Diesel Locomotive Technology

Contents

The Diesel Locomotive - The Diesel Engine - Diesel Engine Types - Size Does Count - To V or not to V - Tractive Effort, Pull and Power - Starting - Governor - Fuel Injection - Fuel Control - Engine Control Development - Power Control - Cooling - Lubrication - Transmission - Parts of a Diesel-Electric Locomotive - Mechanical Transmission - Hydraulic Transmission - Wheel Slip - DMUs - More Information (Links).

The Diesel Locomotive

The modern diesel locomotive is a self contained version of the electric locomotive. Like the electric locomotive, it has electric drive, in the form of traction motors driving the axles and controlled with electronic controls. It also has many of the same auxiliary systems for cooling, lighting, heating, braking and hotel power (if required) for the train. It can operate over the same routes (usually) and can be operated by the same drivers. It differs principally in that it carries its own generating station around with it, instead of being connected to a remote generating station through overhead wires or a third rail. The generating station consists of a large diesel engine coupled to an alternator producing the necessary electricity. A fuel tank is also essential. It is interesting to note that the modern diesel locomotive produces about 35% of the power of a electric locomotive of similar weight.

The UK Class 47 is typical of the general purpose diesel-electric locomotives introduced in the 1960s.

New SD90MAC 6,000 hp heavy freight US diesel-electric locomotives with AC drive first built in 1998

Click on an image for the full size view.

Parts of a Diesel-Electric Locomotive

The following diagram shows the main parts of a US-built diesel-electric locomotive. Click on the part name for a description.

Diesel Engine

This is the main power source for the locomotive. It comprises a large cylinder block, with the cylinders arranged in a straight line or in a V (see more here). The engine rotates the drive shaft at up to 1,000 rpm and this drives the various items needed to power the locomotive. As the

transmission is electric, the engine is used as the power source for the electricity generator or alternator, as it is called nowadays.

Main Alternator

The diesel engine drives the main alternator which provides the power to move the train. The alternator generates AC electricity which is used to provide power for the traction motors mounted on the trucks (bogies). In older locomotives, the alternator was a DC machine, called a generator. It produced direct current which was used to provide power for DC traction motors. Many of these machines are still in regular use. The next development was the replacement of the generator by the alternator but still using DC traction motors. The AC output is rectified to give the DC required for the motors. For more details on AC and DC traction, see the Electronic Power Page on this site.

Auxiliary Alternator

Locomotives used to operate passenger trains are equipped with an auxiliary alternator. This provides AC power for lighting, heating, air conditioning, dining facilities etc. on the train. The output is transmitted along the train through an auxiliary power line. In the US, it is known as "head end power" or "hotel power". In the UK, air conditioned passenger coaches get what is called electric train supply (ETS) from the auxiliary alternator.

Motor Blower

The diesel engine also drives a motor blower. As its name suggests, the motor blower provides air which is blown over the traction motors to keep them cool during periods of heavy work. The blower is mounted inside the locomotive body but the motors are on the trucks, so the blower output is connected to each of the motors through flexible ducting. The blower output also cools the alternators. Some designs have separate blowers for the group of motors on each truck and others for the alternators. Whatever the arrangement, a modern locomotive has a complex air management system which monitors the temperature of the various rotating machines in the locomotive and adjusts the flow of air accordingly.

Air Intakes

The air for cooling the locomotive's motors is drawn in from outside the locomotive. It has to be filtered to remove dust and other impurities and its flow regulated by temperature, both inside and outside the locomotive. The air management system has to take account of the wide range of temperatures from the possible +40°C of summer to the possible -40°C of winter.

Rectifiers/Inverters

The output from the main alternator is AC but it can be used in a locomotive with either DC or AC traction motors. DC motors were the traditional type used for many years but, in the last 10 years, AC motors have become standard for new locomotives. They are cheaper to build and cost less to maintain and, with electronic management can be very finely controlled. To see

more on the difference between DC and AC traction technology try the Electronic Power Page on this site.

To convert the AC output from the main alternator to DC, rectifiers are required. If the motors are DC, the output from the rectifiers is used directly. If the motors are AC, the DC output from the rectifiers is converted to 3-phase AC for the traction motors.

In the US, there are some variations in how the inverters are configured. GM EMD relies on one inverter per truck, while GE uses one inverter per axle - both systems have their merits. EMD's system links the axles within each truck in parallel, ensuring wheel slip control is maximised among the axles equally. Parallel control also means even wheel wear even between axles. However, if one inverter (i.e. one truck) fails then the unit is only able to produce 50 per cent of its tractive effort. One inverter per axle is more complicated, but the GE view is that individual axle control can provide the best tractive effort. If an inverter fails, the tractive effort for that axle is lost, but full tractive effort is still available through the other five inverters. By controlling each axle individually, keeping wheel diameters closely matched for optimum performance is no longer necessary. This paragraph sourced from e-mail by unknown correspondent 3 November 1997.

Electronic Controls

Almost every part of the modern locomotive's equipment has some form of electronic control. These are usually collected in a control cubicle near the cab for easy access. The controls will usually include a maintenance management system of some sort which can be used to download data to a portable or hand-held computer.

Control Stand

This is the principal man-machine interface, known as a control desk in the UK or control stand in the US. The common US type of stand is positioned at an angle on the left side of the driving position and, it is said, is much preferred by drivers to the modern desk type of control layout usual in Europe and now being offered on some locomotives in the US.

Batteries

Just like an automobile, the diesel engine needs a battery to start it and to provide electrical power for lights and controls when the engine is switched off and the alternator is not running.

Cab

Most US diesel locomotives have only one cab but the practice in Europe is two cabs. US freight locos are also designed with narrow engine compartments and walkways along either side. This gives a reasonable forward view if the locomotive is working "hood forwards". US passenger locos, on the other hand have full width bodies and more streamlined ends but still usually with one cab. In Europe, it is difficult to tell the difference between a freight and passenger locomotive because the designs are almost all wide bodied and their use is often mixed.

Traction Motor

Since the diesel-electric locomotive uses electric transmission, traction motors are provided on the axles to give the final drive. These motors were traditionally DC but the development of modern power and control electronics has led to the introduction of 3-phase AC motors. For a description of how this technology works, go to the Electronic Power Page on this site. There are between four and six motors on most diesel-electric locomotives. A modern AC motor with air blowing can provide up to 1,000 hp.

Pinion/Gear

The traction motor drives the axle through a reduction gear of a range between 3 to 1 (freight) and 4 to 1 (passenger).

Fuel Tank

A diesel locomotive has to carry its own fuel around with it and there has to be enough for a reasonable length of trip. The fuel tank is normally under the loco frame and will have a capacity of say 1,000 imperial gallons (UK Class 59, 3,000 hp) or 5,000 US gallons in a General Electric AC4400CW 4,400 hp locomotive. The new AC6000s have 5,500 gallon tanks. In addition to fuel, the locomotive will carry around, typically about 300 US gallons of cooling water and 250 gallons of lubricating oil for the diesel engine.

Air reservoirs are also required for the train braking and some other systems on the locomotive. These are often mounted next to the fuel tank under the floor of the locomotive.

Air Compressor

The air compressor is required to provide a constant supply of compressed air for the locomotive and train brakes. In the US, it is standard practice to drive the compressor off the diesel engine drive shaft. In the UK, the compressor is usually electrically driven and can therefore be mounted anywhere. The Class 60 compressor is under the frame, whereas the Class 37 has the compressors in the nose.

Drive Shaft

The main output from the diesel engine is transmitted by the drive shaft to the alternators at one end and the radiator fans and compressor at the other end.

Gear Box

The radiator and its cooling fan is often located in the roof of the locomotive. Drive to the fan is therefore through a gearbox to change the direction of the drive upwards.

Radiator and Radiator Fan

The radiator works the same way as in an automobile. Water is distributed around the engine block to keep the temperature within the most efficient range for the engine. The water is cooled by passing it through a radiator blown by a fan driven by the diesel engine. See Cooling for more information.

Turbo Charging

The amount of power obtained from a cylinder in a diesel engine depends on how much fuel can be burnt in it. The amount of fuel which can be burnt depends on the amount of air available in the cylinder. So, if you can get more air into the cylinder, more fuel will be burnt and you will get more power out of your ignition. Turbo charging is used to increase the amount of air pushed into each cylinder. The turbocharger is driven by exhaust gas from the engine. This gas drives a fan which, in turn, drives a small compressor which pushes the additional air into the cylinder. Turbocharging gives a 50% increase in engine power.

The main advantage of the turbocharger is that it gives more power with no increase in fuel costs because it uses exhaust gas as drive power. It does need additional maintenance, however, so there are some type of lower power locomotives which are built without it.

Sand Box

Locomotives always carry sand to assist adhesion in bad rail conditions. Sand is not often provided on multiple unit trains because the adhesion requirements are lower and there are normally more driven axles.

Truck Frame

This is the part (called the bogie in the UK) carrying the wheels and traction motors of the locomotive. More information is available at the Bogie Parts Page or the Wheels and Bogies Page on this site.

Wheel

The best page for information on wheels is the Wheels and Bogies Page on this site.

Mechanical Transmission

A diesel-mechanical locomotive is the simplest type of diesel locomotive. As the name suggests, a mechanical transmission on a diesel locomotive consists a direct mechanical link between the diesel engine and the wheels. In the example below, the diesel engine is in the 350-500 hp range and the transmission is similar to that of an automobile with a four speed gearbox. Most of the parts are similar to the diesel-electric locomotive but there are some variations in design mentioned below.

Fluid Coupling

In a diesel-mechanical transmission, the main drive shaft is coupled to the engine by a fluid coupling. This is a hydraulic clutch, consisting of a case filled with oil, a rotating disc with curved blades driven by the engine and another connected to the road wheels. As the engine turns the fan, the oil is driven by one disc towards the other. This turns under the force of the oil and thus turns the drive shaft. Of course, the start up is gradual until the fan speed is almost matched by the blades. The whole system acts like an automatic clutch to allow a graduated start for the locomotive.

Gearbox

This does the same job as that on an automobile. It varies the gear ratio between the engine and the road wheels so that the appropriate level of power can be applied to the wheels. Gear change is manual. There is no need for a separate clutch because the functions of a clutch are already provided in the fluid coupling.

Final Drive

The diesel-mechanical locomotive uses a final drive similar to that of a steam engine. The wheels are coupled to each other to provide more adhesion. The output from the 4-speed gearbox is coupled to a final drive and reversing gearbox which is provided with a transverse drive shaft and balance weights. This is connected to the driving wheels by connecting rods.

Hydraulic Transmission

Hydraulic transmission works on the same principal as the fluid coupling but it allows a wider range of "slip" between the engine and wheels. It is known as a "torque converter". When the train speed has increased sufficiently to match the engine speed, the fluid is drained out of the torque converter so that the engine is virtually coupled directly to the locomotive wheels. It is virtually direct because the coupling is usually a fluid coupling, to give some "slip". Higher speed locomotives use two or three torque converters in a sequence similar to gear changing in a mechanical transmission and some have used a combination of torque converters and gears.

Some designs of diesel-hydraulic locomotives had two diesel engines and two transmission systems, one for each bogie. The design was poplar in Germany (the V200 series of locomotives, for example) in the 1950s and was imported into parts of the UK in the 1960s. However, it did not work well in heavy or express locomotive designs and has largely been replaced by diesel-electric transmission.

Wheel Slip

Wheels slip is the bane of the driver trying to get a train away smoothly. The tenuous contact between steel wheel and steel rail is one of the weakest parts of the railway system. Traditionally, the only cure has been a combination of the skill of the driver and the selective use of sand to improve the adhesion. Today, modern electronic control has produced a very effective answer to this age old problem. The system is called creep control.

Extensive research into wheel slip showed that, even after a wheelset starts to slip, there is still a considerable amount of useable adhesion available for traction. The adhesion is available up to a peak, when it will rapidly fall away to an uncontrolled spin. Monitoring the early stages of slip can be used to adjust the power being applied to the wheels so that the adhesion is kept within the limits of the "creep" towards the peak level before the uncontrolled spin sets in.

The slip is measured by detecting the locomotive speed by Doppler radar (instead of the usual method using the rotating wheels) and comparing it to the motor current to see if the wheel rotation matches the ground speed. If there is a disparity between the two, the motor current is adjusted to keep the slip within the "creep" range and keep the tractive effort at the maximum level possible under the creep conditions.

Diesel Multiple Units (DMUs)

The diesel engines used in DMUs work on exactly the same principles as those used in locomotives, except that the transmission is normally mechanical with some form of gear change system. DMU engines are smaller and several are used on a train, depending on the configuration. The diesel engine is often mounted under the car floor and on its side because of the restricted space available. Vibration being transmitted into the passenger saloon has always been a problem but some of the newer designs are very good in this respect.

There are some diesel-electric DMUs around and these normally have a separate engine compartment containing the engine and the generator or alternator.

The Diesel Engine

The diesel engine was first patented by Dr Rudolf Diesel (1858-1913) in Germany in 1892 and he actually got a successful engine working by 1897. By 1913, when he died, his engine was in use on locomotives and he had set up a facility with Sulzer in Switzerland to manufacture them. His death was mysterious in that he simply disappeared from a ship taking him to London.

The diesel engine is a compression-ignition engine, as opposed to the petrol (or gasoline) engine, which is a spark-ignition engine. The spark ignition engine uses an electrical spark from a "spark plug" to ignite the fuel in the engine's cylinders, whereas the fuel in the diesel engine's cylinders is ignited by the heat caused by air being suddenly compressed in the cylinder. At this stage, the air gets compressed into an area 1/25th of its original volume. This would be expressed as a compression ratio of 25 to 1. A compression ratio of 16 to 1 will give an air pressure of 500 lbs/in² (35.5 bar) and will increase the air temperature to over 800°F (427°C).

The advantage of the diesel engine over the petrol engine is that it has a higher thermal capacity (it gets more work out of the fuel), the fuel is cheaper because it is less refined than petrol and it can do heavy work under extended periods of overload. It can however, in a high speed form, be sensitive to maintenance and noisy, which is why it is still not popular for passenger automobiles.

Diesel Engine Types

There are two types of diesel engine, the two-stroke engine and the four-stroke engine. As the names suggest, they differ in the number of movements of the piston required to complete each cycle of operation. The simplest is the two-stroke engine. It has no valves. The exhaust from the combustion and the air for the new stroke is drawn in through openings in the cylinder wall as the piston reaches the bottom of the downstroke. Compression and combustion occurs on the upstroke. As one might guess, there are twice as many revolutions for the two-stroke engine as for equivalent power in a four-stroke engine.

The four-stroke engine works as follows: Downstroke 1 - air intake, upstroke 1 - compression, downstroke 2 - power, upstroke 2 - exhaust. Valves are required for air intake and exhaust, usually two for each. In this respect it is more similar to the modern petrol engine than the 2-stroke design.

In the UK, both types of diesel engine were used but the 4-stroke became the standard. The UK Class 55 "Deltic" (not now in regular main line service) unusually had a two-stroke engine. In the US, the General Electric (GE) built locomotives have 4-stroke engines whereas General Motors (GM) always used 2-stroke engines until the introduction of their SD90MAC 6000 hp "H series" engine, which is a 4-stroke design.

The reason for using one type or the other is really a question of preference. However, it can be said that the 2-stroke design is simpler than the 4-stroke but the 4-stroke engine is more fuel efficient.

Size Does Count

Basically, the more power you need, the bigger the engine has to be. Early diesel engines were less than 100 horse power (hp) but today the US is building 6000 hp locomotives. For a UK locomotive of 3,300 hp (Class 58), each cylinder will produce about 200 hp, and a modern engine can double this if the engine is turbocharged.

The maximum rotational speed of the engine when producing full power will be about 1000 rpm (revolutions per minute) and the engine will idle at about 400 rpm. These relatively low speeds mean that the engine design is heavy, as opposed to a high speed, lightweight engine. However, the UK HST (High Speed Train, developed in the 1970s) engine has a speed of 1,500 rpm and this is regarded as high speed in the railway diesel engine category. The slow, heavy engine used in railway locomotives will give low maintenance requirements and an extended life.

There is a limit to the size of the engine which can be accommodated within the railway loading gauge, so the power of a single locomotive is limited. Where additional power is required, it has become usual to add locomotives. In the US, where freight trains run into tens of thousands of tons weight, four locomotives at the head of a train are common and several additional ones in the middle or at the end are not unusual.

To V or not to V

Diesel engines can be designed with the cylinders "in-line", "double banked" or in a "V". The double banked engine has two rows of cylinders in line. Most diesel locomotives now have V form engines. This means that the cylinders are split into two sets, with half forming one side of the V. A V8 engine has 4 cylinders set at an angle forming one side of the V with the other set of four forming the other side. The crankshaft, providing the drive, is at the base of the V. The V12 was a popular design used in the UK. In the US, V16 is usual for freight locomotives and there are some designs with V20 engines.

Engines used for DMU (diesel multiple unit) trains in the UK are often mounted under the floor of the passenger cars. This restricts the design to in-line engines, which have to be mounted on their side to fit in the restricted space.

An unusual engine design was the UK 3,300 hp Class 55 locomotive, which had the cylinders arranged in three sets of opposed Vs in an triangle, in the form of an upturned delta, hence the name "Deltic".

Tractive Effort, Pull and Power

Before going too much further, we need to understand the definitions of tractive effort, drawbar pull and power. The definition of tractive effort (TE) is simply the force exerted at the wheel rim of the locomotive and is usually expressed in pounds (lbs) or kilo Newtons (kN). By the time the tractive effort is transmitted to the coupling between the locomotive and the train, the drawbar pull, as it is called will have reduced because of the friction of the mechanical parts of the drive and some wind resistance.

Power is expressed as horsepower (hp) or kilo Watts (kW) and is actually a rate of doing work. A unit of horsepower is defined as the work involved by a horse lifting 33,000 lbs one foot in

one minute. In the metric system it is calculated as the power (Watts) needed when one Newton of force is moved one metre in one second. The formula is P = (F*d)/t where P is power, F is force, d is distance and t is time. One horsepower equals 746 Watts.

The relationship between power and drawbar pull is that a low speed and a high drawbar pull can produce the same power as high speed and low drawbar pull. If you need to increase higher tractive effort and high speed, you need to increase the power. To get the variations needed by a locomotive to operate on the railway, you need to have a suitable means of transmission between the diesel engine and the wheels.

One thing worth remembering is that the power produced by the diesel engine is not all available for traction. In a 2,580 hp diesel electric locomotive, some 450 hp is lost to on-board equipment like blowers, radiator fans, air compressors and "hotel power" for the train.

Starting

A diesel engine is started (like an automobile) by turning over the crankshaft until the cylinders "fire" or begin combustion. The starting can be done electrically or pneumatically. Pneumatic starting was used for some engines. Compressed air was pumped into the cylinders of the engine until it gained sufficient speed to allow ignition, then fuel was applied to fire the engine. The compressed air was supplied by a small auxiliary engine or by high pressure air cylinders carried by the locomotive.

Electric starting is now standard. It works the same way as for an automobile, with batteries providing the power to turn a starter motor which turns over the main engine. In older locomotives fitted with DC generators instead of AC alternators, the generator was used as a starter motor by applying battery power to it.

Governor

Once a diesel engine is running, the engine speed is monitored and controlled through a governor. The governor ensures that the engine speed stays high enough to idle at the right speed and that the engine speed will not rise too high when full power is demanded. The governor is a simple mechanical device which first appeared on steam engines. It operates on a diesel engine as shown in the diagram below. The governor consists of a rotating shaft, which is driven by the diesel engine. A pair of flyweights are linked to the shaft and they rotate as it rotates. The centrifugal force caused by

the rotation causes the weights to be thrown outwards as the speed of the shaft rises. If the speed falls the weights move inwards. The flyweights are linked to a collar fitted around the shaft by a pair of arms. As the weights move out, so the collar rises on the shaft. If the weights move inwards, the collar moves down the shaft. The movement of the collar is used to operate the fuel rack lever controlling the amount of fuel supplied to the engine by the injectors.

Fuel Injection

Ignition is a diesel engine is achieved by compressing air inside a cylinder until it gets very hot (say 400°C, almost 800°F) and then injecting a fine spray of fuel oil to cause a miniature explosion. The explosion forces down the piston in the cylinder and this turns the crankshaft. To get the fine spray needed for successful ignition the fuel has to be pumped into the cylinder at high pressure. The fuel pump is operated by a cam driven off the engine. The fuel is pumped into an injector, which gives the fine spray of fuel required in the cylinder for combustion.

Fuel Control

In an automobile engine, the power is controlled by the amount of fuel/air mixture applied to the cylinder. The mixture is mixed outside the cylinder and then applied by a throttle valve. In a diesel engine the amount of air applied to the cylinder is constant so power is regulated by varying the fuel input. The fine spray of fuel injected into each cylinder has to be regulated to achieve the amount of power required. Regulation is achieved by varying the fuel sent by the fuel pumps to the injectors. The control arrangement is shown in the diagram left. The amount of fuel being applied to the cylinders is varied by altering the effective delivery rate of the piston in the injector pumps. Each injector has its own pump, operated by an engine-driven cam, and the pumps are aligned in a row so that they can all be adjusted together. The adjustment is done by a toothed rack (called the "fuel rack") acting on a toothed section of the pump mechanism. As the fuel rack moves, so the toothed section of the pump rotates and provides a drive to move the pump piston round inside the pump. Moving the piston round, alters the size of the channel available inside the pump for fuel to pass through to the injector delivery pipe. The fuel rack can be moved either by the driver operating the power controller in the cab or by the governor. If the driver asks for more power, the control rod moves the fuel rack to set the

pump pistons to allow more fuel to the injectors. The engine will increase power and the governor will monitor engine speed to ensure it does not go above the predetermined limit. The limits are fixed by springs (not shown) limiting the weight movement.

Engine Control Development

So far we have seen a simple example of diesel engine control but the systems used by most locomotives in service today are more sophisticated. To begin with, the drivers control was combined with the governor and hydraulic control was introduced. One type of governor uses oil to control the fuel racks hydraulically and another uses the fuel oil pumped by a gear pump driven by the engine. Some governors are also linked to the turbo charging system to ensure that fuel does not increase before enough turbocharged air is available. In the most modern systems, the governor is electronic and is part of a complete engine management system.

Power Control

The diesel engine in a diesel-electric locomotive provides the drive for the main alternator which, in turn, provides the power required for the traction motors. We can see from this therefore, that the power required from the diesel engine is related to the power required by the motors. So, if we want more power from the motors, we must get more current from the alternator so the engine needs to run faster to generate it. Therefore, to get the optimum performance from the locomotive, we must link the control of the diesel engine to the power demands being made on the alternator.

In the days of generators, a complex electro-mechanical system was developed to achieve the feedback required to regulate engine speed according to generator demand. The core of the system was a load regulator, basically a variable resistor which was used to very the excitation of the generator so that its output matched engine speed. The control sequence (simplified) was as follows:

1. Driver moves the power controller to the full power position 2. An air operated piston actuated by the controller moves a lever, which closes a switch to supply a low voltage to the load regulator motor. 3. The load regulator motor moves the variable resistor to increase the main generator field strength and therefore its output. 4. The load on the engine increases so its speed falls and the governor detects the reduced speed. 5. The governor weights drop and cause the fuel rack servo system to actuate. 6. The fuel rack moves to increase the fuel supplied to the injectors and therefore the power from the engine. 7. The lever (mentioned in 2 above) is used to reduce the pressure of the governor spring. 8. When the engine has responded to the new control and governor settings, it and the generator will be producing more power.

On locomotives with an alternator, the load regulation is done electronically. Engine speed is measured like modern speedometers, by counting the frequency of the gear teeth driven by the engine, in this case, the starter motor gearwheel. Electrical control of the fuel injection is another improvement now adopted for modern engines. Overheating can be controlled by

electronic monitoring of coolant temperature and regulating the engine power accordingly. Oil pressure can be monitored and used to regulate the engine power in a similar way.

Cooling

Like an automobile engine, the diesel engine needs to work at an optimum temperature for best efficiency. When it starts, it is too cold and, when working, it must not be allowed to get too hot. To keep the temperature stable, a cooling system is provided. This consists of a water-based coolant circulating around the engine block, the coolant being kept cool by passing it through a radiator.

The coolant is pumped round the cylinder block and the radiator by an electrically or belt driven pump. The temperature is monitored by a thermostat and this regulates the speed of the (electric or hydraulic) radiator fan motor to adjust the cooling rate. When starting the coolant isn't circulated at all. After all, you want the temperature to rise as fast as possible when starting on a cold morning and this will not happen if you a blowing cold air into your radiator. Some radiators are provided with shutters to help regulate the temperature in cold conditions.

If the fan is driven by a belt or mechanical link, it is driven through a fluid coupling to ensure that no damage is caused by sudden changes in engine speed. The fan works the same way as in an automobile, the air blown by the fan being used to cool the water in the radiator. Some engines have fans with an electrically or hydrostatically driven motor. An hydraulic motor uses oil under pressure which has to be contained in a special reservoir and pumped to the motor. It has the advantage of providing an in-built fluid coupling.

A problem with engine cooling is cold weather. Water freezes at 0°C or 32°F and frozen cooling water will quickly split a pipe or engine block due to the expansion of the water as it freezes. Some systems are "self draining" when the engine is stopped and most in Europe are designed to use a mixture of anti-freeze, with Gycol and some form of rust inhibitor. In the US, engines do not normally contain anti-freeze, although the new GM EMD "H" engines are designed to use it. Problems with leaks and seals and the expense of putting a 100 gallons (378.5 litres) of coolant into a 3,000 hp engine, means that engines in the US have traditionally operated without it. In cold weather, the engine is left running or the locomotive is kept warm by putting it into a heated building or by plugging in a shore supply. Another reason for keeping diesel engines running is that the constant heating and cooling caused by shutdowns and restarts, causes stresses in the block and pipes and tends to produce leaks.

Lubrication

Like an automobile engine, a diesel engine needs lubrication. In an arrangement similar to the engine cooling system, lubricating oil is distributed around the engine to the cylinders, crankshaft and other moving parts. There is a reservoir of oil, usually carried in the sump, which has to be kept topped up, and a pump to keep the oil circulating evenly around the engine. The oil gets heated by its passage around the engine and has to be kept cool, so it is passed through a radiator during its journey. The radiator is sometimes designed as a heat exchanger, where the oil passes through pipes encased in a water tank which is connected to the engine cooling system.

The oil has to be filtered to remove impurities and it has to be monitored for low pressure. If oil pressure falls to a level which could cause the engine to seize up, a "low oil pressure switch" will shut down the engine. There is also a high pressure relief valve, to drain off excess oil back to the sump.

Transmissions

Like an automobile, a diesel locomotive cannot start itself directly from a stand. It will not develop maximum power at idling speed, so it needs some form of transmission system to multiply torque when starting. It will also be necessary to vary the power applied according to the train weight or the line gradient. There are three methods of doing this: mechanical, hydraulic or electric. Most diesel locomotives use electric transmission and are called "diesel-electric" locomotives. Mechanical and hydraulic transmissions are still used but are more common on multiple unit trains or lighter locomotives.

Diesel-Electric Types

Diesel-electric locomotives come in three varieties, according to the period in which they were designed. These three are:

DC - DC (DC generator supplying DC traction motors); AC - DC (AC alternator output rectified to supply DC motors) and AC - DC - AC (AC alternator output rectified to DC and then inverted to 3-phase AC for the traction motors). The DC - DC type has a generator supplying the DC traction motors through a resistance control system, the AC - DC type has an alternator producing AC current which is rectified to DC and then supplied to the DC traction motors and, finally, the most modern has the AC alternator output being rectified to DC and then converted to AC (3-phase) so that it can power the 3-phase AC traction motors. Although this last system might seem the most complex, the gains from using AC motors far outweigh the apparent complexity of the system. In reality, most of the equipment uses solid state power electronics with microprocessor-based controls. For more details on AC and DC traction, see the Electronic Power Page on this site.

In the US, traction alternators (AC) were introduced with the 3000 hp single diesel engine locomotives, the first being the Alco C630. The SD40, SD45 and GP40 also had traction alternators only. On the GP38, SD38, GP39, and SD39s, traction generators (DC) were standard, and traction alternators were optional, until the dash-2 era, when they became standard. It was a similar story at General Electric.

There is one traction alternator (or generator) per diesel engine in a locomotive (standard North American practice anyway). The Alco C628 was the last locomotive to lead the horsepower race with a DC traction alternator.

face="Times New Roman">Below is a diagram showing the main parts of a common US-built diesel-electric locomotive. I have used the US example because of the large number of countries

which use them. There are obviously many variations in layout and European practice differs in many ways and we will note some of these in passing.

More Information

This page is just a brief description of the main points of interest concerning diesel locomotives. There aren't too many technical sites around but the following links give some useful information:

Diesel Locomotive Systems - A good description of the operation of the equipment of the modern UK diesel-electric Class 60 locomotive. It written in simple terms and gives the reader a basic understanding of the technology.

US Diesel Loco Operating Manuals - Copies of some of the older US diesel locomotive manuals issued to staff. Contains some very interesting details.

Diesel-Electric and Electric Locomotives - by Steve Sconfienza, PhD.D. - >Includes some technical background on the development of diesel and electric traction in the US, an illustration of the PRR catenary system and some electrical formulae related to different traction systems.

Diesel-Electric Locomotive Operation - A general list of US diesel locomotive types, designs and statistics with a summary of their development. A useful introduction to the US diesel loco scene.

Sources:

The Railroad, What it is, What it Does by John H Armstrong, 1993, Simmons Boardman Books Inc.; BR Diesel Traction Manual for Enginemen, British Transport Commission, 1962; BR Equipment, David Gibbons, Ian Allan, 1986 and 1990; Modern Railways; International Railway Journal; Railway Gazette International; Mass Transit; Trains Magazine.

What a Modern Locomotive Is -- The Short Version

This is the really simple version. Modern locomotives have electric motors connected to the drive axles. The electric motors receive electric power either from an on-board power source (e.g., a diesel motor) or from a central power source via a distribution system (e.g., a thrid rail). The link between the electric motor and the source of the electricity is called the transmission. The electrical power lines that criss-cross our towns and cities are called electric "transmission" lines; the link from a diesel motor to the electric motors on a locomotive's axles is called the transmission. That's it!

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Why it looks the way it does

Why do modern freight locomotives look the way they do -- a cab at one end, lots of bulky equipment at the other? Why do Amtrak, LIRR, and other passenger locomotives that have been recently designed without regard to any freight predecessors have one cab with, at most, a hostler's position at the other end?

The issue of cabs on locomotives has a number of "histories" that have converged to produce the style seen today. First, many early U.S. diesel locomotives did have two cabs, such as Baldwins built for Jersey Central (while the same locomotives for other roads had only one cab), as did other diesel and electrics such as various boxcabs and the GG1, and of course the AEM7s of today have cabs at each end. What gnaws at ones mind, though, is really about the big freight locomotives (like the SD80MACs of Conrail). So . . .

When the big frieght roads first dieselized, there were questions about MUs and crews. The railroads did not want to put a crew in each cab of an MUed set, so that brought forth such oxymorons as referring to the evolutionarilly critical A-B-B-A FTs from General Motors as "a locomotive." Calling it one locomotive (one with a cab at each end!) meant it needed only one crew (and note that the B-units had no cab, or if any just a hostler's position). As these evolved into F3s, F7s and F9s, and A-units unpaired and mixed with other units, the ubiquity of single-cab units was assured. Roads taking E-unit derivatives (i.e., double-engine units, even those from other builders) such as the Jersey Central Baldwins (DR-6-4-20) did sometimes take two cabs when it was clear that the unit would only be operating as

a single unit; alternatively, some cab units came semi-permanently coupled back-to-back with a draw-bar instead of a coupler (e.g., PRR's DR-12-8-1500/2), essentially a single unit with a cab at each end (today, similar issues are resovled in passenger operations through push-pull, with a cab at the other end of the train).

The other key development was of the non-hood units, the "road switchers." General Motors again had the critical development with the GP-7. The unit was logically divided into two hoods, with a somewhat centered cab for ease of bi-directional movement. Under one hood -- the longer one -- was the motive equipment, while under the other -- the shorter one -- was usually a steam generator for passenger service. Local builder ALCO had similar locomotives with the RS-1s, RS-2s, and RS-3s, leading ultimately into its Century line. Passenger operations into the 1970s (e.g., the Long Island) took road switchers long-hood forward to protect the engine crew from the steam generator in case of an accident, particularly a grade crossing accident where a vehicle could have flipped over the anti-climber (where the anti-climber would have been had the units been so equipped) and crushed the steam generator into the cab (shades of an exploding steam locomotive!). Much earlier, many roads had begun turning their road switchers around and running them short hood forward for the better visability (who needed a long hood like a steam engines' boiler, anyway?) -- except for The Norfolk and Western [N&W] and The Southern [SOU], which seemed to delight in taking the most incrediably long hood and designating it front, with the cab so configured; and the Erie Lackawanna, which apparently had some SD-45s configured for either direction. Long-hood forward and bi-directional units sometimes had two control stands, one on each side of the cab facing "forward," but sometimes had just a single stand sitting parallel to the cab side for use with the engineer facing in either direction. As the time came when passenger equipment no longer needed steam, the short hood was cut and shortened, and that gave the configuration of the road switcher of today (note that during the overlap when short hoods were being cut but some passenger steam-generators were still needed in operation, GM's SDP-35, SDP-40, and SDP-45 had the steam generators at the coupler-end of the long hood).

At this point, a second cab could have been added, but only a hand-full of units have ever been built that way (some electrics on mining roads come to mind). For the most part, the big roads run with two or more units anyway, so having east-west pairs is not difficult (turning facilities such as wyes and loop tracks seem to be plentiful). The smaller roads simply don't want the expense. And, of course, it seems, N&W and SOU successor Norfolk Southern would just as soon run them long-hood anyway!

[ Motors Graphic ][ back to page index ]

Baisc DC Motor Concepts

The traditional electric motor on a diesel-electric or electric locomotive is a DC motor. Internally, DC motors have two main components: the stator is the stationary outside part of a motor. The armature is the inner part which rotates. To get the armature to rotate, electric motors require two sets of windings, the field winding (on the stator) to develop the magnetic field within which the armature will turn, and the armature winding (which in many DC motors can make transition between series and shunt winding). In series, current passes through both the field and armature windings "in series", that is, one after the other, while in shunt the current is divided and passes either through the field or armature windings. DC motors with series windings develop high starting torque, while motors in shunt develop high speed. (A third category, the compound, combines both series and shunt windings simultaneously, with mixed properties: c.f. a motor that can transition between series and shunt, but not use both at the same time; a fourth category is the permanent-magnet motor, which not surprisingly uses a permanent magnet for the field, and is only used in relatively low-power applications.)

DC motors turn because an electrical field rotates. The field rotates because an electrical current passing into the armature changes polarity, with the armature tugged forward with each change. (N.B., it is the field in the armature that is changing, not the field in the stator.) In order to accomplish this change in polarity, the windings in the armature are connected to the outside world by means of a commutator, a conductive sheaf that allows for the current in the windings to have a change in polarity by breaking and making the connection. The electricity flows into the commutator through conductive brushes (usually carbon). These are sources of friction, heat, and general wear in the DC motor.

Series-wound motors are also called universal motors (see below), universal in the sense that they will run equally well using either AC or DC: simultaneously reversing the polarity of both the stator and the rotor cancel out, thus the motor will always rotate in the same direction regardless of the voltage polarity. Sometimes called "AC motors" instead of "DC series-wound motors" or "universal motors," these are not the motors to which one refers when referring to AC traction motors.

Note: In the motor wiring diagrams, the DC motors do not have separately excited windings. While some first generation diesel-electrics had an auxiliary generator to provide current to separately excited windings, which required manual switching by the engineer, that design is now obsolete. Contemporary U.S. road locomotives do not have separately excited windings; however, there has been other work in this direction, based in computer-control systems, that has included wheel-slip detection and control and wheel-creep systems, in which the windings are under separate control (see below).

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Transmissions

When speaking of a vehicle such as a railroad locomotive, transmission is the process by which power is transmitted from one location and used in another. Often this implies some type of changing process, for example the manner in the rotational force of a crankshaft is converted to electrical force in a generator.

In a modern diesel-electric locomotive, this is a multi-staged process that goes from fuel oil to turning wheels. In the days of steam the intermediate process was, well, it was steam. Coal or oil was burned in a firebox. The heat generated heated water, turning it into steam (and continued to heat the steam), which in turn drove a piston in a back-and-forth motion, which -- through the drive gear -- turned the wheels. In diesel-electric locomotives, the fuel is burned in cylinders, driving pistons in a back-and-forth motion, which -- through the crank shaft -- turns an electricity generating device (a generator or alternator or both), which provides electricity for electric motors that are connected to the axles of the trucks, which turn the wheels.

FIGURE ONE: BLOCK DIAGRAM OF A DIESEL-ELECTRIC LOCOMOTIVE

diesel motor

generator

electric motors

[ Transition Graphic ][ back to page index ]

Transition

Transition is the process by which the transmission of a diesel-electric locomoitve is brought from series wiring to parallel wiring. When in series, all current in the locomotive pass through all motors: this produces maximum low-speed force in the motors, i.e., maximum starting torque. When in parallel, current is divided among the motors: this produces maximum high-end efficency, i.e., highest motor speed. This is just as with the wiring internal to DC motors, where having the motor wound in series develops high starting torque, while placing the motor in parallel will develop high speed. Electrically, as current increases through the motors in a circuit with a given total current and voltage, the voltage drop across each motor will decrease: parallel circuits apply the total voltage to each load (i.e., in this case, motor), while series circuits apply the total current to each load.

Not all locomotives can make transition -- yard locomotives are often wired only for series. The motors on a diesel-electric road locomotives are often capable of making multiple transitions, with both trucks and motors on a truck capable of being switched into series or parallel wiring.

See the motor diagram for an example of a DC motor capable of transition and the transition diagram for examples of two- and three-axle transition schemes. (A note on how the construction of the motors is depicted is above). These diagrams are quite general: some locomotives would put like axles on different trucks in series (first axle with first axle, second with second), or have other arrangements.

[ Catenary Graphic ][ back to page index ]

Electric Locomotives

In straight electric locomotives or M.U. cars (multiple-unit electric), the on-board diesel engine and generator and/or alternator is replaced by Niagara Falls or Indian Point or some other such central power generating source. The power is transmitted to the railroad and delivered to the trains. Electric transmission lines are generally high-voltage AC. This is because of the greater efficiency (i.e., less loss) of AC during transmission over certain distances, and the likewise greater efficiency of high-voltage transmission over low-voltage transmission (see below and also the Formulas and Concepts page under Electric Power Transmission for more extensive notes on AC, DC, and long distance electric transmission). In rail applications (as in most others), the most efficient transmission of electricity from generating stations to the tracks requires transmission lines of high-voltage AC with substations to convert this to line voltage for equipment. The power is delivered to the individual locomotives or cars generally either by a track level third rail (there are some fourth rail systems, too) or through overhead wires known as catenary). While there are some exceptions, AC systems usually use catenary, while DC systems usually use third rail.

FIGURE TWO: BLOCK DIAGRAM OF A ELECTRIC LOCOMOTIVE

central generating facility

distribution system

on-board electrical equipment

(e.g., transformer, rectifier, motor-generator, inverter, etc.)

electric motors

Notes on Electric Power Transmission and Distribution Systems

Long-Distance Transmission, Substations, and Local Distribution

Two principal elements of an electric system are the transmission of the electric power from the source of the electricity (i.e., a generating plant) to the local use area and, ultimately, distributing that power to the consumer (e.g., an electric locomotive or a home). Thus, these parts of the system may be divided into the transmission system and the distribution system, with transmission convenying the power long distances (at high voltages), and the distribution system delivering the power locally (at low voltages).

Long-Distance Transmission

As a general rule, in the United States, DC cannot be transmitted as economically as AC in transmission systems; railroads follow the practice of AC transmission systems, with high voltage AC stepped-down to distribution voltages at substations.

Extensive notes on long distance electric transmission, including some formulas, are on the Formulas and Concepts page under Electric Power Transmission.

Local Distribution

Local distribution is almost universally accomplished by third rail or overhead wires. The highest third rail voltage in use in the U.S. today is the 1,000 volt system on San Francisco's BART system. The highest, historically, is reputed to have been an interurban that ran 2400 volts (historically, only for a brief period): it did not really work very well, as arcing and leakage were such critical issues that the system was conveted to a lower voltage.

As for AC, it is generally delivered at higher volatages than third rail through overhead wires. As for AC third rail, no such systems exist (at least that I know of, certainly not in the U.S.). This may not be practicable: AC's advantage comes from high voltage transmissions that can be readilly stepped up or down, with conversion to DC in the distribution system providing easy control of motors without including on-board rectifiers (but more on that following). (Now, with AC traction in common usage, there may be a rationale for that to change, but distribution is still basically low-voltage DC or higher voltage AC.)

Distribution on the North East Corridor

The NEC uses three different combinations:

• D.C. to New York City: 11kV 25Hz

• N.Y.C. to New Haven: 11kV 60Hz

• New Haven to Boston: 25kV 60Hz

Understandably, Amtrak's engineers (the slide-rule type) want everything at 25kV 60Hz, and that is the standard for new track, such as the latest electrificationm, from New Haven to Boston. Sixty hertz has the advantage of being compatible with the commercial grid (25Hz requires frequency converters, which run [reportedly] $40,000,000 each), and 25kV is not an unusual voltage, so equipment is available.

Higher voltages are also more efficient to transmit than lower: in fact, when the voltage is doubled the amperage is halved for the same power level ( P = I * V: increasing voltage results in a linear decrease in current at the same power level). Since transmission losses are a function of amperage only (dissipated power = I2R, where R is the constant line resistance [or impedance, in the case of AC]), 25kV power can be transmitted over twice as far as 11kV power at the same loss levels. One should note, however, that this does not solve the problem of drawing down the current in a section by multiple trains running within it: high train density will still require short segments (remember that this concerns only local distribution via the catenary and its local feeders, not long-distance transmission from powerplants).

Unfortunately, upgrading track from 11kV to 25kV is expensive, because it is necessary to rebuild catenary to accomodate the higher arc distance at the higher voltage, (e.g., better insulation and insulators).

Phase

While it is theoretically possible to run an entire rail line, hundreds of miles long, on a single, synchronized AC phase, in practice it is not practical. Instead, lines are generally broken into ten to twenty mile segments, each one running on a different phase (usually 120 degrees apart). The boundry of each segment is called a "phase break." On former Pennsy track, these were marked by a phase-break signal, which looked like a typical position-light signal with all positions in the entire circle lit. To prevent arcing between the sections, an insulating section of catenary is run across the phase break. By segmenting the catenary into sections, it is a simple matter -- with respect to stringing the catenary -- to have not only different phases but also different frequencies, 25 or 60 hertz, or voltatges, 11kV or 25kV, on the two sides of a phase break.

Unlike former equipment, which had to stop and change internal settings, Acela trains are capable of changing both frequency and voltage while at speed. This is done as part of the normal "approaching phase break" message that is sent to trains via ACSES, which includes the frequency and voltage that will be on the other side of the break (typically no change). When the pantograph hits the insulator between phases, the train temporarily cuts the input power, reconfigures the leads to the windings on the primary of the main transformer, and reconnects the input power -- all in less than a second. To the equipment downstream from the transformer, all that is visible is an AC voltage that drops out briefly every five to 15 minutes, as the locomotive hits the various phases. The blip is short enough there should be no noticeable traction-motor stutter or hotel-power disruption.

FIGURE THREE: REGIONAL EXAMPLES OF MAINLINE ELECTRIC OPERATIONS

• Northeast Corridor

o 25kv, 60Hz AC via Catenary

The PRR originally built this as 11kv, 25hz and supplied its own

electricity, as this system was not compatible with commercial 60Hz

systems (complete change-over not yet completed: see above).

• Long Island Rail Road

o 600v DC via 3rd rail

• Delaware, Lackawanna, and Western (metro New Jersey lines)

o 3000v DC via Catenary

• Montreal Suburban

o 2500v DC via Catenary

• Other Systems

o there are also some 50kv, 60hz catenary systems

o some DC operators generated their own 25Hz AC for distribution to

substations

Substations

Substations sit between transmission and distribution systems. They are fairly straightforward: a transformer steps down the AC voltage, then, if using a DC distribution system, a rectifier converts the AC to DC. With their transformers to step-down the high voltage transmission voltages to distribution levels, they are located periodically throughout the system. For the railroad, these are much like the ubiquitious substations with their tranformers located throughout suburban neighborhoods.

In electric locomotive (or MU) applications, the use of DC (as on the Metro North [ex New York Central] Hudson and Harlem lines and on the LIRR) requires closely spaced substations to convert AC to DC, stations more closely spaced than might be required for a similar AC distribution system. This is because of the higher line losses at the lower distribution voltages (this is explained elsewhere under Electric Power Transmission).

Rectification

Because of long-established AC motor issues of low starting torque and of power control (more on that follows), the traction motors themselves have (up until recently) been DC. This has meant that at some point in the process AC has had to be coverted ("rectified") to DC, either at the substation or in the locomotive.

AC, which reverses direction 60 times a second (the U.S. standard), generally resembles a sine wave in the distribution systems. A simple rectifier is an electrical check valve: flow is only permitted in one direction, while retaining the characteristic sine curve (one-half of the curve, just the "positive" half, let's say). This is referred to as half-wave rectification. A more sophisticated approach is to allow the negative alternations to pass also, but in the same direction as the

positive alternations (i.e., no direction change in the current). The AC thus becomes a pulsating DC, with all pulsations of the sine wave in one direction from zero. This is referred to as full-wave rectification.

FIGURE FOUR: RECTIFICATION

Substation-Based Rectification:

The rectifiers in modern substations are solid state, sillicon diode based. They

are efficient (the voltage drop is a fraction of a volt through the rectifier) and

reliable. Earlier systems, such as used on the Long Island Rail Road, used mercury

arc rectifiers, only slightly less efficient, but requiring much support (these were

known as "ingitron" systems). They were quite large, housed in large structures,

and required much cooling. Other systems, such as used by the New York City

Transit Authority, used rotary converter based substations - - very large, very

maintenance intensive.

Substations are almost always fed with three phase AC, and the three phases overlap coming out of the rectifier, so the DC pulsates only slightly (filtering can remove the pulsations altogether: see figure seven below for an example). From here, the DC is fed to the third rail (or catenary) by way of breakers, current sensors, switchgear, and whatever else.

Locomotive-Based Rectification:

Prior to the advent of a solid-state technology for converting high-power AC

to DC, massive locomotives were often the only solution to this issue when using

all AC systems: an AC motor turned a DC generator, which in turn supplied DC to

the motors on the axles. A rectifier that takes the form of an AC motor turning a

generator is called, not surprisingly, a "motor-generator."

Some railroads, such as the Pennsylvania and New Haven, had MUs with ignitrons on them. Both of these roads also had ingitron based locomotives (known as "rectifiers," locomotives such as the EP-5, E-44, and E-33, but not the PRR's GG1: one of the most massive locomotives, it was actually an all-AC unit, with power control through tranformer taps).

In the mid-1960s, high-power solid-state rectifiers became feasible, and smaller, lighter weight electric locomotives -- and AC transmissions on diesel-electric locomotives -- became available. In the straight-electric market, the last GM (GMD [Canada]) motor-generator unit was the SW1200MG (2300v, 60hz), produced from 1963 to 1971 (1971 being well after the move to solid-state rectification, but the unit had gone into production in 1963 and was maintained for an existing customer).

[ Catenary Graphic ][ back to page index ]

The conversion to AC/DC transmission

An alternator is generally smaller and simpler than a generator of like capacity. This is because generators, like DC motors, are equipped with a commutator and carbon brushes, which are what reverses the electrical current as the armature turns, preventing the current from alternating, keeping the current direct. This simpler, lighter structure means that a diesel-electric locomotive using an alternator instead of a generator should be more economical. With the advent of economical and compact solid-state rectifiers, which could be routinely installed on locomotives (see above), the greater efficiency of the alternator could finally be realized in rail applications, and AC/DC transmission became a reality. In the mid-1960s, all three major manufacturers begin offing AC/DC transmission units, Alco and GM in 1965 and GE in 1966.

FIGURE FIVE: BLOCK DIAGRAM OF A DIESEL-ELECTRIC LOCOMOTIVE WITH AN

AC/DC TRANSMISSION

diesel motor

alternator

rectifier

electric motors

The block diagram in figure five illustrates the AC/DC transmission. A diesel motor turns an alternator; the AC produced by the alternator is rectified to DC for the locomitive's DC traction motors.

GM's first applications of AC transmission were in the GP40 and SD40 of 1965 and 1966, respectively. General Electric's first AC transmission were the U28B/U28C offerings of 1966 (earlier production of these models was straight DC). Alco offered the top-end of its Century line with AC/DC transmissions, the C430/C630, in 1966/1965 respectively.

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The move away from DC traction motors

One of the most important advances in locomotive technology in recent years is the AC traction motors. AC motors have been around for many years (the kitchen clock that plugs into a recessed electrical socket directly behind it is an example of one). However, AC motors were never able to match the starting torque of the DC and are notoriously difficult to control in varrying load and speed implementations. Unfortunately, while DC motors provide high starting torque they also have critical limitations (as was noted above). These limitations have long made it desirable that a substitute be found.

Like generators, DC motors are equipped with a commutator and carbon brushes, which are subjected to very high current loads. (In a generator, these are what reverses the electrical current as the armature turns, preventing the current from alternating -- keeping the current direct; in the motor, the commutator and brushes reverse the current, creating the moving magnetic force that rotates the armature.) A DC motor that would have high current loads while not in motion or while moving slowly would receive major damage or burn-out if such a high current were to be applied for too long a period of time. At low speeds, the high amperage damage would occur within minutes. Because of this, until recently, all DC locomotives all have minimum continuous speeds (for example, SD40 & 45 at 11 to 12 MPH, SD50 at 10 MPH, GP40 at 12 MPH, some swithcers and regeared road units, such as some CSX GP38s at 7 MPH).

Power in a DC circuit is simply equal to the voltage times the current. This is expressed as power (in watts, "P") = voltage (in volts, "E" [for Electromotive force) times current (in amps, "I"), or

P=E*I, and

Power (in horsepower) = watts * 0.00134102

(going the other way, watts = horsepower * 745.6999)

In DC motors, the power relationship is simple: at a constant voltage Ohms law requires more current to produce more power (watts = voltage * current). This means that in DC high current levels will be needed to produce high power, lacking a good way to vary voltage on the fly. This becomes expensive, having necessitated heavy conductors throughout the system to carry the high current; further, the high current produce a great deal of heat, further limiting DC traction motors.

For example, to compute the current flow in a 1000 horsepower switcher with DC traction motors at 600 volts,

• 1000 horsepower = 745,699.872 watts

• 745,699.872 watts / 600 volts = 1242.83312 amps.

Using today's high-horsepower DC units, e.g. a 4400 horsepower, 6 axle unit, where each of the six motors contribute 733 horsepower to the total unit horsepower, one can get up to 5500 amps per motor in a 600 volts system. (Remember that in DC motors that current goes across the commutator and brushes.) Specifically,

• 4400 horsepower / 6 motors = 733 horsepower/motor

• 733 horsepower/motor = 546,598 watts/motor

When operating in parallel, with a 600 volt drop across each motor,

• 546,598 watts/motor / 600 volts = 910.99667 amps/motor

When operating in series, with a 100 volt drop across each of six motors,

• 546,598 watts/motor / 100 volts = 5465.98 amps/motor

Note that when operating in parallel, 911 amps * 6 motors is 5466 amperes total in the system.

These modern units -- like their AC brethren -- use computer control to reduce (hopefully to eliminate) wheel slip, but even so they can still slip (and stall), and even with arc suppressors and damping material around the brushes, flashovers and destroyed brushes still occur, caused by low speed, wheel slip, rough track, etc., all of which contribute to the woes of a DC traction motor.

Power-wize, contemporary DC traction motor size is getting very close to the practical limits. This is based on such elements as magnetic saturation and the current capacity of the electrical conductors used to build them, coupled with the physical limits of the structure (it would be necessary to use physically larger motors to forestall magnetic saturation: see note below).

In the 1960s, the Southern Pacific and the Rio Grande both acquired diesel-hydraulic locomotives. In the hydraulic transmission, a driveshaft connects the power-plant to the axles, just as in an automobile. In 1961, both roads acquired German-built Krauss-Maffei locomotives, twin-engined 3450 hp, c-c units with a cowl carbody. In 1963, the SP took an additional 15 units with a road-switcher carbody. In 1964 SP acquired the Rio-Grande units. ALCO also made a forray into the diesel-hydralluc experiments, the DH-643, a double-engine, 4300 hp, c-c unit: three units were built, all going to SP in 1964 after testing on the New York Central. In 1970 SP retired its German units, while the ALCOs were scrapped in 1973. The world still had two decades to wait for a better locomotive transmission.

Note: Magnetic saturation is a rather abstract concept that may best be thought of as the limited ability of an object to be magnetized. In the case of a motor the object is usually a piece of iron wound with wires conducting an electrical current. With an applied voltage to the wound wires, a current is caused to flow, and that current flow causes a magnetic field to be created. With more applied voltage, more current and more magnetic field in proportion to the applied voltage. At some point, the iron becomes saturated, increasing the current does not create more magnetic field, and the linear relationship is broken: increasing voltage no longer causes a linear increase in current but instead creates a geometric increase in current -- that is, lots and lots of current, creating lots and lots of heat, burning out the motor. For more on magnetic saturation, including some formulas, see our Formulas and Concepts page under AC Motor Facts.

[ back to page index ]

The move to AC traction motors

It has long been known that AC motors can be more economical than DC motors, just as with their near cousins, alternators and generators. Like alternators, AC motors are not equipped with wear-prone commutators and brushes, eliminating these sources of limitations of the low speed-high throttle position. AC motors would allow locomotives to (1) have more pulling power, (2) avoid stall burns in the traction motors, and (3) have correspondingly lower maintenance requirements.

An early example of AC in a railroad application is the GG1 (designed in 1934), which utilized 12 six-pole motors, 400 volts AC at 25 Hz. Each motor was rated at 385 hp, with the 12 motors mounted in pairs over each of the six driving axles (see our GG1 page for details of the GG1 electricals). In June of 1989, GM began the modern AC traction motor era with its demonstrator, the F69PH-AC, an AC traction version of the F59, followed in 1991 by the SD60MAC. GM delivered its first production unit to Burlington Northern in 1993. GE delivered its first AC-traction unit to CSX in June of 1994.

As a brief technical aside to provide some background and standardize terminology, series-wound DC motors (i.e., motors with commutators and brushes where the field winding and the rotor winding are connected in series) are also called universal motors, universal in the sense that they will run equally well using either AC or DC: simultaneously reversing the polarity of both the stator and the rotor cancel out, thus the motor will always rotate the same direction regardless of the voltage polarity. So a universal motor is in a sense a type of an AC motor in as much as it will operate on AC. The term "universal motor" differentiates it from the more generally thought of AC motor, the AC induction motor, which lacks commutators and brushes. Unfortunately for universal motors, the fact that they do not lack commutators and brushes means that they do lack all of the advantages of what are more typically thought of as AC motors -- the induction motors -- which is the very lack of commutators and brushes! So to say the universal motor "will run equally well using either AC or DC" may be a slight misphrasing: perhaps one should say, "it will run equally badly!" Therefore, the universal motor does not have a role to play in modern electric traction (although universal motors were used in early AC applications in locomotives); rather it is the induction motor that

is the "AC motor" to which one refers when speaking of AC traction motors today. That means no brushes to maintain, no flashovers, no commutator to get damaged, no armatures to rewind, and less potential for damage at high power/low rpm situations.

AC locomotives are more expensive due to the control problems inherent in the AC design. An AC motor's speed is traditionally dependant on its design, but it may be controlled by varying the frequency of the input voltage. Being able to vary frequency has been a significant issue in the development of AC motors in high-horsepower traction applications. To deal with the power control problem, both EMD and GE use an AC to DC to AC conversion, control taking place in the DC phase. In an AC traction motor application, the diesel engine drives an alternator, crating AC. This AC is rectified (i.e., converted to DC) and power control takes place in this stage. This is the same place that power control would take place in a conventional AC/DC transmission. At this point, the DC (called the DC link) goes through a solid-state "inverter," which converts the DC back to AC. This AC then powers the motors.

FIGURE SIX, BLOCK DIAGRAM OF A DIESEL-ELECTRIC LOCOMOTIVE WITH AC

TRACTION MOTORS

diesel motor

alternator

rectifier

== DC LINK ==

inverter

electric motors

FIGURE SEVEN, VOLTAGE/FREQUENCY IN A DIESEL-ELECTRIC LOCOMOTIVE WITH

AC TRACTION MOTORS: OUTPUT OF ALTERNATOR TO OUTPUT OF INVERTER

Control takes place in the stages around the DC Link. The inverter converts the DC back to AC, with the conversion frequency and voltage specifically controlled (this is what then determines the motor's speed). However, this is not simply an inverter, for in modern applicatons of AC motors, with a reliance made on varying the voltage and frequency of the AC to control power more than on simply the brute force approach of the application of current, the inverter must do more than simply convert DC to AC. Complex electronic circuitry in the form of on-board computers now is used to control the inverter. (This has eliminated the need for

that classic of the diesel age, the ammeter, in the cab of the AC-motored locomotive, which has been replaced by a tractive effort display.)

The inverter stage is actually a group of inverters, depending on manufacturer either one for each truck (GM) or one for each motor (GE). Each individual inverter consists of six "gated turn-on (GTO) devices," high-power thyristors (that is, "silicon-controlled rectifiers"), three each for the positive and the negative phases of the AC wave in positive/negative pairs. Each positive/negative pair alternate turning-on, chopping the DC into a square wave AC. Each of the three positive/negative pairs turn-on 120 degrees out of phase from each other (turning-on at 0 degrees, 120 degrees, and 240 degrees), producing three-phase AC. While the phase remains constant, the frequency -- how many cycles per second this is repeated -- is varried. Also able to be controlled at this stage is the voltage, how positive and negative the AC becomes. Thus, the frequency and the voltage of the AC arriving at the AC motor is fully controlable, providing the speed control for the locomotive.

Since the frequency and voltage are closely controlled by onboard computer systems, motors cannot run away as they would on a DC locomotive, and the AC motor will not be subject to damaging wheel slip. The use of AC traction motors, coupled with computer controlled wheel creep systems, has allowed AC units to achieve much higher adhesion levels than similar DC units, up to 45% adhesion, versus the 20% range on other units. This has permitted two-for-three and one-for-two replacement of units, with resulting economies in size and maintenance expenses that offset the added initial investment in the purchase of AC units. (Note, however, that there are other issues with such power reductions: for example, a two-for-one reduction on a tradtionally two locomotive run means one locomotive, and if that one locomotive develops problems enroute [not entirely unheard of] there is no backup.)

Computer control technology has also been applied to DC traction motors, including wheel-slip detection and a wheel-creep systems allowing for brief [we're talking fractions of seconds here] applications of power to facilitate very low speed operations. While, this does not fully eliminate problems with high current flow at low speeds in DC motors, these DC wheel-creep systems and wheel-slip detection systems provide dramatically increased adhesion in DC units as well as in AC units and have eliminated many of the operational issues with DC traction: CSX, for example, does not place a minimum continuous speed on its DC-traction GM SD60s and SD70s and GE Dash 8 and Dash 9 locomotives, the same as for all of its AC locomotives [see also note above].)

While the AC traction motor is less complex and has proven itself dependable in long term railroad use (the PRR GG1 used 12 385 hp AC motors ), the purchase of new units with AC traction motors is an expensive undertaking, representing an investment in new technology with maintenance and operational issues not previously encountered, and the new generation of 1000 hp AC traction motors in railroad use represents a new and untested technology, with some railroads still very reluctant to make the transition. (An interesting W3 site on AC motors is http://www.drivesys.com/asdis.html.)

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Expanded AC Motor Principals

The Short Version

This isn't expected to make sense, so don't worry. When an AC motor is at rest and an AC voltage is first applied to it, the difference between the aramature speed and the rotating field is 100%. Under these conditions, a high current will flow at the moment the aramature starts to turn. At the moment of starting, the torque is at 0% of the full load torque, but as the speed increases the torque likewise increases. This is in part because, at low speeds, the motor reactance is high, and the current and voltage are very much out phase. This contributes to the low power factor. In an AC motor, maximum power will be generated when the voltage and current are closest to being in phase, so it can be seen that when the voltage and current are out of phase the motor will not be very efficient.

The Long Version

(See the Formulas and Concepts page for more detail on AC motor operation and on

these formulas).

Power in a DC circuit versus Power in an AC circuit.

Power in a DC circuit

As noted above, Power in a DC circuit is simply equal to the voltage times the current. This is expressed as power (in watts, "P") = voltage (in volts, "E" [for Electromotive force) times current (in amps, "I"), or

P=E*I

For example, ten volts times ten amps equals 100 watts. This relationship can be used in reverse to analyze a circuit. A 40 watt bulb on a 12 volt DC circuit must be drawing 3.333 amps. Further, since Ohm's law states that voltage = current tims resistance (E=I*R), it may be seen that the load here is 3.6 ohms. This is all simple and straightforward because this is a DC circuit.

Power in an AC circuit

AC Motors

One of the miricals of the AC motor is that in the AC induction motor, one of the of the two principal components (these two components in the AC motor are the stator and the rotor), the rotor has no visable electrical contacts to the outside world. Instead, it has an electrical field induced into it by the electrical field of the stator -- no commutator, no brushes! (Acutally, some induction motors have brushes and slip rings, but these are used for connecting control and starting equipment to the windings). The induction of the electrical field into the rotor happens because of the characteristic pulsing flow of current in AC. However, this has other affects as well.

• Reactance

In an AC circuit, things are different, because in addition to there being a pure resistive load in the circuit there is also reactance in the circuit. Reactance is the unique effect that is displayed in opposition to AC current flow. There are two types of reactance, inductive reactance (that is, a coil), the tendency of the circuit to absorb and store an electrical potential, and capacitive reactance (that is, a capacitor), the tendency of the circuit to absorb and store current. AC circuits can always be quantified in terms of these three forces: resistance, inductive reactance, and capacative reactance. The total oppostion to the AC current flow is called impedance, and it is the vectored sum of the circuit resistance plus the total reactance, inductive and capacitive. Since inductive and capacitive reactance are forces of opposite direction, they counter each other, thus,

1. Inductive Reactance, Xl, = 2PiFL

2. Capacitive Reactance, Xc, = 1/(2PiFC)

where

• Xl = Inductive Reactance in Ohms,

• Xc = Capacitive Reactance in Ohms,

and

• F = the frequency of the applied AC in Hertz (cycles per

second),

• L = the inductence of the circuit in Henries, and

• C = the capacitence of the circuit in Farads

3. Impedance, Z, = (R2 * X2)1/2, where X2 = (Xl - Xc)2

where

• Z = Impedance in Ohms,

• R = Resistance in Ohms, and

• X = Reactance in Ohms

AC induction motors are primarilly inductive circuits, so effectively their impedence may be expressed by the formula

Z = (R2 * X l2)1/2

• Power Factor

In an AC circuit, voltage times current does not equal power; it equals the effective value of voltage and current, which is measured in "voltamperes" (VA). Correcting voltamperes for "power factor" produces the useful or actual power in the circuit, which is measured in watts. So,

P = VA * pf

and the value of pf is determined by how much the voltage and current are out of phase. An incandescent light bulb has a power factor of anywhere from 0.95 to 0.99; AC motors may have power factors ranging from .6 to .9; in all of these situations, the current is lagging the voltage -- inductive circuits.

• Phase Angle

A purely reactive circuit has a phase angle between the current and voltage of 90 degrees, which results in a power factor of 0.0. The relationship between phase angle and power factor is that power factor equals the cosine of the phase angle. Therefore, power equals the cosine of the phase angle times the voltamperes. In the above example, the cosine of 90 degrees = 0.0. So, at rest, with 90 degree phase angle (purely reactive

circuit -- the resistance of the motor's windings is minimal), the useful power of the motor is . . . 0 watts! There are starting strategies, for example, any substantive resistance in the circuit will reduce the phase angle below 90 degrees, thus increasing power factor above 0 and allowing some work to get done. More typically, capacitor-based systems can reduce the phase angle and can be used to start the motor.

The situation that has developed is that the power developed in an AC motor is related to the magnitude of the voltage, the current, and the internal resistance of the motor (i.e., the simple resistance of the wires), and the frequency of the AC applied to the motor, because the frequency will change the phase angle. (This concept is expanded upon on the Formulas and Concepts page under Power Facts/AC Motor Facts.)

• Speed Control in AC Motors

Since an AC motor's speed is based on the frequency of the AC, a change in frequency directly results in a change in speed; however, the change in frequency also changes the reactance of the circuit (because a reduction in the frequency causes a linear reduction in inductive reactance). This in turn changes the impedance of the circuit, the oppositon to the flow of AC current. Speed control may be accomplished in these motors by utilizing solid-state, micro-processor control devices that vary the frequency and voltage of the AC applied to the motor.

If it were intended to slow an AC motor, the frequency of the applied AC would be reduced: as frequency decreases, circuit reactance decreases, and therefore impedance also decreases. Given a constant voltage, current would increase, potentially to the point where the motor would be damaged. Therefore, a decrease in the frequency must be accompanied by a decrease in voltage sufficient to stabilize the current.

As one last reminder, there is much more detailed information on our Formulas and Concepts page under Power Facts/AC Motor Facts.

GASP!

Kilo Newtons, kilo Watts, kilometres per Hour

So just what do terms used to describe the performance of locomotives and multiple units like Maximum Tractive Effort, Power At Rail, and Continuous Power mean? Here is a guide to such things showing how they influence journey times and speeds.

Some School Physics Revision

A few basic physical relationships link the various factors that influence the acceleration and speed of an object, in this case a train! The following notes explain those relationships.

The application of a force to a mass will cause it to accelerate as governed by one of Newton's laws of motion. The relationship is that the force necessary is the product of the mass and the acceleration rate.

i.e. Force = Mass x Acceleration (1)

Here it is useful to point out that, in strict scientific terms, weight is the force acting on a mass resulting from the influence of the acceleration due to gravity (which is constant for all objects).

The energy consumed in moving an object over a distance is the product of the force required and the distance.

i.e. Energy = Force x Distance

Now, power is the rate of energy usage

i.e. Power = Energy/Time

And speed is the rate of travelling a distance

i.e. Speed = Distance/Time

These relationships may therefore be combined

so Power = Force x Speed (2)

This introduction provides two relationships that will reappear later on.

Units of Measurement

All physical quantities have some unit of measurement assigned to them in order to support these relationships numerically. The standard system of units across the world is the Systeme International (SI), from which many units are known colloquially as "metric". Within this system, the quantification of units is based on 10s, 100s etc, with the main divide points every 1000 (e.g. millimetres, metres and kilometres). Before this system was introduced, various other units were used, often referred to as "imperial", where the links between sub-units were not so mathematically straightforward (e.g. inches, yards, miles).

The rest of this article will use SI units for all but miles, but the following section explains the units for each of the quantities already introduced, and shows their conversion to imperial units which may well be more familiar to many readers.

Quantity SI Unit Name

SI Unit Symbol

Imperial Unit Name

Imperial Unit Symbol

ConversionSI Unit Imperial

Unit (approx.)

Force Newton N Pound force lbf 1 N 0.22 lb f

Mass Kilogram kg Pound lb 1kg 2.2 lb

Distance Metre m Yard yd 1 m 1.09 yd

Distance Kilometre km Mile mile 1 km 0.62 mile

Time Second s

Speed Metres per second

m/s Miles per hour mph 1 m/s 2.2 mph

Speed Kilometres per hour

km/h Miles per hour mph 1 km/h 0.62 mph

Acceleration Metres per second per second

m/s/s orm/s2

Energy Joule J

Power Watt W

With the SI unit system, a largely standard means of sub-dividing the units using a prefix is employed so as to keep the figures quoted sensible. These are broken down in intervals of 1000, although some intermediate intervals occur. The following table lists the commonly used prefixes. Note that the one exception to these is the base unit of mass being the kilogram, with a thousandth of a kilogram being a gram and a thousand kilograms being a tonne!

Prefix Symbol Interval

milli m 1/1000

centi c 1/100

deci d 1/10

1

kilo k 1000

mega M 1 000 000

Anyway, now we get to the trains at last……..

Getting Going

Tractive Effort

Tractive Effort (TE) is the name for the force applied to the rail by the wheel of the train to cause movement. The size of that force is determined by the characteristic of the power equipment installed on the train, and how the driver uses it.

By necessity, this tractive effort is not constant throughout the speed range, and most traction units have a characteristic that looks something like Fig 1.

Fig 1:

In the example characteristic shown, the TE is constant up to 20 mph, therefore in this speed range, from relationship (1) above, the acceleration will be constant. As a result of this, speed will build up uniformly with time as shown in Fig 2. This is the region of Maximum Tractive Effort.

Fig 2:

Above this speed, the TE falls, and in consequence the acceleration will start to fall and speed will not build up so quickly. The plot of speed with time, now starts to curve as shown in Fig 3.

Fig 3:

Power

Relationship (2) above says that power is the product of force and speed. Now, if the force, or TE were to remain constant with increasing speed, the power requirement would continue to rise throughout the speed range. Practically, this is not possible as the necessary equipment becomes unfeasibly big and costly, so, when the maximum power capability (or rating) of the equipment is reached, the TE must start to be reduced as speed increases to compensate. This occurs at the "knee" point at 20mph on the above TE-speed curve (Fig 1).

So, in the example given, the maximum TE of the unit is 100kN, and hence the maximum power may be calculated as follows:

Speed in m/s from above table = 20/2.2 = 9.1 m/s

Power = Force x Speed

= 100kN x 9.1 m/s

= 910kW

Fig 4:

As this is the power needed to actually move the train it is strictly referred to as the Maximum Power at Rail.

In reality, the total power drawn from the supply (whether overhead wire, third rail, or fuel tank) will be greater than 910kW, due to the need for additional auxiliary loads (for lighting, heating, cooling etc) and due to losses in the conversion process, as nothing is 100% efficient.

Further, it is highly unlikely that the equipment is capable of running at this power level continuously, and indeed for many types of service, it would offer little advantage relative to the associated cost. Again, for reasons of rating the characteristic of the equipment will not follow the curve of maximum power to top speed, as indicated by the dip from 70mph onwards in Figs 1 & 4. Consequently a continuous power rating will often also be quoted.

This continuous power rating may be derived from a number of factors based around the equipment characteristic and will including assumptions of proportion of time at a lower tractive effort demand (driver's controller) or coasting.

Train Resistance

So that's how a train is controlled to get it moving, but in practice there are a number of other forces which act to make life difficult.

Friction is always present where motion is concerned, and indeed, there is a certain minimum amount which must be overcome before any movement can take place (often known as stiction!).

Air resistance, or drag, is another important factor which becomes increasingly significant with speed. Pointed noses help reduce this.

These factors are accounted for mathematically using results found by measurement and experience, as theoretical calculation would be far too complex.

Generally train resistance is expressed as:

R = a + bv + cv2 where v = speed

The factors a, b and c characterise the particular train, with a being the stiction referred to above, b arises from other mechanical considerations, and c is due to the air resistance.

The train resistance typically looks something like that shown in Fig 5.

Fig 5:

There are further factors to take into account which depend on the route. The main one of these is gradient, which brings in the effect of gravity.

If the train was travelling vertically upwards (i.e. it thought it was the space shuttle at take off), it would incur the full effect of gravity. As explained earlier, the acceleration due to gravity is constant. Mathematically, it is known as g (as in the term g forces in also the best quality intellectual films!) and is 9.81 m/s2.

For example, for a 150 tonne (150 x 1000 kg) train, the gravitational force acting on it is:

Force = Mass x Acceleration

= 150 x 1000 x 9.81

= 1 471 500 N

= 1 471.5 kN

This is the weight of the train.

Now, even the Lickey incline isn't that steep, so the gravitational resistance practically encountered isn't nearly so great. While it's not completely accurate, for the gradients encountered by trains, it suffices to divide the weight by the gradient to obtain the value for this resistance.

So, for example if the above train were climbing a 1 in 200 gradient, the resistance due to gravity would be:

1 471.5/200

= 7.3575 kN

This resistance is constant irrespective of speed and thus simply adds to the train resistance. When the train is going downhill, this figure is subtracted from the train resistance - i.e. it assists the train.

The effect of gradient is seen in Fig 6.

Fig 6:

Now, how do these forces look compared to the Tractive Effort developed by the train

Fig 7:

As long as the train produces Tractive Effort greater than the overall train resistance, then it will accelerate. The point at which the two curves cross is when it will cease to accelerate and is known as the balancing speed and is the maximum speed attainable on that particular track. In the example here it is 95 mph on the level, but 75 mph on a 1 in 100 gradient.

The force available to accelerate the train is the difference between the Tractive Effort and the train resistance. Thus it will be realised that an earlier statement about constant acceleration, when the TE is constant, is not strictly correct. In practice the acceleration will reduce as the resistance increases with speed. Additionally it will be noted that train resistance becomes increasingly significant as speed increases.

The following curve shows the actual build up in speed allowing for train resistance (Actual Characteristic) compared with the theoretical build up in speed seen earlier in Fig 3 (Ideal Characteristic):

Fig 8:

Gear Ratio

In all the above discussions, gear ratio has not been mentioned. A gearbox links the traction motor shaft to the train axle in order to step down the rotational speed since motors run much faster than axles! As power = force x speed, and assuming that there are no losses in the gearbox, as the rotational speed at the axle is reduced, the torque at the axle is increased. Consequently, re-gearing is often used as a means of obtaining a revised traction characteristic to suit alternative service patterns without other significant change to the traction equipment.

Wheel Diameter

Before finishing, it is also worth noting that this performance will not be maintained throughout the life of the train, since, as the wheels wear down, the tractive effort characteristic will change! A change in the wheel diameter is effectively a change of gear ratio, and consequently as the wheels get smaller the starting TE will increase. However, as this also means that the axle speed becomes higher for any given train speed, the TE at higher speeds will fall off more rapidly. When train performance is being predicted, it is normal to assume the average half-worn wheel diameter.

Fig 9 illustrates the effect of wheel diameter on the TE characteristic.

Fig 9:

With all this information, it is therefore possible to calculate the performance of a train over a given route.

Example Route Performance Calculation - Appleby to Settle

To provide an example of such a calculation illustrating the various influences, a train with the above TE characteristic (based on the average wheel diameter) is shown running over the Appleby to Settle section of the Settle & Carlisle route (Fig 10), with stops at each of the intermediate stations. In this example, the line speed limit has been falsely set to 85mph between Kirkby Stephen and Garsdale so as to illustrate the effect of gradient on speed (see expanded profile Fig 11).

In the following two diagrams, the train speed is indicated by the bold red line, with line speed restrictions indicated by the pink line. The gradient profile is illustrated by the green line, and is not to any scale.

Fig 10:

Fig 11:

The train is capable of reaching and maintaining the 60mph line speed limit even when climbing the 1 in 100 gradient shortly after departure from Appleby (Fig 10). On leaving Kirkby Stephen (Fig 11) speed increases with the classic curve illustrated in Fig 8, albeit up the 1 in 100 gradient, before hitting a short stretch of less arduous climb around Mallerstang. At this point, the train accelerates more (i.e. speed builds up more quickly) to around 75mph until a further stretch of 1 in 100 is reached. As is seen above in Fig 7, the balancing speed on such a gradient is 75mph and thus speed remains constant until the

summit at Ais Gill is reached and a short downhill stretch is encountered allowing speed to increase to the 85mph line limit shortly before braking for Garsdale.

Consequently with such information, journey times may be calculated, although margins and allowances for other factors, such as driving technique, track curvature and wind need to be included.

Footnote

All the above curves have been generated for the illustrative purposes of this article and do not represent any one particular equipment.

Gradient profile information for the Settle & Carlisle route is based on information from "British Rail Main Line Gradient Profiles - Ian Allan.

Tony Woof B.Eng C.Eng MIEE

[ D.C. Circuits ]

[ Ohm's Law ]

[ A.C. Circuits ]

[ Capacitance ] [ Inductance ] [ Impedance ] [ Resonant Circuits ]

[ Power & Other Electrical Concepts ]

[ Power & AC Motors ] [ Electric Power Transmission ]

[ TOP ]

D.C. Circuits

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Ohm's Law

E = I * R

I = R / E

R = E / I

where

E = Electromotive Force (in Volts); also abbreviated as V

I = Current (in Amperes)

R = Resistence (in Ohms)

Power, in Watts

= I2R

= E2/R

A.C. Circuits

[ back to page index ]

Capacitance

Capacitive Reactance

(XC) = 1/(2PiFC) [in Ohms]

where

F = Frequency in Hertz

C = Capacitance in Farads

If using microfarads instead of farads, the formula is: 1,000,000/(2PiFC)

µf =

106

(µf is

"microfarads)

(106 is

Million)

pf =

1012

(pf is

"picofarads)

(109 is

Billion)

Pi = 3.14159265358979

Time Constant

To charge a capacitor to 63.2% of the source voltage.

or

To discharge a capacitor to 36.8% of its initial stored charge.

T = RC

where

T = time in seconds,

R = resistance of circuit in Ohms,

C = capacitance in farads

For multiple time constants,

Two time constants will charge to 86.5% or discharge to 13.5%.

Five time constants will charge to approximately 99% of source voltage.

(See the time constant graph under Inductance.)

Energy Stored

To charge a capacitor to 63.2% of the source voltage.

En = CE2/2

Quantity of Charge

Q = CE

where

C = Capacitance in farads

E = Electromotive Force (in Volts); also abbreviated as V

En = energy stored joules (wattseconds)

Q = quantity of charge in coulombs

Above ~10 MHz, capacitors will start acting like tuned circuits due to their inductance [in the leads, etc]: they will block AC and a capacitor of less capacitance will be required to pass higher frequencies.

As the capacitance or frequency increases, the capacitive reactance decreases; as the capacitive reactance decreases, the more AC that will pass, specifically, the higher the frequency of AC that will pass.

Table One A: Capacitive Reactance, 60 Hz - 50 KHz Power and Audio Frequencies

Capacitive Reactance in Ohms

Frequency:

Power Audio . . . . . .

Capacitance:

60 Hz 1000 Hz 3000 Hz 5 Khz 50

KHz

100 µf 26.53 1.59 XC is less than one ohm

1 µf 2,653 1.59 53 32 3.2

0.01 µf 2.653

105

15,920 5,300 3,183 318

100 pf

1.591

106

5.300

105

3.183

105

31,318

1 pf XC is greater than 2,000,000 ohms

Table One B: Capacitive Reactance, 250 KHz and over RF Frequencies

Capacitive Reactance in Ohms

Frequency:

LF MF . . . HF VHF . . . UHF . . .

Capacitance:

250 500 1

5 MHz 50 100 500 1

KHz KHz MHz MHz MHz MHz GHz

1 µf XC is less than one ohm

0.01 µf 63 32 16 3.2 XC is less than one ohm

100 pf 6,264 3,183 1,591 317 32 16 3.2 1.6

1 pf 6,264

105

3.183

105

1.591

105

31,830 3,183 1,591 318 159

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Inductance

Inductive Reactance

(XL)= 2PiFL [in Ohms]

where

F = Frequency in Hertz

L = Inductance in Henries

mL = 103 (mL is "milli-

henries")

(103 is Thous

and)

µL = 106 (µL is "micro-

henries")

(106 is Millio

n)

Pi = 3.14159265358979

Coils

A single layer, air-core coil of length approximately equal to its diameter

approximates the following:

µL = (r2N

2)/(9r + 10l)

where:

µL = inductance in micro-henries

r = radius in inches

N = number of turns

l = length of coil in inches

A coil has 1 Henry of inductance for a current change of 1 amp per second, which

produces an average counter force of 1 volt within the coil.

Time Constant

T = L/R

for current to rise to 63% of its maximum through the coil

where

L = inductance of coil in Henries

R = resistance of coil (or of the L/R circuit) in Ohms

Table Table Two: Time Consant Curve

Time Consants: Percents Change

RC

RL

Time

Constant

t

% of

Change

in t

% of Final

Q or V

on C

when

Charging

% of Initial

Q or V

on C

when

Discharging

% of Final

I

When

Increasing

% of Initial

I

When

Decreasing

1

63.2

63.2

36.8

63.2

36.8

2 23.3 86.5 13.5 86.5 13.5

3 8.5 95.0 5.0 95.0 5.0

4 3.2 98.2 1.8 98.2 1.8

5 1.1 99.3 0.7 99.3 0.7

Energy

LI2/2

(in joules [watt-seconds]) in a coil's magnetic field

where

L = inductance of coil in Henries

I = current through the coil in Amps

Table Three A: Inductive Reactance, 60 - 50 KHz Power and Audio Frequencies

Inductive Reactance in Ohms

Frequency:

Power Audio . . . . . .

Inductance:

60 Hz 1000 Hz 3000 Hz 5 Khz 50 KHz

30 L 11,310 188,495 565,485 942,477 9.425 106

10 L 3,770 62,831 188,493 314,159 3.142 106

1 L 377 6,283 18,849 31,416 314,159

0.1 L 37.7 628 1,885 3,142 31,416

10 mL 3.77 62.8 188 314 3,142

3.3 mL 1.25 20.7 62.1 104 1,037

1 mL

6.28 18.8 31.4 314

100 µL

1.9 3.14 31.4

10 µL

3.14

1 µL XL is less than one ohm

Table Three B: Inductive Reactance, 250 KHz and over

RF Frequencies

Inductive Reactance in Ohms

Frequency:

LF MF . . . HF VHF . . . UHF . . .

Inductance:

250 KHz 500

KHz 1 MHz 5 MHz 50 MHz

100

MHz

500

MHz 1 GHz

1 L 1,570

106

XL is greater than 2,000,000 ohms

0.1 L 157,079 314,159 628,318 3.142

106

10 mL 15,708 81,416 62,831 314,159 3.142

106

3.3 mL 5,184 10,367 20,734 103,673 1.037

106

1 mL 1,570 3,142 6,283 31,416 314,159 628,318 3.142

106

6.283

106

100 µL 157 314 628 3,142 31,416 62,831 314,159 628,318

10 µL 15.7 31.4 62.8 314 3,142 6,283 31,416 62,832

1 µL 1.57 3.14 6.28 31.4 314 628 3,142 6,283

0.1 µL

3.14 31.4 62.8 314 628

0.01 µL XL is less than one ohm 3.14 6.28 31.4 62.8

0.001 µL

3.14 6.28

[ back to page index ]

IMPEDANCE

Impedance (Z)

equals (in Ohms)

Series:

Z = (R2 + X

2)

1/2, where X = XL-XC

Parallel:

Y [i.e., 1/Z] = (G2 + B

2)

1/2, where B = BL-BC

Definitions:

X = Reactance, in ohms

B = Susceptance (B = 1/X), in mhos (mhos = 1/ohms)

XL = Inductive Reactance

XC = Capacitive Reactance

BL = Inductive Susceptance

BC = Capacitive Susceptance

G = Conductance, in mhos (G = 1/R)

Y = Admitance, in mhos (Y = 1/Z)

Formula Review

XL = 2PiFL

XC = 1/(2PiFC) -- or -- 1,000,000/(2PiFC) where C = µf

BC = 2PiFC

BL = 1/(2PiFL)

Vectors

Xc: V = -j, I = j

(Voltage lags -- voltage has negative "J Operator")

Xl: V = j, I = -j

(Current lags -- current has negative "J Operator")

Figure One, Diagram of Vectors [d]

Note that the two formulas for computing impedance,

Z = (R2 + X2)1/2 and Y [1/Z] = (G2 + B2)1/2,

both build a right triangle based on the above diagram, with impedance being the hypoteneuse of the triangle. If the nature of the circuit is of importance (i.e., is it capacitive or inductive), then the direction of the vector can also be indicated based on the sign of the reactance. Note also that this sign is lost when the reactance is squared in computing impedance, as X-squared always has a positive sign.

Parallel circuits with series elements:

First compute the series impedance in each branch, then . . .

G (in any branch) = R/Z2

B (in any branch) = X/Z2

Y2 =

(G1 + G2 + G3 + . . . ) +

(B1 + B2 + B3 + . . . )

[ back to page index ]

RESONANT (TUNED) CIRCUITS

Tuned circuits are an integral part of inductance, capacatance, and impedance. Applications for resonance and tuned circuits are usually in broadcast and other radio frequency applications (so if you're listening-in you are using a resonant circuit of some sort!).

The frequency of a tuned circuit equals:

1/(2Pi * (LC)

1/2) =

0.159/(LC)

1/2 or

0.159/L1/2C1/2

Q, the figure of merit of the circuit, equals:

of a series circuit = (XL)/R or (XC)/R

of a parallel circuit = R/X

For resonant circuits,

Qp = R/(L/C)1/2

Qs = (L/C)

1/2/R

Using Q, the frequency (F) of a tuned circuit is:

F = (1 - 1/4Q2)1/2/2Pi(LC)1/2

When L or C are increased, F is decreased;

When L or C are decreased, F is increased.

Half-Power Bandwidth, BW, is related to Q. It is defined as the difference

between the upper (f2) and lower (f1) half-power frequencies. It is computed as

follows:

BW = Fc/Q

where

BW = Half Power Bandwidth

Fc = center frequency of the tuned circuit

Power & Other Electrical Concepts

[ back to page index ]

POWER

AC MOTORS

Measuring Power

In D.C. circuits and in non-reactive A.C. circuits,

Power = I x E

where

Power = Watts

I = Current (in Amps)

E = Electromotive Force (in Volts; also abbreviated as V)

alternatively,

Power = E2/R = I

2R

In AC circuits, these relationships are different. AC circuits also have Reactance, the tendency of an inductor or capacitor to resist AC current flow (to DC, an inductor -- a coil -- is a short circuit, while a capacitor is an open circuit). To correct the above DC formulas for AC, the vector of Resistance and Reactance must be computed, which is Impedance (see above). Correcting the DC power formula for AC is done by applying the "power factor."

Power factor:

For parallel circuits:

• IR/IS

-- or --

• G/Y

For series circuits:

• ER/ES

-- or --

• R/Z

For both parallel and series circuits:

• I2R/EA

-- or --

• P/EA

Using cosines:

For parallel circuits:

• cosine [phase angle] = IR/IS

For series circuits:

• cosine [phase angle] = R/Z

Notes:

R

Resistive current or voltage

S

Source current or voltage

In a DC circuit, EA is the power; in an AC circuit, EA is the "Volt-Amperes" (sometimes "VA")

Also, see Impedance (above) for full explanations of G (Conductance, 1/R) and Y (Admittance, 1/Z)

AC/DC Power Relationships:

• DC

o 1 volt DC across 1 ohm = 1 watt

o 1 amp DC through 1 ohm = 1 watt

• AC

For the following,

o Assume that IR = IS (phase angle = 0, power factor = 100%)

o P-P is "Peak-to-Peak," i.e., in one oscillation of the sine wave the

voltage measured from the top (positive) peak to the bottom

(negative) peak.

o Vrms is "Volts root-mean-square," the effective total voltage under

the sine wave.

o 1 volt AC [P-P] across 1 ohm = 0.125 watt:

� 1 volt AC [P-P] =

� 0.5 volt pulsating DC; 0.5 x 0.707 =

� .3535 Vrms

� Power = E x E / R = (.3535 x .3535)/1 = 0.125 watt

o 2 volts AC [P-P], 1 volt pulsating DC, across 1 ohm =

� (.7072)/1 = 0.4949 watt

Using Sines:

An AC voltage, v, can be described mathematically as a function of time by the following equation:

v(t) = A * sin(ωt)

where

o A is the amplitude in volts (also called the peak voltage)

o ω is the angular frequency in radians per second

o t is the time in seconds.

This formula is commonly rewritten as the following:

v(t) = A * sin(2πft)

where

o π is "pi" -- 3.14 . . .

o f is the frequency in hertz

Note the similarity here between this formula (2πft) and the various formulas above:

o 2πfl

o 1/(2πfc)

o 1/(2π * (lc)1/2)

Since, for any angle x, sin(x) can have a maximum value of is +1 and a minimum value is -1, an AC voltage swings between +A and -A. The peak-to-peak voltage, written as VP-P, is therefore

o (+A) - (-A) =

o (+A) + (+A) =

o 2A

AC Motors

• Power Computation

In an AC motor with an essentially reactive circuit (i.e., the impedence is approximately equal to the inductive reactance), the voltamperes may be computed as

E² / Xl

where Xl is the Inductive Reactance (see Inductance above) So again,

1 volt AC [P-P] across 1 ohm = 0.125 voltamperes (VA) . . .

1 volt AC [P-P] = 0.5 volt pulsating DC; 0.5 x 0.707 = .3535 Vrms

VA = E x E / R = (.3535 x .3535)/1 = 0.125 VA

2 volts AC [P-P], 1 volt pulsating DC, across 1 ohm =

(.7072)/1 = 0.4949 VA

But in this purely reactive circuit, with a phase angle of 90%, the power factor is 0, and watts = 0! Changing the motor slightly, if the motor were to have an internal resistance of 2 ohms and a total inductance of 6 milli-henrys (see the table of inductances under Inductance above), and an AC of 60 Hz were applied to it, it would have the following characteristics:

• its inductive reactance at 60 Hz would be approximately 2 ohms

• its impedance (Z=[R² * X²]½) would be

o Z = (2² * 2²)½

o Z = (4 * 4)½

o Z = 16½ = 4 ohms

• its power factor (R/Z, assuming it to be a simple series circuit) would be

.5000 (2 ohms resistance / 4 ohms impedance)

• and its phase angle (not really important here) could be computed as

follows:

o cosine (angle x) = R/Z

o cosine (angle x) = 2/4 = .5000

o .5000 = cosine 60 degrees

Applying 10 volts across this motor would yield 25 voltamperes ((10 * 10)/4) and 12.5 watts (25 * 0.5), with a current of 2.5 amps. If an AC voltage of a different frequency were to be applied to the motor, it would yield the following characteristics:

• it's inductive reactance at 120 Hz would be approximately 4 ohms

• it's impedance (Z=[R² * X²]½) would be

• Z = (2² * 4²)½

• Z = (4 * 16)½

• Z = 64½ = 8 ohms

• its power factor (again assuming it to be a simple series circuit) would be

.2500 (4 ohms R/16 ohms Z)

• and its phase angle could be computed as

• cosine = R/Z

• cosine = 2/8 = .2500

• .2500 = cosine 75.522 degrees

Applying 10 volts across this motor would yield 12.5 voltamperes ((10 * 10)/8) and 3.125 watts (12.5 * 0.25), with a current of 1.25 amps. Reducing the AC to 30 Hz would be . . .

• Inductive Reactance: 1 ohms

• Impedance: 2.236 ohms

• Power Factor: 0.8945

• Phase Angle: 82.81 degrees

And now 10 volts produces 44.723 voltamperes and 40.004 watts, with a current of 4.4723 amps.

So changing the frequency of the AC has changed the power dramatically. This has a number of consequences. First, changing the frequency (at a constant voltage) will also change key operating characteristics of the motor, such as the power produced and the current flow. Second, since changing the frequency changes the flow of current through the motor, reducing the frequency may result in an unacceptably high current flow causing damage to the motor. Finally, changing the frequency of the AC changes the speed of the rotor.

• Speed Control in AC Motors

To give away the punch-line first . . . Practically speaking, the frequency of the AC is how the speed of any given AC motor is controlled. This is so because of the specific characteristics of AC.

To develop that idea more fully, the speed of any given AC motor is based on the frequency of the applied voltage, the permanent internal construction of the

motor, and on the load. Critical in the internal construction of the motor is the number of poles in the stator windings, along with the nature of the wire in the windings and of the component iron (meaning how much current can be applied to the motor and how much of a magnetic field will that current produce). Essentially it is frequency, poles, and load (see AC Motor Speed Table following for how these elements interact).

The load is assumed to be within the ability of the motor to turn. An infinitely large load would be beyond the ability of any motor to turn, while a "too big" load will be beyond the ability of some motor to turn, with the concept of "too big" being based on the motor's internal characteristics: how large is the motor, how much current is it rated for, how much torque does it provide, etc. The ability of the windings to conduct an appropriately high current is necessary for a high-horsepower motor.

Assuming the ability of the motor turn the load (that is, an appropriately rated motor for the load), there will still be some "slip" from the computed speed. The computed speed is called the "synchronous speed," which is when the rotor turns at the same rate as the magnetic field is advancing around the stator. This slip is usually in the area of about 5%, and results in what is called the "full load speed."

By the way, if there were no slip (i.e., if the motor were turning at its synchronous speed, the maximum possible speed for an induction motor), the relative velocity between the stator flux and the rotor motion is zero, thus there is no voltage induced in the rotor windings, hence there is no current flowing in those winding: there is zero torque. Of course, this condition cannot exist for any time under load, slip reappears, and current flows again. This is also the starting problem -- getting the rotor turning, getting slip, getting torque.

Poles are based on the windings of the motor, specifically how the windings are set up inside the motor by their placement and connection, and are in fact the actual magnetic entities of the motors. Since magnetic entities always come in pairs (North & South) [o.k., physics Ph.D.s, show me a real magnetic monopole], the poles of an AC motor also always come in pairs. So a motor may have two poles, four poles, six, eight, and so forth.

The speed of the motor is based on how the AC rotates around the stator, the resulting magnetic field dragging the rotor along with it. The AC energizes the magnetic field in the stator as it passes along the poles. Thus, a formula for computing the synchronous speed of an AC motor is suggested, based on the

frequency of the AC and the number of poles. In the real world, the speed of motors is expressed in "revolutions per minute" (rpm) while the frequency of AC is expressed in "cycles per second" (cps or Hz), so a correction of 60 is also required to convert the seconds-based frequency of the AC into the minutes-based speed of the motor. So, since poles always come in pairs, divide the total number of poles by two, then multiply the AC by this number, then multiple by 60 to convert from seconds to minutes. For example, an 18 pole motor at 60Hz would run at . . .

• 18 poles / 2 = 9

• 60 Hz / 9 = 6 6/9ths revolutions per second

• 6 6/9ths rps * 60 = 400 rpm

[Alternatively, if you want to think about it this way, dividing the number of poles into the product of the AC frequency times 120 determines the motor's synchronous speed. For example, as above, for 60 cycle house current that is 60 * 120 = 7,200, 7,200 divided by 18 poles equals 400 rpm. For some reason the formula is sometimes expressed this way.]

In the case above, this same motor, at 120 Hz, would have a synchronous speed of 800 rpm:

• (120 Hz / [(18 poles) / 2]) * 60 seconds = 800 rpm.

Correcting for slip would then mean multiplying this synchronous number by about 0.95, depending on the motor and the load.

This is nice to know: varying the number of poles is a possibility, but in practice it is not widely used, as it is not generally not possible to change the number of poles on the fly. Inherently, the number of poles is typically fixed in an AC motor; however, the stator can be wired so that it can be switched from two poles to four poles to six poles when needed. If the number of poles are doubled, the speed is reduced by one-half, By a special design of the stator windings, leads can be brought out to switch connections that change the number of poles (in the aforementioned two to one ratio: six poles, four poles, two poles). Multiple speeds can be achieved by winding the stator with two or more separate windings. So it is possible, for example, to imagine using transformer taps or a solid-state switch to change the energized segments of the stator, and There are "pole-changing" motors, but that gets very complicated, may require handling huge amounts of current through a solid-state switch, and is genrerally not considered a good idea in very high horsepower applications.

In addition, it is still a rather primative means of control, as it allows for only gross speed changes. A two pole goes twice the speed of a four pole, with nothing in between. If dealing with large numbers of poles, finer speed control may be obtained (24 poles, 26 poles, 28 polse, etc.), but then the synchronous speed of the motor is severely limited ([60*cps]/[poles/2] becomes a very small number when poles is very large). Nevertheless, changing the number of poles is one method of obtaining speed regulation in an induction motor.

Voltage control is obviously an option in controlling any motor. Just like in a DC motor, changing the applied voltage in an AC motor can push more or less electrons through the motor, creating more or less torque to run against the motor's load. So it may seem that one method of controlling the speed of an AC motor is by changing the applied voltage. If the voltage is reduced or increased, the torque produced by the motor is also reduced or increased (and again this is in proportion to the square of the voltage change, the "Vrms" noted above, meaning that a small change in voltage produces a very large change in torque). For most loads, a reduction in driving torque results in a reduction in speed. Varying the applied voltage can, therefore, be considered as a form of speed control for AC induction motors. At low speeds, however, rotor losses become unacceptably high, and it is not possible to achieve stable low-speed, high-torque operation (and this is, after all, the reason not to use a DC traction motor, the intrinsic problems with DC traction at low speeds). So variable voltage as a means of speed control is not normally used with any AC motors. (However, reduced voltage is a strategy for starting AC motors.)

Alternatively, the speed of an AC motor may be controlled by directly controlling the frequency of the applied AC. Since motor speed depends more or less directly on the speed of the rotating field produced by the stator, and this is directly related to the supply frequency, this approach offers many benefits and is the basis of all modern inverter drives (recall that in a modern AC locomotive an inverter changes the DC in the DC link back to AC). Varying the frequency of the AC is not, however, sufficient, for the motor, an inductive electrical load, has a lower impedance with falling frequency, as demonstrated above. With no corrective action taken with regard to the supply voltage, this means the motor current rises as the frequency of the AC is reduced. To compensate for this, the supply voltage must be reduced at the same time as the frequency. By properly reducing the voltage a constant current may be maintained while also maintaining the appropriate torque as the speed is reduced. This process is likewise followed reciprocally as speed is increased.

Using the example of the motor above, and keeping the power developed by the motor constant at 12.5 watts as the speed is changed, yields the following:

1. at 30 Hz:

o speed: 200 rpm

o resistance: 1 ohm

o inductive reactance: approximately 1 ohm

o impedance: 2.236 ohms

o phase angle: 82.81 degrees

o power factor: .8945

To yield 12.5 watts from this motor at 30 Hz requires the voltage to be set

at 5.590 volts:

5.590 volts across this motor yields

13.975 voltamperes ((2.364 * 2.364)/2.236) and

12.5 watts (13.975 * 0.8945), with a current of 2.5 amps.

2. at 60 Hz:

o speed: 400 rpm

o resistance: 1 ohm

o inductive reactance: approximately 2 ohms

o impedance: 4 ohms

o phase angle: 60 degrees

o power factor: .5

To yield 12.5 watts from this motor at 60 Hz requires the voltage to be set

at 10.0 volts:

10.00 volts across this motor yields

25.0 voltamperes ((10.0 * 10.0)/4.) and

12.5 watts (25.0 * .5000), with a current of 2.5 amps.

3. at 120 Hz:

o speed: 800 rpm

o resistance: 1 ohm

o inductive reactance: approximately 4 ohms

o impedance: 8 ohms

o phase angle: 75.522 degrees

o power factor: .2500

To yield 12.5 watts from this motor at 120 Hz requires the voltage to be set

at 20.0 volts:

20.00 volts across this motor yields

50.0 voltamperes ((20.0 * 20.0)/8.) and

12.5 watts (50.0 * .2500), with a current of 2.5 amps.

Note that the current remains constant while maintaining a constant power (wattage), as the terms in I2R remain constant.

AC Motor Speeds

The following table describes the relationship between some standard AC frequencies and the speed of some standard design AC induction motors. The number of poles in the motor is constant, so the speed is controlled by the frequency of the AC applied. In "normal" circumstances, that is, running an AC motor off 60 cycle AC house current, the speed of the motor will be constant, based solely on the number of poles (and the slippage due to the load); where a variable-speed AC motor is desired some means of frequency control (and therefore also necessarily corresponding voltage control) will be required.

Table Four: AC Motor Speed Table

Table of Motor Speeds (rpm):

Number of Poles / AC Frequency

Synchronous Speed & Full-Load Speed

Number

of Poles

400 Cycle AC

R.P.M.

100 Cycle AC

R.P.M.

60 Cycle AC

R.P.M.

50 Cycle AC

R.P.M.

40 Cycle AC

R.P.M.

30 Cycle AC

R.P.M.

25 Cycle AC

R.P.M.

Sync.

Full

Load Sync.

Full

Load Sync.

Full

Load Sync.

Full

Load Sync.

Full

Load. Sync.

Full

Load Sync.

Full

Load

2 24,000 23,200 6000 5800 3600 3500 3000 2900 2400 2310 1800 1750 1500 1450

4 12,000 11,600 3000 2900 1800 1770 1500 1450 1200 1150 900 860 750 720

6 8000 7680 2000 1920 1200 1170 1000 960 800 770 600 575 500 480

8 6000 5800 1500 1450 900 870 750 720 600 575 450 375 375 360

10 4800 4600 1200 1150 720 690 600 575 480 460 360 340 300 285

12 4000 3840 1000 960 600 575 500 480 400 385 300 285 250 240

14 3424 3280 856 820 514 490 428 410 343 330 257 247 215 205

16 3000 2880 750 720 450 430 375 360 300 288 225 215 187 180

18 2664 2542 666 638 400 380 333 319 266 256 200 190 167 160

20 2400 2280 600 570 360 340 300 285 240 230 180 170 150 143

22 2224 2080 546 520 326 310 273 260 218 208 163 155 138 130

24 2000 1920 500 460 300 285 250 240 200 192 150 143 120 115

30 1600 1552 400 388 240 230 200 192 160 153 120 115 100 96

Magnetic saturation

This is a rather abstract concept that may best be thought of as the limited ability of an object to be magnetized. In the case of a motor the object is usually a piece of iron wound with wires conducting an electrical current.

A coil of wire is an inductor, that is a magnetic field may be induced within the coil (see inductors above). When a voltage is applied to the wound wires in the motor (the coils or inductors), a current is caused to flow, and that current flow causes a magnetic field to be created. With more applied voltage, more current flows and there is more of a magnetic field in proportion to the applied voltage. This is a linear relationship.

At some point, the iron becomes saturated: that is, increasing the current does not create more magnetic field, and the linear relationship is broken: increasing voltage no longer causes a linear increase in current but instead creates a geometric increase in current -- that is, lots and lots of current, creating lots and lots of heat, burning out the motor.

This may best be thought of in terms of a graph. The graph of a magnetic field can be thought of as starting at the origin (0,0) and increasing/decreasing linearly

from there (in opposite directons) as the magnetic field magnetizes the iron of the core, ultimately reaching a point (in either direction) where the effect levels.

Figure Two, Magneic Saturation Applied Voltage / Magnetic Field Strength [d]

Any motor (AC or DC) is an electro-magnet. When voltage to the motor, thus to the electro-magnet, is increased, current increases in direct proportion (I=V/R), but this only works (in the electro-magnet) up to a point. After that point current increases exponentially. That is, because the iron core or any material (in the real world of working motors) can only conduct a limited amount of magnetic flux, once that point is reached current will have the tendency to become very high with a very small increase in voltage. This is called magnetic saturation and is sometimes seen in motor applications. Correspondingly, current can drop from that very high level with a small adjustment of voltage down, but this is too dangerous an area of operation for that principal to be of any operational use: the point is to avoid this point. The point is actually to operate the motor as close to saturation as possible, but not to go let it go into saturation.

Figure Three, Magnetic Saturation Applied Voltage / Current Flow [d]

Figure Two is also the basic, s-shaped, B-H curve, the graph of

• B, the magnetic flux density, expressed in units of gauss (generally

measured in milligauss), which is the total magnetic effect that results from

the applied force, and

• H, the magnetic field, expressed in units of amperes per meter (A/m),

which is the the magnitude of the magnetic field vector, i.e., tendendcy to

magnetize space.

The actual slope of the curve, u, in the region of the origin (0,0) is expressed by the formula

u = u0ur

where

u0 is the permeability of free space, and

ur is the relative permeability of the material.

B and H are approximately linked with the simple equation

B = H * u

This results in the aforementioned s-shaped curve that crosses the origin linearly (slope of 1/1 or some such, whatever the above equation yields) and flattens on the ends (to a slope of 0/1).

Eventually, all the magnetic domains align with the applied field, and the curve flattens out as the iron core becomes magnetically saturated. As the applied magnetic field is reversed, the iron eventually becomes magnetized in the reverse direction until it again saturates. When saturated, the application of an increased voltage will not be attenuated (in part) by the work spent magnetizing: rather, current will increase dramatically. Motors may burn-out in a matter of seconds in this state.

[ back to page index ]

Electric Power Transmission

When utilizing a power system where the underlying power itself is remotely produced, that is, when utilizing a central generating plant to produce power consumed in remote locations, the means of transport for the power, between the generation site and the consumers, is of critical importance. The quality of the electrical supply to the users, in the case of electric railroads the users being the electric locomotive or MU power cars, is essentially the quality of the voltage provided. While power is derived from the flow of electrons (the flow of electrons -- the current flow -- as measured in amps) through a circuit (in the case of moving a train, the current flow through electric motors), it is the maintenance of a constant voltage that is critical to the uninterrupted and stable delivery of current.

Many factors influence the quality of the voltage delivered. These include those intrinsic in the infrastructure (transmission lines) as well as the results of power consumption itself. Problems may be manifested by short- or long-term periods of variation from the normal voltage, along with rapid voltage changes, deviations, dips (or sags -- "brown-outs"), fluctuations and flicker, or unbalance of 3-phase voltages (i.e., different voltages among the phases in a three phase system). In addition, there may occur other irregularities, which may include variations in frequency and the presence of non-linear system or load impedances

that will distort the voltage waveform, along with transient spikes and surges that may be propagated along circuits in a supply system. In an ideal AC power system, the voltage and frequency at every supply point would be constant and free from harmonics, and the power factor would be one. Various approaches are used to mitigate these problems. One of the most critical areas to be addressed is the stablity of the transmission system.

The Transport of Large Amounts of Electrical Power over Long Distances: High-Voltage Transmission Lines

In rail applications (as in most others), the most efficient transmission of electricity from generating stations to the tracks requires transmission lines of high-voltage. In the United States this is done (almost universally) with AC transmission lines and with substations to convert this to line voltage for local use.

Electric transmission lines criss-cross the United States, with their characteristic sets of three wires (or goupings of three wires). Each of the three wires (or wire groups) is one phase of a three-phase AC set. There are also characteristically ground wires above or below the transmission wires. This is the standard long distance, high voltage transmission line in the United States. In fact, AC transmission is so ubiquitious that the possibility of using DC is sometimes forgotten; however, in certain long distance applications, DC may be more economical than AC.

The transmission of large amounts of electrical power over long distances is is done with high-voltage lines. High-voltage lines are used because the line losses are much smaller than with low-voltage lines.

All wires currently used have some internal resistance (the development of high-temperature superconductors suitable for long-distance transport would change). The total resistance of the transmission line leading from a power station to the local substation may be called R. The demands of the local conusmer for power from that substation may be expressed in the formula

P=IV

where P is power, I is current, and V is voltage (we're going to use V here for "voltage" instead of E for "electromotive force" as we want to stay focused on the concept of voltage in the power lines). This means the current drawn by the substation (rearranging algabraicly) is

I=P/V

Current and voltage have an inverse relationship, so the higher the transmission line voltage, the smaller the current.

The line loss (that is, the power consumed in the line) may be expressed by the formula

Ploss=I2R

Note: the formula above and all those following assume a phase angle of zero, which in fact is what one strives for in transmission lines.

Doing some substitution (for I, V/R; for R, V/I; for P, V2/R),

1. divide both sides of the equation by power through the line,

Ploss / P = I2R / P

2. on the right side of the equal sign, substitute for the R in the numerator

and for P in the denominator,

Ploss / P = ( I2*[V/I] ) / ( V

2/R )

3. which simplifies to

Ploss/P = ( I * V ) / ( V2/R )

4. which rearranges to

Ploss/P = ( I * V ) * (R / V2)

5. which simplifies (finally) to

Ploss/P = ( P ) * (R / V2)

6. so

Ploss/P = PR/V2

The fraction Ploss/P is the percentage loss in the line, or the "loss fraction."

Since P is fixed by community demand (as it exists at any given time), and R is as small as can be made (using heavy copper cable, for example) and generally fixed, line loss decreases dramatically with increasing voltage (decreasing logarithmicly, as the voltage in the denominator is raised to the second power). So the point is to use the smallest amount of current that can deliver the power being demanded, this done by using the highest voltage possible.

Another important note: the loss fraction (what was computed above)

Ploss/P

increases with increasing load P: power transmission is less efficient at times of higher demand. As P in the numerator is at the first power, the loss fraction increases linearly with increasing power demand.

PR/V2

Again, this is because power is proportional to current but line loss is proportional to current squared (see formula one above). Line loss can be quite large over long distances, up to 30% or so. By the way, line loss power goes into heating the transmission line cable which, per meter length, is not very much heat, but may be enough to make the cable sag: under extreme loads, it may be sufficient for the cable to sag enough to contact objects underneath the transmission lines, causing direct shorts to ground (and failure of the transmission system).

Alternating Current versus Direct Current

Note that the above formulas treat the transmission medium as a purely resistive load to the AC: that is, at 60Hz, a straight wire has essentially zero

inductance (thus no inductive reactance). The medium has high, but not infinite, capacitance, and the parallel wires act as a shunt capacitor (i.e., a capacitor across the load): thus it does have capacitive reactance. The loads on power lines are almost all inductive (motors, light bulbs, toasters), so there is a tendency (one thinks; one hopes) for the inductive reactance of the loads and capacitive reactance of the transmission lines to cancel each other. In practice, at any given time, the total system may be capacitive or inductive, (current may be leading or lagging); therefore, it is generally close to, but not completely, a purely resistive load (there is some phase angle, preferably not much, and in practice the line is most efficient when phase angle is zero).

There may be significant radiation with the transmission lines acting as antennas. At a frequency of 60 Hz, the wavelength of the AC is about 3,100 miles.

γ=V/ƒ

where γ is wavelength, V is velocity, and ƒ is frequency.

γ=[300,000,000 meters/second]/[60 cycles/second]

γ=5,000,000 meters/cycle

(That is, one wave is 5,000 kilometers, or 3,100 miles, long.)

These long lines are frequently in the range of quarter waves (1250 kilometers, 775 miles). These would be long enough for considerable radiation.

There are numerous examples of long distance, high voltage transmission lines that use DC. These are generally what are called a bipole system, referring to a positive (+) and a negative (-) pole across an earth ground (not unlike the grounded neutral in +/0/- AC systems), thus generally indicated as +/- V. Transmission is possible over many hundreds of miles, far greater distances, theoretically, than AC, which has practical limits of around 750 miles (1200 kilometers).

The principle of high voltage DC transmission is simply converter stations on each end of a transmission line: at the source there is one converter station housing the rectifier system (AC to DC), then there is a transmission line, and at the destination a second converter station housing the inverter system (DC to AC). (Generation and distribution are still accomplished in AC, generation because AC machinery is less complex and less costly to maintain [no brushes], and distribution because it is easier to step down voltages at various stages in the local

system.) The rectifier is a standard 3-phase AC rectifier that gives the +/- voltages. (It can be single, +V voltage, but it is generally more simple to use two half voltage lines than one full, which is (again) similar in principal to the three-wire residential service most homes in the United States have.) The transmission line has two or three wires in the -V,0,+V voltage system (with the grounded neutral).

A leader in energy transmission via DC lines is Russia: they have air-lines running +/-750 kV that are several thousands kilometers long. Manitoba Hydro (in Canada) has two bipole lines in their Nelson River DC Transmission System, one +/-450 kV, the second +/- 500 kV, each approximately 900 kilometers long (running to just northwest of Winnipeg). In the United States, Minnesota Power (now called Allete) is using DC from a power plant at the mouth of a coal mine in Montana that sends very high voltage to Duluth. The Duluth line runs two wires and ground (two wire is 95% efficient, and if one wire is out, they can run one wire and ground at 92% efficiency). The station ground is located some distance from the plant, and reportedly consists of huge pits filled wth salt.

In DC transmission (as in any DC applications), the inductance and capacitance of the conductor have no negative effects, as there are no inductive or capacitive effects, thus no inductive or capacitive losses. The electrical field in a DC cable is generally evenly disposed, especially in round cables. Corona effects (ionization of the air around the transmission wires) are similar to, although not identical to, AC. Underwater DC cables are also specifically different than AC cables. In submarine lines, water all around the cable gives a shielding effect, so the voltage applied to the DC cable can be considerably higher than the voltage in an AC cable.

With respect to the transmission of high quantities of electrical energy over long distances as the only criteria, DC transmission is effective because DC lines are less expensive than AC (typically two wire instead of three) and DC has considerably less losses (no reactive - - specifically capacitive - - losses and no radiation with long air lines): some estimates put DC at about 30% more efficient than AC. Other issues at the super-high voltage levels such as corona are as much or more pronounced with AC than DC. In the case of underwater transmission there is the additional reason of DC cables being able to support very high voltages and transmit a correspondingly higher energy than AC cables. These cables have less energy losses and the price of the cables is less than the AC equivalent. For these reasons, a DC cable can generally have less copper than AC cable, thus the transmission medium itself can be less expensive than in AC systems.

With all of its advantages, DC has at least one critical flaw: high voltage conversion is an issue. Modern inverters (the DC to AC converter) are generally thyristor based: they have a large number of ultrafast thyristors connected in serial. These are very efficient, but are a very expensive part of DC transmission; likewise, solid state rectifiers are very efficient but very expensive. These elements of the infrastructure simply do not exist with AC transmission systems. Further, progressively stepping down the voltage in the local distribution network confronts the same issues of size and expense: it is an expensive proposition to reduce a high DC voltage to a lower DC voltage

With AC, stepping down the voltage in the distribution system may be done on the fly, so to speak. It is a simple matter to reduce a high AC voltage to a lower AC voltage using step-down transformers (these may be seen at substations and on power-poles). A step-down transformer reduces voltage and increases current so that the power (voltage * current) is constant (and, ideally, loss-less, or as near so a technically possible). A neighborhood substation typically reduces the voltage to a reasonable value for street lines, say 13.8kV, and then a small transformer on the pole reduces it to +/- 110 volts (220 volts in Europe) (see more on substations under Electric Locomotives on the Locomotive Information page). (The alternation frequency is 60 cycles/sec [60 Hz] in the US [50 cycles/sec (50 Hz) in Europe].)

The choice between AC and DC is central to the effort to reduce line loss by using high voltage. For the reasons enumerated above, in DC transmission systems conversions at both ends of the transmission line are necessary, making short-distance DC transmission not cost-effective. However, when very long distances are involved, greater than about 750 miles (1200 killometers) AC may be impracticable, while DC would become quite cost-effective.

So, overall, DC transmission systems are not used as standard systems in the United States for economic reasons as much as for technological reasons; in fact, they present technological advantages, but in electric systems with numerous, relatively local generating facilities, the costs of the converter stations outweigh the economies of the transmission. What we see here in the U.S., serving our communities and along our railroad rights-of-way, is AC.

AC Frequency Usage

Various frequencies are in common use. Northeast railfans know 25 hertz as the frequency for the Pennsylvania Railroad's mainline electrification. However, it is generally accepted that Nikola Tesla chose 60 hertz as the his standard for power

distribution as it was the lowest frequency that would not cause street lighting to flicker visibly and it had efficiencies in transmission over lower frequencies, and is an efficient multiple of the time base (of 60). The origin of the 50 hertz frequency used in other parts of the world is generally conceeded as a concession to the metric system, although this frequency may have significantly higher line losses than 60 hertz, with losses in some applications greater than 60 hertz in the 10% to 15% range.

Other frequencies were common in industrial use in the first half of the 20th century, and some remain in use: 25 Hz AC (much of it generated at Niagara Falls), was used in Ontario and the northern USA. Some 25 Hz generators were in use at Niagara Falls up until the mid-1990's for large industrial customers who did not want to replace existing equipment.

The lower frequency eases the design of low speed electric motors, especially commutator-type motors for electric traction applications such as railways (e.g., the commutator-based AC motor in the GG1), but would cause a noticeable flicker if used in lighting. Along this line, 16.67 Hertz (which multiples times-3 to 50.0) is used in some European rail systems (e.g., Sweden).

Some aircraft, spacecraft, computer mainframe, off-shore, marine, and textile industry applications use 400Hz. This is for the benefits of the reduced weight of apparatus or the higher motor speeds obtainable in synchronous motors.