The Physics of Flying! Lecture 27. - University of...

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

The Physics of Flying!Lecture 27.

Views of New York State from 9000’.


Course Information

• Optional homework set # 11 is due at noon totday.

• The results of Exam # 3 were distributed via email onMonday.

• You can pick up your exam today.


Results Exam # 3.

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Course Information

• You will receive an estimate of what you need to receive onthe final exam to earn an A-, a B-, and a C- in this course.

• The final exam will take place on Tuesday 12/20 at 4 pm inHoyt. The exam will cover Ch 1 – 12 plus Supplement plusequilibrium. But NOT error analysis.

• The TAs will have extra office hours on Monday 12/19.Details will be distributed via email.


And now for something completely different:

The Physics of Flying


The Physics of Flying! Outline.

• What makes an airplane fly?• Weight and balance.• Airplane control and stability.• Lift and Bernoulli.• Take off and landing.

• What is the physics behind ourinstruments, and why should wetrust them?

• Forces of flight.• The grave-yard spiral.• The gyro system.

• Summary

12/17/1903


Where did I learn everything I know about flying?

Joe d’Arpino, World’s best flight instructor.


The physics of flying.What can we cover in such a short time?

• In this talk I will focus on a fewexamples of the physics of flying.

• I have decided to focus on thoseareas of the physics of flying thatare in general not well understoodby the members of the physicscommunity.

• Given the time allocated to me,this certainly will not be an “allyou need to know about flying”type of talk.

The pilot’s handbook of aeronautical knowledge, Paul E. Illman


The forces of flying.• In order to understand the art of

flying we need to understand thebasic forces that act on anairplane:

• Weight: the gravitational forcethat depends on the mass ofairplane.

• Lift: the upward force generatedby the wings. The lift depends onthe attitude of the airplane, itsspeed, and the design of thewings.

• Thrust: the forward forcegenerated by the engine(s). Thethrust depends on engine designand operating conditions.

• Drag: the backward force thatslows the airplane down.



Airplane stability.The tail force.

• Although the total mass of theairplane is an important factor indetermining the required lift, thedistribution of the mass alsoeffects the required lift, and is akey factor in determining thestability of the airplane.

• If lift and weight are the onlyvertical forces acting the airplane,the plane will only be stable if thecenter-of-gravity coincides withthe center-of-lift.

• In all other cases, a tail force isrequired to provide stability to theairplane. The pilot’s handbook of aeronautical knowledge, Paul E. Illman


Airplane stability.The tail force.

In this example, a 9” change in the location of the center of gravity changes therequired lift by 135 lb. Changes in the location of the center of gravity occurduring flight due to for example fuel consumption.

The advanced pilot’s flight manual, William K. Kershner


Airplane stability.A serious calculation, often ignored.

• Since the location of the center ofgravity has a significant impacton airplane stability, it needs tobe evaluated before each flight.

• Improper loading might preventstable operation of the airplane.

Allowed

Notallowed

Photographer:Radomir Zaric

Picture from airliners.netWeight-and-balance chart for an Archer (pilot operating hand book).


Airplane control.• To control an airplane requires

control of its orientation withrespect to the following the threeaxes:

• Pitch axis: controlled with theelevator.

• Roll axis: controlled with theailerons.

• Yaw axis: controlled with therudder.

• Most airplane operations requirethe use of more than one controlsurface. For example, to turn anairplane requires simultaneoususe of the rudder, the elevator,and the ailerons. The pilot’s handbook of aeronautical knowledge, Paul E. Illman


Airplane control.An example: the constant altitude turn.

• In level flight, the magnitude ofthe lift is equal to the magnitudeof the weight (yes, I have ignoredthe tail force ….).

• An airplane changes its headingby banking, and the horizontalcomponent of the lift provides thecentripetal force required for theturn.

• The vertical component of the liftis now smaller than the weight,and unless the total lift isincreased, the airplane will loosealtitude. The advanced pilot’s flight manual, William K. Kershner


Generating lift.Who needs Bernoulli?

• Most people who claim tounderstand the generation of lift,will rely on the Bernoulli effectto explain the principle of flight.

• If you are one of them, I am sorryto have to tell you that you do notunderstand the principle of flight.

• Although the Bernoulli effect hasbeen used for many decades toexplain the principle of flight, theBernoulli effect can only accountfor a few percent of the liftgenerated by a wing, and it cannot account for phenomena suchas inverted flight.

http://www.aa.washington.edu/faculty/eberhardt/lift.htm

This wing does notgenerate lift!


NY Times, January 2004100 Year Anniversary of Flight

• What keeps them up there?

• “it is disconcerting that physicistsand aeronautical engineers stillpassionately debate thefundamental issues”

• Jef Raskin, one of the creators ofthe Macintosh, was send to theprincipal’s office when he arguedwith his science teacher that theBernoulli effect could not explainwhy paper airplane’s fly.According to the science teacherpaper airplanes use a differentscientific principle to fly.



• In order for a wing to generate lift(producing an upward force) itmust force the air down.

• The vertical component of themomentum associated with thedownwash, must balanced by thevertical component associatedwith the lift generated by thewing.

• Thus, unless the air is forceddownwards, the wing will notgenerate lift.


This wing does notgenerate lift!

This wing does generate lift!



• The lift of a wing is generated bythe downwards deflection of air.

• Consider an elastic collisionbetween an air molecule of massm and velocity V. The change inthe vertical component of themomentum of the wing as a resultof this single collision is equal to:

• The lift generated will increase ifV increases, if the air densityincreases, and if the angle ofattack increases.

�

plift = mV sin(α)


Generating lift.An example.

• Consider a Piper Warrior. Thisplane has a maximum weight of2450 lb, and the required lift ontakeoff is about 11,000 N.

• On takeoff, the airspeed is 60knots = 31 m/s. Assume that ontakeoff the angle of attack is 5°.

• To generate this lift requires that

• This requires that

www.newpiper.com

�

Lift =dpliftdt

= dmdtV sin(α)

�

dmdt

= LiftV sin(α)

= 4100 kgs


Generating lift.Certainly not a surface phenomenon.

• The Warrior has a wing span of35.0 ft (10.7 m) and a wingsurface area of 170 ft2 (15.8 m2).

• The density of air at sea level isabout 1 kg/m3.

• In order to generate an airdeflection rate of 4100 kg/s, theheight of the layer of air involvedmust be about 12 m.

• Clearly, the generation of lift isnot a surface phenomenon.

12 m

31 m/s

The Rochester Flying Club



Generating lift.What does it take to lift a Boeing 737?

• At 6.02 am on 3/22/03, CO 282took of from San Antonio (TX).For this particular flight, theweight of the plane was 106,000pound and the rotation speed was131 knots (numbers provided byMark d’Arpino, the first officeron this flight).

• For this flight:• dm/dt = 80,000 kg/s (80,000 m3/s)• Note: (dm/dt)/M = 1.7 for this 737

compared to 3.7 for the Warrior.• The wingspan of this 737 is 94.9

ft, which indicates that a 41 mthick layer of air is involved in thegeneration of lift. Pictures from airliners.net

Photographer:B. Leibowitz

Photographer:M. Abbott


Generating lift.

• The effect of the downwash ofthe wing of this citation, flyinglow over a fog layer, is clearlyvisible.

• More details about the generationof lift can be found in“Understanding Flight” byAnderson and Eberhardt. Note:Anderson is a retired high-energyphysicists.

Photograph by Paul Bowen, courtesy of Cessna Aircraft, Co.


S-C WangFSU

Generating lift.Certainly not a surface phenomenon.

• The lift generated by the wingincreases with increasing angle-of-attack.

• The increase in the lift with anincreasing angle continues untilthe angle-of-attack exceeds acertain critical value, abovewhich the air above the wingbecomes turbulent, at which pointthe wing loses half of its lift.

• At this angle, the airplane stalls.

CirrusAircraftCompany


Generating thrust.The physics of the propeller.

• The generation of thrust with apropeller relies on the samemechanism that allows the wingto produce lift.

• The thrust generated by asegment of the propeller relies onthe angle of attack and theairspeed (which is a function ofthe engine rpm and the distancefrom the center of the propeller).

• Since the airspeed increases withincreasing radius, the angle ofattack must be decreasing inorder to minimize the structuralforces inside the propeller. The pilot’s handbook of aeronautical knowledge, Paul E. Illman


Generating thrust.The physics of the propeller.

• Consider a typical propellerinstalled on a Piper Warrior:

• Diameter d = 74”

• Maximum engine rpm = 2700

• The velocity of the tip of thepropeller is equal to

• This velocity is close to the speedof sound in air, which is

v = 331 + 0.6 * T m/s�

Vtip =1.88π 270060

= 266ms

The Rochester Flying Club


Take off.

• The airplane will take off whenthe lift generated by the wingsexceeds the weight of the plane.

• An increase in weight impacts therequired runway length:

• The increase in weight requires anincrease in lift: lift is proportionalto velocity.

• The increase in mass decreasesthe acceleration of the airplane(since the thrust provided by theengine(s) remains constant). The advanced pilot’s flight manual, William K. Kershner


Many factors influence the length of the runway required to take off.



Many factors influence the length of the runway required to take off.

• A PA-28-181 will take off whenthe airspeed reaches 60 knots.

• A 15 knots head wind, requires aground speed of 45 knots.

• A 15 knots tail wind, requires aground speed of 75 knots.

• Assuming a constant accelerationa, the ground roll x required toachieve a velocity v is equal tov2/2a.

• The difference in ground roll forthe PA-282-181 in the exampleabove is x75/x45 = 752/452 = 2.8.

Takeoff chart for an Archer(pilot operating hand book)


Landing.

• Key issues during landing:• Slow the airplane down: increase

the angle of attack.• Extend wing flaps: produce extra

lift by increasing the angle ofdeflection of the “bottom” air.

• Align wheels with the direction ofmotion.

AoTExtend flaps.

Picture from airliners.net

Photographer:J. Derden

Runway 10KSYR

A Boeing 747 on final approach for 26L in Gatwick


The Physics of the North Pole. An interesting effect before getting serious again.

• The numbering of runwaysreflects the magnetic direction oftheir centerline.

• For example, to approach runway10 in KSYR your heading will besomewhere between 95 degreesand 105 degrees.

• But ……. the magnetic Northpole of the earth is moving, andas a result the orientation ofrunways are changing as functionof time.

• KSYR recently had to renumberone of their main runways due tothis effect.

Runway 10KSYR


Instrument Flying

Frank, there is one simplerule in IFR: you trust yourgut, you die!

Joe d’Arpino, World’s best flight instructor.


Instrument Flying.You trust your gut, you die!

• In instrument conditions, the pilotdoes not have any outsidevisibility.

• Without being able to view thehorizon or the ground, the pilothas to rely to his/her instrumentsto determine the attitude of theairplane.

• The pilot is also exposed tovarious forces which often givethe impression that the airplane isin a different attitude.

• Who is right? The instruments orthe pilot?

Sporty’s: Volume 1, Instrument Flying Fundamentals.


Instrument Flying.You trust your gut, you die!

• There are three senses that arecommonly used to maintainequilibrium and orientation:

• Sight: location of horizon andground, and instrumentindications.

• Inner ear: senses up/down motion,turning motion, and changes inorientation.

• Postural: the “seat-of-the-pants”feeling, which senses up/downmotion.

J.R. Williams, The Art of Instrument Flying


Instrument Flying.Sight.

• In most circumstances, sightdominates the senses generatedby the inner ear and the “seat-of-your-pants” (e.g. the attitude canbe determined immediately onthe basis of the orientation of thenose of the airplane with respectto the visible horizon).

• When an airplane entersinstrument meteorologicalconditions, the horizon is nolonger visible, and the sensesgenerated by the inner ear and the“seat-of-your-pants” can start todominate.

Sporty’s: Volume 1, Instrument Flying Fundamentals.


Instrument Flying.The inner ear.

J.R. Williams, The Art of Instrument Flying


Instrument Flying.The seat-of-your-pants force.

• The pilot is experiences a numberof different forces during a flight:

• Examples:• During take-off, the pilot is

pressed into his/her seat. Anincrease in this “seat-of-your-pants” force is frequentlyassociated with an increase inaltitude.

• During the initiation of a descent,the “seat-of-your-pants” forcedecreases, and this decrease isfrequently associated with adecrease in altitude.

• However, these “seat-of-the-pants”forces can also be generated duringother phases of flight when thealtitude is constant. The advanced pilot’s flight manual, William K. Kershner



• Let us consider the constantaltitude turn:

• To maintain altitude in this turn,the lift must be increased.

• The “seat-of-the-pants” force feltby the pilot increases.

• If the pilot trusts his/herinstruments, the airplane willmaintain its altitude.




• If the pilot trusts his/her “seat-of-the-pants” feeling (continued):

• The pilot will “feel” the planegoing up, and pushes the yokeforward.

• The airplane will loose altitude andincrease its speed.

• The increase in speed results in anincrease in the lift.

• Assuming the the pilot maintains astandard-rate turn, the horizontalcomponent of the lift will beproportional to its speed and willthus increase.

• The pilot will “feel” the planegoing up even further, and pushesthe yoke further forward.

• ………• The graveyard spiral.



Instrument Flying.The gyro instruments.

• Although the instrument panelvaries greatly between differentplanes, the following six basicinstruments can be found inalmost every plane:

• Airspeed indicator• Attitude indicator• Altitude indicator• Vertical speed indicator• Directional indicator• Turn indicator

• Three of these six instrumentsrely on gyroscopes for theiroperation.

www.newpiper.com

KLM 747 @ 31,000’ over Hudson Bay.

Photographer:B. Wang



• The gyroscopes in aviationinstruments are either vacuum orelectrical driven.

• The gyroscope will maintain itsorientation in space, independentof the orientation of the airplane.

• In the attitude indicator, the gyroaxis points in the verticaldirection.

• The artificial horizon is attachedto the gyro axis, and it will thusremain aligned with the realhorizon. Attached to the airplane

Attached to the gyro



• By comparing the position of theairplane with respect to theposition of the artificial horizon,the pilot can judge the attitude ofthe airplane (in this example, theairplane is nose high, and in a leftturn).

• The directional gyro is used todetermine the heading of theairplane, and is stable in turbulentconditions and in turns.

• The turn indicator is used tomake constant rate turns (2minutes for 360 degrees).


The Physics of FlyingSome Final Remarks

• Many of our lecture demonstrations have important ties toaviation, although quite often most of us are not aware theimportant ties.

• Some of the most obvious ones are:• The gyroscope: does not only provide the basis for our most

important flight instruments, but also are the basic components ofmost autopilots.

• The jumping ring: a neat demonstration in Physics 122/142, but theoperation of electric fuel pumps, used as backups for the mechanicalpumps, rely on this effect for their operation.

• The simple radio: a nice demo to illustrate the properties of radioemission. The relation between the signal size and antennaorientation forms the basis of the ADF. It allows you to use WHAM1180 to fly home from as far away as Washington DC.


The Physics of Flying.Summary.

• Although the world of aviationhas changed a lot in the last 100years, the physics of flying hasnot changed.

• There is a lot of physics in flying,more than many people realize.

• If you remember one thing fromthis talk, please remember thatthe lift generated by a wing relieson the downward deflection ofair, and that the Bernoulli effectdoes not explain why planes fly. From: A 747 pilots-eye-view.


The end of Physics 141 Lectures!

Good luck with all your finals.

See you on Tuesday 12/20 in

Hoyt at 4 pm!


Physics 141.Now you are free (and so am I)!

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