TEAM NAME:

TEAM # 027

SAE Aero Cargo aircraft Design Report

March 24, 2011

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Contents1 Introduction 4

1.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Requirement Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Design Process 52.1 Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Discussion of Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Test and Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Design Analysis, Review Process and Selection . . . . . . . . . . . . . . . . . . . . . . . 122.2.1 Component Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.2 Design Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Calculations 183.1 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1.1 Drag Analysis and Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.1.2 Performance Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.1.3 Competitive Scoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Stability and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2.1 Servo Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Aircraft Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.4 Weight Build-Up and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.5 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4 Innovations 274.1 Manufacturing Process Innovations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5 Conclusion 28

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1 Introduction

The SAE Aero design series aims to give a real world engineering design opportunity to universities across

the world. The engineering design goal is to take off and land an aircraft while carrying as much weight

as possible. This engineering goal can only be met by applying the principles aerodynamics, material

mechanics, physics, and other engineering principles. There are also challenges with design process:

time management, budget, and team dynamics all create unforseen obstacles. The design process for this

competition starts in the early fall and continues through competition in April. During the design process

there are many problems that arise. In order to be successful in this competition, the design must be

adapted and enhanced along the way.

1.1 Objective

The Huskies Aero Design Team aims to design and build an aircraft that maximizes lift at low airspeeds

while maintaining a robust, stable, lightweight, modular, and easy to machine design. With a combination

of experience, new research, testing, and critical assessment, the Huskies design team is meeting that

objective.

1.2 Requirement Statement

SAE Aero 2011 design requirements are listed in Table 1.

Table 1: SAE Aero 2011 Design Requirement

Wing No lighter-than-air or rotary wing aircraftDimension Maximum combined length, width, and height of 225

inchesGross Weight No more than 55 pounds with payload and fuelMaterial FRP is prohibited for all parts. Commercially avail-

able engine and propeller onlyEngine O.S 61FX (unmodified) or Magnum XLS-61A En-

gine (unmodified)Payload No dimensional requirements, must be fully enclosed

within the fuselageRunway Maximum Take off distance 200 ft

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2 Design Process

2.1 Research

2.1.1 Discussion of Concepts

Based on the team objective, a set of collaborative concept sessions occurred to discuss new ideas and

improvements on previous years aircraft designs. This collaboration has lead to the development of a

set of goals that were implemented into this year’s design. Last year’s competition aircraft proved to be

exceptionally stable, robust, and easy to fly; however, the fuselage frame was heavier than expected and

the aircraft’s lifting ability was a few pounds below the first place competitor. Another issue encountered

was the aircraft’s extremely low rolling resistance. Although great for takeoff, it caused the aircraft to

repeatedly fail to stop before the end of the runway. The performance characteristics of past aircraft

have given insight into how improvements can be implemented into this year’s design. The following list

outlines the specific goals that were implemented into this year’s design.

• Eliminate any component weight possible

• Improve wing structure and fuselage structure to reduce weight

• Design a weight box that can be installed within the given time limit

• Change fuselage manufacturing process to eliminate excess weight in welds, slag, etc

• Create a mechanism to slow the aircraft down after a touchdown or an aborted takeoff

• The aircraft is extremely stable and easy to pilot

• Do not compromise aircraft robustness

• Keep the modularity of the design for ease of transportation

• Optimize the thrust of the aircraft

To better understand how to meet each of the goals outlined above, research into aircraft engineering

principles, and the possible materials that could be used for the aircraft was conducted. The following

sections outlines what came out of that research.

Material

The selection of strong, lightweight materials for the aircraft is very important, because it is a limiting

factor in how much weight can be carried. The material selected also dictates how much the aircraft will

weigh. The wing accounts for a large percentage of the aircraft’s total volume so its material selection is

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especially important. Through testing, a foam core wing with a balsa sheet covering has been determined

to give the lightest structure possible while maintaining strength, durability, and ease of manufacturing.

The balsa selected this year is 1/32 inch, half the size of previous year’s 1/16 inch balsa. The balsa thick-

ness effectively reduces the weight of the total balsa used by about one-half while maintaining the strength

of the wing. The foam core of the wing is a low density extruded polystyrene, similar to the type used

in packaging materials because of its light weight and durability. A foam core wing can be manufactured

more easily and precisely than an all balsa ribbed aircraft with the use of a computer numerical control

(CNC) foam cutter. To further lighten the core of the wing, holes are cut at specified dimensions along

the wing. The combination of these materials and manufacturing methods makes for a strong, lightweight

wing perfect for maximizing the lift to weight ratio.

The selection of fuselage material was based on weight, strength, cost, ease of manufacturing, and

availability of sizes and shapes. Based on these desired characteristics, aluminum was decided on as the

material to be used. Determining the type of aluminum to be used required testing of many different types

and comparing the features of each. The results of the testing are provided in Table 2. Al 6061-T6 was

selected as the material to be used for the fuselage structure, due to the fact that it is the easiest material to

weld. Al 2024-T3 was chosen as the spar material because it had the best strength to weight ratio.

Table 2: Material Properties

Density(lb/in3)

YieldStrength(ksi)

ElasticModulus(ksi)

Poisson’sRatio

ShearStrength(ksi)

ShearModulus(ksi)

StrengthtoWeightRatio

BalsaWood

0.00324 1.015 0.232 13.92 313

Al 2024-T3 0.1 50 10600 0.33 41 4060 500Al 4032-T6 0.0968 46 11400 0.34 38 3770 475Al 5182-O 0.0957 18.9 10100 0.33 21.8 3770 197Al 6061-T6 0.0975 40 10000 0.33 30 3770 410Al 6151-T6 0.0979 42.8 10000 0.33 31.9 3770 437

Takeoff

The competition has a maximum runway length of 200 feet, so it is crucial to have a aircraft that can take

off on a short runway. The added payload in the aircraft will make it harder for the aircraft to take off in

this short distance. Due to the short runway the wings will have to be designed to have maximum lift at

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low airspeed.

Airfoil Selection

Choosing the airfoil of the wings was an important step in the wing design process. Previously used airfoils

for the competition included: FX 63-137, Selig S1210, and Selig S1223. According to the University of

Illinois online airfoil database the S1210 was designed specifically for the SAE heavy lift competition [3].

The most recent airfoil designed for the competition is the Selig S1223 which is an even more refined

version of the Selig S1210 and produces 30% more lift than the FX 63-137 [3]. Using computational

fluid dynamics (CFD), testing on various airfoils has proven that the S1223 is the most efficient airfoil for

the speeds that will be experienced in the competition. The reason for this is the S1223 is designed for a

Reynolds number below 200000, this means that the wing chord needs to be fairly small and experience

slower speeds [3]. To increase efficiency of the wing, chord length has been increased from the previous

year’s design from 13 inches to 15 inches. This increase will be more effective than a shorter chord, since

it adds wing surface area without adding too much extra drag. While the Selig has slow airspeed and high

lift properties, the required manufacturing tolerance is stringent. This requires the accurate manufacture

process with a CNC foam cutter.

Drag Reduction

Reducing drag is critical to the flight of an aircraft. For a wing, induced drag results from the production

of lift created by the wing. This drag is created by differential pressures acting on the surfaces of the wing.

There is a migration of airflow to the wingtips of the aircraft, causing a vortex. Another vortex is created

at the inner portion of the trailing edge of the wing. These vortices increase drag due to turbulence. With

an increased angle of attack (AoA), the induced drag is increased [5]. An increase in speed reduces drag;

however, this aircraft is designed for slow speeds. In order to reduce the wings chance of stalling with high

AOA and slow speeds we have designed our wing to make use of winglets. Winglets are used because

they reduce drag associated with those vortices at the tips of the wing [7].

Stability

Stability was recognized as a crucial characteristic of a well designed aircraft. Having a stable aircraft

in this competition will reduce the chances for a crash by making the aircraft easier to fly for the pilot.

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Stability in the aircraft refers to the ability of the aircraft to return to an equilibrium position. If an aircraft

is stable it will naturally go back to its neutral position, which is straight, level flight [6]. An aircraft that

tends to roll back to level flight is said to have positive lateral stability. This is one of the performance

characteristics that is desired for this year’s aircraft. According to Aircraft Engineering Principles by

Lloyd Dingle, and Michael H. Tooley to make an aircraft have positive lateral stability it should have a

parasol wing, sweep-back, and wing dihedral [6]. A parasol wing aircraft is an aircraft that has a center

of lift above the center of gravity. This creates a pendulum like effect that tends to bring the wing back to

level flight. A sweptback wing is one that has the wing leading edge placed at an angle that is more than 90

degrees to the fuselage. Wing dihedral refers to the upward inclination of the wings from the horizontal.

Wing dihedral and sweep-back were not implemented in the design as they present many manufacturing

issues that would end up adding more weight and thus hurting the performance more than improving it.

The parasol wing design was implemented because it is relatively easy to manufacture, and has proven in

past competitions to be a very effective design. Using a parasol wing design, the aircraft will have positive

lateral stability, which will make it easy to fly when there are environmental disturbances and pilot error.

Washout and Taper

In order to increase controllability at low airspeeds and avoid sudden stalls, wing washout has been in-

corporated into the design. This lowering of the AoA towards the tip keeps air flowing over that part of

the wing even after the center of the wing has entered into a stall. By implementing washout, the aircraft

enters into a stall more gradually and maintains effective aileron control well into the stall.

Wing taper from the full 15 inch cord to 11 inch cord over the last 18 inches of each wing also improves

the stall characteristics of the aircraft. The shorter cord length at the end of the wing provides that area

of the wing to stall after the main area of the wing. This occurs because the tips of the wing is at a lower

Reynolds number than the main area of the wing. The lower Reynolds number allows the wing tips to have

a lower stall speed and remain effective even if the main area of the wing stalls. This allows the aircraft

to maintain roll control and not tip stall, which would cause the aircraft to possibly roll completely over

before recovering from the stall.

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Weight Box

The new rules for 2011 took away the dimension constraints for the payload bay. This allowed for a better,

more efficient way to utilize the space of the payload bay. Another new constraint for 2011 was the time

required to load and unload the payload. The time allowed to load the payload was a minute as well as the

time to unload it. In order to be able to achieve a loading and unloading time of less than a minute, a new

design had to be created.

The weight box design consisted of a box that encased the weights that were positioned on a removable

weight bar in the center of the box. The weights could be adjusted on the weight bar to change the center of

gravity of the aircraft. The weight bar also featured a quick release mechanism that allowed for the quick

removal, and a special handle can be used to pick up the weight bar to make the loading and unloading

easier. The box is secured with six bolts. Designing the payload system as a two part system to reduce

loading and unloading time.

2.1.2 Test and Experiment

Static Thrust Testing

The purpose of static engine testing was to narrow down propellers to be analyzed in dynamic engine

testing. After reviewing the results, a decision was made for all propellers tested during static testing to be

also tested in a dynamic air stream. Six different propellers varying in sizes and materials where tested.

The strain, temperature, and revolutions per minute (rpm) were recorded during each test.

Three test runs were completed for each propeller size and type. The engine was started and allowed to

warm up. Full throttle was applied, the engine ran for approximately a minute to allow the air-fuel mixture

to adjust and obtain maximum rpm. While the engine was running at maximum throttle, the average thrust

was measured using a force transducer. Strain readings were transformed to thrust forces. Once the test

values (rpm, thrust, and engine temperature) had been recorded three times for each propeller, the engine

was throttled down and allowed to cool before the next test was performed.

The strain gauge was used to convert mechanical motion into an electrical signal. The cantilever

aluminum beam acts as a resistor. The beam was attached to the engine mount. After zeroing the strain

indicator, the gauge factor was set to a range between 0.5 and 2.0. The beam conducts electricity but

resists part of the flow when deflected. When bent, the resistance is raised since the electricity has a

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further distance to travel. Wires are attached to the engine mount which are attached to a Wheatstone

bridge on the other end. A Wheatstone bridge is a device that measures its resistance.

Dynamic Thrust Testing

Dynamic thrust testing is important because propeller driven aircraft have different thrust characteristics

when they are moving versus when they are static. In general, the thrust from a propeller engine decreases

with increased airspeed by

F = 0.5ρA(V 2s − V 2

0 ) (1)

F is the thrust generated by the engine, ρ is the density of the air, A is the circular area that the propeller

occupies when it spins, Vs is wind velocity behind the propeller, Vs and Vo is the incoming wind velocity.

This equation is derived using a simplified model of a propeller spinning in a laminar velocity field.

In reality, the characteristics of a propeller generating thrust are complex and empirical testing of various

propellers is the best way to determine which propeller is best for this application.

From this equation it can be seen that incoming air velocity decreases the force produced by the

propeller. The dynamic engine testing will determine which propeller produces the most thrust at lower

airspeeds. The reason it is important to have more thrust at lower airspeeds is because the aircraft will, in

general, be moving fairly slow. Also from the takeoff distance restraint, producing more thrust at lower

airspeeds will produce more acceleration, and thus velocity on the runway.

To simulate an engine moving, the test apparatus used in the static engine testing was placed in the

exhaust of a wind tunnel; this is shown in Figure 1. This allows the airspeed to be controlled by increasing

the fan speed of the wind tunnel. To try and eliminate any error in the testing, the exhaust speed of the

wind tunnel was tested at various points to determine where the most consistent wind velocities were. It

is important to have consistent wind speeds so the thrust measured by the strain gauge does not fluctuate a

lot while the test is occurring. The resulting data will determine how the thrust generated by the engine at

a wide open throttle varies with airspeed.

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Figure 1: Dynamic Engine Test Setup

Dynamic Engine Testing Results

Figure 2 shows the thrust generated at various wind velocities. The range of velocities between five and

thirty miles an hour was selected because the aircraft will always have an airspeed under thirty miles an

hour. Six data points were taken to fully characterize the thrust characteristics of the propeller driven

engine.

As can be seen from Figure 2 the thrust decreases as wind velocity increases. Although the propellers

only varied slightly in diameter and pitch they showed different thrust characteristics. Some propellers,

like the 13-6, had the thrust drop very quickly as the wind speed increased. The 13-8, 12-4, and 12-7

propellers all had very similar thrust characteristics, losing about two pounds of thrust over an increase of

25 miles an hour wind velocity increase. The 13-4 propeller generated more thrust than any of the other

propellers tested at all airspeeds.

Figure 2: Wind Velocity (mph)

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2.2 Design Analysis, Review Process and Selection

2.2.1 Component Review

Propeller Review

Selection of the propeller was fairly straight forward after looking at the data generated from the dynamic

engine testing. In both cases the 13-4 propeller outperformed all the others. The 13-6 prop performed

almost as well as the 13-4 in the static thrust testing, but due to the rapid decline in the thrust it generated

in the dynamic engine testing it was determined that it was inferior to the 13-4 prop. By selecting the 13-4

prop the aircraft will have at least two more pounds of thrust available to it at maximum throttle over using

any of the other props. This translates to a higher acceleration of the aircraft on the runway and thus more

velocity and in the end more lift.

It should also be noted that the manufacturer of the Magnum XLS-61A engine recommends using the

13-4 propeller [2]. This fact verifies the test data and makes an even stronger argument in favor of the 13-4

propeller.

By characterizing the thrust characteristics of the propeller that will be used in competition, the sim-

ulation for takeoff of the aircraft will be that much more accurate. This accuracy is crucial to a high

competition score. Therefore the lift curve had a second order polynomial fit to it. This equation is shown

in Equation 2.

T (lbs− f) = −0.0024v(mph)2 + 0.0312v(mph) + 7.854 (2)

The variable T is thrust, in pounds force, being generated by the engine with a 13-4 propeller attached,

and v is the incoming wind velocity or airspeed of the aircraft in miles per hour.

Fuselage

The fuselage review was done by designing four different fuselages that each had certain advantages and

disadvantages. The four models developed are shown in Figures 3. Model B is a model of last year’s

fuselage design. This is important because this year’s design should be an improvement from last year.

To help select which fuselage is the best possible design four categories were identified as characteristics

that a good fuselage should have. These categories are: overall weight, frontal area, strength, and FEA

analysis. The scores that each of the models received in each of these categories is shown in Table 3.

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Table 3: Fuselage Model Decision Matrix

Fuselage WeightRanking(1− 4)

FrontalAera

Ranking(1− 4)

Strength(0.5− 2)

FEAAnalysis(1− 4)

TotalPoints

Total(1− 4)

A 1.003 1 3.75x3.50 1 1 1 4 1B 1.4303 3 3.5x3.75 1 2 2 8 2C 7.853 4 4.75x4.125 4 0.5 4 12.5 4D 1.0736 2 4.5x4.25 3 1.5 3 9.5 3

Figure 3: Fuselage Selection

Spar Selection

The spar is a vital aspect of a high lifting aircraft. It needs to be both strong and rigid, but within reason as

to maintain the lightest aircraft possible. The three candidates for a spar design are listed below in Table

4, along with the criteria to decide them.

Table 4: Spar Decision Matrix

Candidates

Weighting Factor (%)Balsa Al Spar Al Spar w/ Guy Wire

Rating Score Rating Score Rating ScoreWeight 30 3 90 7 210 9 270Added Drag 10 1 10 1 10 0 0Strength 50 4 200 6 300 9 450Ease of Manu-facturing 10 6 60 8 80 6 60

Total 100 360 600 780

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Landing Gear

The landing gear design needed to be strong, lightweight, produce a small amount of drag, and be easy to

manufacture. With this in mind there were three types of landing gears that were reviewed. These three

were chosen because they have proven in the past to be solid designs. Table 5 shows how each of the three

landing gears scored in four different categories. To clarify, the triangulated landing gear is a bent landing

gear that has aluminum attaching the ends of the gear to the spar. This transfers force to the strongest part

of the aircraft.

Table 5: Landing Gear Decision Matrix

Candidates

Weighting Factor (%)Triangulated Bent Gear Square Tube

Rating Score Rating Score Rating ScoreWeight 40 10 400 6 240 4 160

Induced Drag 20 5 100 7 140 3 60Strength 30 8 240 5 150 7 210

Ease of Manufacturing 10 3 30 6 60 5 50Total 100 770 590 480

Wheels and Braking System

High precision bearings were used to reduce rolling resistance and improve acceleration during takeoff. A

0.375 inch diameter ABEC 7 bearing, seen in Figure 4, was specked out for its small size and minimum

weight. This bearing is rated for 113 lbs of dynamic loading, which is 2.5 times the maximum load the

bearings are expected to see during a hard landing. The wheels themselves are machined out of aluminum

to fit these bearings along with 0.25 inch diameter rubber o-rings for use as tires. The current wheels

seen in Figure 5a weigh 2.2 oz each, but FEA analysis was been done to reduce the weight of each wheel

while maintaining adequate strength. The newly designed wheels seen in Figure 5b will be 0.8 oz per

wheel, which is a 63% reduction in weight. FEA analysis verifies adequate strength after the reduction of

material. The wheel was simulated with a maximum predicted load of 65 lbs, assuming impact loading

from the gross weight of the aircraft freefalling 3 feet (simulating a stall during takeoff or landing). The

FEA results, seen in Figure 5c, predicted a maximum stress of 32 ksi, which is 20% below the yield stress

of the aluminum. This custom wheel and bearing assembly will provide a great advantage over the use of

commercially available R/C aircraft wheels.

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Figure 4: ABEC 7 Bearings

(a) Current Design (b) Weight Reduction (c) High Precision Bearings

Figure 5: Wheel Design

Having highly efficient, low rolling resistance wheels introduces a small problem, the ability to slow

the aircraft down before the end of the runway. To solve this problem a lightweight brake was designed.

This brake, seen in Figure 6, makes use of a small wooden cantilever beam that is actuated by a servo in

the avionics bay. The entire brake system weighs only 2.1 oz and through testing, has shown the ability to

stop the aircraft at gross weight in less than 65 feet from approximately 20 mph. This brake system has

the potential to keep the aircraft from being damaged in the event that the momentum is too great to stop

the aircraft under normal means, such as turning to scrub away speed.

Figure 6: Brake System

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2.2.2 Design Selection

Propeller

The 13-4 type propeller was chosen after comparing the dynamic engine test data to a variety of other

propellers. It maintained the highest thrust in comparison with the other propellers over the whole range

of velocities tested.

Fuselage

Model A in Figure 3 was chosen as the design for the fuselage. It scored the best overall and will be

the lightest and strongest possible design. It is the best design because it uses less material while still

maintaining strength. Although it has the least amount of material, it is the strongest design. This is a

testament to the application of engineering mechanics. Another advantage that this design has over the

other ones is that it has the most room for loading the weight box. This is very important due to the new

design constraint of loading the weight box in under a minute.

Spar

The front spar, Al 2024 with a guy wire, was chosen for its high strength to weight ratio and its ability to

minimize the wing tip deflection. This was chosen over just an aluminum spar because it is slightly lighter

and stiffer in flight. The material chosen for the guy wire is a high strength braided fish line. This material

was chosen due to its light weight, high strength, and resistance to stretching.

Landing Gear

The triangulated landing gear was selected as the best design to use on the aircraft. Table 5 shows that the

triangulated landing gear outperformed the others by a wide margin. This is a new innovation this year

that allows some of the load to be transferred to the strongest part of the aircraft, the wing spar. This will

prevent the gear from buckling while the aircraft is landing.

Brake

The brake design in Figure 6 was chosen for this year’s aircraft. This design is essentially an upgrade

from the first attempt at a braking system. Since this is a new concept this year the design is still being

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improved on and will only continue to improve.

Wheels

The wheels will be constructed of aluminum hubs and rubber o-rings as tires. With the use of high

precision bearings, these wheels have proven to have very low rolling resistance and can stand up to the

loads to be experienced during competition. The wheels are easy to manufacture and assemble.

Parasol versus Low Wing

While low wing aircrafts tend to generate a bit more lift near the ground due to ground effect, the natural

positive roll stability of a parasol wing aircraft is extremely valuable with such a slow flight aircraft.

The parasol wing has also proven itself in past competitions to be the ideal configuration for a high load

carrying aircraft. The parasol wing was chosen because of positive stability and past experience.

Tail Attachment

A boom style tail was chosen for its high strength to weight ratio and its ease to detach, keeping the

aircraft modular and easy to transport. Other types of tails include a blended tail that would reduce drag,

but increase weight. The manufacturing and transportation of the aircraft would also be more difficult

with a blended tail. In the past a blended tail was used because composite material was allowed. Due

to competition rules preventing the use of composites to be used a more simplistic boom style tail was

adopted.

Center of Gravity (CG) Location

While a slightly aft CG seems to improve roll performance, the aircraft also becomes more unstable and

harder to fly. For this reason, the CG will be placed at 30% chord length downwind of the leading edge of

the wing; this still gives a positive static margin so the stability of the aircraft will be maintained. During

competition there are often unforeseen variables that may require the CG to be moved slightly away from

it designed position. The design of the weight box allows the CG to be adjusted slightly to account for

these variables.

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Design Conclusion

The Michigan Technological University’s Huskies Aero Design Team has successfully implemented the

design process to meet this year’s aircraft goals. With a drastically lighter design and an increase in wing

area, the Huskies’ craft will be capable of higher lift than ever before. A sleeker fuselage will keep the drag

down so the aircraft can reach its maximum lift. An adjustable CG will keep the aircraft positively stable,

and the high wing design and innovative washout will keep the aircraft easy to fly for the pilot. A new

brake design will keep the low rolling drag design from rolling off the runway. All and all, a successful

collaborative design process will keep the Huskies aircraft on the competitive edge.

3 Calculations

3.1 Performance

3.1.1 Drag Analysis and Calculations

To calculate drag it is broken up into three separate parts: wing drag, body drag, and rolling drag.

Rolling Drag

Rolling drag can be found experimentally by calculating the coefficient of friction (Cf ). This is done by

finding the distance versus stop time of the aircraft’s wheel assembly, finding the negative acceleration

caused by friction, finding the friction force, then finding Cf . A several trial average generated a Cf of

0.0315. Equation 3 shows the equation for rolling drag.

FD,rolling = 0.0315mg (3)

Where m is mass of the aircraft and g is the acceleration due to gravity

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Body Drag

Body drag was estimated by splitting the aircraft geometry up (not including the wing) into simple shapes

with known coefficients of drag (CD,i), each given by equation 4.

FD,body =

[i∑

i=1

1

2CD,iAiρv

2

](4)

Where CD,i is determined by geometry and orientation to relative airflow, Ai is the frontal area, ρ is

ambient air density, and v is velocity of the aircraft through air. The sum of the components drag equals

the total body drag. At standard pressure, the body drag at 30mph airspeed (maximum velocity of the

aircraft) is .64lbf.

Wing Drag

Wing drag is available based on experimental data available for the Selig 1223 airfoil. The coefficient of

drag is a function of AoA. The drag equation in equation 4 is again used.

FD,wing =1

2CDAiρv

2 (5)

In this instance, the area Ai is the chord length of the wing multiplied by the wingspan. The total drag

force is the sum of these three drag forms. See section 3.1.2 for calculations of drag/lift optimization.

3.1.2 Performance Optimization

Lift optimization requires many calculations. The most crucial governing equation is the lift equation,

shown in equation 6.

FLift =1

2ClAρv

2 (6)

Cl represents the coefficient of lift, which, like CD, is a function of AoA. A is area and is, again, the

chord multiplied by the span.

To begin the optimization, one looks to the three designer-alterable variables: Cl (AoA), A, and v. For

the beginning of the calculation, the AoA is set to negative 2 degrees AoA, the approximate minimum drag

angle (the aircraft has an adjustable AoA wing). The next equation that has to be applied is the overall

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force balance for forward motion. This is shown in equation 7.

FResultant = FThrust − FDrag (7)

Thrust and drag are both functions of velocity, based on the equations discussed earlier in this section.

The following equation collects all the summed terms and lays them out in a differential equation for the

total force balance. Essentially the force multiplied by acceleration equates to a sum of all the forces. The

forces as discussed earlier are all a function of velocity.

mdv

dt= c1v

2 + c2v + c3 (8)

Where c1,c2, and c3 are the collection of terms from the components of FThrust and FDrag. This

relationship represents a Bernoullis Differential Equation. By setting velocity as a function of time, one

can numerically integrate the general solution v[t] this will allow the distance needed for take off to be

calculated. Equation 9 shows that runway position is a function of time and wing area. It needs to be

solved for 180 ft because this gives a twenty foot cushion on takeoff for unexpected variables.

x(t, A) = 180 (9)

The variable x is the runway position as a function of time and wing area.

Now, one can plug time and area back into the velocity equation. Taken a step further, the equation can

be substituted in for velocity in the lift equation. The reason this is done is because once we have lift as a

function of area and time it can be optimized for various loads that the lift force has to generate. Equation

10 combines the lift equation and the velocity functions.

FLift =1

2ClAρv[time, area]

2 (10)

Optimizing this equation yields a velocity of almost 42 ft/sec, while in the optimized condition of -2

degree AoA, 128 in. wingspan, 15 in. chord, and standard pressure. The lift was more efficient at a higher

wing area, but was not worth the increased weight. Increasing the wings AoA for the last 20 ft. of takeoff

to 4 degrees bears a final maximum lift force of 40.9 lbs.

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3.1.3 Competitive Scoring

To place high in the design competition it is important to understand the competition dynamic. The scoring

for this competition contains three main areas of scoring: the design report, oral presentation, and flight

score. The design report and oral presentation are both worth fifty points and have in the past combined

to account for approximately 30 to 50 % of the total score. The remaining portion comes from the flight

score where there is technically no maximum score. Last year for the Aero Design East in Georgia the top

flight score was 149 points. The top flight score for Aero Design West for 2011 in Texas was 162 points.

The large difference in score from year to year has to do with the change in the dimensional constraints

and the operational availability bonus. To be competitive in this years competition a flight score of close

to 150 points has to be achieved.

The scoring goes as follows for the flight score, there is a 10 point bonus for flying empty weight in

the first round, there is a possible 20 point bonus for lifting exactly the predicted payload, there is a raw

flight score that is based on the maximum weight lifted, and the new scoring this year gives a bonus for

flying every round. After combing the equations and equating to 150 points with the assumption that the

aircraft will successfully fly 80 % of the time and achieve both bonuses, the aircraft has to lift at least 26.6

pounds.

3.2 Stability and Control

To ensure inherent aircraft stability and effortless control, research into aerodynamic stability paved the

way for many aircraft design features. Before dimensioning the aircraft, a decision needed to be made

about the overall configuration of the aircraft. The research yielded results in the direction of a traditional

style, raised mono-wing aircraft. Raised wing aircraft have innate advantages over mid and low wing

aircraft, the most important being the theory of positive stability. A vertically raised wing acts much like

a wing with dihedral, but in a manufacturing sense, is much easier to construct. An aircraft that has been

rolled to one side encounters what is known as a side slip. This is a change in angle from the original

attitude of the aircrafts heading. When a raised wing or a wing with dihedral encounters a side slip, more

lift is generated on the inside wing causing a counteracting roll moment that naturally returns the aircraft

to level flight.

Many small, stable aircrafts use this aerodynamic principal, including one of the most popular pilot

training aircrafts, the Cessna. Other advantages of the raised wing in this year’s design is the increased

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Figure 7: Natural Aircraft Response to A Pitch Disturbance, for Different Amounts of Pitch Stability

lifting area at the center of the wing, where in other designs that have the wing attached to the fuselage,

this lifting surface is lost. Likewise, due to the vertical position of the wing, less interference drag exists

between the wing and fuselage.

There are many more aerodynamic principles that factor into the stability of an aircraft, even if an

overall stable configuration is selected. These include pitch stability and yaw stability and are governed

by factors such as center of gravity (CG) position, neutral point (NP) of the aircraft, and vertical and

horizontal stabilizer sizing. Each one of these parameters directly affects the stability of the aircraft design.

Pitch stability is a factor of CG location relative to the aircrafts NP. This stability factor is also known as

the stability margin (S.M.) and is expressed by Equation 11.

S.M ≡ xnp − xcgc

(11)

A stability margin of zero would effectively be a neutral flying aircraft where any disturbance in pitch

would not be corrected by the stability of the aircraft. This makes it very sensitive to pitch input and

requires constant input from the pilot to counteract disturbances such as wind gusts. A small S.M. in the

range of +.05 to +.15 is desired because any pitch upsets caused by outside disturbances results in damping

affect that brings the aircraft back to the trimmed level flight as seen in Figure 7 [1].

The neutral point of the aircraft can be closely approximated with equation 12. Where xvp is the

distance of the neutral point from the mean aerodynamic cord leading edge as shown in Figure 8 [1].

xnpc' 1

4+

1 + 2/AR

1 + 2/ARh

(1− 4

AR + 2)Vh (12)

The variables c, AR, ARh, and Vh and are the mean cord length, wing aspect ratio, (HS) aspect ratio

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Figure 8: Length, Areas, and Angles Used in Simple Stability Criteria

and horizontal stabilizer volume coefficient, respectively. Vh can be calculated equation 13,

Vh =ShlhSc

(13)

Where the variables S and Sh are the areas of the wing and (HS) respectively. The variable lh is the

moment arm measured from the CG location to the aerodynamic center of the (HS). Typical values for Vh

on stable aircraft range from 0.30 to 0.60 [1].

Yaw stability is only a factor of the vertical stabilizer volume coefficient Vv expressed in equation 14,

Vv ≡SvlvSb

(14)

Where Sv is the vertical stabilizer (VS) reference area, lv is the moment arm measured from the CG

location to the aerodynamic center of the VS and b is the wingspan. Typical values for Vv are in the range

of 0.02 to 0.05 for stable aircraft [1]. Since many of the stability equations are dependent on each other,

an iterative process was used to finalize these dimensions and ensure that each value maintained in the

appropriate range.

3.2.1 Servo Forces

The maximum torque due to the forces on the control surfaces, assuming 20mph airspeed, were calculated

using MATLAB. The maximum possible torque upon the servo arms were computed by these forces. The

max torque are the control surfaces are shown in Table 6. The max torque that the servos (Futaba S3004)

can handle is 2.75 lbsin determined from testing consisting of hanging weight from the servo arm and

seeing whether it could lift it or not. The servo operating the engines throttle was not calculated because

the resistive load is insignificant. The nose gear servo was also not calculated, loads were considered to

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be similar to the rudder, except for metal gears were used which will be more accepting to jolts received

from the run way.

Table 6: Servo Force Requirements

Servo TorqueLocation Required Max Servo OutputAileron 1.3002 lbs-in 2.75 lbs-inElevator 5.7209 lbs-in 2.75 lbs-inRudder 3.1329 lbs-in 2.75 lbs-in

3.3 Aircraft Sizing

Deciding how to distribute the 225 inches constraining dimension between the height, wingspan, and

length of the aircraft was performed by a series of calculations and structural expectations that the airframe

must meet. The aircraft incorporates a parasol wing design, which provides stability while carrying a

heavy payload but draws a larger dimension from our total. Another determining factor for aircraft height

was prop clearance, which is large comparatively to standard aircraft because of the over sized prop. To

compensate for its size the landing gear length is adjusted. The remaining size will be distributed among

the wingspan and length. The wing span and length are dependent of each other so they must be adjusted

accordingly. The benefits of a longer wingspan is it provides more overall lift for the aircraft but the

remaining dimension for the tail boom would have to be shorter which can cause the aircraft to become

unstable in flight. From an iterative process using MATLAB it was concluded that the best dimensions to

use are a height of 22.6 in, a length of 72.5 in, and a wingspan of 128 inches.

3.4 Weight Build-Up and Analysis

An essential part of a cargo aircraft’s effectiveness is in the ability to build the aircraft around the true

center of gravity (CG). The CG for most aircraft should be located between 25− 30% of the chord length

from the aft of the leading edge. From past experience and various calculations, this aircraft should have a

true CG at 30% of the chord. This however, is easily adjusted to 28% and 26% if need be on this particular

aircraft due to the adjustable weight box. Once the 30% CG was decided on, and the overall dimensions

were calculated for the aircraft, the design process started. Many dimensions of the aircraft came from

a simple moment diagram. The engine assembly is the object of greatest mass, so to counteract this the

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much lighter tail must be much farther from the CG. Once these dimensions were set most of the design

stage was spent making the frame fit these dimensions, strong enough, and have a balanced CG.

In order to cut weight on the aircraft, a weight budget was conceived before the design stage. This

forced a more purposeful design process and more in-depth thought on construction process. This weight

management was updated once the final solid model was finished. The results are shown in table 7. In the

last two columns the weight of this aircraft is compared to last year’s aircraft. Also the actual CG (distance

from true CG) is calculated in Table 7. This indicates that the CG is very close to the desired location.

Table 7: Weight Buildup

3.5 Structural Analysis

The structure of this aircraft was analyzed by means of both FEA and MATLAB code. The FEA, figure

14, model looked at a force equal to a 3ft. drop on the frame and gear. This force (approx. 180lbf) resulted

in a max stress of 25 ksi, only half the yielding of aluminum.

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Figure 9: FEA Analysis (Left) and MATLAB Wing Simulation (Right)

The spar was analyzed analytically and through finite element analysis for a 3-g bank turn. A free

body diagram is provided in Figure 10 , which illustrates the forces acting on the spar. The final strengths

from this analysis are recorded in Table 8. As seen in the table not only does a guy wire reduce the stress

in the wing, but it also stiffens the wing. The strength values were found using the bending stress equation

as shown in Equation 15. The spar can be modeled as this because normal stress is minimal, and vertical

sheer can be neglected.

σb =My

Ix(15)

(a) Original Spar With 1.25” Max Outer Diameter and Without Guy-Wire

(b) Upgraded Spar with 1” Max Outer Diameter with Guy-Wire

Figure 10: Spar Evolution

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Table 8: Bending Strength of Spar

DesignStrength(ksi)

SafetyFactor

1.25” Center Spar and 1” Outer Spar 32 1.561” Center Spar and 0.875” Outer Spar w/ FishLine Guy-Wire

23 2.17

1” Center Spar and 0.875” Outer Spar w/ 22Gauge Steel Wire

16 3.13

4 Innovations

4.1 Manufacturing Process Innovations

The wing for the 2011 S.A.E. Aero West Competition was not only designed for performance, but for ease

of manufacture. The manufacturing process employs a CNC foam cutter to precisely cut the wing profile

into a foam core. After the foam profile is cut, the balsa sheeting is glued and the spar is inserted the wing

is laid back into the foam negatives and pressure is applied via and vacuum pump and bag. This helps

remove excess epoxy and create a very accurate airfoil across the entire wing.

4.2 Design

There are new innovations to the design that improve its functionality and performance. The wings have

a washout from 4 to 0 degrees AoA. This washout will provide a relief in the stall characteristics of

the wingtips, especially during stalls and turns. A VAoA system has been designed for the entire wing

allowing the aircraft an increase in acceleration down the runway, generating more lift within the 200 foot

takeoff zone. High precision bearings reduce the rolling friction on takeoff and landing therefore a simple

yet lightweight braking system was designed to keep the aircraft on the runway. Also, the aircraft has an

adjustable CG built into the wing strut. This provides the ability to place the aircraft on a stand to balance

the aircraft at predetermined percentages of the chord length.

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4.3 Application

A prominent part of the design is to make the aircraft modular, because our team has very limited space

to transport the aircraft. This lack of space requires that the aircraft design be able to separate into the

smaller component pieces; the fuselage, landing gear, empennage, and the two wing sections. The other

reason the team chose to have a modular design is so in the event of a damaged component, it can be easily

removed for repair.

5 Conclusion

In conclusion, after much research, and testing an aircraft that is capable of lifting 27 pounds of payload

was designed. The design applies the principles of fluid and aerodynamics to reduce drag, and increase lift.

Material mechanics were applied to design an extremely light aircraft that will still be able to withstand

any load that it experiences during a normal flight. The aircraft was also designed with a parasol wing

and wing washout to ensure that it is highly stable and can recover from pilot error and environmental

disturbances. Throughout the design process many challenges were overcome to improve upon previous

designs and through new innovations, such as the braking mechanism, and variable AoA wing this year’s

aircraft will be highly competitive and has great promise to place high in the Aero Design East competition.

References

[1] Aircraft design for stability and control. Spring, 2006.

[2] Magnum xls .61a rear needle valve aircraft engine manual. retrieved Janurary 22, 2011.

[3] S1210 airfoil description. retrieved October 25, 2010.

[4] T. Benson. Propeller thrust, July 2008. retrieved Janurary 22, 2011.

[5] T. Benson. Induced drag coefficient, August 2010. retrieved Octover 2, 2010.

[6] L. Dingle and M.H. Tooley. Aircraft Engineering Principles. Oxford: Elsevier Butterworth-

Heinemann, 2005.

[7] B. Dunbar. Fact sheets - winglets, March 2008. retrieved October 25, 2010.

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