Airplane Performance and Design

8/20/2019 Airplane Performance and Design

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© 2012 Randal Allen, PhD

1

AIRPLANE PERFORMANCE and DESIGN

Dr. Randal Allen


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Phases of Airplane Design

2

Conceptual Design

Preliminary Design

Detail Design


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Conceptual Design

3

Major drivers are

Aerodynamics

Propulsion

Flight performance.

The first-order question is…

Can the design meet the specifications?

If so, then the next question is… Is the design optimized, i.e. is it the best design that meets the

specifications?


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Preliminary Design

4

Serious structural and control system analysis and design take

place.

Substantial wind tunnel testing will be carried out, and major

computational fluid dynamic (CFD) calculations of the completeflow field over the airplane configuration will be made.

At the end of the preliminary design phase, the airplane

configuration is frozen and precisely defined.

The drawing process called lofting is carried out whichmathematically models the precise shape of the outside skin of

the airplane, making certain that all sections of the aircraft

properly fit together.


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Detail Design

5

The airplane is now simply a machine to be fabricated.

The precise design of each individual rib, spar, and section of

skin now takes place.

The size, number, and location of fasteners (rivets, welded joints,

etc.) are determined.

Manufacturing tools and jigs are designed.

At this stage, flight simulators for the airplane are developed.


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7 Pivot Points for Conceptual Design

6

Requirements

Initial weight estimate of the airplane

Critical performance parameters

Maximum lift coefficient

Lift-to-drag ratio

Wing loading

Thrust-to-weight ratioConfiguration layout (shape/size of the airplane on a drawing)

Better weight estimate

Performance analysis (does the airplane meet/exceed the req’ts?)

…iterate steps 3 to 6… Optimization (is it the best design?)


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Requirement Aspects (1/4)

7

Remember thrust required and power required are associated

with the airframe, while thrust available and power available

are strictly associated with the power plant (engine/motor).

Range

Propeller

Takeoff distance

0

1ln

W L

R cD W

2

,0.7

1.44

LO

LO

L MAX r V

W s

g SC T D W L


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8

Stalling velocity

Endurance

Propeller

Maximum velocity

,

2 stall

L MAX

W V

SC

3/2

1 0

1 12

2

L

D

C S E

cC W W

1/22

,0

,0

4 D A A

MAX MAX

MAX

D

C T T W W

W S S W eARV

C


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9

Rate of climb

Propeller

Maximum turn rate

Maximum turn radius

3/ 2,0

/ 1

( / ) 0.8776 / MAX MAX D MAX

P W S

R C W C L D

,

2 /

L MAX MAX

MAX

C n g

W S

min

,

2

L MAX

W R

gC S


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10

Maximum load factor

Service ceiling

Cost

Reliability and maintainability

Maximum size

,212

/

L MAX

MAX

C n V

W S

1/21/4

,0

3/4

0,0

0.7436219,867ln

D

A MAX

C W W H

S P eAR


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11

Design of a Propeller-Dr iven Airplane


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Requirements

12

1. Maximum level speed at midcourse weight: 250 mph

2. Range: 1,200 mi

3. Ceiling: 25,000 ft

4. Rate of climb at sea level: 1,000 ft/min

5. Stalling speed: 70 mph

6. Landing distance (to clear a 50-ft obstacle): 2,200 ft

7. Takeoff distance (to clear a 50-ft obstacle): 2,500 ft


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Initial (gross) Weight Estimate (1/2)

13

(empty: historical data for 19 propeller-driven airplanes)

(fuel: see Anderson, section 8.3.2, pp. 400-405)

Crew: 1 pilot at 170 lb

Payload: 5 passengers (5 x 170 lb) and luggage (6 x 20 lb)

0 0 01 / /crew payload

f e

W W W

W W W W

0

0.62eW

W

0

0.159 f W

W

170crewW

970 payload W


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Initial (gross) Weight Estimate (2/2)

14

Note: For each 1 lb increase in passenger weight, there is 4.525

lb increase in gross weight

Aviation gasoline

Density

Minimum needed fuel capacity

0 0 0170 970 1140

(1140 )(4.525) 51581 0.159 0.62 0.2211 / /

crew payload

f e

W W lb lb lbW lb lb

W W W W

0

0

(0.159)(5158 ) 820 f

f

W W W lb lb

W

820145.4

5.64 /

lb gal

lb gal


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Critical Performance Parameters

Maximum Lift Coefficient

15


5-digit NACA airfoils preferred over 4-digit NACA airfoils

because the maximum camber is closer to the leading edge

(0.15c), which implies a higherWings are usually thicker at the root then taper toward the tip

While stall may occur at the root, the tips are still in the flow

for effective aileron

Assume root is NACA 23018

Assume tip is NACA 23012

Use the average

To assist in takeoff and landing performance, trailing edge

flaps are added

, L MAX C

, 1.6l MAX c

, 1.8l MAX c

, 0.9l MAX c

, 1.7

l MAX c

,l MAX c

, 1.7 0.9 2.6

l MAX c , ,0.9 (0.9)(2.6) 2.34 L MAX l MAX C c


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Wing Loading

16

Wing loading

Wing loading plays a role in stall velocity, landing distance,

and maximum velocity.

Consider each requirement then determine based onstrongest constraint

Stall velocity requirement (#5) of 70 mph = 102.7 fps…

(sea level)

Landing distance requirement (#6) of 2,200 ft…

The stronger constraint is

/W S

3 2

2 2

,

1 1(0.0023769 )(102.7 ) (2.34) 29.3

2 2

slug ft lb stall L MAX s ft ft

W V C

S

241.5 lb

ft

W

S

229.3

lb

ft

W

S

2 2

25159 17629.3 29.3lb lb

ft ft

W lbS ft


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Thrust-to-Weight Ratio

17

Thrust-to-weight ratio

Consider each requirement then determine the ratio based on

strongest constraint

Takeoff distance requirement (#7) of 2,500 ft…

Rate of climb requirement (#4) of 1,000 ft/min…

Maximum velocity requirement (#1) of 250 mph…

The stronger constraint is

Recall for a propeller-driven aircraft, the power-to-weight

ratio is the performance parameter and is often quoted as

power loading (the reciprocal of power-to-weight ratio).

/T W

119 P hp363 P hp

303 P hp

363 P hp

363 0.075158

hplb P hp

W lb 14.2 lbhpW

P


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Maximum lift-to-drag ratio

Wing loading

Power loading

Takeoff gross weight

Fuel weight

Fuel tank capacity

Wing area

High-lift device, single-slotted trailing-edge flaps

Zero-lift drag coefficient

Drag-due-to-lift coefficient

Aspect ratio

Propeller efficiency 0.8 Engine power, supercharged to 20,000 ft

Summary

Minimum Needed for Conceptual Design

18

, 2.34 L MAX C

/ 14 MAX

L D

2/ 29.3 lb

ft W S

/ 14.2 lbhp

W P

0 5158W lb

820 f

W lb

145.4 gal 2176S ft

,0 0.017

DC

0.075 K

7.07 AR

363 P hp


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Configuration Layout (1/4)

Overall Configuration

19

The weight of 5158 lb is on the borderline of single- and twin-

engine general aviation airplanes. We need 363 hp. Examining

the available piston engines, we find the Textron Lycoming

TIO/LTIO-540-Vis rated at 360 hp supercharged to 18,000ft.


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Tractor Configuration

20

(+) The heavy engine is at the front, which helps to move the

center of gravity forward and therefore allows a smaller tail for

stability considerations.

(+) The propeller is working in an undisturbed free stream. (+) There is a more effective flow of cooling air for the engine.

(-) The propeller slipstream disturbs the quality of the airflow

over the fuselage and wing root.

(-) The increased velocity and flow turbulence over the fuselagedue to the propeller slipstream increase the local skin friction on

the fuselage.


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Pusher Configuration

21

(+) Higher-quality (clean) airflow prevails over the wing and

fuselage.

(+) The inflow to the rear propeller induces a favorable pressure

gradient at the rear of the fuselage, allowing the fuselage to closeat a steeper angle without flow separation. This in turn allows a

shorter fuselage, hence smaller wetted surface area.

(+) Engine noise in the cabin area is reduced.

(+) The pilot’s front field of view is improved. (-) The heavy engine is at the back, which shifts the center of

gravity rearward, hence reducing longitudinal stability.

(-) Propeller is more likely to be damaged by flying debris at

landing. (-) Engine cooling problems are more severe.


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22

Because we need a rather large, powerful reciprocating engine

for our airplane, we wish to minimize any engine cooling

problems. Therefore, we will be traditional and choose the

tractor configuration.


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Wing Layout (1/2)

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Aspect ratio

Wing sweep, subsonic therefore no need for swept wings

Taper ratio

(+) Smaller taper ratio implies a lighter wing structure (based oncentroid of the lift distribution)

(-) Smaller taper ratio exhibits undesirable flow characteristics

Compromise with which determines the geometry of the

trapezoidal wingVariation of airfoil shape and thickness along the span, root

NACA 23018, tip NACA 23012

Geometric twist, unnecessary since aileron control is maintained

Anhedral – wings bent upDihedral – wings bent down

2176 7.07 35.27b S AR ft ft

/ , 0 1t r c c

0.5


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Wing Layout (1/2)

24

High-wing: good for loading/unloading cargo; more stable re:

lateral/rolling motion; dihedral also enhances lateral stability;

possibly too much stability inhibiting rolling motion; anhedral

Mid-wing: lowest drag because wing-body interference isminimized; structural disadvantages with support running

through the fuselage; okay with passengers above and cargo

below

Low-wing: landing gear disadvantages; ground clearance neededfor propeller

We choose a low-wing configuration due to structural and

landing gear considerations.


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Fuselage Configuration

25

Store the fuel in the wings

Volume is given for the Lycoming engine, seating is referenced,

baggage

Note: Tapering should be less than 15 degrees to avoid flowseparation.


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CG Location – First Estimate

26

Used to locate the wing relative to the fuselage such that the

mean aerodynamic center of the wing is behind the c.g. of the

airplane for static longitudinal stability.

Estimate the weight of the wing. 2 2 22.5 2.5 176 440lb lbwing ft ft W S ft lb


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Horizontal and Vertical Tail Size (1/)

27

Horizontal tail: longitudinal stability

Elevator: provides longitudinal control and trim

Vertical tail: directional stability

Rudder: provides directional control

Size may be based on stability and control analysis or historical

approach.

Horizontal tail volume sizing: (historically, )

Vertical tail volume sizing: (historically, )

0.7 HT

V

0.04VT V


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Horizontal and Vertical Tail Size (2/)

28

Tail types: Conventional, T-tail, Cruciform

We choose the conventional tail for its light-weight structure

and reasonable stability and control then calculate

and . It makes no sense to use a cambered airfoil forthe tail, therefore, use symmetric airfoils, e.g. NACA 0012.

Wings of lower AR, although aerodynamically less efficient,

stall at higher angles of attack than wings with higher AR.

Hence, if the horizontal tail has a lower AR then the wing, whenthe wing stalls, the tail still has some control authority.

Select with the same taper ratio as the wings, .

Then calculate wingspan, root chord and tip chord length, and

mean aerodynamic chord for the horizontal tail.

237.2 HT

S ft 2

15.5VT S ft

4 AR 0.5


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Horizontal and Vertical Tail Size (3/3)

29

For the vertical tail, is typical. Choose .

Then, calculate the height of the vertical tail, and with ,

calculate the root chord and tip chord lengths as well as the mean

aerodynamic chord for the horizontal tail.

1.3 2.0VT

AR 1.5VT AR

0.5


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Propeller Size (1/2)

30

Propeller efficiency is improved as the diameter of the propeller

gets larger.

1. Propeller tips must clear the ground when the airplane is on

the ground. 2. Propeller tips speed should be less than the speed of sound to

avoid compressibility effects.

Two-blade (diameter in inches)

Three-blade (diameter in inches)

1/4

22 D hp

1/4

18 D hp


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Propeller Size (2/2)

31

With a two-blade: , the wing tip velocity is

1,089 ft/s

Add this vector to the forward velocity vector (250 mph = 367

fps) to attain 1,149 ft/sThe speed of sound at sea level is 1,117 ft/s which is undesirable.

With a three-blade: , the wing tip

velocity is 889 ft/s

Add this vector to the forward velocity vector (250 mph = 367fps) to attain 962 ft/s

Therefore, we choose the three-blade propeller with

(adjust to what is available off the shelf)

1/4

18 360 78.4 6.5 D in ft

1/4

22 360 95.8 8 D in ft

6.5 D ft


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Landing Gear/Wing Placement (1/3)

32

Landing gear configurations: tricycle, tail dragger, and bicycle

Tricycle: cabin is level when on the ground, forward visibility is

improved, requires the c.g. to be ahead of the main wheels,

enhanced stability during ground rollTail dragger: allows for a larger propeller, greater lift at takeoff,

main wheels must be ahead of the c.g., unstable during a ground-

roll turn

Bicycle: useful for high wing airplanes, light-weight outriggerwheels are required near each wing tip

We choose the tricycle configuration. (Complete texts are

written on landing gear design.)


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33

The landing gear should be long enough to give the propeller tip

at least 9 inches of clearance above the ground. (We choose 12

inches or 1 ft.) The diameter of the propeller was determined to

be 6.5 ft, so that the radius is 3.25 ft. The landing gear length

should be at least 4.25 ft.

Note: since the landing gear folds up into the wing, the wing

location may have to be adjusted to distribute the loading on the

wheels – keeping the aerodynamic center behind the c.g. to

maintain longitudinal stability.


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34

Tire sizing

From a load analysis, the load on the main gear is 4,301 lb andthe nose gear is 857 lb. Therefore, the main wheels are 22.0

inches in diameter and 7.8 inches wide; while the nose wheel is

15.9 inches in diameter and 5.9 inches wide. (adjust according to

what is available off the shelf) Note: Keep in mind the c.g. shifts as fuel is consumed.

Therefore, a detailed analysis should be conducted to account for

the range of the c.g.

A B

Wheel diameter (inches) 1.51 0.349

Wheel width (inches) 0.715 0.312


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Better Weight Estimate (1/3)

35

Reference: “Aircraft Design: A conceptual Approach” by Daniel

Raymer, AIAA

Wing weight = 2.5(Sexposed wing planform)

Horizontal tail weight = 2.0(Sexposed horizontal tail planform)Vertical tail weight = 2.0(Sexposed vertical tail planform)

Fuselage weight = 1.4(Swetted area)

Landing gear weight = 0.057(W0)

Installed engine weight = 1.4(Engine weight)

All else empty = 0.1(W0)


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36

Wing weight = 370 lb

Horizontal tail weight = 70.6 lb

Vertical tail weight = 28.8 lb

Fuselage weight = 428.8 lb

Landing gear weight = 294 lb Installed engine weight = 765.8 lb

2

exp 148osed wing planformS ft

2

exp 35.3

osed horizontal tail planformS ft

2

exp 14.4

osed verticaltail planformS ft

2306.3wetted areaS ft

0 5158W lb

547 Engine weight lb


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37

All else empty = 515.8 lb

With this new we recalculate landing gear weight 0.057(W0)

and all else empty 0.1(W0) and recalculate . Repeat until

convergence occurs. Finally…

2474eW lb

0 crew payload fuel emptyW W W W W

170crewW lb

970 payload

W lb

820 fuel W lb

0 170 970 820 2474 4434W lb lb lb lb lb

2308eW lb 652 f W lb 0 4100W lb


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Performance Analysis (1/8)

38

Updated performance parameters…

Wing loading

Power loading

Still assume…

22

410023.3

176

lb

ft

W lb

S ft

410011.4

360lbhp

W lb

P hp

,0 0.017

DC

0.075 K

, 2.34 L MAX C

/ 14 MAX

L D


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39

Power required and power available curves

Plotted curves show

Requirement #1: Maximum level speed at midcourse weight: 250

mph

437 298 ft MAX s

V mph


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40

Rate of climb and ceiling

Plots show with a ceiling of 33,300 ft

Requirement #4: Rate of climb at sea level: 1,000 ft/min

Requirement #3: Ceiling: 25,000 ft

min/ 1572 ft

MAX R C

f A i (4/8)


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41

Range

Calculations show range meets the range requirement.

Requirement #2: Range: 1,200 mi

P f A l i (5/8)


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42

Stalling speed

Requirement #5: Stalling speed: 70 mph

2

3,

2 1 2 123.3 91.5 62.4

0.0023769 2.34

ft lb stall s slug ft

L MAX ft

W V mph

S C

P f A l i (6/8)


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43

Landing distance

Calculations show

Requirement #6: Landing distance (to clear a 50-ft obstacle):

2,200 ft

1751landing s ft

P f A l i (7/8)


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44

Takeoff distance

Calculations show

Requirement #7: Takeoff distance (to clear a 50-ft obstacle):

2,500 ft

761takeoff s ft

Performance Anal sis (8/8)


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45

Clearly we meet all the performance requirements (in some

cases considerably). This is due to the change from the initial

weight estimate of 5,158 lb to a new weight estimate of 4,100

lb.

Iterate


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Iterate

46

…iterate steps 3 to 6…

There really is no reason to iterate on the design. But if you did,

it’s best to have this information in MATLAB or an Excel

spreadsheet for iterative purposes.

Optimize


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Optimize

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Optimization – Is it the Best Design?

With the new, lighter weight, we could choose a less powerful,

more light-weight engine. Hence the airplane will be less

expensive.

References


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References

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Aircraft Performance and Design, by John D. Anderson

Aircraft Design: A Conceptual Approach, by Daniel P. Raymer

Airplane Performance and Design

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