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# Aircraft

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Submitted By am3556
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MEM425: Aircraft Performance and Design
(drag-polar)

Dr. Ajmal Yousuff Dept. MEM Drexel University

“Engine Selection”
In a cruise flight:
2 T  D  qSCD  qS CD,0  KCL   

(5.3.2)

1  q (T / S )  (T / S )2  4CD ,0 K (W / S ) 2   2CD,0 

Yousuff

MEM 425 Aircraft

2

Altitude effects (5.3.2)
Ta  Ta 0 (  / 0 )

VTmin

 2W   S 

K CD ,0

   

Yousuff

MEM 425 Aircraft

3

Drag Polar manipulation
2 CD  CD,0  KCL
3/2 1/2 CL / CD , CL / CD , CL / CD  is important 

Maximization of

CD / CL  (CD,0 / CL )  KCL

Yousuff

MEM 425 Aircraft

4

The drag-polar
2 CD  CD,0  KCL

Drag-polar reflects the aerodynamic efficiency of the vehicle While the design parameters {CD,0,K} are fixed, CL could be changed in flight.

Three important ratios:
3/2 1/2 CL CL CL , , CD CD CD yousuff MEM425 Aircraft Design 5

The ratio:

3/2 C L / CD

3/2 CL CD

max

yousuff

MEM425 Aircraft Design

6

The ratio:

CL / CD

CL CD

max

yousuff

MEM425 Aircraft Design

7

The ratio:

1/2 C L / CD

1/2 CL CD

max

yousuff

MEM425 Aircraft Design

8

Velocity in cruise flight

3/2 (CL / CD )max

(CL / CD )max

1/2 (CL / CD )max

V

2

2W  S

K 3CD ,0

2W  S

K CD ,0

2W  S

3K CD ,0

a yousuff MEM425 Aircraft Design 9

An example
Consider HW2 aircraft:

@ sea-level, Pmin = 27547 ft.lb/sec occurs at V = 110 ft/sec.
Determine drag-polar parameters:

2W @ Pmin , V   S
2

K 3CD ,0

and

P 1  T  D  V 2 S (4CD,0 ) V 2

W = 2950 lbs, S = 174 ft2 - given

yousuff

MEM425 Aircraft Design

10

Example, contd.
If

CL CL  aa ; a   0.2deg 1 a
Determine the corresponding angle of attack.

If V=1.5 VP_min, determine a.

yousuff

MEM425 Aircraft Design

11

V and a, in cruise
In a cruise flight,

1 W  L  V 2 S (aa ) 2

yousuff

MEM425 Aircraft Design

12

Limits on cruise velocity?
Is V=1.5 VP_min possible?

Yes, if sufficient power is available.
Is V=0.75 VP_min possible?

CL

a

yousuff

MEM425 Aircraft Design

13

Fuel needed
If we are in Pmin cruise flight, how much fuel do we need to cover R?

Rprop

 W0   ln   c CD  W1 

 CL

Propeller and engine characteristics given, ie. {,c} yousuff MEM425 Aircraft Design 14

Fuel needed, 2
If we are cruising with V=1.5 VP_min how much excess (?) fuel do we?

Rprop

 W0   ln   c CD  W1 

 CL

{CL , CD } recalculate

 W0 / W1.

W1  W0  W fuel  W0  W1

Propeller and engine characteristics given, ie. {,c} yousuff MEM425 Aircraft Design 15…...

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