AS 309- Aerodynamics Final Project

Final project required some math and writing report about aircraft and how the aircraft is flying.

AS

309- Aerodynamics Final Project

1

AS 309- Aerodynamics Final Project

You have been hired to assist the director of operations for a large and very well-known flight school.
The director of operations has asked you to analyze aerodynamics and performance data of the Cessna
172 S NAV III Skyhawk in order to buy 45 new aircraft to replace their old fleet. You are to calculate the
information and present a report of your findings to the Director of Operations of the organization.

The Project will consist of two parts:

I. Answers to the aerodynamics and performance questions in Canvas quiz (80% of Grade)
II. Technical report (minimum of 3 pages, not including the cover page) to the company Director of

Operations to describe the following: (20% of Grade)

a. cover page that includes the names of each group member, the class title and number, and
semester and year.

b. A brief description of the aircraft

c. Answers to report questions (20 questions total) in grey boxes at the bottom of each section.

d. Peer/self-evaluation form

Because of the limitations of Canvas, each individual person must submit answers and documents

online. If you fail to submit the assignment, you will receive a zero. All parts need to be submitted

(report and numerical answers), in order to receive a grade for the final project. Failure to submit one

of these elements, will result in a zero on the final project

AS 309- Aerodynamics Final Project 2

1. Lift

Questions to be answered in Canvas quiz:

Utilizing the aircraft information provided in Appendix A, calculate the following:

@ 2550 lbs

1. Vs1-Stall speed no flaps (in knots) @ 2550 lbs

2. Vr (in knots) @ 2550 lbs

3. Vs2 – Stall Speed with full flaps (in knots) @ 2550 lbs

4. Vref (in knots) @ 2550 lbs

5. CL (coefficient of lift)@ 115 kts @ 2550 lbs

6. What is the angle of attack for zero lift? (make sure to indicate + or – sign)

@2200 lbs

7. Vs1-Stall speed no flaps (in knots) @ 2200 lbs

8. Vr (in knots) @ 2200 lbs

9. Vs2 – Stall Speed with full flaps (in knots) @ 2200 lbs

10. Vref (in knots) @ 2200 lbs

11. CL @ 115 kts@ 2200 lbs

@ 2100 lbs

12. Vs1-Stall speed no flaps (in knots) @ 2100 lbs

13. Vr (in knots) @ 2100 lbs

14. Vs2 – Stall Speed with full flaps (in knots) @ 2100 lbs

15. Vref (in knots) @ 2100 lbs

16. CL @ 115 kts @ 2100 lbs

Questions to be answered in Report:

1. In the report include a description of how stall speed, rotation speed and approach speed

change with weight and how the values obtained above compared to the book values in the

C-172 Owner’s Manual (see Appendix B)

AS 309- Aerodynamics Final Project 3

2. Drag

Questions to be answered in Canvas quiz:

Utilizing the aircraft information provided in Appendix A, calculate the following (Use Appendix A1 and
A2 for the best L/D speed questions!)

1. Wing Di @2550lbs & 100 kts

2. Wing Dp @2550lbs & 100 kts

3. Wing Dtotal @2550lbs & 100 kts

4. Best L/D speed @2550lbs

5. Wing Di @ 2100lbs &100 kts

6. Wing Dp @ 2100lb & 100 kts

7. Wing Dtotal @ 2100lbs & 100 kts

8. Best L/D speed @ 2100lbs

Questions to be answered in Report:

2. In the report make a table to explain which of the following factors will affect which kind of drag
(induced or parasite)

1. load factor
2. air density
3. wing area
4. weight
5. air speed
6. wing span
7. aspect ratio

AS 309- Aerodynamics Final Project 4

3. Lift to Drag Ratio

Questions to be answered in Canvas quiz:

Utilizing the aircraft information provided in Appendix C, determine the following:

9. Velocity for minimum sink in knots @ 2,550 lbs

10. Value for minimum sink in ft/min @ 2,550 lbs

11. Velocity for best L/D in knots @ 2,550 lbs

12. Value for best L/D @ 2,550 lbs

13. Velocity for minimum sink in knots @ 2,100 lbs

14. Value for minimum sink in feet/min @2,100 lbs

15. Velocity for best L/D in knots @ 2,100 lbs

16. Value for best L/D in knots @ 2,100 lbs

Questions to be answered in Report:

In the Report:

3. The wing drag data calculated in section 2 are based on theoretical data for wing drag only. The

lift to drag ratio information in Appendix C is based on flight test data and calculations based on the

drag and power of the entire aircraft. Explain whether the best L/D speeds are different in

questions 4,8; 11 and 15. If so explain why are they different and compare values for the C-172 in

Appendix C based on experimental data.

4. Explain how L/D, sink rate and L/D change or don’t change with weight. Include graphs in the

report.

AS 309- Aerodynamics Final Project 5

4. Power and Thrust

Questions to be answered in Canvas quiz:

Utilizing the aircraft information provided in Appendix D, determine the following:

1. Max level airspeed in knots

2. Best range speed in knots

3. Best endurance speed in knots

4. Vx in knots

5. Vy in knots

6. Value in feet per minute for best rate of climb

Questions to be answered in Report:

In the Report:
5. Include the following:

a. Power v. Velocity graph
b. Thrust v. velocity graph
c. ROC v. velocity graph
d. Indicate where the maximum level flight speed is, Vx, Vy, Best L/D, best range and

best endurance in graphs.

5. Slow flight, stalls, spins

Questions to be answered in Canvas quiz:

1. The C-172 has a lot of twist/washout on the wings

2. Twist or washout is designed to maintain the ailerons less stalled when the aircraft has exceeded critical
angle of attack

3. The C-172 has a wing that is nearly

4. In a slip the stall speed is:

5. In a skid the stall speed is:

6. In a skid the inclinometer or ball will be

AS 309- Aerodynamics Final Project 6

7. In a slip the position of the flight controls will be

8. In a skid the position of the flight controls will be

Questions to be answered in Report:

In the Report:
6. What can you say about the lift distribution on the wing in the C-172 (What part will stall first,

does the wing have twist or washout?)

7. What is the spin recovery procedure for the C-172?

8. Why is the spin recovery order important?

9. What are the differences between a slip and a skid (position of the flight controls, inclinometer,

stall speed)?

1. Vg Diagram

Questions to be answered in Canvas quiz:

Utilizing the aircraft information provided in Appendix E, determine the following:

1. What is Vs or stall speed at 1G without flaps and maximum gross weight of 2,550 lbs (KIAS) for the C-172
2. Vs or stall speed at 2G without flaps and maximum gross weight of 2,550 lbs (KIAS)
3. Vs or stall speed at 3G without flaps and maximum gross weight of 2,550 lbs (KIAS)
4. Vs or stall speed at 1G without flaps and weight of 2,100 lbs (KIAS)
5. Va or maneuvering speed at 2550 (KIAS)
6. Va or maneuvering speed at 2100 (KIAS)
7. Vs or stall speed at 1G with flaps and weight of 2,100 lbs (KIAS)

Questions to be answered in Report:
In the Report:

10. Draw a VG diagram for the C-172 at 2,500lbs

11. Calculate Va and Vs at 2,100 lbs and draw the VG diagram at 2,100 lbs

12. Explain what airspeeds change and what airspeeds do not change with weight. Make sure to

include vs, Va, Vne and Vno.

13. Explain what Va is and how it changes with weight

AS 309- Aerodynamics Final Project 7

6.Stability and control

Questions to be answered in Canvas quiz:

A pilot performs a landing roll in a tailwheel airplane with no crosswind correction. There is a

strong cross wind. Neglecting engine effects please fill in the following blanks:

The airplane will start to yaw _____________________ (away from, into) the wind due to

______________ (dihedral effect, weather vane stability, scuff effect). This turn is due to lack of

proper __________________ (elevator, rudder, aileron) control. As a result, the airplane will be

on the _________________ (upwind, downwind) side of the centerline. The proper placement

of the ailerons would be _____________(towards the centerline, away from the centerline, into

the wind, downwind). The airplane will tend to roll__________________ (away from, into) the

relative wind. The effect that can further aggravate this yawing situation is

__________________ (dihedral effect, adverse yaw, spiraling slipstream)

The worst thing that can be done in this situation is to apply ________________ (downwind,

into the wind) ailerons.

Questions to be answered in Report:
In the Report:

14. What kind of longitudinal static stability would you expect a C-172 to have? Positive/negative –

explain

15. What kind of longitudinal dynamic stability would you expect a C-172 to have?

Positive/negative – explain

16. Where would the CG be located in relationship with the neutral point?

17. What will provide dihedral effect to C-172 Explain in report

18. How does a PIO occur?

19. How does a ground loop occur?

20. What would happen if the pilot takes off with the CG aft of the aft CG limit. Explain

AS 309- Aerodynamics Final Project 8

Appendix A1

Airplane Information
Length: 27 ft
Wingspan: 36 ft
Wing area: 174 sq ft
CLmax no flaps: 1.22
CLmax full flaps: 1.7
Max Gross Weight 2,550 lbs
Standard density: 0.002377
Airfoil: modified NACA 2412
n=1
e (Oswald’s Efficiency number) =0.8
K-factor= 0.030049
Cdo=0.01

AS 309- Aerodynamics Final Project 9

Appendix A2

Wing Drag @ 2,500 lbs

Airspeed
(kts)

Induced
Drag
(lbs)

Parasite
Drag (lbs)

Total

Drag
(lbs)

40 198.40 9.45 207.85
45 156.76 11.96 168.72
50 126.98 14.76 141.74
55 104.94 17.86 122.81
60 88.181 21.26 109.44
65 75.136 24.95 100.09
70 64.78 28.94 93.72
75 56.43 33.22 89.65
80 49.60 37.80 87.40
85 43.93 43.67 86.61
90 39.193 47.84 87.03
95 35.17 53.30 88.47
100 31.74 59.06 90.80
105 28.79 65.11 93.91
110 26.23 71.46 97.70
115 24.00 78.11 102.11
120 22.04 85.05 107.09
125 20.31 92.28 112.60
130 18.78 99.81 118.60
135 17.41 107.64 125.06
140 16.19 115.76 131.96
145 15.09 124.18 139.28
150 14.10 132.89 147.00
155 13.21 141.90 155.11
160 12.40 151.20 163.60

0

100

200

300

400

500

0 50 100 150 200 2

50

D
ra

g

Airspeed

Drag vs Airspeed

Induced

Parasi

te

Total

AS 309- Aerodynamics Final Project 10

Appendix A3

Wing Drag @ 2,100 lbs

Airspeed
(kts)
Induced
Drag
(lbs)

Parasit
e Drag
(lbs)

Total
Drag
(lbs)

40 139.99 9.45 149.44
45 110.61 11.96 122.57
50 89.59 14.76 104.36
55 74.04 17.86 91.91
60 62.22 21.26 83.48
65 53.01 24.95 77.97
70 45.71 28.94 74.65
75 39.82 33.22 73.04
78 36.81 35.93 72.75
80 34.99 37.80 72.80
85 31.00 42.67 73.67
90 27.65 47.84 75.49
100 22.39 59.06 81.46
105 20.31 65.11 85.43
110 18.51 71.46 89.97
115 16.93 78.11 95.04
120 15.55 85.05 100.60
121 15.29 86.47 101.77
125 14.33 92.28 106.62
130 13.25 99.81 113.07
135 12.29 107.64 119.93
140 11.42 115.76 127.19
145 10.65 124.18 134.83
150 9.95 132.89 142.84
155 9.32 141.90 151.22
160 8.74 151.20 159.95

0
100
200
300
400
500

-50 50 150

250

D
ra
g
Airspeed
Drag vs Airspeed
Induced
Parasite
Total

AS 309- Aerodynamics Final Project 11

Appendix B

Stall Speed Information from Cessna Manual

AS 309- Aerodynamics Final Project 12

Appendix C

Sink rate v. Velocity

Figure 1. Sink rate v. Velocity

e 0.8 hp 180 rho 2.38E-03
cdo 0.05 eta 0.75 weight 2550

weight 2100

Vkts Vfps e ta Thrus t Dra g @ 2550 R/C L/D @ 2550
Si nk Ra te @

2550l bs i n ft/mi n a ngl e dra g a t 2100 L/D a t 2100
s i nk ra te a t

2100l bs i n ft/mi n

40 67.55556 0.6 879.2763 415.3281576 737.4653 6.139723381 654.4352051 9.235286 296.8605858 7.074027677 569.216446
45 76 0.62 807.6316 350.5980078 817.2836 7.273287192 623.0454482 7.815395 256.9940004 8.171396984 555.2830533
50 84.44444 0.64 750.3158 309.3400224 876.1871 8.243356228 611.6477183 6.905181 233.5207764 8.992775857 561.109978
55 92.88889 0.65 692.7632 283.932203 893.5495 8.981017204 618.0224858 6.342862 221.2716691 9.490595919 585.0890804
60 101.3333 0.67 654.5724 269.7890305 917.4442 9.451829806 640.877551 6.029309 217.1367764 9.671323463 626.4365345
65 109.7778 0.68 613.2389 264.01756 902.0409 9.658448474 679.5378237 5.90125 219.1541009 9.582298445 684.8993846
70 118.2222 0.71 594.5583 264.7195273 917.5122 9.632836784 733.7418612 5.916828 226.0362385 9.290545683 760.5719823
75 126.6667 0.72 562.7368 270.6074829 870.6601 9.423242745 803.5091644 6.047464 236.9100402 8.864124111 853.7788947
80 135.1111 0.73 534.8931 280.783265 807.8367 9.081737831 889.0523104 6.273083 251.166372 8.360991891 964.9979586
85 143.5556 0.74 510.3251 294.6048384 728.655 8.655662322 990.7173955 6.579222 268.3698052 7.825023378 1094.807934
90 152 0.75 488.4868 311.6033969 632.6184 8.183479467 1108.942539 6.95521 288.202395 7.28654597 1243.851518

100 168.8889 0.75 439.6382 353.8212956 341.0239 7.207028044 1397.114534 7.886344 334.8664841 6.271156117 1602.373072
110 185.7778 0.75 399.6711 405.5314616 -25.6173 6.288044803 1757.954502 9.021082 389.8663282 5.386461585 2046.090988
120 202.6667 0.75 366.3651 465.5875152 -473.155 5.476950985 2196.02392 10.32998 452.4244517 4.641658938 2580.314148
130 219.5556 0.75 338.1832 533.2662201 -1007.8 4.781851735 2715.722898 11.79195 522.0503553 4.022600461 3209.765095

-3500

-3000

-2500

-2000

–

1500

–

1000

-500

0

0 20 40 60 80 100 120 140

S
in

k
ra

te

V(kts

)

sink rate

2100 lbs
2550 lbs

AS 309- Aerodynamics Final Project 13

Appendix D

Power Available & Power Required

Figure 2. Power Available & Power Required v. Velocity

e 0.8 hp 180 rho 2.38E-03
cdo 0.05 eta 0.75 weight 2550
weight 2100

Vkts Vfps

eta
(Propeller
Efficiency)

Thrust
(lbs) Drag (lbs)

RoC
(ft/min) L/D

Sink Rate
in ft/min

angle of
climb in
degrees

drag at 2100 in
lbs

L/D at
2100

sink rate
at 2100

Excess
Thrust in

LBS

Power
Required

in

HP

Power Available in

HP

Excess
Power in

HP
40 67.55556 0.75 1099.095 415.3282 1086.877 6.139723 654.4352 9.235286 296.8605858 7.074028 569.2164 683.7672 51.11731 135.2732794 84.15597
45 76 0.75 976.9737 350.598 1120.107 7.273287 623.0454 7.815395 256.9940004 8.171397 555.2831 626.3757 48.54434 135.2732794 86.72894
50 84.44444 0.75 879.2763 309.34 1132.422 8.243356 611.6477 6.905181 233.5207764 8.992776 561.11 569.9363 47.59077 135.2732794 87.68251
55 92.88889 0.75 799.3421 283.9322 1126.491 8.981017 618.0225 6.342862 221.2716691 9.490596 585.0891 515.4099 48.05007 135.2732794 87.22321
60 101.3333 0.75 732.7303 269.789 1103.797 9.45183 640.8776 6.029309 217.1367764 9.671323 626.4365 462.9412 49.80721 135.2732794 85.46607
65 109.7778 0.75 676.3664 264.0176 1065.1 9.658448 679.5378 5.90125 219.1541009 9.582298 684.8994 412.3488 52.80351 135.2732794 82.46977
70 118.2222 0.75 628.0545 264.7195 1010.689 9.632837 733.7419 5.916828 226.0362385 9.290546 760.572 363.335 57.01651 135.2732794 78.25677
75 126.6667 0.75 586.1842 270.6075 940.5424 9.423243 803.5092 6.047464 236.9100402 8.864124 853.7789 315.5767 62.44788 135.2732794 72.8254
80 135.1111 0.75 549.5477 280.7833 854.425 9.081738 889.0523 6.273083 251.166372 8.360992 964.998 268.7644 69.11588 135.2732794 66.1574
85 143.5556 0.75 517.2214 294.6048 751.9491 8.655662 990.7174 6.579222 268.3698052 7.825023 1094.808 222.6165 77.0505 135.2732794 58.22278
90 152 0.75 488.4868 311.6034 632.6184 8.183479 1108.943 6.95521 288.202395 7.286546 1243.852 176.8834 86.29017 135.2732794 48.98311

100 168.8889 0.75 439.6382 353.8213 341.0239 7.207028 1397.115 7.886344 334.8664841 6.271156 1602.373 85.81686 108.8681 135.2732794 26.40519
110 185.7778 0.75 399.6711 405.5315 -25.6173 6.288045 1757.955 9.021082 389.8663282 5.386462 2046.091 -5.86041 137.2568 135.2732794 -1.98352
120 202.6667 0.75 366.3651 465.5875 -473.155 5.476951 2196.024 10.32998 452.4244517 4.641659 2580.314 -99.2224 171.9092 135.2732794 -36.636
130 219.5556 0.75 338.1832 533.2662 -1007.8 4.781852 2715.723 11.79195 522.0503553 4.0226 3209.765 -195.083 213.3065 135.2732794 -78.0332

0
50
100

150

200
250
0 20 40 60 80 100 120 140

Power Available v. Power Required

Power Required in HP Power Available in HP

V(TAS) in kts

Po
w

er
A

va
ila

bl
e

&
P

ow
er

R
eq

ui
re

d
in

L
bs

AS 309- Aerodynamics Final Project 14

Appendix D (Continued)

Thrust & Drag

Figure3. Thrust & Drag v. Velocity

Figure 4. Rate of Climb v. Velocity

0
200
400

600

800

1000

1200

0 20 40 60 80 100 120 140

Thrust and Drag

Thrust (lbs) Drag (lbs)

-1500

-1000

-500
0
500
1000
1500
0 20 40 60 80 100 120 140

RoC (ft/min)

RO
C

(F
t/

M
in

)

V(TAS) in kts

V(TAS) in kts

Th
ru

st
a

nd
D

ra
g

in
L

bs

AS 309- Aerodynamics Final Project 15

Appendix E

C-172 Envelope Information from Cessna Manual