Aerodynamics
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ASCI 309 Aerodynamics: Extra Credit
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An (almost) real-world application of what we’ve been discussing in
ASCI 309, “Aerodynamics”………
Eagle Airlines Flight 007 departs from the Anytown USA International
Airport (KAOK) and is scheduled to arrive at the Vacationland Regional Airport (KFUN). It is a routine flight that occurs twice daily. Today’s flight is the last of the day and is very full - with almost every seat occupied and with a significant amount of cargo.
The weather forecast predicts calm winds throughout the intended flight path; however, there is a significant chance of a winter storm forming at the destination that could include icing.
Proper flight planning prescribes that an alternate airport be identified in the event that the flight must be diverted. The selected alternate airport is the Grumpyville Cargo Hub (KBAD), an airport with a very long runway that is located on the opposite side of the Great Sugar Mountain from Vacationland. The facilities there are poor and the passengers must endure a bumpy bus ride from there over the mountain to Vacationland (hence the name, Grumpyville).
Diverting to the alternate airport, however, increases the overall cost significantly. It also will result in extremely poor customer satisfaction.
Eagle Airlines is committed to the safety of passengers, crew and cargo and is very proud of their perfect safety record.
For this exercise you are asked to estimate the takeoff, cruising, and landing performance for Eagle Airlines Flight 007.
PART 1: Takeoff
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Given:
Aircraft Information
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Empty weight |
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| 110,000 | pounds |
Fuel loaded |
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| 40,000 | pounds |
Cargo & passengers
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| 60,000 | pounds |
Max takeoff Weight
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| 215,000 | pounds |
CL @ takeoff configuration |
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| 2.05 |
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Clmax @ takeoff configuration |
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| 2.32 |
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Wing Area
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| 1250 | sq ft |
Total thrust at sea-level |
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| 52,500 | pounds |
Average drag at sea-level |
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| 2,000 | pounds |
Average friction at sea-level
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| 750 | pounds |
BGS Units for Gravitational Accel |
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| 32.2 | ft/s2 |
Conversion: Knots to ft/s
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| 1.69 | ft/s/K |
Limit Load Factor - Positive |
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| 2.5 | G |
Limit Load Factor - Negative |
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| -1 | G |
Assume sea-level, standard day atmospheric conditions
PART 1: Takeoff
Find the following:
Does the (loaded) aircraft weight exceed the maximum takeoff weight? (Circle)
YES NO
Speed at takeoff
Stall speed at takeoff sqrroot(2*210000*9.81/1.225*1250*2.32)
34.05 KTS
Average Acceleration
Runway used
Time for takeoff
PART 2: Cruise
Given:
Aircraft Information
Cruising Altitude | 30,000 | ft |
Baro-Altimeter Setting | 29.57 | in Hg |
Outside Temperature at Altitude
Aircraft Performance Figure 1 (attached) Atmosphere per Table 2.1 (attached)
Assume cruise at best endurance speed.
| -12 | F |
Total weight of aircraft
| 210,000 | pounds |
Limit Load Factor - Positive | 2.5 | G |
Limit Load Factor - Negative
| -1 | G |
Cl @ cruise configuration | 1.77 |
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Clmax @ cruise configuration | 1.99 |
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Wing Area
| 1250 | sq ft |
BGS Units for Gravitational Accel | 32.2 | ft/s2 |
Conversion: Knots to ft/s | 1.69 | ft/s/K |
PART 2: Cruise
Find the following:
Pressure Altitude
Pressure Ratio
Temperature Ratio
Density Ratio
Stall speed at cruise PART 2: Cruise
Find the following:
Maneuvering Speed
Maximum Endurance Velocity
Maximum Specific Range Velocity
Fuel Flow
True Airspeed at Cruise
Max Specific Range
PART 3: Landing
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Given:
Aircraft Information
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Empty weight |
| 110,000 | pounds |
Fuel remaining |
| 12,500 | pounds |
Cargo, passengers & crew
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| 60,000 | pounds |
Max landing Weight
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| 205,000 | pounds |
Clmax @ landing configuration |
| 2.32 |
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Wing Area
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| 1250 | sq ft |
Approach speed factor
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| 1.2 |
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Total thrust at idle |
| 7,000 | pounds |
Average drag
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| 1,500 | pounds |
% of weight on Main Gear |
| 80% |
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% of weight on Nose Gear Total braking friction
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| 20% |
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Wet Runway, braking Friction coeff
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| 0.32 |
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BGS Units for Gravitational Accel |
| 32.2 | ft/s2 |
Conversion: Knots to ft/s |
| 1.69 | ft/s/K |
Assume sea-level, standard day atmospheric conditions
PART 3: Landing
Find the following:
Does the (loaded) aircraft weight exceed the maximum landing weight? (Circle)
YES NO
Stall speed at landing
Approach speed
Main wheel friction
Nose wheel friction
Average Acceleration
Runway used
PART 4: WEATHER EMERGENCY
Shortly before reaching its destination the aircraft enters some very poor weather. At that point in the flight a significant amount of structural ice begins to accumulate. It is highly desirable to continue to land at the intended destination, however, safety concerns may require that the flight be diverted to the alternate airport.
Given:
Aircraft Information
Empty weight | 110,000 | pounds |
Fuel remaining | 12,500 | pounds |
Cargo, passengers & crew | 60,000 | pounds |
Weight of accumulated ice
| 20,000 | pounds |
Max landing Weight
| 205,000 | pounds |
Clmax @ landing configuration w Ice | 1.74 |
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Wing Area | 1250 | sq ft |
Approach speed factor
| 1.2 |
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Total thrust at idle | 7,000 | pounds |
Average drag
| 1,500 | pounds |
% of weight on Main Gear | 80% |
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% of weight on Nose Gear
| 20% |
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Icy Runway, braking Friction coeff
| 0.19 |
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BGS Units for Gravitational Accel | 32.2 | ft/s2 |
Conversion: Knots to ft/s | 1.69 | ft/s/K |
Assume sea-level, standard day atmospheric conditions
PART 4: WEATHER EMERGENCY
Find the following:
Does the (loaded and iced) aircraft weight exceed the maximum landing weight?
(Circle)
YES NO
Stall speed at landing
Approach speed
Main wheel friction
Nose wheel friction
Average Acceleration
Runway used PART 4: EMERGENCY
Find the following:
Vacationland (KFUN) Runway Length 8200 feet
Grumpytown Regional (KBAD) Runway Length 11500 feet
Which Airport must be used?? (Circle) Support your answer
Vacationland (KFUN) Grumpytown (KBAD)
Why did you choose that airport?
If the airplane must make a turn in the iced condition what is the maximum angle of bank that can be sustained without stall?
Using figure 14.10, the angle of bank from above, and the iced-aircraft approach speed what rate of turn and radius of turn can be expected?
Extra Space for additional work - - - Indicate Problem Number
Extra Space for additional work - - - Indicate Problem Number
Dole, C.C and Lewis, J.E, Flight Theory and Aerodynamics, 2nd Ed, Wiley, 2000
Figure 1
Figure 14.10
LINEAR INTERPOLATION
Example from Table 2.1
Pressure Altitude Density Ratio
(x-values) (y-values)
10,000 ft 0.7385
12,000 ft ?????
15,000 ft 0.6292
Y=0.7385 + (0.6292-0.7385)
Y = 0.6948 -> OR the density ratio at 12,000 ft. (interpolated) from Table 2.1 is 0.6948
10 years ago
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