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Problem Sets 1

MA6641 Flight Performance and Dynamics

These problems are for practice only. No submission i s necessary.

1. Instruments on an aircraft measure an air temperature of 28oC and a pressure

altitude of 2,500 m. What is the density altitude? (See Appendix for the Standard

Atmosphere table)

2. By using the hydrostatic relation and by noting that the gravitational acceleration

at a geometric altitudeGh can be expressed by

2)( G

E

hr

GMg

whereE

GM is

Earth gravitational constant and r is the radius of the Earth, show that the relation

between the geometric and geopotential altitudes can be written as:

G

G

hhr

rh

3. A NACA 2412 airfoil with a 2 m chord and 5 m span is being tested in a wind

tunnel at standard sea level conditions and a test section velocity of 42 m/s at an

angle of attack of 8 degrees. How much lift, drag, and pitching moment about its

aerodynamic center is the airfoil generating?

4. A wing with a rectangular planform, a NACA 2412 airfoil, a span of 5 m and achord of 2 m is operating in standard sea level conditions at a free stream velocity

of 42 m/s and an angle of attack of 8 degrees. Ifthe wings span efficiency factoris 0.9, how much lift and drag is it generating?

5. A turbojet engine produces a thrust of 45,000 N at sea level. The inlet diameter is

1 m. If an airplane equipped with this engine is flying at standard sea level with

airspeed of 300 m/s, estimate:

a. the jet velocity relative to the airplane, and

b. the propulsive efficiency.

6. A turbojet engine is intended to produce a thrust of 100,000 N at a takeoff speed

of 70 m/s at sea level. At takeoff, the gas velocity at the exit of the engine (relative

to the engine) is 550 m/s. The fuel-air ratio by mass is 0.03. Calculate the engine

inlet area necessary to obtain this thrust.

7. A turboprop engine is rated at 4910 equivalent shaft horsepower at zero velocity

at sea level. An airplane that uses this engine is flying at 170 m/s at sea level

condition. If the jet thrust is 800 N and the propeller efficiency is 0.9, calculate the

equivalent shaft horsepower at this flight condition.

8. The specific fuel consumption of a reciprocating engine is 1.910-7 lb/[(ft.lb/s)s].

When this engine is installed on an airplane which is flying at 300 ft/s with a

propeller efficiency of 0.85, calculate the equivalent thrust specific fuelconsumption.

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APPENDIX

Characteristics of the International Standard Atmosphere, SI UnitsAltitude, h

kmTemperature, T

KPressure, P

N/m2Density,

kg/m3

Speed ofSound, a m/s

0 288.16 101325 1.225 340.3

0.5 284.91 95461 1.1673 338.4

1 281.66 89876 1.1117 336.4

1.5 278.41 84560 1.0581 334.5

2 275.16 79501 1.0066 332.5

2.5 271.92 74692 0.95696 330.6

3 268.67 70121 0.90926 328.6

3.5 265.42 65780 0.86341 326.6

4 262.18 61660 0.81935 324.6

4.5 258.93 57752 0.77704 322.6

5 255.69 54048 0.73643 320.5

5.5 252.44 50539 0.69747 318.5

6 249.2 47217 0.66011 316.5

6.5 245.95 44075 0.62431 314.4

7 242.71 41105 0.59002 312.3

7.5 239.47 38299 0.55719 310.2

8 236.23 35651 0.52578 308.1

8.5 232.98 33154 0.49575 306

9 229.74 30800 0.46706 303.9

9.5 226.5 28584 0.43966 301.7

10 223.26 26500 0.41351 299.6