Flight Dynamics Problems and solution - part 1

Flight Dynamics Problems and solution - part 1
[Useful for GATE - AEROSPACE ENGINEERING (AE )]

An aircraft cruises at a calibrated airspeed of 320 kt in FL 200. The outside air temperature is -23 °C. a) Calculate the air pressure p in FL 200.
b) Calculate the air density r in FL 200 under given conditions.
c) Determine the equivalent airspeed EAS from a suitable diagram.
d) Calculate the equivalent airspeed EAS.
e) Calculate the true airspeed TAS.
f) Calculate the Mach number.

An aircraft is equipped with a wing of symmetrical airfoils:-

During an IFR flight, a passenger looks out the window while relaxing in his seat. He observes a turn and estimates the bank angle to be 30°. At the same time, the passenger observes the free surface of the orange juice in his glass: it is parallel to the tray.
a) The passenger assumes the turn being flown as a rate one turn. Explain the term rate one turn. Why is it correct to assume a rate one turn.
b) The passenger assumes the turn being flown as a coordinated turn. Explain the term coordinated turn. Why is it correct to assume a coordinated turn.
c) Calculate the aircraft's true airspeed

An aerobatic airplane flies a perfect circular looping. The pilot reads an altitude of 5000 ft at the highest point of the looping and an altitude of 4000 ft a the lowest point of the looping. The looping is flown at such a speed that the lowest load factor in the looping is n = 0. Assume that aircraft speed is nearly constant in the looping. a) During which part of the looping does the airplane experience the highest load factor? b) What is the aircraft's speed in the looping? c) Calculate the highest load factor n during the looping.

A jet cruises with constant lift coefficient and constant Mach number of 0.82 in the stratosphere. The take-off mass with full fuel tanks is 271000 kg, the maximum fuel volume is 135000 liters, fuel density is 800 kg/m³. The specific fuel consumption is 16 mg/(Ns). The aircraft has a specified range of 7200 NM.
a) Write down the appropriate equation for these flight conditions from which the range can be calculated. How is this equation named?
b) Calculate the aircraft's mass without fuel.
c) On its fuel reserves, the aircraft could fly additional 920 NM plus further 30 min. How far could the aircraft fly in these 30 min. if we assume that the 30 min. are also flown at cruise speed? How far could the aircraft fly on its fuel reserves?
d) Calculate the aircraft's lift-to-drag ratio.

Derive an equation for the range of a jet aircraft in a (shallow) steady climb with constant airspeed and constant lift coefficient.