# Aircraft Performance Questions and Answers – Aerodynamic Relationships

This set of Aircraft Performance Multiple Choice Questions & Answers (MCQs) focuses on “Aerodynamic Relationships”.

1. The minimum drag speed is given by ___________
a) $$\big(\frac{2W}{\rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{4}$$
b) $$\big(\frac{2W}{\gamma \rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{4}$$
c) $$\big(\frac{2W}{\rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{2}$$
d) $$\big(\frac{2W}{\gamma \rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{2}$$

Explanation: The correct formula for minimum drag speed is given by $$\big(\frac{2W}{\rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{4}$$ where W is weight, ρ is density, K is constant, S is span area and CDz is coefficient of lift dependent drag.

2. The minimum drag mach number is given by ___________
a) $$\big(\frac{2W}{\rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{4}$$
b) $$\big(\frac{2W}{\gamma \rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{4}$$
c) $$\big(\frac{2W}{\rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{2}$$
d) $$\big(\frac{2W}{\gamma \rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{2}$$

Explanation: The correct formula for minimum drag mach number is given by $$\big(\frac{2W}{\gamma \rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{4}$$ where W is weight, ρ is density, K is constant, S is span area, γ is ratio of specific heats and CDz is coefficient of lift dependent drag.

3. At steady state flight condition
a) T>D
b) T<D
c) T=D
d) T≠D

Explanation: At steady state flight condition the thrust produced by the aircraft is same as the drag produced by the aircraft i.e. T=D. At this state the minimum power speed is given by $$\frac{1}{\sqrt{3}}$$=Vmd where Vmd is minimum drag speed.

4. Which of the following is the correct relation between minimum power speed and minimum drag speed?
a) Vmp=$$\frac{1}{\sqrt{3}}$$Vmd
b) Vmp=$$\frac{1}{\sqrt{3}}$$Vmd
c) Vmp=$$\frac{1}{\sqrt{3}}$$Vmd
d) Vmp=$$\frac{1}{\sqrt{5}}$$Vmd

Explanation: At steady state flight condition the thrust produced by the aircraft is same as the drag produced by the aircraft i.e. T=D. The relation between minimum drag speed and minimum power speed is given by Vmp=$$\frac{1}{\sqrt{3}}$$Vmd where Vmd is minimum drag speed and Vmp is minimum power speed.

5. What is the value of minimum power speed when minimum drag speed is 300m/s?
a) 173.21 m/s
b) 227.95 m/s
c) 134.16 m/s
d) 200.62 m/s

Explanation: The correct answer is 227.95 m/s. Given Vmd is 300m/s. From the formula Vmp=$$\frac{1}{\sqrt{3}}$$Vmd substitute the values.
On substituting we get, Vmp=$$\frac{1}{\sqrt{3}}$$*300
Vmp=227.95m/s.
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6. Airspeed with minimum power speed relates to the performance of the aircraft with power producing engine.
a) True
b) False

Explanation: Airspeed with minimum power relates to the performance of the aircraft with power producing engine whereas minimum drag speed relates to the performance of aircraft with thrust-producing engine.

7. In a glider the engine used is thrust producing engine.
a) True
b) False

Explanation: Airspeed with minimum power relates to the performance of the aircraft with power producing engine whereas minimum drag speed relates to the performance of aircraft with thrust-producing engine. In a glider the engine uses both minimum power speed and minimum drag speed but does not have any engine present.

8. What is the relative airspeed of an aircraft whose airspeed and minimum drag speed are 500m/s and 150m/s?
a) 3.33
b) 0.3
c) 33.33
d) 0.333

Explanation: The answer is 3.33. Given, airspeed is 500m/s and minimum drag speed is 150m/s. From the formula u=$$\frac{V}{V_{md}}$$ where V is airspeed and Vmd is minimum drag speed. On substituting the values we get u= $$\frac{500}{150}$$
u=3.33.

9. What will be the drag to minimum drag ratio when the relative airspeed is 3.33?
a) 5.49
b) 1.51
c) 5.59
d) 1.82

Explanation: The answer is 5.59. Given u=3.33. From the equation $$\frac{D}{D_{min}}$$=$$\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]$$where $$\frac{D}{D_{min}}$$ is drag to minimum drag ratio and u is relative airspeed. On substituting the values,
We get $$\frac{D}{D_{min}}$$=$$\frac{1}{2}\big[3.33^2+\frac{1}{3.33^2}\big]$$
On solving we get $$\frac{D}{D_{min}}$$=5.59.

10. Which of the following is the correct performance equation?
a) $$\big[\frac{\lambda}{u}+τ\big]+\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]$$=Emax$$\big\{sin\gamma_2-\frac{V}{g}\big\}$$
b) $$\big[\frac{\lambda}{u}+τ\big]-\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]$$=Emax$$\big\{sin\gamma_2-\frac{V}{g}\big\}$$
c) $$\big[\frac{\lambda}{u}+τ\big]+\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]$$=Emax$$\big\{sin\gamma_2+\frac{V}{g}\big\}$$
d) $$\big[\frac{\lambda}{u}+τ\big]-\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]$$=Emax$$\big\{sin\gamma_2+\frac{V}{g}\big\}$$

Explanation: The correct equation is $$\big[\frac{\lambda}{u}+τ\big]-\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]$$=Emax$$\big\{sin\gamma_2+\frac{V}{g}\big\}$$ where λ is dimensionless power, u is relative speed, τ is dimensionless thrust, Emax is maximum efficiency, sinγ2 is horizontal component, V is airspeed and g is gravitational force.

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