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) \(\big(\frac{2W}{\gamma \rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{2}\)

View Answer

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 C

_{Dz}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) \(\big(\frac{2W}{\gamma \rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{2}\)

View Answer

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 C

_{Dz}is coefficient of lift dependent drag.

3. At steady state flight condition

a) T>D

b) T<D

c) T=D

d) T≠D

View Answer

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 \(\frac{1}{\sqrt[4]{3}}\)=V

_{md}where V

_{md}is minimum drag speed.

4. Which of the following is the correct relation between minimum power speed and minimum drag speed?

a) V_{mp}=\(\frac{1}{\sqrt[2]{3}}\)V_{md}

b) V_{mp}=\(\frac{1}{\sqrt[4]{3}}\)V_{md}

c) V_{mp}=\(\frac{1}{\sqrt[3]{3}}\)V_{md}

d) V_{mp}=\(\frac{1}{\sqrt[4]{5}}\)V_{md}

View Answer

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 V

_{mp}=\(\frac{1}{\sqrt[4]{3}}\)V

_{md}where V

_{md}is minimum drag speed and V

_{mp}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

View Answer

Explanation: The correct answer is 227.95 m/s. Given V

_{md}is 300m/s. From the formula V

_{mp}=\(\frac{1}{\sqrt[4]{3}}\)V

_{md}substitute the values.

On substituting we get, V

_{mp}=\(\frac{1}{\sqrt[4]{3}}\)*300

V

_{mp}=227.95m/s.

6. Airspeed with minimum power speed relates to the performance of the aircraft with power producing engine.

a) True

b) False

View Answer

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

View Answer

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

View Answer

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 V

_{md}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

View Answer

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) \(\big[\frac{\lambda}{u}+τ\big]+\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]\)=E_{max}\(\big\{sin\gamma_2-\frac{V}{g}\big\}\)

b) \(\big[\frac{\lambda}{u}+τ\big]-\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]\)=E_{max}\(\big\{sin\gamma_2-\frac{V}{g}\big\}\)

c) \(\big[\frac{\lambda}{u}+τ\big]+\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]\)=E_{max}\(\big\{sin\gamma_2+\frac{V}{g}\big\}\)

d) \(\big[\frac{\lambda}{u}+τ\big]-\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]\)=E_{max}\(\big\{sin\gamma_2+\frac{V}{g}\big\}\)

View Answer

Explanation: The correct equation is \(\big[\frac{\lambda}{u}+τ\big]-\frac{1}{2}\big[u^2+\frac{1}{u^2}\big]\)=E

_{max}\(\big\{sin\gamma_2+\frac{V}{g}\big\}\) where λ is dimensionless power, u is relative speed, τ is dimensionless thrust, E

_{max}is maximum efficiency, sinγ

_{2}is horizontal component, V is airspeed and g is gravitational force.

**Sanfoundry Global Education & Learning Series – Aircraft Performance.**

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