# Aircraft Performance Questions and Answers – Aerodynamic Relationships

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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

Answer: a
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) $$\big(\frac{2W}{\gamma \rho S}\big)^{\frac{1}{2}}\big(\frac{K}{C_{Dz}}\big)^\frac{1}{2}$$
View Answer

Answer: b
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
View Answer

Answer: c
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 $$\frac{1}{\sqrt[4]{3}}$$=Vmd where Vmd is minimum drag speed.
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4. Which of the following is the correct relation between minimum power speed and minimum drag speed?
a) Vmp=$$\frac{1}{\sqrt[2]{3}}$$Vmd
b) Vmp=$$\frac{1}{\sqrt[4]{3}}$$Vmd
c) Vmp=$$\frac{1}{\sqrt[3]{3}}$$Vmd
d) Vmp=$$\frac{1}{\sqrt[4]{5}}$$Vmd
View Answer

Answer: b
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=$$\frac{1}{\sqrt[4]{3}}$$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
View Answer

Answer: b
Explanation: The correct answer is 227.95 m/s. Given Vmd is 300m/s. From the formula Vmp=$$\frac{1}{\sqrt[4]{3}}$$Vmd substitute the values.
On substituting we get, Vmp=$$\frac{1}{\sqrt[4]{3}}$$*300
Vmp=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

Answer: a
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

Answer: b
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.
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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

Answer: a
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
View Answer

Answer: c
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.
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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$$\big\{sin\gamma_2+\frac{V}{g}\big\}$$
View Answer

Answer: d
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.

Sanfoundry Global Education & Learning Series – Aircraft Performance.

To practice all areas of Aircraft Performance, here is complete set of 1000+ Multiple Choice Questions and Answers.

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