# Aircraft Performance Questions and Answers – Measurement of Air Temperature

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This set of Aircraft Performance Multiple Choice Questions & Answers (MCQs) focuses on “Measurement of Air Temperature”.

1. The ratio of indicated temperature rise to ideal pressure rise is known as recovery factor.
a) True
b) False

Explanation: The ratio of indicated temperature rise to ideal pressure rise is known as recovery factor. It is given by the expression r=$$\frac{T_i-T}{T_t-T}$$ where r is known as recovery factor, Ti is known as indicated total temperature, Tt is known as total temperature and T is known as static temperature.

2. Which of the following is the correct expression for recovery factor?
a) r=$$\frac{T_i+T}{T_t+T}$$
b) r=$$\frac{T_i-T}{T_t-T}$$
c) r=$$\frac{T_i+T}{T_t-T}$$
d) r=$$\frac{T-T_i}{T+T_t}$$

Explanation: The expression for recovery factor is given by r=$$\frac{T_i-T}{T_t-T}$$ where r is known as recovery factor, Ti is known as indicated total temperature, Tt is known as total temperature and T is known as static temperature. The ratio of indicated temperature rise to ideal pressure rise is known as recovery factor.

3. What is the recovery factor if the total temperature is equal to the indicated total temperature?
a) 1
b) 2
c) -1
d) -2

Explanation: The answer is 1. The expression for recovery factor is given by r=$$\frac{T_i-T}{T_t-T}$$where r is known as recovery factor, Ti is known as indicated total temperature, Tt is known as total temperature and T is known as static temperature. In the formula if Tt=Ti then
r=$$\frac{T_i-T}{T_i-T}$$
r=1.

4. What is the relation between speed of object and temperature?
a) T0=T$$\Big[1+\frac{\gamma-1}{2}(\frac{V}{a})^2\Big]$$
b) T0=T$$\Big[1-\frac{\gamma-1}{2}(\frac{V}{a})^2\Big]$$
c) T0=T$$\Big[1+\frac{\gamma+1}{2}(\frac{V}{a})^2\Big]$$
d) T0=T$$\Big[1-\frac{\gamma+1}{2}(\frac{V}{a})^2\Big]$$

Explanation: The relation between speed of object and temperature is T0=T$$\Big[1+\frac{\gamma-1}{2}(\frac{V}{a})^2\Big]$$ where T is the temperature at that altitude, T0 is the stagnation temperature, γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume, V is speed of object and ‘a’ is speed of sound.

5. What is the relation between recovery factor and temperature?
a) Ti=T[1+r$$\frac{\gamma-1}{2}$$M2]
b) Ti=T[1+r$$\frac{\gamma+1}{2}$$M2]
c) Ti=T[1-r$$\frac{\gamma-1}{2}$$M2]
d) Ti=T[1-r$$\frac{\gamma+1}{2}$$M2]

Explanation: The relation between recovery factor and temperature is Ti=T[1+r$$\frac{\gamma-1}{2}$$M2] where T is the temperature at that altitude, Ti is indicated total temperature, r is recovery factor, M is Mach number and γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume.

6. What is the indicated temperature of an aircraft having mach number 2 and when temperature and recovery factor are 300K and 2?
a) 780K
b) 128K
c) 345K
d) 435K

Explanation: The answer is 780K. Given r=2, T=300K, M=2 and we know that γ for air is 1.4. From the formula Ti=T[1+r$$\frac{\gamma-1}{2}$$M2].
On substituting the values we get Ti=300[1+2$$\frac{1.4-1}{2}$$22]
On solving above equation we get Ti=780K.

7. What is the mach number of the aircraft which is moving in air at an indicated total temperature is 780K and the temperature, recovery factor at that point are 300K and 2?
a) 1
b) 2
c) 0.1
d) 0.2

Explanation: The answer is 2. Given r=2, T=300K, Ti=780K and we know γ of air is 1.4. From the formula Ti=T[1+r$$\frac{\gamma-1}{2}$$M2].
On substituting the values in the formula, we get 780=300[1+2$$\frac{1.4-1}{2}$$M2].
On solving we get M=2.

8. The difference in indicated values and local values of altitude, airspeed and mach number is known as system pressure error.
a) True
b) False

Explanation: The difference in indicated values and local values of altitude, airspeed and mach number is known as system pressure error. The indicated values of the altitude, airspeed and mach number resulting from the measured values of the local or system, pressures will differ from the values that would occur when using the undisturbed freest stream pressures. This error is known as system pressure error.

9. Calculate the indicated temperature rise when indicated total temperature is 400K and temperature at that point is 389K.
a) 11
b) 5.5
c) 6
d) 12

Explanation: The answer is 11. Given Ti=400K and T=389K. The indicated temperature rise is measured by the formula, Ti-T.
On substituting the values we get the indicated temperature rise=400-389
The indicated temperature rise=11.

10. Calculate the ideal temperature rise when total temperature is 440K and temperature at that point is 369K.
a) 71
b) 70
c) 75
d) 78