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GATE 2021 AE – Question 22

Flight Mechanics & Space Dynamics · Aircraft classification and configuration, pressure altitude, equivalent, calibrated and indicated air speeds · 1 mark · Multiple choice

The ratio of true airspeed to equivalent airspeed is

  1. $\rho/\rho_0$
  2. $\rho_0/\rho$
  3. $\sqrt{\rho_0/\rho}$
  4. $\sqrt{\rho/\rho_0}$

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Correct answer: (C) $\sqrt{\rho_0/\rho}$

Explanation

**Equivalent airspeed** (EAS) is the speed at sea level that would give the same dynamic pressure as the actual flight condition:
$$\tfrac12\rho V_{TAS}^2=\tfrac12\rho_0V_{EAS}^2 .$$

Rearranging,
$$\frac{V_{TAS}}{V_{EAS}}=\sqrt{\frac{\rho_0}{\rho}} .$$

At altitude, $\rho<\rho_0$, so the true airspeed is larger than the equivalent airspeed. Answer **$\sqrt{\rho_0/\rho}$** (C).