Question

Let $V_{TAS}$ be the true airspeed of an aircraft flying at a certain altitude where the density of air is $\rho$, and $V_{EAS}$ be the equivalent airspeed. If $\rho_0$ is the density of air at sea-level, what is the ratio $\frac{V_{TAS}}{V_{EAS}}$ equal to?
 

• A. $\dfrac{\rho}{\rho_0}$
• B. $\dfrac{\rho_0}{\rho}$
• C. $\sqrt{\dfrac{\rho_0}{\rho}}$
• D. $\sqrt{\dfrac{\rho}{\rho_0}}$

Hint:

TAS depends on actual air density, while EAS is referenced to sea-level density. Lower density → higher TAS for the same EAS.

Answer 1

The Correct Option is C

Step 1: Definition of EAS.
Equivalent airspeed is defined as: \[ V_{EAS} = V_{TAS}\sqrt{\frac{\rho}{\rho_0}} \]

Step 2: Rearranging the formula.
\[ \frac{V_{TAS}}{V_{EAS}} = \frac{1}{\sqrt{\frac{\rho}{\rho_0}}} = \sqrt{\frac{\rho_0}{\rho}} \]

Step 3: Final conclusion.
Thus the ratio is: \[ \boxed{\sqrt{\frac{\rho_0}{\rho}}} \]