Question

For an aircraft moving at 4 km altitude above mean sea level at a Mach number of 0.2, the ratio of equivalent air speed to true air speed is ............ (rounded off to 2 decimal places). The density of air at mean sea level is \(1.225 \,\text{kg/m}^3\) and at 4 km altitude is 
\(0.819 \,\text{kg/m}^3\).

Hint:

Equivalent Air Speed accounts for compressibility and density effects. For subsonic flight, the ratio $EAS/TAS = \sqrt{\rho/\rho_0}$ is commonly used.

Answer 1

Step 1: Definitions.
- True Air Speed (TAS): actual speed of aircraft through air. - Equivalent Air Speed (EAS): corrected for density, defined as: \[ V_{EAS} = V_{TAS} \sqrt{\frac{\rho}{\rho_0}} \] where \(\rho\) = actual density at altitude, \(\rho_0\) = reference density (sea level). Step 2: Ratio expression.
\[ \frac{V_{EAS}}{V_{TAS}} = \sqrt{\frac{\rho}{\rho_0}} \] Step 3: Substitution.
\[ \frac{V_{EAS}}{V_{TAS}} = \sqrt{\frac{0.819}{1.225}} = \sqrt{0.668} \] \[ \frac{V_{EAS}}{V_{TAS}} = 0.817 \approx 0.82 \] \[ \boxed{0.82} \]