Question

True airspeed (TAS) is \[ (\rho_0 = \text{Air density at sea level},\ \rho = \text{Air density through which aircraft flying}) \]

• A. \( EAS \sqrt{\frac{\rho_0}{\rho}} \)
• B. \( IAS \sqrt{\frac{\rho_0}{\rho}} \)
• C. \( CAS \sqrt{\frac{\rho_0}{\rho}} \)
• D. \( EAS \sqrt{\frac{\rho}{\rho_0}} \)

Hint:

TAS increases with altitude even if indicated airspeed remains constant due to decreasing air density.

Answer 1

The Correct Option is A

True airspeed (TAS) is a critical parameter in aerospace engineering representing the actual speed of an aircraft relative to the air through which it flies. It is different from other airspeed measurements such as Indicated Airspeed (IAS), Calibrated Airspeed (CAS), and Equivalent Airspeed (EAS), as it accounts for variations in air density. The relationship between TAS and EAS is given by the equation:

TAS = EAS × \(\sqrt{\frac{\rho_0}{\rho}}\)

where:

• \(\rho_0\) = Air density at sea level
• \(\rho\) = Air density through which aircraft is flying
• EAS = Equivalent Airspeed

This formula arises because True Airspeed (TAS) adjusts the Equivalent Airspeed (EAS) for the actual air density (\(\rho\)) the aircraft is operating in, compared to the standard sea-level density (\(\rho_0\)). Hence, the expression \(EAS \sqrt{\frac{\rho_0}{\rho}}\) correctly represents the TAS as it incorporates the density correction factor \(\sqrt{\frac{\rho_0}{\rho}}\), ensuring that the airspeed reflects real ambient conditions.