# For a turbojet-powered airplane with the altitude variation of thrust given by Eq. (3.19), show that as the altitude increases, the maximum velocity decreases.

For a turbojet-powered airplane with the altitude variation of thrust given by Eq. (3.19), show that as the altitude increases, the maximum velocity decreases.

\[\frac{T_{A}}{\left ( T_{A} \right )_{0}} = \frac{\rho }{\rho _{0}}\]

\(\left(T_{A} \right )_{0}\) is the thrust available at sea level. \(\rho _{0}\) is the standard sea level density.

From the equation we can see that the thrust produced by the turbojet engine is proportional to density of air. At sea level density of air is maximum so the amount of thrust produced by the turbojet engine is maximum. As the altitude increases, density of air decreases, so thrust produced by the turbojet engine also decreases.

Since thrust produced is proportional to velocity of aircraft, so as altitude increases thrust decreases and so velocity also decreases. Maximum thrust occurs at sea level, so maximum velocity is also at sea level.