Question

An airplane with wing planform area $S=20\,\text{m}^2$ and weight $W=8\,\text{kN}$ is flying straight and level with a speed of $V=100\,\text{m/s}$. The total drag coefficient is $C_D=0.026$ and the air density is $\rho=0.7\,\text{kg/m}^3$. The total thrust required to introduce a steady climb at angle $\gamma=0.1$ radians is ............. N. (round off to the nearest integer)

Hint:

In steady climb or descent, $T=D\pm W\sin\gamma$ (plus for climb). Use the drag from $qSC_D$ and add the component of weight along the flight path.

Answer 1

Step 1: Drag in level flight.
Dynamic pressure: \[ q=\tfrac12 \rho V^2=\tfrac12(0.7)(100^2)=3500\ \text{N/m}^2 \] Drag: \[ D=q\,S\,C_D=3500(20)(0.026)=1820\ \text{N} \]

Step 2: Thrust for steady climb.
For a steady climb, force balance along the flight path gives \[ T=D+W\sin\gamma \Rightarrow T=1820+8000\sin(0.1)=1820+798.67=2618.67\ \text{N} \]

Step 3: Rounding.
\[ \boxed{T\approx 2619\ \text{N}} \]