Lift coefficient needed at cruise

A 1200 kg light aircraft with a 16.2 m² wing cruises at 65 m/s at 3000 m, where the standard-atmosphere density is 0.9093 kg/m³. In level flight lift equals weight. Find the dynamic pressure and the lift coefficient required.

Given

Solution

1. 1.Weight, which lift must equal
   $$W=mg$$
   $$W=11.77\mathrm{kN}$$
2. 2.Dynamic pressure
   $$q=\frac{1}{2}\rho V^2$$
   $$q=1921\mathrm{Pa}$$
3. 3.Required lift coefficient
   $$C_L=\frac{W}{qS}$$
   $$C_L=0.378$$

Worked in ProveCalc

A lift coefficient is dimensionless, and the engine shows the units cancelling. Enter a density in the wrong unit and the result keeps leftover units instead of passing as a plausible number.

The results above were evaluated by ProveCalc's compute engine (SymPy and Pint), the same engine the desktop app runs on your machine.

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