Basic aircraft performance: how can you calculate the required power? [closed]

Question

How can we determine the minimum power required for a propeller aircraft?

1. How can we determine the minimum power required at standard altitude of h=3km

and

2. What is the maximum airspeed at standard sea level conditions ?

   if :

   • Wingspan = 10m
   • Wing area =15m‌‌ Squared
   • Mass = 1500 kg
   • Power plant = one-piston engine of 230hp power available at sea level
   • Parasite drag coefficient= 0.025
   • Oswald efficiency = 0.8
   • Air density at 3 km = 0.9093 kg/m³

Answer 1

Hints for your first question:

1. Power required is the product of drag and true airspeed.

$P_r = D\cdot V$

2. You can calculate drag as a function of airspeed.

$D=\frac{1}{2}\rho V^2 S C_D$

3. The drag coefficient is the sum of the parasite drag coefficient and the induced drag coefficient.

$C_D = C_{D,0} + C_{D,i}$

4. The induced drag coefficient is a function of the lift coefficient, the wing geometry and the Oswald efficiency factor.

$C_{D,i} = \frac{C_L^2}{\pi A e}$

5. The lift coefficient can be calculated as function of the speed, the density of the air, the weight of the aircraft and the wing area.

$C_L = \frac{2 L}{\rho V^2 S}$ and for horizontal flight $L = W = mg$

Substituting yields:

$P_r = \frac{1}{2}\rho V^3 S C_D = C_{D,0}\frac{1}{2}\rho V^3 S + \frac{2 W^2}{\pi A e \rho V S}$

Now you need to find the minimum of that function, which occurs when it's derivative equals zero.

All the constants you need are given in the table, apart from the density at 3 km altitude, but I believe you have been given that as well.

The same power formula derived above will also help to solve your second question.