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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

  1. 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
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    $\begingroup$ if you are the same person, you could have edited your previous question $\endgroup$ – Federico May 31 '15 at 16:29
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    $\begingroup$ I'm voting to close this question as off-topic because If you are going to get help on blatant homework type questions the best you can really hope for is for someone to point out the error you are making in your reasoning or work. Without seeing your work, we cannot do that. We will not just do your work for you. $\endgroup$ – Federico May 31 '15 at 16:32
  • $\begingroup$ anyways thx 4 ur advise sir $\endgroup$ – Mohammed Nouri May 31 '15 at 16:34
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    $\begingroup$ Hello Mohammed, welcome at aviation.SE. This looks like a homework exercise. That's not a problem, we can help you to understand the fundamentals behind the questions. Please show what you have done so far, and where you get stuck. We will not just solve your assignments for you to hand them in. In the end, the purpose of studying aerospace engineering is to become a good engineer with a prosperous future; if we would just solve your homework we would do you a disservice. $\endgroup$ – DeltaLima May 31 '15 at 17:04
  • $\begingroup$ Hello dear friend DeltaLima and thank you for your comment actually i am studding to be a pilot and i am not going to be engineer in the future so that is why i do not need to focus in this subject however this is the final take home exam and the last deadline is tomorrow morning and to be honest with you tomorrow i have an Air Law exam and i want to focus on it bcz its more important than this one that is why i shared it here and if there is someone who can help me i would be thankful for that THANK YOU again :) $\endgroup$ – Mohammed Nouri May 31 '15 at 17:27
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Hints for your first question:

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

$P_r = D\cdot V$

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

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

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

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

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

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

  1. 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.

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