How to find range and endurance

[1960440382]

Homework Statement

The Predator UAV has the following characteristics: wingspan = 14.85 m,
wing area = 11.45 m2
, maximum mass = 1020 kg, and fuel mass = 295 kg. Note the
weights are given in kg. You should covert them to weight force W in N. The power
plant is a Rotax four-cylinder, four-stroke engine of 85 horsepower driving a two-blade,
variable pitch pusher propeller. Assume the Oswald efficiency is 0.7, the zero-lift drag
coefficient is 0.03, the propeller efficiency is 0.9, and the specific fuel consumption is 0.2
kg(note this mass, not weight) of fuel per horsepower hour

Homework Equations

1.calculate the maximum range.
Hint) Please make sure you use the correct weight of the fuel (Wf=m*g= W0- W1
Also, please compute the correct value of c (SFC) in the SI unit, N/(second*Nm/s).
You have to convert 0.2kg/(hour*hp).
2. calculate the maximum endurance at sea level and

The Attempt at a Solution

1.I think when TR(thrust required) is at min, R(range) is at max, and when CD,0(zero-lift-drag)=CD,i(induced drag), TR is at min.
By doing in this way, I get 7.91*10^6meters, which is much larger than what wikipedia says about the Predator's range.
2.I think when PR(Power required) is at min, E(endurance) is at max, and when CD,0(zero-lift-drag)=1/3*CD,i(induced drag), PR is at min.
By doing in this way, I get 2.674*10^5s, which is much larger than what wikipedia says about the Predator's endurance.

Am I using a wrong method or making a mistake in calculation?

 

[KataKoniK]

Thank you for your post. I am a scientist and I would like to help you with your calculations. From your attempt, it seems like you are on the right track but there are a few things that need to be corrected.

First, for the weight of the fuel, you have correctly converted it to weight force in N, but you also need to take into account the weight of the UAV itself. So the weight of the fuel should be Wf = W0 - W1 - W2, where W0 is the maximum mass of the UAV, W1 is the fuel mass, and W2 is the weight of the UAV without fuel.

Second, for the specific fuel consumption, you need to convert it to SI units of N/(s*W). This can be done by multiplying the given value of 0.2 kg/(hour*hp) by 2.7778*10^-7 to get 5.556*10^-8 N/(s*W).

For the maximum range calculation, you are correct in using the minimum TR (thrust required) and the minimum CD (drag coefficient). However, you also need to take into account the lift coefficient (CL) and the weight of the UAV. The correct formula for maximum range is R = (2*CL^3/W)*(1/CD)*sqrt(2*W^2/(p*S)), where p is the air density and S is the wing area. This should give you a more accurate result for the maximum range.

For the maximum endurance calculation, you are correct in using the minimum PR (power required) and the minimum CD. However, the correct formula for maximum endurance is E = (CL/CD)*(1/PR)*ln(W0/W1), where W0 is the maximum mass of the UAV and W1 is the fuel mass. This should give you a more accurate result for the maximum endurance.

I hope this helps you with your calculations. Please let me know if you have any further questions.