## Helicopter UAV - Required Power

Hey guys,

I'm currently doing conceptual performance analysis of a UAV helicopter in hover. I'm having some conflicting results however, and if anyone could help me out, that would be great. Here are some of the basic design constants I'm working with:

GTOW: 95kg
κ = 1.15 (induced power factor)
σ = 0.07 (solidity ratio)
A = 6.16m^2 (main blade area)
ΩR = 204.17 m/s (tip speed)
CDo = 0.01 (profile drag coefficient)
P(available) = 15,221 W

I'm using this equation, from Principles of Helicopters - Leishman:

P(required) = P(induced) + P(profile)
P(required) = {[κW^(3/2)]/sqrt(2*ρ*A)} + {[ρA(ΩR)^3]*(σ*CDo/8)}

I'm trying to find my performance ceiling in hover, which occurs at P(excess) = P(available) - P(required) = 0.

However, I'm getting that my required power decreases with increasing altitude. This is contrary to helicopters with greater GTOW's. Now, from the equation, I can see that as my density decreases, my induced power term increases and my profile power decreases. This is of course, what I would expect, because of the following:

- while maintaining a constant tip speed (RPM) at a higher altitude, you need more torque and subsequently more power to maintain the same amount of thrust, as thrust=weight (in hover)
- the profile power decreases because the amount of skin friction reduces due to the lower density

Now, I'm trying to determine the maximum ceiling for my UAV. What this essentially tells me, is that, at this particular GTOW (and anything smaller than 150kg), my ceiling is infinite? Ahhh please help me make sense of this. Thanks.
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 The Power required might be decreasing, but so is the thrust, as it's also dependent on density, there is a differential in the rates, however. Too tired to work it out properly, but using Momentum Theory (hover) T=2pAVi^2 P=T*Vi=sqrt(T^3/(2pA)) then rearranging T^3/(2A*P^2)=p p is the target air density T=mass*g A=disk area P=Power ideal(only induced) FOM=0.8(guess) P=FOM*MaxShaftPower Spreadsheet came up with 0.44 Air is 1.22 ASL Can't find a density TO altitude calculator, but chart puts it about 9km or 30,000ft Momentum theory is not accurate, that altitude is pushing the tropopause, and I pulled the FOM out of a hat, so consider that an unobtainable upper theory limit. Need more data(and time) to increase accuracy, like an actual FOM, min/max collective, etc. Your vessel has to actually be able to climb to the altitude also, no teleportation like the math pretends.
 At 0.5 FOM(lowest bound) ~1.1358 maybe 1300m W=FV You have 15211W, and gravity gives you 932N resistance for 16.32m/s ideal ascent FOM(0.8)=9000m/16.32m/s=552s to reach alt FOM(0.5)=1300m/16.32m/s=80s to reach alt 15211W*552s = 8,396,472J energy required 15211W*80s = 1,216,880J Assuming fuel fraction of 0.9(rocket mass to orbit) 85.5kg fuel 9000m=0.0987MJ/kg needed 1300m=0.014MJ/kg needed 0.5 (aircraft fuel fraction) 47.5kg fuel 0.177MJ/kg 0.025MJ/kg Lead-acid battery=0.1MJ/kg Lithium battery=1.8MJ/kg gas=46MJ/kg H2=123MJ/kg So it is ideally possible with electric or chemical fuel.