Calculation of rate of climb for UAV (pusher propeller)?

Question

At the moment, I'm doing an estimation and analysis of flight performance for UAV (unmanned aerial vehicle). During climbing flight analysis, I have a problem regarding rate of climb (vertical velocity), my calculation value of rate of climb seem weird, the vertical velocity (RC) bigger than velocity vector. I hope someone can help me to solve this problem quickly, I have already calculate it many time but the result still same. I want to attach xls file here but can't do it, so I really want a help from all of you here, perhaps an email to discuss.

Answer 1

my advice is to pay a lot of attenction to put the right numbers in the right place(for example if in the formula there is thrust, do not put in power avaiable, remember to divide it by airspeed), pay attenction to units(for example weight sometimes expressed in mass units sometimes in force units...pound, kilogram-force, newton).

however in the case of prop an approximation of vertical (steady) speed can be calculated quite simply. you know the power avaiable(consider constant with speed),

From weight=lift you can calc the CL at that speed,

CL=(2 * W)/(rho * S * V^2)

W=weight, rho=air density, S=wing area

and with parabolic polar approx. from CL you can calc Cd.

Cd=Cd0+(CL^2)/(e * AR * 3.14)  

Cd0 is a constant

AR=aspect ratio

"e" is "oswald factor" depends from wing plane shape(straight,tapered,elliptical) usually consider 0.8-0.85-0.9

now you know Cd at that speed, so you can calc the "power required" at that speed.

Pr=1/2 * rho * S * Cd * V^3.

Pay attenction:" Power required = drag * airspeed" contains an approximation that is usually good, it considers 0 the  component of weigth in thrust-drag direction, but this approximation is good only if the angle of climb is quite small(gamma<<1 in radiants, so much smaller than about 60°). the more steepest the climb is the worst this approximation will be. so if your UAV has a big specific excess power, it will climb quite steepy and the results can  be not so good.

You already knew the power avaiable from powerplant (consider it constant for props or thrust*airspeed in jets)

now you can calc the vertical speed Vz:

Vz=(Pa-Pr) / W