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trouble with rotor thrust equation

trouble with rotor thrust equation

(OP)
koschur@graffiti.net

I am trying to calculate thrust from a rotor in the simplest way. I am using the general equation:

(explained in much more detail at http://www.natefisher.com/rotorthrust.html)

My problem is that when I increase the pitch of the blade, the total thrust amount always decreases, and when I increase the lift-curve slope value, the thrust always seems to increase. Common sense seems to tell me that this would be the opposite case I should be getting. Anyone out there know what may cause this? I tried to make it as easy as possible to read what I am doing at the website above.
http://www.natefisher.com/rotorthrust.html

also, is the relative pitch (p in the equation) in radians or degrees, i assumed degrees.

thanks,
nate

koschur@graffiti.net

RE: trouble with rotor thrust equation

I think you have three problems with the derivation

a) Wrong expression for thrust
b) Wrong expression for induced velocity
c) Using the induced velocity expression incorrectly

The blade pitch is in radians (to match the lift curve slope of 4.5 which is in per radian).

Here are the correct equations

Thrust in terms of coefficient

T = Ct * (rho * A * (Omega * R)^2)

rho = density = 0.002378  (lb sec^2 / ft^4)
A = disk area = pi * R^2   (ft^2)
Omega = rotation rate  (radians / sec)

Equations for a uniform pitch (flat) blade

Tip Loss Factor

Kp = 1.15  (nondimensional)

sigma = Nb * chord * R / A   (nondimensional)

Nb is the number of blades

Induced velocity

lambda = sigma * a / (16 * Kp)
* {-1 + sqrt[1 + 64/3 * Kp^2 / (sigma * a) * theta0] }

a - lift curves slope, per radian

Thrust coefficient

Ct = sigma * a / 2 * (theta0 / 3 - lamda / 2)

Ct should increase with theta0 (blade pitch in radians) and also increase with "a" (lift curve slope in radians).  An increase lift curve slope is an improved airfoil section.

Reference: Class notes, University of Maryland, Helicopter Dynamics

Cheers
J. Vorwald

RE: trouble with rotor thrust equation

(OP)
well, that all looks good to me too! as I am jsut strating out my AE career and am not very familiar with common math. And thank yo ufor your time in replying! It is greatly appreciated.

The formulea I used were gathered from Chapter III on blade element theory from "Intro to Helipcopter Aerodynamics" by W.Z. Stepniewsk. (1950)

I dont know if anyone is familiar with that book and can tell me what I interpreted wrong?

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