Member Login

Remember Me
Forgot Password?
Join Us!

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!

Join Eng-Tips
*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.
Jobs from Indeed

Link To This Forum!

Partner Button
Add Stickiness To Your Site By Linking To This Professionally Managed Technical Forum.
Just copy and paste the
code below into your site.

trouble with rotor thrust equation

trouble with rotor thrust equation


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

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.

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


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)
R = blade radius  (ft)

Equations for a uniform pitch (flat) blade

Blade twist

theta(r) = theta0   (radians)

Tip Loss Factor

Kp = 1.15  (nondimensional)

Blade solidity

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

J. Vorwald

RE: trouble with rotor thrust equation

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?

Red Flag This Post

Please let us know here why the post below is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close