Formula for Aircraft Propeller Thrust

[tilopa]

I'm trying to understand thrust for a real world application. I found this formula:

T= pi / 4 x D(squared) x (v+V1/2) x p x V1

Where:

T thrust [N]
D propeller diameter [m]
v velocity of incoming flow [m/s]
V1 additional velocity, acceleration by propeller [m/s]
P density of fluid [kg/m³]
(air: = 1.225 kg/m³, water: = 1000 kg/m³)

I understand how increasing the propeller diameter would increase the "amount" of air and therefor increase thrust. But the equation does not account for the increased pitch angle of the propeller blades. Intuitively (and by Newton's Third Law of Motion) if you increase the angle of the blade against the air you will be pushing more air (greater "amount" of air), correct? So, does anyone have an equation for thrust that includes the propeller angle. Or an equation that I can use that includes pitch angle to replace the D2 value in this equation?

Thanks.

 

[CWatters]

the equation does not account for the increased pitch angle of the propeller blades.

I think it does. Changing pitch would change the V1 term.

I think if you find one that has pitch in it explicitly it will also have unknown constants that relate to the blade design. For example the torque won't be zero at zero pitch. It might not be a maximium at max pitch either.

 

[CWatters]

Looks like a good read...
http://www.free-online-private-pilot-ground-school.com/propeller-aerodynamics.html

http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/propeller/prop1.html

 

[tilopa]

Thanks, I'll check out those links.

 

[learninphysics]

tilopa, I know this thread is old, but I wanted to share with you an equation I came across recently for propeller thrust that *does* include pitch angle. Here is the simplified version of the equation:

F = 4.3924e-8*RPM*d^3.5/sqrt(pitch)*(4.23333e-4*RPM*pitch – Vac).

F is thrust in Newtons, RPM is rotations per minute, d is prop. diameter in inches, pitch is prop. pitch in inches, Vac is aircraft airspeed in m/s. The full derivation of the equation begins with Newton’s laws, and is shown here: http://electricrcaircraftguy.blogsp...tatic-dynamic-thrust-equation-background.html