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# Propeller Thrust and Power Coefficients Formulas

Posted by Glosh | Dec 28, 2017 @ 07:05 PM | 2,312 Views
In order to have a preliminary design tool for propeller-motor matching and in lack of public propeller performance data tables for many propellers manufacturers, I've been trying to obtain 2 simple formulas that approximates the propeller’s Thrust and Power coefficients (CT and CP) as a function of only Diameter(D), Pitch(P), RPM and advance ratio (J = V/(n*D)). The first two are usually the only parameters made available and RPM and J are inputs.

CT = CT(D,P,RPM,J)
CP = CP(D,P,RPM,J)
T = CT*rho*n^2*D^4
P = CP*rho*n^3*D^5

In reality, dimensional analysis proves that both coefficients are a generic function of the following parameters:

CT = CT(J,Re,Ma,Beta,shape)
CP = CP(J,Re,Ma,Beta,shape)

Where Re is the Reynolds number, Ma is the Mach number at the tip and Beta is the angle of incidence at ¾ of the wing span.

I figured that besides from the general shape of the propeller, Diameter, Pitch and RPM should be sufficient to represent Re, Ma and Beta. J we have as an input, Re and Ma can be written as functions of D and RPM, as for Beta, pitch is defined as how much would the propeller travel forward with one revolution, so we can argue that the P/D ratio is somewhat related to a “average angle of incidence” of the propeller.

To derive such formulas, I applied metaheuristic research algorithms (PSO and GA) on data from UIUC propeller database (http://m-selig.ae.illinois.edu/props/propDB.html) and Tmotor propellers (http://store-en.tmotor.com/). Almost...Continue Reading