What's the formula for calculating thrust using prop size and rpm's?

Thanks.

It's not a simple thing. I don't remember where I got this from, so I give credit to whom ever gave it to me.

"
Engine Thrust Calculation:


This is a good general purpose thrust calculation that will provide results, for most Zingers and APCs as close as a fish scale will measure thrust over the usual range of sport flying setups. But, see note #5 below.


Thrust in lbs = 2.83E-12 x RPM^2 x D^4 x Cp x ((In. Hg)/29.92) x (528/(460+deg F))
Where:
RPM = revolutions per minute;
D = propeller diameter in inches;
Cp = propeller coefficient, use 1.00 for Zinger wood props or APC nylon props. See note below for Master Airscrew, K-series, black nylon props and others;
(In. Hg) = barometric pressure in inches of mercury;
deg F = ambient temperature in degrees Fahrenheit

NOTES:

(1) Don't worry about not having a pitch term. I questioned that too. The basic equation is from the Marks Mechanical Engineer's Handbook. The equation in the handbook does not include pitch as a variable, but expects the user to empirically determine a coefficient (my/your Cp) that is adjusted for variation in propeller geometry. Although my data is limited, I have found that pitch variation in the 6" to 10" range has no appreciable affect on thrust prediction of props of 11" to 15" diameter, tested below 10,000 rpm. Test with a new, unblemished Zinger prop and you will be a believer! There are great variations in propeller geometry though, so you should determine your own Cp for the style of prop that you prefer to use (refer to note 5 below)

(2) Don't be concerned about the units not working out to lbs. The constant 2.83E-12 isn't dimensionless. It includes standard air density (lb/ft^3) divided by the gravitational acceleration constant (ft/sec^2). It also contains units conversions, to allow you to input rpm rather than rps, and prop. diameter in inches rather than feet. In addition, it contains an empirically determined value that allows thrust prediction using a Cp value of 1.00 for Zinger or APC props.

(3) If you don't want to mess with temperature and barometric pressure just leave out the terms following Cp.

(4) I have a reasonable amount of data on Zinger and APC props, but just enough data on Master Airscrew (MA) K-series Nylon props to show that they are definitely a different breed. Data taken on the same day, with the same engine and the same fuel showed a Cp of 1.33 with a 13x8 MA when compared with a 13x8 APC (baselined at Cp=1.00). My engine rpm dropped considerably (1000 rpm) running the MA, so, though thrust was higher overall performance was not. The bright side is, if you need more engine load because of ground clearance problems use a MA prop. You will get the thrust, if not the airspeed.

(5) Determine your own coefficient (Cp) for your props. I have found certain sizes/pitches of my Zingers and APC's don’t precisely hit the 1.00 Cp. I am sure that there are variations in all brands and sizes. All you need is a good thrust measuring technique. Using a fish scale and a hard level surface, you should be able to measure thrust while the engine is mounted on the plane.

(6) Results will not be predictable for any prop that has been deformed, shortened, or reshaped in any way. My experience is that the prop efficiency will always be reduced if you mess with it! But then, I don’t design props, and some folks are masters at prop carving.
"

Here are some other from AMA mag Oct 86 :


Load = Prop Diameter^4 * Pitch
Speed = Pitch * rpm * 0.000947
Horse Power = Load * rpm^3 / 1.4 * 10^17
Static Thrust = 0.00000000000283 * rpm^2 * Prop Diameter^4 * Air Density/29.92 * CF value

If I have time, I'll make a spreadsheet for the values.

I played with it with Excel, and came up with 2 sheets. The 1st seems very accurate, but the second needs some more empirical data to come up with a better formula. Basically, you type in the values in the yellow, and it figures out the red. Here it is:
http://www.cwoi.net/spad/PropPredict.zip