What is the best way to calculate power and thrust for model aero engines?

[ken]

Hi I am helping someone with the aerodynamics to program a model aircraft flight simulator however my aero study has been aimed at radio controlled gliders so I'm a bit lacking on the power side of things.

We need to relate power and thrust for various model aero engines.

I did a static thrust test on a 2.5cc Taipan glow plug racing motor. This is a 2 stroke motor running on 80% methanol, 20% castor oil.
The prop is an 8 * 4 which is a dia of 203.2mm and pitch 101.6mm
Static thrust measured at 9.5 Newtons.

Now I found a statement that power = force * distance in unit time.
The test was made with the plane on a level surface, a string attached to the plane, round a pulley and attached to a small bucket.
I pored water in the bucket until the system a ballanced. I moved things about a bit the see if friction was affecting the outcome and found it insignificant. The mass of bucket and water was found to be .97 Kg.

Reasoning that thrust of 9.5 ballanced the weight of a .97 Kg mass, it could also accelerate that same mass at 9.81 m/s/s on a level surface therefore I could find distance from :

S = U * T + 1/2 A * T^2

Asssuming acceleration from rest and unit time 1 sec, I get:

S = A / 2

Now if power is force * distance in unit time I get :

P = 9.5 * 9.81 /2

P = 46.6 Watts

Is this correct?



If I knew bhp, can I use the reverse the above to find static thrust?

Is prop efficency a factor in the above and if so, are there good estimates we can adopt?

Would I be better off just scaleing thrust based on engine capacity?

The motor I used is a racing motor, designed to produce enough thrust for a racing model at well over 20,000 rpm. Would that mean less static thrust than a standed or stunt motor usually rated at 15,000 rpm.

Is there any way to relate turust to rpm as piston motor thrust reduces with rpm?

 

[paults2]

The measurement you did on your engine gives only the thrust at zero airspeed, which is 9.5N. It doesn't give the engine power.

For comparison, the power for a 2.5cc OS Max engine is listed on the OS website as 0.41 brake HP at 17,000 rpm, which is about 306 W. This is a maximum power and will be lower at lower rpm. Your engine is probably similar.

You can download the program Prop Selector from the following site. It gives absorbed power (power provided by the engine) and thrust as a function of airspeed for a given type prop and rpm. The program uses data based on NACA model prop tests.


http://www.gylesaero.com/freeware/propcalc.shtml


I plugged in your prop specs (8x4 inch, 2-blade) into the Prop Selector program. To get 9.5N thrust at zero air speed, the prop would be running at 14,000 rpm. The program shows an absorbed power of 175W. This is the power the engine would need to put out to get a thrust of 9.5N at 14,000 rpm for the given prop. Based on this model, your engine was probably putting out about 175W of power during your static test.

For a fixed-pitch prop, thrust is maximum at zero airspeed and decreases with airspeed. Eventually, the thrust reaches zero at some air speed where the angle of attack of the blade becomes slightly negative (prop 'lift' becomes zero).

Output power is defined as the airspeed times the thrust. At zero airspeed, the output power is zero, even though the thrust is max. Output power increases with airspeed, reaches a max, and then drops with increasing airspeed.

Absorbed power is the power needed to drive the prop. It supplies the output power plus power that is lost in the prop wake and prop vibrations.

Power efficiency is the output power divided by the absorbed power. Power efficiency is zero when the airspeed is zero, increases with airspeed, reaches a max, and then decreases with airspeed.

As an example, according to Prop Selector, for an airspeed of 35MPH, 14,000 rpm, and an 8x4 prop, the thrust is 6.5 N (lower than the 9.5 N at zero airspeed), the output power is 102 W, and the absorbed power (engine power) is 155W. The power efficiency is 65% (101/155). The Prop Select program shows a maximum power efficiency of 72% at an airspeed of 47 MPH for the given prop.

For your computer simulator, as a first approximation, you could assume that your engine is capable of putting out some maximum power for all rpm and then use the Prop Selector values to get a curve of thrust vs. rpm and airspeed for a given prop. This is approximate, because the engine power itself varies with rpm.

To be more exact, you would need the power vs. rpm curve for your engine, which you might be able to get from the manufacturer. Power for a glow engine usually increases with rpm and reaches a max at a relatively high rpm and then decreases. One gets a precise power vs. rpm curve using a brake measurement system (a dynamometer like those used for car or motorcycle engines).

In your simulator, you would read a throttle position which translates to a certain engine rpm. Knowing rpm and airspeed, you could get the thrust using data from the Prop Selector program. The thrust would then be used to determine the acceleration of the plane (thrust=F=ma, a=thrust/mass). The drag force would also need to be considered.

Let's say you assume your engine is capable of putting out power up to 200W at all rpm. Assume that a 50% throttle stick position means 10,000 rpm. For this rpm (and an 8x4 prop), Prop Selector shows the following for airspeed, thrust, and absorbed power:

--------------------
0 MPH, 4.8 N 64 W
20 MPH, 3.8, 60 W
40 MPH, 1.3 N, 37W


Assume 75% throttle stick means 13,000 rpm. Then Prop Selector shows:

----------------------
0 MPH, 13.9 N, 140 W
20 MPH, 7.1 N, 136 W
40 MPH, 4.5 N, 80 W


Try some higher rpm values, such as 15,000, which requires over 200 W absorbed power for airspeeds below 32 MPH. If your engine can't put out power above 200W at 15,000 rpm, then the rpm will never reach 15,000 for airspeeds below 32 MPH, and you won't get as much thrust as you expect. For example, using Prop Selector, at an airspeed of 20 MPH, the thrust will be only 9.3N at 200W and 14,700 rpm instead of the expected 9.7N at 212W and 15,000 rpm.

The thrust might be limited below a certain airspeed due to limited engine power. It depends on the engine, prop, rpm, and airspeed. The simulator software would need to account for this if you want a very accurate simulator.


References:

http://ntrs.nasa.gov/?method=advanced

Propeller tests to determine the effect of number of blades at two typical solidities
Lesley, E P (Daniel Guggenheim Aero. Lab., Stanford University)
National Advisory Committee for Aeronautics (NACA)
NACA TN-698 , April 1939

Comparison of model propeller tests with airfoil theory
Durand, William F Lesley, E P
National Advisory Committee for Aeronautics (NACA)
NACA Report 196 , 1925.

http://www.grc.nasa.gov/WWW/K-12/airplane/propth.html

http://142.26.194.131/aerodynamics1/Performance/Page8.html

http://www.mh-aerotools.de/airfoils/propuls4.htm


The following website gives prop power as a function of prop Dia, pitch, and rpm. I assume the results are for zero airspeed.

http://www.andersonparkflyers.org/wattage.htm

This site gives higher power values than Prop Selector software. For example, it shows that 237 W are required for a Master Airscrew 8x4 prop at 14,000 rpm and 199 W for an APC brand prop. These values are larger than the 175 W that Prop Selector gives. The variations are due in part to differences in the design of the prop and errors due to trying to scale results from tests of larger props (NACA tests) to smaller model aircraft props.

 

[ken]

Thanks Paul

That's very helpfull.

I knew that thrust and power varied with airspeed and RPM but the only practical test I could think to do was static. The links should help greatly. I could measure airspeed and crunch some numbers for drag. With the links, that would give me an idea of in flight power and rpm.


Many thanks,
Ken

 

[paults2]

Here's another report from the NACA server that discusses relations between airspeed, thrust, rpm, and engine power:

NACA Technical Note 237
Propeller Design: A Simple System Based on Model Propeller Test Data III
Fred E. Weick
May 1927

 

[paults2]

Ken,

I don't know if you're familiar with the motocalc software. It's made for modeling performance of rc airplanes. Among other things, it calculates a table of thrust vs. rpm, prop make and type, and airspeed. It also estimates airframe drag. They give a 30-day free trial. It's made for modeling electric powered airplanes, but it can be applied to gas planes. It's a handy program and worth buying. The data base has many types of rc motors and props.

http://www.motocalc.com/motodown.htm


Two other electric modeling programs are pcalc and electricalc:

http://brantuas.com/ezcalc/dma.asp

http://www.slkelectronics.com/ecalc/