Model Aircraft Prop Calculations

Vince,

NACA Technical report number 237 shows data and plotted curves for wind tunnel measurement of a family of 3 foot diameter props runnung in a wind tunnel at Reynolds numbers (measured at .75R) of from about 180k to 300k - in a range similar to that of our model props.

The props tested have pitch/diameter ratios of .5 to 1.1 and the data and plots show thrust coefficient, power coefficient and efficiency versus advance ratio. The planform and thickness distributions of these props a close enought to Master Airscrew that the coefficients will probably get you predictions within 10% of of real life performance.

Most Master Airscrew props that I have measured have actual pitch, as measured to the flat bottom of the airfoil, that is close to the claimed pitch and it is pretty uniform along the radius.

The NACA reports can be found by searching on the NASA tech report server at

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Are we really that far apart? Sure, I know that stall speed is not a linear function of air density. But we are talking to model airplane people. So the altitude range is not greatly different from a normal light plane. More or less sea level to 12000 feet. Over that altitude range using a linear calculation is a decent approximation. Particularly for a group that may be a bit math challenged. A linear approximation has several advantages. It slightly over estimates the stall speed. No one ever crashed because he thought his stall speed was a couple of % higher then it really was. It is easy to do in your head. And it avoids making math errors such as you made when you said it increased 14%.

I am also well aware that some combinations of prop, airframe and power plant can fly a plane at or very slightly faster level flight air speed than a simple pitch-rpm calculation would suggest. Of course those who think a props purpose is to blow air probably chock a bit on this idea.

I am also aware if you happen to have the above combination and want more low gear and are willing to sacrific a very small amount of cruising air speed the way to get there is to chop the prop diameter a little bit. I would think the prop works by blowing air crowd would insist that more pitch is needed not less diameter.

In models altitude should make next to no difference if you are using electric. If the plane flys fine at sea level it should fly just fine at any altitude a model normally reaches. This is not quite so true of a IC powered model. Engine power output drops with decrease in air pressure. As output drops rpm drops also. This combination can cause pretty dramatic losses in thrust. So altitude effects can demand prop changes in such situations. Particularly when you consider that model people need or at least want a lot more forgiveness between stall speed and cruise speed as they have no instruments or on board stick feel to help them fly the plane. I have seen very few if any models that did not have cruise speeds of 4X the power off stall speeds. In fact I do not know if I have ever seen a model that was not so overpowered that you could even do a power on stall unless you were pulling a tight turn. For sure you could not do a level flight power on stall like you can with most light man occupied planes.

So where do we really differ?

On many things. The aerodynamics of models follow the same rules of physics as real airplanes, and the air density has the same effect on both. The 14% was not done in my head. I don't do mental algebra easily, like I can arithmetic. I used a calculator. You would get the same result if you did the math yourself.

Internal combustion engines lose power with altitiude, as you say, but you are forgetting the drag reduction that also occurs with altitude. I can get full redline RPM in level flight at 8000' just like I can at sea level, on a fixed pitch prop, on the same airplane. The throttle setting will be the same: pretty much full open. Much less horsepower is being developed, but the lowered density reduces the drag on the prop and nothing much changes, except that the true airspeed rises and I go farther per gallon of fuel. These are actual observations I have made while flying real airplanes. I have heard arguments that Reynolds numbers make big differences between models and FS, but they're not so big. Some of the smallest real airplanes are smaller than some models. Where's the difference there, except perhaps in power-to-weight ratios? The models I have flown behaved exactly as I expected them to, based on experience as a pilot. Airfoils interact with air along well-defined lines, regardless of their size; that's why aircraft designers used models for many years when developing new designs. Computers changed all that.

Dan

Well Dan I suggest you either get a new calculator or put the correct numbers in your present calculator. One or the other is not happening or you would not get 14%.

I think probably what you did to get 14% was to take the square root of 2. Am I correct? Sorry but that is not how you do it.

Keep trying until you figure out the right answer is 11.8% increase in stall speed. This is a perfect illustration of why you should just use a linear estimate. Even after given a hint you blew it you still blew it.

After you figure out you really did blow it go back and ask yourself how many other things you may have blown.

So why did you say this in an earlier post:

My 14% was a lot closer to your 12% than your initial 20% was.

Dan

I said it because lift is linear with air density. I also said a 20% increase in stall speed as it is a perfectly good approximation that does not cause confusion with math challenged folks like you. After all you clearly demonstrated you could not do exponential math calculations.

Now to what you said: "Internal combustion engines lose power with altitiude, as you say, but you are forgetting the drag reduction that also occurs with altitude. I can get full redline RPM in level flight at 8000' just like I can at sea level, on a fixed pitch prop, on the same airplane. "

According to your simple minded analysis the above statement is equivilent to saying your light plane has a peak altitude capability of 60,000 feet making the very conservative assumption it has a level flight, power off, stall speed of half its cruising speed at sea level! ie suppose we put a radio control system on it to avoid the oxygen requirement of a pilot that plane could fly up to 60,000 feet. Now anyone with a brain knows that is pure nonsense.

I sure hope you never kill anyone other then yourself due to lack of understanding of lift, drag, stall speeds, various power plants, etc.

Cruise speed is the issue here, not climb rate. An airplane will cruise faster at altitude, but its climb rate diminishes with altitude so that every airplane has a service ceiling. The climb rate is horsepower-related, and an unsupercharged engined airplane will have lower service ceilings. And again: stall speed and lift are not linear with air density. They're a function of the square root of any change in air density. We've been over that, and using a straight 20% increase in stall speed for 7000 feet is nonsense. I posted the websites for that earlier.

Here's a performance chart for the P-51. Note that its peak cruise speed comes at around 23,000 feet, while its rate of climb drops with alititude until it reaches zero. The vertical sections of the lines reflect the supercharger shifting to a higher RPM and improving the performance for that altitude.

And the performance charts for the Cessna 172R: Note that the cruise speed improves with altitude. Doing the interpolations for the usual 75% power setting, we get:

110 kt at 2000' 112 kt at 4000' 114 kt at 6000' 116 kt at 8000' 118 kt at 10,000' and 119 kt at 12,000 feet, at 73% power because the engine can't get enough air anymore.

Do these figures look like decreasing cruise speeds with increasing altitude to you?

Dan (Commercial Pilot, Flight Instructor, Aircraft Maintenance Engineer. Took a lot of years of study to get all that.)

My oh My. This explains a lot. Clear back in 7th grade you should have learned that in an equation any two variables that carry the same exponent are linear with each other just as I said about density and lift. I now understand why you make so many conflicting statements and are unable to do calculations correctly even with a calculator. You never learned 7th grade math. Totally hopeless.

Maybe TNP will help tutor you up to 8th grade level. He at least never makes stupid math errors like you consistantly make.

altitude.http://www.wwiiaircraftperformance.org/mustang/xp-51g-chart.jpg>

172R:

So, what do you make of those tables and charts? Are North American (P-51) and Cessna all wet and you're not?

I run into this all the time with some modelers. Somehow models follow different rules of physics than real airplanes. How much flight experience--in REAL airplanes--do you have? Have you ever taken any flight groundschooling? BTW, "consistantly" is spelled "consistently."

"There are none so blind than those who will not see." John Heywood, 1546

Dan

altitude.http://www.wwiiaircraftperformance.org/mustang/xp-51g-chart.jpg>>> And the performance charts for the Cessna

172R:>> Note that the cruise speed improves with altitude. Doing the

No, but they are probably not talking about te smae thing.

No, just that the actual physics of flight is really pretty complicated, and most modellers have less than rudimentary understanding of newtonian mechanics, cant do calculus, are are totally lost when it comes to complex turbulent flow, which is where I peg out as well.

None whastoever, but I have flown a lot of models ad designed a lot of powertrains from scratch.

People in glass houses..

You need to fly faster to stay up as you get higher,. I believe its around 35,000 miles an hour in low earth orbit ;-)

To fly faster with an RPM limited electric motor, you need more pitch. Since the L/D ratio of your wing is substantiually the same or a little more, you will need a bit more thrust. But not much., Since MASS of air moved wont increase at your poptimum cruise, where pitch speed is nearly airspeed, you need a bit bigger prop.

That's the qualitative analysis. As to how exactly the pitch and diameter increase with altitude, its been covered pretty well.

You can believe anything you want to, BUT Low Earth Orbit velocity is MUCH closer to 17,500 Miles per hour,

Escape Velocity is only around 25,000 miles per hour.

And both of those have nothing to do with aerodynamic lift. They have to do with centrifugal forces and gravity.

Dan

Well thanks for correcting it.

The point still stands tho ;-)

Oh dear. Another man who can't see the smiley in there.

Sorry. Didn't look closely enough. I guess I get a little annoyed at some posters grasping at straws instead of responding to legitimate evidence, and start to reply a little too quick.

Anyhow, I give up on this one. It just ain't worth it. I have airplanes to fix and fly and students to teach and a house to paint and a Hummelbird sitting in the garage waiting to get finished and can't spend any more time at this.

Dan