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Author Topic: Horsepower determined by prop and RPM  (Read 636 times)

Offline Paul Smith

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Horsepower determined by prop and RPM
« on: July 09, 2024, 09:32:11 AM »
Has anybody come up with a formula to determine an engine's horsepower from RPM and propeller size?

One horsepower is defined as 746 watts.  So the HP of a DC electric motor is volts times amps.
If we defined a set of tach props, such as the APC 7-4, 8-6, and 9-6, we should be able to compute HP based on a tachometer reading. 
I've been using piston engines for decades, but I still don't know what the actual HP is.
Paul Smith

Offline Colin McRae

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Re: Horsepower determined by prop and RPM
« Reply #1 on: July 09, 2024, 11:04:56 AM »
I'm not sure engine HP can be calculated by prop diameter, pitch and rpm.

The typical equation for prop 'thrust horsepower' is HP = Thrust (pounds) x velocity (mph) / 375

It got me thinking. Maybe one could attach a digital scale (I have a digital fish scale) to the model on the ground and see what the static thrust is being generated by the engine. Then fly the model and calculate the tangential velocity based on lap speed and line length. Then put the results in the equation above and see the resultant HP.

But not sure of the overall accuracy. The static thrust on the ground will be a bit higher compared to level flight as I understand the engine unloads a bit once in level flight.

(But I really don't worry about it. If my model/engine/prop combination flies well, then I have enough power.) :)
« Last Edit: July 09, 2024, 03:08:03 PM by Colin McRae »

Offline Robert Zambelli

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Re: Horsepower determined by prop and RPM
« Reply #2 on: July 09, 2024, 12:09:42 PM »
Horsepower is indeed a function of torque and rotational velocity.

The normal equation is HP = TxN/63025 where torque is measured in inch-pounds force and N in RPM.

Years ago, we made an engine stand the could rotate around the crankshaft axis of the engine.
An arm extended outward from the stand, the end of which pushed downward opposite crankshaft rotation.
A load cell was placed under the end of said arm, measuring downward force. the load cell signal was sent to an oscilloscope via a charge amplifier.
Knowing the arm length and force, we could then calculate torque.
A stroboscope provided RPM.
The device worked well enough to get us an "A" in a course called "Applied Engineering".
Bob Z.



Offline Paul Smith

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Re: Horsepower determined by prop and RPM
« Reply #3 on: July 09, 2024, 01:20:44 PM »
I guess I got my answer.

I was hoping to convert 15,000 RPM with an APC 9-6 into horsepower.

The old Scotty, James Watt, rated his steam engines in units of how many mining horses they replaced.  Later on it was deduced that Scottish coal mines had really weak horses and a modern athletic man can also outperform a Scottish work horse.
Paul Smith

Offline Brett Buck

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Re: Horsepower determined by prop and RPM
« Reply #4 on: July 09, 2024, 01:28:57 PM »
I guess I got my answer.


  The missing element is how much drag/load the prop represents. People have used calibrated props to do exactly as you suggest. Otherwise, yes, in principle you can do what you want.


Quote
I was hoping to convert 15,000 RPM with an APC 9-6 into horsepower.

   On the ground? A good bit, maybe about .8-1 hp. 

    Brett

Offline Colin McRae

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Re: Horsepower determined by prop and RPM
« Reply #5 on: July 09, 2024, 02:27:50 PM »
Fundamentally any engineering equation used to calculate HP has to have one of the factors in the equation to be based on energy. Thrust force, torque, etc.

Prop diameter, pitch and rotational speed are not energy factors. So direct calculation won't get you there.



« Last Edit: July 09, 2024, 03:01:10 PM by Colin McRae »

Offline Paul Smith

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Re: Horsepower determined by prop and RPM
« Reply #6 on: July 09, 2024, 05:59:30 PM »
It seems to me that a workable test apparatus would be an electric motor (maybe an E Flite 46) with a voltmeter and an ammeter in the circuit.

Then the scientist could regulate the RPM and check it with a tachometer, noting the amps and volts and thus the watts which could be converted to HP using 746 watts per HP.  Just like lab testing a V8 car engine, this would be a static, not dynamic number.

So then result might be a table showing the HP required to turn a test prop (APC 9-6) at various RPM's within the operating range of engines. 

This might be an interesting project for student looking for a project.

Paul Smith

Offline Brett Buck

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Re: Horsepower determined by prop and RPM
« Reply #7 on: July 09, 2024, 07:35:30 PM »
It seems to me that a workable test apparatus would be an electric motor (maybe an E Flite 46) with a voltmeter and an ammeter in the circuit.

Then the scientist could regulate the RPM and check it with a tachometer, noting the amps and volts and thus the watts which could be converted to HP using 746 watts per HP.  Just like lab testing a V8 car engine, this would be a static, not dynamic number.

So then result might be a table showing the HP required to turn a test prop (APC 9-6) at various RPM's within the operating range of engines. 

This might be an interesting project for student looking for a project.

    You are right with one exception, conversion efficiency of the input power to the shaft. It's pretty efficient but not nearly 100% - lots of stuff heats up.

    Bob was right above- you need some method of measuring the applied torque. There are plenty of pretty easy ways to do that, even with strictly mechanical means, like a spring (that also has to be calibrated with a pulley and weights, or something), a swing weight, a load cell on an arm like described.
 
     Ted Fancher has a model-sized dynamometer that he bought that used a swing weight. It appeared to be reasonably accurate and we got good results from it. I am not sure where he got it.

     Brett

Offline Brett Buck

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Re: Horsepower determined by prop and RPM
« Reply #8 on: July 09, 2024, 07:45:28 PM »
Fundamentally any engineering equation used to calculate HP has to have one of the factors in the equation to be based on energy. Thrust force, torque, etc.

Prop diameter, pitch and rotational speed are not energy factors. So direct calculation won't get you there.

   You definitely need the RPM, and you do not need the thrust (at least to calculate the shaft power). The missing element is the torque, or if you use calibrated propellors, a torque curve VS rpm for that prop. For the most part at model RPM you can probably assume that the torque curve is a RPM^2 function, that is, a parabola. The tip speed at 15,000 rpm is about 588 fps, so there are negligible compressibility effects. So, if you could measure the torque the prop takes to spin at 10000 RPM, you could probably construct the rest of it pretty easily and assume that the power goes with the cube of the RPM.

  The weak spot of the calibrated props is that you need a lot of them and to switch back and forth to get an HP curve using them .

    Brett

Offline Brett Buck

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Re: Horsepower determined by prop and RPM
« Reply #9 on: July 09, 2024, 08:03:19 PM »
I'm not sure engine HP can be calculated by prop diameter, pitch and rpm.

The typical equation for prop 'thrust horsepower' is HP = Thrust (pounds) x velocity (mph) / 375

It got me thinking. Maybe one could attach a digital scale (I have a digital fish scale) to the model on the ground and see what the static thrust is being generated by the engine. Then fly the model and calculate the tangential velocity based on lap speed and line length. Then put the results in the equation above and see the resultant HP.

But not sure of the overall accuracy. The static thrust on the ground will be a bit higher compared to level flight as I understand the engine unloads a bit once in level flight.


   You cannot determine the shaft HP from the static thrust, even on the ground. I can tell you now what the static drag HP is without even a measurement, it is zero, because no work it being done on the airplane.

   One thing that you seem to be muddling is shaft power and the airframe power/drag power that the airplane is absorbing.

     The unload it not "a bit", it is a factor of 2 or more, and varies greatly depending on the prop efficiency in the actual position. The shaft HP is function of the torque and the RPM, as stated above. The power being absorbed by the airplane in a static condition is the drag x the speed.

    The shaft HP relationship to the thrust power is a function of the prop efficiency, which is very optimistically 60-70% (large high pitch at low RPM) and very low, maybe in the 30% range or lower (small diameter, low pitch, high RPM) and exactly zero either on the ground - it's not moving so no power is transferred to the airplane - or when it if moving forward with enough speed that the thrust goes to zero - the airspeed equals the effective pitch x RPM.

  While I think it is important to understand the basic relationships and in this case, the terminology, it's usually not terribly critical to know your torque curve, drag HP, etc, to more than in the ballpark values, since you select everything by how it functions rather than by analysis. We have done a fair bit of actual real testing over the years, with good precision, but more-or-less to confirm our observations rather than using it directly to design or trim anything.

    Brett

Offline Brian Hampton

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Re: Horsepower determined by prop and RPM
« Reply #10 on: July 09, 2024, 08:23:36 PM »
Back in the early 1950's Aeromodeller magazine published an article based on the experiments done by David-Andersen from Norway on the HP needed to drive a range of props at various revs. These results were then converted to a graph which gave the curves for HP required to turn these various sized props from 2K-20K revs. If you go to https://www.adriansmodelaeroengines.com/catalog/main.php?cat_id=57 you'll find a copy of that graph down near the end of Adrian's article.

Offline Air Ministry .

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Re: Horsepower determined by prop and RPM
« Reply #11 on: July 09, 2024, 09:43:15 PM »
People once used ' a stick ' , say 1/2 x 1 inch . a Torque Stick .

Say you runem on a lectric motor & measure the watts / rpm Cuttem to length of even modules reqd. Lable each .

So , a variety , Measure rpm & correlate on your rpm / watt table ( graph )

If you  dont use a seperate fan , there may be a thermal issue .

Offline Brett Buck

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Re: Horsepower determined by prop and RPM
« Reply #12 on: July 09, 2024, 10:08:18 PM »
Back in the early 1950's Aeromodeller magazine published an article based on the experiments done by David-Andersen from Norway on the HP needed to drive a range of props at various revs. These results were then converted to a graph which gave the curves for HP required to turn these various sized props from 2K-20K revs. If you go to https://www.adriansmodelaeroengines.com/catalog/main.php?cat_id=57 you'll find a copy of that graph down near the end of Adrian's article.

    That's an excellent article that tells you what you need to know to be able to calibrate your own props. And shows there isn't a lot new about this problem.

    I would just add that the prop-to-prop variation, even from the same notional manufacturer and design, is enough that you can tell, particularly with wood props. So you really need to calibrate a set of specific props and keep them in pristine shape to get repeatable results. I also note that using props directly as a known torque load is also prone to air density/pressure, etc. variations.

    Brett

Offline Motorman

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Re: Horsepower determined by prop and RPM
« Reply #13 on: July 10, 2024, 10:24:39 AM »
Is this an LA46? Just look in the back of the manual.

Offline Brian Hampton

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Re: Horsepower determined by prop and RPM
« Reply #14 on: July 10, 2024, 07:43:04 PM »
Just to add to my previous mention of the Aeromodeller article, these are the 2 pages of the article itself. Unfortunately the scans don't show who wrote the article.

Offline spare_parts

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Re: Horsepower determined by prop and RPM
« Reply #15 on: July 10, 2024, 08:54:17 PM »
We've been doing it to choose props for electric for decades. Each prop design has a constant, so this has to be known in addition to diameter, pitch, and RPM.

Prop Watts (2 blade) = Kprop x dia^4 x pitch x kRPM^3
dimensions in ft. APC sport props K= 1.11

I have seen curves for APC props in an article as well. Actually, APC has predicted data for every one of their props on their site. Use it for reference until you prove it's correct. Some seem to be strange.

You'll find calculators online also, but some are simply wrong. Some are very complicated. If you want to be very accurate, you want to calibrate a load, either prop or stick.

Greg
Greg

Offline Paul Smith

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Re: Horsepower determined by prop and RPM
« Reply #16 on: July 11, 2024, 10:07:46 AM »
The Page 2 graph from Aeromodeler is what I was looking for.

With it, I can use an APC 7-4, 9-4, or 10-6 to find the horsepower of an engine or motor. 
I don't plan to take this to court or challenge the accuracy of the data. 
But with that chart and a magnifying glass I can get a good idea of the HP of an engine or motor and compare them.
Paul Smith

Offline Steve Helmick

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Re: Horsepower determined by prop and RPM
« Reply #17 on: July 11, 2024, 10:09:19 AM »
Aero Modeller's (and Model Airplane News') great engine reviewer PGF Chinn made occasional reference to using a calibrated set of propellers to create his torque and HP curves. I'm pretty sure the props came in a set from Germany. Kavan, maybe?

He also gave rpm results for commonly available propellers. Usually, he pushed the engine's desires with propellers that were too small or too big and gave the rpm results for those, too. Very helpful to the average bloke.  y1 Steve
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Offline Paul Smith

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Re: Horsepower determined by prop and RPM
« Reply #18 on: July 13, 2024, 07:52:51 AM »
I recall reading Peter Chinn's engine reviews.  He didn't seem to have a problem putting HP numbers on engines.  Maybe some of the whiz-bang experts of today would find reason to challenge his methods.  I always accepted him as THE authority on engines.

In one of George Aldrich's writings he mentioned that he a had a tach prop, tach fuel, and tach engine that he used to do comparative studies on the Rossi 15 and other 2.5 cc engines.  The base line data from this trio was used to measure changes in ONE of the variables.
Paul Smith

Offline Brett Buck

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Re: Horsepower determined by prop and RPM
« Reply #19 on: July 13, 2024, 02:20:53 PM »
I recall reading Peter Chinn's engine reviews.  He didn't seem to have a problem putting HP numbers on engines.  Maybe some of the whiz-bang experts of today would find reason to challenge his methods.  I always accepted him as THE authority on engines.

  They wrote and referred to their use of both calibrated props and a dynamometer. Nothing has changed much about since the time of James Watt, so I am not sure what you are talking about "whiz-bang experts" doing differently. The only real change is that some people  replaced the spring scale or the swing weights with an arm and a load cell. That just makes it easier to use, not any better or more accurate.

   BTW, you used to be able to buy a set of calibrated props for doing exactly what you are doing. But to come up with the curves in the plot from above, you have to have a dynamometer of some type.

   When Ted and I did power and torque testing, we used a swing-weigh dynamometer than was available as a kit and would have been completely familiar to PGF Chinn and his bunch. The only issue I have ever had with his results, or any other engine tester, is the tendency to jump to conclusions based on static tests. Almost any engine for any specific  application has to be tested in that application, and maybe you can make some sense of the results by looking at dyno tests, but you sure can't tell without actually testing in the specific application*.

    The other objection I have had (after PGF Chinn), is that people following him wanted to write things like he did, and ended up with the most pompous and overwrought Proper English, you could almost read it with an RP accent!  That is a big problem with all technical writing, I end up rejecting papers *all the time* trying to get it cut down to only the necessary information. Write like Hemingway, not Edgar Rice Burroughs. In Chinn's case, you get the impression that it was not an act, but everybody else since, yes, it seems like an affectation.

    The best-ever example of this was a series of articles in Stunt News where a proclaimed "engine expert" inspected and tested a series of engines, and came to the conclusion that the OS 40VF was "unsuitable for stunt" because the timing was "typical radio numbers" - shortly after it won 4 NATS in a row and a WC!, while in the process of redefining the standards for the entire event. Some of the others, traditional baffle-piston chug motors like giant Foxes, all passed his muster!

   Brett

 *p.s. Chinn frequently waited until some engine was showing itself as competitive before testing it, like when the Olympic 15 and even more so, the Tee Dee 15 flew up FAI FF Power. He even refers to the contest success frequently in the articles. So, what he was doing made more sense than testing it first and them proclaiming it good or not just based on the test.
« Last Edit: July 13, 2024, 02:38:51 PM by Brett Buck »

Offline Motorman

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Re: Horsepower determined by prop and RPM
« Reply #20 on: July 13, 2024, 07:40:02 PM »
Using a set of calibrated props to determine HP? IDK. The slippage at different rpms, air temp, ect. You would almost always get a different rpm than the calibration rpm.

Maybe if you do the reverse and trim several props to give you 1K rpm increases in the suspected range. Then measure the props on an electric system that would measure the amp draw at that rpm for each prop and develop a power curve from there.

Another thing, it's kind of a skill to tweek the very maximum rpm out of an engine. Heat and mixture have to be just right at the same time and it don't last long. If you just lean down the needle untill you get the highest reading on your tach you're leaving something on the table.

They do make inertia dynos for model enignes but how far down the rabbit hole do you want to go.

MM 8)



   

Offline Brett Buck

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Re: Horsepower determined by prop and RPM
« Reply #21 on: July 13, 2024, 09:30:46 PM »
Using a set of calibrated props to determine HP? IDK. The slippage at different rpms, air temp, ect. You would almost always get a different rpm than the calibration rpm.

   As noted above, and in the article, the air density effects certainly do affect it. That, and in the extreme inconvenience of having to swap props to get a curve, suggest the use of a real dynamometer. However, over the small range we are likely to use, you can correct it based on temperature and pressure. Of course, the engine power itself is also affected by air density and has other correction factors.

   Trying to determine the engine performance with any sort of precision is a tricky issue and takes exacting care to consider all the factors. Most of the time, people (including Paul who asked initially) are just trying to get a ballpark number, maybe to 1/100 of a HP, two significant figures. To actually use that for anything practical, particularly in stunt, also would have to consider a huge number of other things that we only know in general terms.

    Brett
   


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