Can we come up with an easy system for matching a propeller to a motor and an airplane?

#### The Challenge

I started flying electric RC model airplanes about twenty years ago. The advances in the technologies since that time have been breathtaking. But we still fumble when it comes to putting together an efficient electric power system.

The task has gotten a little easier over time for a couple of reasons. The incredible popularity of electric flight helps. There is a lot of knowledge available on what types of power systems work better. Tools like my free power system calculator help, too.

But I have been wondering for a long time if we can come up with a better set of simple guidelines to make the job easier. My power system rule was an attempt at doing that for a power system as a whole.

Of course, there is no substitute for actual performance measurements of the components. The goal here is not ”100% accurate” but “good enough to serve as a starting point for further fine tuning”.

#### Work In Progress

The community that has built up around this website has a huge amount of knowledge. I continue to be amazed at the depth of knowledge evident in many of the comments posted with the articles.

What I am about to describe is a work in progress. Right now it is just an interesting idea. I am hoping to engage our collective wisdom and ingenuity. Let us see how far we can take this, shall we?

#### The Idea

Look at the performance graph for a propeller (RPM vs. efficiency). All propellers exhibit clear drop-off points in efficiency at very low and very high RPMs. What causes them? Can these drop-off points be predicted? Could we come up with a simple rule for predicting the best RPM range for a given propeller diameter?

#### Gas and Electric Propellers

Propellers made for gas engines are generally a lot thicker than propellers made for electric motors. They need to be stronger to better handle the higher RPMs that many gas engines turn at. Just like flying with a thicker wing, the thicker propeller blades behave differently. The focus here is on propellers for electric motors. It would not be hard to generalize my observations to gas propellers, but for the sake of simplicity I am not going to do so.

#### Low RPM

Propellers turning slowly run into the same low Reynolds number efficiency issues that our model airplane wings run into. Just like our model airplane wings, it can be hard to predict when the big drop in efficiency is going to happen. From my experience, a thin electric propeller blade is probably going to be in trouble at a Reynolds number below 100,000.

#### High RPM

At high RPMs, an entirely different performance problem comes into play. It is due to Mach, or speed of sound, effects. The entire propeller blade does not need to be turning at close to the speed of sound for you to notice a drop in performance.

You see, the air speeds up as it goes over the top of an airfoil. That is a direct consequence of the lift generation process. So Mach effects are felt first based on the highest speed of the air going over the airfoil.

Putting it into more practical terms, a gas propeller blade could start to experience a drop in efficiency at a Mach number as low as half the speed of sound. That is a Mach number of 0.5.

A thinner electric propeller produces less lift. Therefore, it will be efficient up to a higher Mach number. For the sake of argument, let us say that is Mach 0.7.

The typical plastic electric propeller cannot efficiently handle high RPMs. So bear with me. If it makes you feel better, imagine it is a thin carbon fiber propeller.

#### Some Numbers

I put together the attached sample spreadsheet to help me put all of this into perspective. It assumes that you are at sea level under standard atmospheric conditions. It takes the performance measurements at the propeller’s 75% radius, in accordance with propeller theory. The aspect ratio is assumed to be 15, though I know that small diameter electric propellers tend to have a lower aspect ratio.

For each propeller diameter, I found RPM values that were close to 100,000 Reynolds and to 0.7 Mach. For the smaller diameter propellers I also added a row with the typical RPMs that those propellers are normally flown at.

The propeller pitch does not affect the Reynolds or Mach numbers, so it can be ignored.

#### Surprise!

Do you see what I see? If the propeller diameter is less than 10 inches (25 cm), getting high efficiency out of a model airplane propeller is pretty much mission impossible. We are not going to be running our electric slow flyer motors (with 8 inch propellers) at 15,000 RPM to get decent efficiency.

With a four inch (10 cm) diameter propeller, the high efficiency window is tiny and at an extremely high RPM (60,000). It is just not going to happen.

Once the diameter gets bigger, we are in much better shape. A 10 inch propeller starts getting decent efficiency at about 10,000 RPM. That is doable. A 16 inch prop has a 11,000 range in RPM speed where it will work well.

If you thought that the main challenge with the smaller models was making the wing efficient, think again. The propeller is probably in deeper trouble.

#### Next Steps?

Coming up with a table with a recommended RPM range per propeller diameter is now easy. Again, my goal here is to come up with a set of rough rules of thumb. Matching the number of battery cells to the motor’s Kv is not out of the question. Using an estimate of the model’s cruising airspeed to pick the propeller pitch speed is also doable.

How do you estimate the cruising airspeed of a model airplane? I am not sure.

Could we use the propeller diameter and estimated RPM to compute the expected power requirement? Maybe. Then using the battery pack voltage, we could compute the current in amps.

This is all highly speculative. The point of this article is more to stimulate some brainstorming than to provide answers.

More than any time before, I want to hear what you think. It is a lot easier to say that something is impossible than to figure out a solution. How would you solve this problem?

Propeller Speed Limits Spreadsheet (xls)

http://t.co/lVtIabUE Propeller Speed Limits: Can we come up with an easy system for matching a propeller to a motor and an airplane? #rc

Hi Carlos,

Since different propellers, even within the same size range across manufacturers can be wildly different, I take the following approach with my designs:

Estimate the speed range that I want, and use a thrust calculator to estimate flying speed. I tend to try to keep pitch as low as possible but still achieving the pitch speed I want in order to maximize static thrust over the usable speed range of the plane. I ignore thrust out of the calculator since static thrust isn’t all that useful for a dynamic plane, as well as the final results are often 25% lower than the calculator estimated, but flying speed is usually pretty close. Then I adjust the prop pitch and recalculate so the plane ends up in the speed range I want.

Then I use the watts per pound of power to figure out how much motor power I need. Then I use the thrust calculator to check how many watts a certain prop at a certain rpm will take, using the pitch I figured out above. And then tweak the rpm and diameter to keep the watts the same, but the tip speed well below the mach figures you discussed above.

This gets me a prop size that’s at least absorbing a correct enough amount of power to fly the plane. The rest is determined experimentally.

Then I try out all the brands I can get a hold of in that prop range to pick the best one for that plane and flying style. I’ll also try an inch of diameter or pitch either way to tweak things that way.

I think it’s going to be difficult to find any cut and dry method of selecting a prop off of charts when most manufacturers don’t publish wind tunnel tests for their props, but I do enjoy hearing people thinking of ways to make the way we think of things better and easier, so keep it up! Innovation comes from thought processes like this.

Thank you for writing. I like your approach for finding the right propeller. It is similar to what I do. I have to admit, I am usually not that thorough. My goal is almost always just “good enough”, not top level competition performance.

Yes, wind tunnel results would be fantastic. We can only dream…

I am also very glad to hear that you understood the purpose of the article. Getting comments like yours was exactly my goal.

Actually I didn’t describe that well. I mean to say, I adjust rpm and pitch to find a prop/rpm combo that’s close. Then adjust diameter to get watts close. Then go fly and test.

That’s what I understood. Thanks for the clarification.

Also, one of the most popular ways of selecting a prop is seeing what someone else did for a similar plane! The most powerful calculator we have is the group of experimenters like you that we have access to across the planet.

Absolutely.

Carlos,

Something else to consider when looking at Mach number, is that you have to add the forward velocity component to the radial component at the tip to get the actual tip speed. For a slow flyer, it isn’t much of a problem. However, as the forward velocity increases, it can make a difference. Also, you will start to get a small amount of compressibility at ~0.5M, and should probably start having a noticeable affect around 0.7M. So, it’s a vector problem when you’re looking at tip speed, and not a big deal with a slow flyer, but it could become a problem with a higher performance airplane. Also note that the speed of sound is related to the square root of the absolute temperature. This shouldn’t be an issue in normal flying weather, but if one is flying a very high performance airplane in very cold weather, it should be looked at.

I enjoy your tips; thanks,

Dennis

Good points. My calculator takes forward velocity into account, but I was trying really hard to keep it simple for the article.

Hi Carlos,

Thanks for the challenge – it would be a great achievement if a relatively simple method was developed. To try to frame the difficulty consider that the information desired is prop pitch, prop diameter, motor max power, motor Kv and battery voltage. That is five variables so analytically five independent equations are needed for a solution if a unique one exists. So the real challenge is to define those five conditions, or at least find ways to reduce the number of independent variables. Good luck – I’ve tried and failed so far.

I do not know if an ultimate solution exists, but I can at least chip away at the problem. If nothing else, I found the exercise very educational.

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