Tuesday, March 27th, 2012 09:03 am GMT -6 Tuesday, March 27th, 2012 09:03 am GMT -6Tuesday, March 27th, 2012 09:03 am GMT -6
 
Propeller Samples

Your propeller may just be a chunk of wood, but understanding how it works is key.

 

 

 

Propeller spreadsheet

Propeller Spreadsheet

I put together a simple spreadsheet to help you try out and understand better what I am about to say.

Click here to download it. As I have done before with other spreadsheets, the green cells are the ones to edit. Yellow cells are constants that should not need editing. Red numbers are computed results. I provide columns for U.S. customary and metric units of measure.

To help illustrate my points, the cells towards the bottom of the spreadsheet will add colored background dots. Red dots are bad. It means the value is outside the recommended range. Green dots are good. It means the value is in a specially good range.

For the sake of illustration, the spreadsheet assumes that you are using a thin propeller suitable for an electric motor. For a much more accurate and comprehensive set of results, use my free online calculator.

Blade Angle of Attack

Propellers are measured using diameter and pitch values. There is a simple formula to convert the pitch value into an actual propeller blade pitch angle. Think of this blade pitch angle as the angle of incidence of the wing in an airplane. It is important, but not the most important angle.

What we really care about is the angle that the air makes with the propeller blade. This angle is called the angle of attack. It is comparable to the airplane wing’s angle of attack.

Note that we are actually measuring the propeller blade angle of attack at the 75% radius position. In other words, we assume that the propeller blade only exists three quarters of the way out from the propeller hub. Do not let this bother you. This is a simplification that works well in practice.

Electric propellers like this one use thin airfoils. This thin airfoil has a stall angle of about 11 degrees. Beyond that, we are really just adding drag instead of lift.

We are similarly in trouble if the angle of attack is less than zero. Then we are just generating negative lift, which is just as bad.

Our propeller blade is most efficient at an angle of attack of about 7 degrees. At this angle the drag is still relatively low but the lift generated is good. This is the sweet spot we want to aim for.

Propeller Blade Reynolds Number

The Reynolds number relates the size of an object, its speed, and the fluid it is moving through. In our case, the fluid is air at sea level on a typical day. Propellers have an aspect ratio of about 15, so that is how I compute the width of the blades. This blade width is what I use in the spreadsheet as the size of the object.

The higher the Reynolds number, the easier a time the air has going around the propeller. This leads to less drag overall. Above a Reynolds number of about 200,000 we are in pretty good shape. As an aside, this is also true of our model airplane wings.

At the same time, low Reynolds numbers lead to very high drag. Below about 100,000, the drag gets really high. Yep, this is also true of thin model airplane wings. We need to avoid this.

We use thin propellers for our electric motors because they turn slower than comparable propellers on gas engines. The slower turning propellers have a lower Reynolds number and benefit from being thinner.

Mach Number

The Mach number is the fraction of the speed of sound that the propeller is moving at. Again, we take the speed measurement at 75% of the way out from the propeller hub.

I am not talking about the speed of the propeller moving forward. That is the speed of the airplane. I am talking about the speed of the propeller blades as they turn around in a circle. The forward speed of the airplane does contribute to the Mach number, but the effect is relatively small.

As the propeller blade speed approaches Mach 1.0, the drag on the propeller goes up dramatically. We need to avoid that at all costs.

But it is even worse than that. You see, even if the overall Mach number is well below 1.0, the local Mach number over parts of the propeller blades could be much higher. Remember that the air speeds up as it goes over an airfoil. As a safe rule of thumb, we need to keep the overall Mach number below 0.5. It would be even better to stay below 0.25.

Sample Propellers

Propeller Efficiency

The efficiency of a propeller is (amount of thrust produced) * (airspeed) / (power required to turn the propeller).

Why is airpeed a part of this equation? Here is a non-technical explanation. It is used as a scaling factor for the thrust. It is a way of crediting the thrust for the airspeed it has to overcome. The faster you are flying, the harder it is to produce any thrust at all.

I know what you are thinking. This equation cannot be right. It says that if the airspeed is zero, then the efficiency of the propeller has to be zero. Bingo! If the airspeed is zero, then no useful work is being produced. I know this is counter-intuitive, but trust me on it.

There is enough information in the spreadsheet to estimate the propeller efficiency. But the equation is a bit complicated, and I wanted to only include real simple equations in the spreadsheet. I decided to leave it out.

The efficiency can be roughly estimated by looking at the blade angle of attack, blade Reynolds number, and blade Mach numbers. Red dots mean bad efficiency, for example.

The lift and drag of the propeller blade airfoil have a direct correlation to the thrust available and power required by the propeller, respectively.

The Challenge

The challenge with using a propeller is to stay out of all the red dot zones. Preferably, we want to always be in the green dot zones. Let us change the values in the green cells and see how they affect the overall propeller efficiency.

We could try using a small, fast revving propeller. As the propeller’s RPM goes up, the Reynolds number goes up which is good. But then we risk hitting a high Mach number which is very bad.

The alternative is to use a slowly rotating large diameter propeller. We can stay in the relatively low blade angle and high efficiency sweet spot of the propeller. Problem is, then we risk having a low Reynolds number on the propeller blades at lower throttle settings, which causes lots of drag and is very inefficient.

There is another big problem which I have ignored so far. In practice, we want good efficiency over a range of airspeeds and RPM settings. That is really hard to do. Since we spend most of our time at the cruise airspeed and throttle setting, that is the flight condition we should be optimizing for. As long as we can also get enough thrust during take off, we should be fine.

Bonus

Here is a great video showing how a full-size airplane wood propeller is made.

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