Propeller Basics

March 1, 2002 for  Sailplane & Electric Modeler Magazine

The majority of powered model airplanes use a propeller as part of their power system, and electric models are no exception. Some models use a ducted fan to simulate jet flight, and some even use propane or kerosene powered turbines (real jet engines). There are also a very few models that use flapping wings as a source of motive power (known as ornithopters). However, propellers are still the most efficient way to power a model.

What Does a Propeller Do?

In short, a propeller moves air. It converts the torque of its power source (a motor or engine) into thrust, and the rotational speed (rpm) into linear speed. The combination of an electric motor and a propeller turns current (Amps) into thrust and voltage into speed.

There are two values that express the most important characteristics of all propellers: diameter and pitch. The diameter is really the diameter of the circle in which the propeller rotates. This corresponds to twice the distance from the center of the propeller hub to the tip of one blade (for a propeller with an even number of blades, that’s just the distance from tip to opposite tip).

Slicing the end off of a propeller blade reveals an airfoil just like that found on a wing. Different propellers use different airfoils. Some modern electric flight propellers have undercambered airfoils. This glow propeller has a flat-bottomed airfoil.

Slicing the end off of a propeller blade reveals an airfoil just like that found on a wing. Different propellers use different airfoils. Some modern electric flight propellers have undercambered airfoils. This glow propeller has a flat-bottomed airfoil.

The pitch is a measure of how far the propeller would move forwards in one revolution if it were treated as a screw and screwed into some solid material.

Although the measure of pitch treats the propeller as if it were a screw, one shouldn’t think of it as an airscrew (the name of a certain model airplane prop manufacturer notwithstanding). It is really a rotating wing, and if you were to take a propeller and slice it across the blade, you’d see a typical airfoil cross-section.

The size of a propeller is usually expressed in the form diameter x pitch. For example, an 8×4 propeller has an 8 inch diameter and 4 inch pitch.

As a very rough approximation, the diameter of the propeller controls the thrust produced, and the pitch controls the speed of the air leaving the back of the propeller. In reality, pitch also affects thrust somewhat, but thinking of the two separately helps to envision how propeller changes will affect performance.

Measuring Pitch

Most propellers are labeled with their pitch and diameter, but it is possible to determine both given an umarked prop. The diameter is straightforward to measure of course.

Measurements needed to determine the pitch of a propeller should be taken 3/4 of the way from the hub to the tip.

Measurements needed to determine the pitch of a propeller should be taken 3/4 of the way from the hub to the tip.

To measure the pitch, lay the propeller flat on a table, measure 75% of the way from the hub to the tip, and draw a line across the propeller blade. Measure the width of the blade at this point, along the surface of the table (i.e. the width of the blade’s shadow if there were a light on the ceiling overhead). Next, measure the height of the front and the back of the blade, and compute the difference between these two to determine the height.

The pitch is then given by the formula:

pitch = 2.36 diameter height/width

There’s nothing magical about the number 2.36; it’s just 75% of π (pi), because we’re measuring pitch at the 75% diameter mark.

The reason we measure pitch at 75% of the diameter is two-fold. Generally, the pitch of a propeller is not completely constant, varying somewhat from hub to tip to optimize it for the different linear speeds at each point along the blade. The pitch at 75% corresponds roughly to the average effective pitch of the propeller. Secondly, the propeller is sufficiently wide at 75% to allow one to get reasonably accurate measurements of blade width and height.

Measuring the pitch of a propeller is easily done on a flat surface with an accurate ruler.

Measuring the pitch of a propeller is easily done on a flat surface with an accurate ruler.

Power Requirements

Both pitch and diameter affect how much output power the motor must produce to turn the propeller at a given rpm. The following equation shows the relationship between motor output power (also called shaft power, or propeller input power), rpm, pitch, and diameter:

power = k rpm3 diameter4 pitch

The factor k depends on the units used to express power, pitch, and diameter, and also on characteristics of the propeller such as the airfoil it uses, its overall shape, thickness, and so on. For power in Watts, and diameter and pitch in inches, k is about 5.3×10-15 for an average model airplane propeller.

This formula tells us a number of things. First, it tells us that rpm is not directly proportional to power. Doubling the shaft power and keeping pitch and diameter the same will only increase rpm by a factor of 1.26 (the cube root of 2).

It also tells us that increasing the pitch slightly will increase the power requirements slightly, whereas a slight increase in diameter will result in a dramatic increase in power needed to maintain the same rpm. For example, going from a 10 inch propeller to an 11 inch propeller of the same diameter would require 1.46 times the power to maintain the same rpm (11/10 to the fourth power). Or, if the shaft power were kept the same, the rpm would drop to 88% of what it was (the reciprocal of the cube root of 1.46 from the previous result).

The fact that pitch affects power requirements only slightly is very important, because it means that we can make small changes in pitch to improve model performance without having to worry too much about increasing current. For example, if we have a model with a 10×7 prop that has good take-off and climb performance, but poor high-speed performance, we can switch to a 10×8 prop and only increase power required by about 14%. Assuming the motor is near its maximum efficiency point, current will also increase by about 14%, say from 25A to 29A. Larger changes in pitch should be accompanied by a slight reduction in diameter to keep the current levels reasonable.

In practice, changing from one propeller to another will change both the rpm and the power. This is because changing the load on a motor shaft will change the rpm, which will change the power required, which will change the rpm, and so on. The motor and propeller combination will find a new operating point at which the shaft power produced equals the propeller input power required. Next month, I’ll talk about how motor output power is related to input voltage, current, and rpm, and how this can be mathematically connected to the propeller formula above to predict what will actually happen.

Airflow

As was mentioned earlier, a propeller is really a rotating wing, and as such, is subject to the same aerodynamic effects as a wing. As a propeller rotates, the blades meet the oncoming air. The angle at which this happens is a function of how fast the air is moving towards the propeller and how fast the propeller is turning. If the air were stationary, the angle of attack of a given section of the blade would be exactly equal to the blade angle at that point.

The relative angle of attack of the airflow to the propeller blade depends on the rotational speed of the blade, and the speed of the incoming air flow.

The relative angle of attack of the airflow to the propeller blade depends on the rotational speed of the blade, and the speed of the incoming air flow.

In reality, the air is not stationary, even if the plane is not moving, because the air accelerates before it reaches the propeller. As a result, from the blade’s point of view, the air is meeting it at some relatively low angle, which is the blade’s angle of attack.

Like any wing, a propeller blade can stall if the angle of attack is too high. This can happen with a very highly pitched blade when moving at too low an airspeed. It is for this reason that high pitch propellers, like a 10×9 or 12×12 often exhibit poor performance at low airspeeds. A plane equipped with such a propeller will often exhibit poor launch or take-off performance, and then come alive once the model is up to speed.

Also like a wing, if the angle is too low, no lift will be produced. A low pitched propeller on a fast plane (for example, 8×3, 12×5, etc.) can get to the point where it produces no thrust (in a dive, when gravity is providing the force to keep the plane moving). In high speed level flight, thrust from such a propeller can drop too low to overcome drag long before the plane has reached its designed flying speed. According to Astroflight’s Bob Boucher, such propellers should be relegated to stirring paint. Of course, this statement was made in the days before slow-flyer models, which often sport very large low pitch props.

For many aircraft, a good compromise is a propeller with a diameter to pitch ratio of about 3:2 or 4:3 (for example, 8×6, 9×6, 10×7, 11×8, 12×8, 12×9, and so on). Such a propeller will become unstalled at relatively low airspeeds (usually below the model’s stall speed), and will remain efficient at relatively high flying speeds.

In many full scale aircraft, the propeller has in-flight adjustable pitch, so that it can have a low pitch for maximum take-off thrust, and a higher pitch for optimal cruising efficiency. Some small full-scale aircraft can be fitted with one of three different propellers depending on the need at the time: low pitch for getting heavy loads off the ground but slow cruising, standard for general use, or high pitch for light loads but fast cruising.

Three or More Blades

Most model propellers have only two blades because a two bladed propeller is generally more efficient than a larger propeller that produces the same thrust and air speed. A common misconception is that this is due to the blades operating in each others’ wakes, but this is only a small factor. Remember that the air in which the propeller is turning is moving away from the back of the propeller, so the wake from each blade will move backwards too, leaving clean air for the next blade to bite into. A reasonably pitched propeller would have to have a large number of blades before they start interfering with each others’ air.

That being said however, a multi-bladed prop does have more induced drag caused by tip vortices (air spilling over the blade tips, just like wingtip vortices on a wing), because there are more tips. So, overall efficiency is lower, in much the same way that a biplane (even one without struts and bracing wires) is less efficient than a monoplane with the same wing area. A multi-bladed prop often has a larger total blade surface area than the equivalent larger two-bladed prop, further reducing efficiency (due to parasite drag).

For best performance, reduced noise, and increased motor life, all propellers should be balanced before use. I use a Top Flite magnetic balancer, which due to its nearly frictionless bearings, will show even the slightest imbalance.

For best performance, reduced noise, and increased motor life, all propellers should be balanced before use. I use a Top Flite magnetic balancer, which due to its nearly frictionless bearings, will show even the slightest imbalance.

Multi-bladed propellers do have the ability to turn power into thrust and airspeed in less space than a larger two-bladed prop though, which makes them advantageous when ground clearance is an issue (or fuselage clearance for wing or pylon mounted propellers).

Practical Considerations – Balancing

As electric flyers, balancing a propeller is very important. It’s important on glow powered models too, but the result of an unbalanced propeller is a lot less apparent, due to the noise and vibration of the engine. On an electric model, an unbalanced propeller is far noisier than a balanced one. Furthermore, an unbalanced propeller wastes power, because it is putting a sideways force on the motor shaft, pushing it against one side of the bearing. It also can also cause the shaft to bend somewhat, which means the motor armature (in a direct drive application) runs off-center, further reducing efficiency.

I use a Top Flite magnetic balancer, and sand material off the back side of the heavy blade as close to the tip as possible (the further from the center you remove material, the less you will have to remove). One of my direct drive models which sounds like a glow model when flown with an unbalanced prop, becomes inaudible at 200 feet when flown with a well balanced prop of the same brand.

Making It Turn

A propeller with no source of power is useless, so next month we’ll look at how an electric motor interacts with the propeller to convert electric power to the form that we need it for flight, namely thrust and airspeed.

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34 Comments

  1. Lynn Demers
    February 20, 2008

    I want to thank you for the pitch explanation and measurement process. I have been looking for that answer for awhile.

  2. Shehar Bano Safeer Awan
    October 11, 2010

    its too good to learn it from here!!!!!!!!

  3. Robert Pegg
    November 06, 2010

    Good, simple explanation of the basics!

  4. Shazad Irani
    February 02, 2011

    good stuff

  5. Zohair Kanga
    February 02, 2011

    well explained,

    “thumbs up”

  6. Anant Saraogi
    March 09, 2011

    very helpful article

    thanks for it

    sir can you plz tell me the source from where you got the formula…

    power = k rpm3 diameter4 pitch

    as i have to show the calculations with the source of the used formulae

  7. Stefan Vorkoetter
    March 09, 2011

    That formula is taken from Robert Boucher’s “Electric Motor Handbook”, published by AstroFlight.

  8. Ayberk Okan
    May 29, 2011

    Helpful article sir.An unbalanced airscrew powered by a glow engine can also cause dramatic situations depending on the degree of unbalance factor and the diameter/mass of the propeller.I can’t stop myself thinking that can absolute factory prebalance be possible because most beginners do not balance their propellers.They think its unneccessary i guess.It may be ok with a cox engine maybe but if you are running an OS 140RX it can be very dangerous both for the humans and investment.

  9. Agus Suprianto
    August 15, 2011

    please explain to me how to calculate slip, geometric pitch, and effective pitch..??thank’s before

  10. Loreann Wells
    August 26, 2011

    can you please explain to me how propeller size effect thrust?

  11. Stefan Vorkoetter
    August 26, 2011

    Loreann, thrust is equal to input power times efficiency divided by pitch speed (where all units are SI).

  12. Les Clark
    August 29, 2011

    I have a Hendrickson Wood 2 blade prop. The only markings i could find are h68f82 21659 .

    Can anyone tell me what that means? Thanks Les.

  13. Stefan Vorkoetter
    August 29, 2011

    Les, I assume you’re not talking about a model airplane prop. I would guess that one of 68 and 82 is the diameter, and the other is the pitch. If you measure the diameter and it’s one of these, then you’ll know. :)

  14. Abdul Wahhab
    September 07, 2011

    awesomely explained !

  15. Padmanabhan Vijayaraghavan
    September 19, 2011

    hi give a name of a book where i can find more abt this and marine prop

  16. Jesse Nderitu
    September 30, 2011

    am working on a small plane and need some advice,i would like to know why my plane is failing to lift,has a wooden propeller one piston engine NEED HELP PLIZ(currently in Uganda )

  17. William Herrmann
    October 04, 2011

    I am having trouble getting the pitch from my airfield T28 prop as it is a multi piece prop and the hub i tall there is no listing of pitch i am trying to replace it with a master airscrew when i replace the motor with a power 32 770kv from a power 25 520kv so i want to get the right prop. plane is 1400mm and about 5.5lbs. motor is a little under powered or not enough kv for prop size..is about 13in 3 blade. guessed at a 7 pitch ???? want to use original prop if possible…?????

  18. Bruce Parrott
    October 18, 2011

    i’m looking for a cheap three blade prop 5″ dia for a de havalland beaver i’m building out of scrap for fun hanging ornament. Pitch of no importance, just needs to turn and look right, any help please?

  19. Vikas Agarwal
    November 08, 2011

    very good and informative

  20. Dixansh Sharma
    February 06, 2012

    What is the relation b/w thrust and pitch of the propeller..

  21. Paulo
    March 09, 2012

    A very interesting and informative read !
    Thank you sir !

  22. chuck
    March 24, 2012

    How do you choose an airfoil for a propeller? I need to carve a 1:4 scale Vs11 3-bladed german propeller for the 1:4 scale Ju87 i’m building

  23. shubham sharma
    July 12, 2012

    thankyou for this page………….very helpful

  24. Fred G
    November 05, 2012

    I would like to know how to calculate thrust to payload push/pulling capacity of a propeller.
    Example: If I have a hovercraft that has a gross loaded weight of 600lbs. What size propeller would I need to push the craft forward at 30 miles per hour, using an 18hp gas engine?
    I am concerned about the propeller failing because of load pushing/pulling stresses on the blade itself
    How do I determine how strong a propeller is? I am concerned about a blade breaking. How do I calculate how much weight a propeller can pull or push with out blade failure?

  25. Joseph L. McCauley
    April 04, 2013

    The formula above is not for the motor hp, it’s for the power transmitted by the prop to the air. This is less than the motor output, which is simply torque times RPM. The amount by which it’s less is the mechanical efficiency=power output/(power input).

  26. Joseph L. McCauley
    April 04, 2013

    Book: Marine Hydrodynamics, by Newman. MIT Press in the 1970s. The ideas apply to props in air, props submerged in water, and surface-piercing marine props. Same physics/hydrodynamics so far as power, etc are concerned.

  27. Stefan Vorkoetter
    April 04, 2013

    Sorry Joseph, that formula is for the power _absorbed_ by the propeller, not the power that is turned into useful thrust and velocity. Thus, it _is_ equal to the power that the motor must output. To get the power _produced_ by the propeller, you have to multiply by an additional factor that represents the efficiency of the propeller (and that factor will vary with speed, medium, etc., so it can’t be included in the constsant k).

  28. Antonio Silva
    October 14, 2013

    Hi Stefan,

    We use CF ground adjustable custom made blades in our prop hubs. These are 1/5 scale of the Corsair. I have a pitch adjusting tool I purchased from GSC of Canada, but this measures in DEGREES pitch. I need to know the equivalent in inches of pitch (and vice-versa). The length of the blade is 325 mm from the hub to the tip and I suppose to set the dial at 25% of this distance from the tip, thus 81.5 from the tip. At this point the blade is 55.2 mm wide.
    Is there any software that can do this conversion automatically?
    Thank you for any information.

  29. Sander Liivandi
    March 10, 2014

    Greetings,

    I am a student of the Estonian Aviation Academy. I am writing a paper on construction of a thrust stand for propeller driven UAV engines and I would like to request permission to use your image about relative angle of attack (in the chapter titled “Airflow”).

    Yours faithfully,

    Sander Liivandi

  30. nabil hilmi
    April 13, 2014

    one thing though.there is another article they did not take 75% of pi.and then again pi is constant for any circle .that not mean to find the pitch at the position 75% of(r) you take 75% of pi..for any circle what ever it is pi is the same pi which it is constant value ..

  31. Stefan Vorkoetter
    April 14, 2014

    Nabil, 75% of pi, times the diameter, is the same as pi times 75% of the diameter. I merely combined the 75% (0.75) with pi (about 3.14) so that one wouldn’t have to compute 75% of the diameter. That is,

    0.75 * pi * d = pi * 0.75 * d = 2.36 * d (approximately).

  32. Val Resnick
    June 04, 2014

    Stefan, I’m trying to design a ducted fan. It’s small. It is 30mm OD. with a 12mm dia. hub leaving small blades.

    Does the pitch start at the hub and go to the OD ?

    How would you calculate the pitch ? The same formula as above?

    I’m thinking I could use the tangent of the chord at 75% instead of h/w ?
    (I’m designing this in CAD)

    Thanks for your time.

  33. Stefan Vorkoetter
    June 04, 2014

    Val, the blade should be twisted, so that the pitch is constant. So you’ll get a different angle at each distance from the hub, but the pitch should remain the same. The only reason we use the 75% point for a propeller is because the blade is typically the widest there, or near there, thus minimizing measurement error.

    So to compute pitch at any given distance from the centre, use pi * d * height / width where d is the distance from the centre, and height and width are as measured at that distance. Or, as you’ve noticed, you can use tan(c) instead of height / width, where c is the angle of the blade.

  34. santhosh
    July 29, 2014

    Hello sir …may I know what kind of propeller used in mini rc hover craft for thrust and air bag fill up ..I’m dng mini project …I need ur help sir thanq

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