Efficient Propeller Design

Objective

The goal of this project is to investigate how changes in chord length affect the efficiency of propellers.

Introduction

A propeller, like an airplane wing, is an airfoil: a curved surface that can generate lift when air moves over it. When air moves over the surface of a moving propeller on an airplane, the air pressure in front of the propeller is reduced, and the air pressure behind the propeller is increased. The pressure imbalance tends to push the airplane forward. We say that the propeller is generating thrust.

The same principle applies to helicopter propellers, only now the propeller rotates around the vertical axis. The pressure on top of the propeller is reduced, and the pressure underneath is increased, generating lift.

The illustration below (Figure 1) defines some terms that are used to describe the shape of a propeller. The radius (r) of the propeller is the distance from the center to the tip. The chord length (c) is the straight-line width of the propeller at a given distance along the radius. Depending on the design of the propeller, the chord length may be constant along the entire radius, or it may vary along the radius of the propeller. Another variable is the twist angle (β) of the propeller, which may also vary along the radius of the propeller.

Figure 1. Illustration of terms used to describe propellers. The radius, r, of the propeller, is the distance from the center to the tip, along the center line. The chord length, c, is the straight-line width of the propeller at a given distance along the radius. The twist angle, β, is the local angle of the blade at a given distance along the radius (Hepperle, 2006).

In this project you will investigate how changing the chord length affects the efficiency of the propeller. You will keep the other design features (radius and twist angle) constant, changing only the chord length of the propeller. To measure the efficiency of the propeller, you'll connect the propeller to the shaft of a small DC motor. You will use the breeze from a household fan to make the propeller turn, which will cause the shaft of the motor to spin. In this configuration, the motor will act like a generator. You'll monitor the voltage produced by the motor to determine the efficiency of the propeller.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

propeller terms:
- chord,
- radius,
- pitch,
- rotational speed (measured in revolutions per minute or RPMs);
airfoil,
forces on an airplane in flight:
- thrust,
- drag,
- lift,
- weight.

Questions

How do you think increasing the chord length will affect the efficiency of the propeller?

Bibliography

Wikipedia is a good place to start for basic information on propellers:
Wikipedia contributors, 2006. "Propeller," Wikipedia, The Free Encyclopedia [accessed November 21, 2006] http://en.wikipedia.org/w/index.php?title=Propeller&oldid=88680042.
You'll definitely want to check out the Propellers section (among others) of NASA's Beginner's Guide to Aeronautics. This site is packed with useful information on the science of flight:
NASA, 2006. "Beginner's Guide to Aeronautics," NASA Glenn Research Center [accessed November 22, 2006] http://www.grc.nasa.gov/WWW/K-12/airplane/guided.htm.
For more advanced students, these webpages on aerodynamics of model aircraft by Martin Hepperle will be useful. There is even a Java program that you can use to test your design ideas on the computer before building them:
- Hepperle, M., 2005. "Propulsion by Propellers," Aerodynamics for Model Aircraft [accessed November 21, 2006] http://www.mh-aerotools.de/airfoils/.
- Hepperle, M., 2003. "JavaProp - Design and Analysis of Propellers," Aerodynamics for Model Aircraft [accessed November 21, 2006] http://www.mh-aerotools.de/airfoils/javaprop.htm.
- Hepperle, M., 2006. "Propellers for F3D Models," Aerodynamics for Model Aircraft [accessed November 21, 2006] http://www.mh-aerotools.de/airfoils/pylonprops_1.htm#F3DOptimumPropeller.

Materials and Equipment

To do this experiment you will need the following materials and equipment:

four (or more) propellers:
- You'll need to make these with varying chord lengths (but identical radius and twist angles).
- One potential source for materials to make these can be found at Freedom Flight Models (scroll down to see the propeller kits).
- Another potential source for propellers would be a local hobby shop that sells airplane models.
- If you are handy with tools and experienced with model building, you could also try carving propellers from a soft wood, like pine. It takes quite a bit of skill and patience to keep the twist angle the same for the different propellers!
small 1.5-3 V DC motor (e.g., Radio Shack part number 273-223),
1/4 Watt, 4.7 kΩ resistor (e.g., Radio Shack part number 271-1124),
jumper leads with alligator clips (e.g., Radio Shack part number 278-1156),
digital multimeter (e.g., TM-162 from TechBuys.Net),
fan.

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Experimental Procedure

Do your background research so that you are knowledgeable about the terms, concepts, and questions, above.
First you will need to make four (or more) different propellers, keeping the propeller radius and twist angle (pitch) constant, while systematically varying the chord length.
For testing, attach a propeller securely to the shaft of the DC motor. Depending on the materials used for the propeller, it could be taped on to the motor shaft, or drilled and press-fit.
Connect the 4.7 kΩ resistor across the terminals of the motor, and also connect the terminals to the voltage inputs for the multimeter.
Turn the multimeter to read DC volts, in the range for tens of millivolts.
Starting with the fan on low speed, hold the propeller/motor assembly in front of the fan. You'll want to test in the exact same spot each time.
The propeller may need a small push to start turning in order to overcome the internal friction of the motor. The moving air from the fan should keep the propeller turning after this. If not, turn the fan to the next speed and try again.
Observe and record the reading from the multimeter in a data table in your lab notebook. The reading will fluctuate slightly. You can round the reading to the nearest millivolt. Note that the reading will be quite sensitive to distance from the fan. Make sure that all of your measurements are taken at the same distance from the fan.
The mounting of the propeller to the motor may also affect the reading. If you are taping the propeller in place, you should repeat your measurements after removing and remounting the propeller to see how consistent your results are.
Repeat the measurements for each propeller.
Calculate the average voltage reading from the measurements for each propeller. More advanced students should also calculate the standard deviation.
Make a graph of the voltage produced (y-axis) vs. chord length of the propeller (x-axis). Is there a systematic relationship between chord length and rotational speed of the propeller?

Variations

Test different propellers with different chord lengths while holding twist angle and mass of the propeller constant. To keep the mass constant, you will need to reduce the radius somewhat as the chord length increases. Do you find the same results as when the radius was held constant? Why or why not?
Test the propellers at different fan speeds and compare the results. Do the same relationships between the propellers hold at all fan speeds?
There are a number of possible variations on this project. Instead of examining the effect of the propeller's chord, you could investigate:
- twist angle (pitch), Freedom Flight sells a handy jig for measuring the twist angle of a propeller (see Figure 2, below), or you could make one of your own.
  Figure 2. Propeller pitch gauge from Freedom Flight Models.
- airfoil shape (camber of the propeller),
- blade shape,
- number of blades,
- sweep (like a swept wing).
This project uses an indirect method for measuring the propeller's rotational speed. Devise a way to measure the thrust produced by the propeller directly. For example, you could design a low friction mount for the motor that allows the motor to slide back and forth (along the propeller mount axis). Connect the motor to a gram spring scale to measure the force produced when the motor turns the propeller. How does thrust produced change with voltage applied to the motor? (Increasing voltage increases the rotational speed of the propeller.) How does the thrust measurement compare to the rotational speed measurement from this project?