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Propeller Dynamics

Essential reading for model aircraft contest fliers. This is the only book on the market explaining propeller theory in non-mathematical terms. A rattling good read, I know, I wrote it.


The Breguet range equation


Getting speed in F2C and Bendix is not too hard, but getting range to match is another matter. We need to examine the parameters which affect an aircraft's range, and these may be found in the classic Breguet range equation: 

Range = 375 * (n / sfc) * (L/D) * ln(gross weight/empty weight)

Here, range is in miles, n is the propeller efficiency and sfc the specific fuel consumption. The term (L/D) is the aircraft lift-to-drag ratio, and ln stands for logarithm to the base e.

In an aircraft like Rutan's Voyager (range 25000 miles non-stop around the world), the last term in the equation above required the aircraft to lift 4 times its own weight in fuel! Definitely not an option in F2C !

Thus, we need only consider the remaining terms n, sfc and L/D. In an aircraft like Voyager, the wing design determines the greater part of L/D. However, for F2C or Bendix, line drag has a profound effect on the value of D. Clearly drag must be minimised, especially in Bendix style aircraft where the rules set out to make the fuselage a large source of drag.

Low sfc means the engine should not leak raw fuel, or shovel raw half-burnt fuel out the exhaust port. This leaves propeller efficiency as a determining factor to be considered in obtaining range. Unfortunately prop efficiency is a complex topic to be treated on its own, which I will treat in another issue. However, for the moment here are some pointers, in order of importance, for F2C and Bendix:

1. The high drag in the vicinity of the engine and fuselage means that the airflow velocity over these components is less than the free-stream velocity. This reduction in axial velocity is seen even before the air reaches the propeller. Consequently, the pitch of the propeller in the root area must be reduced to match the slowed inflow. This is not a trivial effect, the pitch must be markedly reduced, the more so for Bendix than for F2C.
2. The propeller must have good airfoils. Symmetrical airfoils have poor L/D's, while rearward high points give poor acceleration from a standing start. Well-cambered airfoils with high points at 30% or less are required. An airfoil sculpted-in with a file can never consistently match a machine carved airfoil. This is one of the reasons APC props are such splendid performers, their airfoils are excellent.
3. The pitch must be a reasonable match for the airspeed and RPM, although there exists a considerable range of tolerance over which pitch variations have little effect. Some argue that lower pitches are better in traffic, as the model is then flying in disturbed air which reduces propeller thrust. It sure does, but I would rather have a pilot who could change the altitude enough, just a few inches, to get out of this wake.
4. The diameter likewise is not a critical factor, especially in high speed aircraft like F2C and Bendix. Normally one tries to maximise diameter as this maximises acceleration from a standing start. However, when the speed exceeds about 20 MPH, the effect of diameter is minimal and quite amazingly small diameters can suffice, even 5.5" for F2C is acceptable.

To retain the acceleration, such a small prop must have a well forward airfoil high-point. Well that ended up being a bit of a lecture, I wouldn't mind betting some of you race-hardened pro's out there don't agree with all of that. 
Next month: The Prop Doctor makes a house call !

If you have a question on props, send it to Supercool, c/- 42 Hepburn Way, Balga 6061 WA , or Fax it on 08 9247 2481.

Best question as judged by me wins a copy of my book "Propeller Dynamics" or propellers to the value of $30 (G/Y, Bendix or F2C). I will offer the question and reply to the Editors for their consideration to print. Your name will be used, no anonymouse please.

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