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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.




From Graham Patterson of Upper Orara in NSW comes this months winning question, straight off the Internet. Over now to our patient.

Q. An article on the Internet was extolling the virtues of fitting an unbalanced propeller with the heavy blade opposite the piston at TDC to help balance the engine. My interest is in vintage team race engines with iron pistons: my question is whether a weighted hub or blade on the propeller would have any benefit or am I having myself on?

A. My diagnosis is idiopathic delusions arising from too much rotation at F2C speeds. In short, I don't know the answer to your question. The system you are describing is complex, involving a reciprocating piston, an oscillating conrod and rotating counterweights and propeller: all of these have some degree of elasticity, and I aint Euler or Newton. There is a theory that may help us to some degree, so lets consider.. With Mp the mass of the piston, r the crank length, w the angular velocity and that the momentary angle between the crank and line of motion of the piston, the primary disturbing force Frecip caused by motion of piston alone is given by:

Frecip = Mp * r * w * w * COS(t)

This primary unbalance could be cancelled by a second piston moving the opposite way, as in a horizontally opposed twin. However all we have is a rotating counterweight, so lets look at that. With Mb the mass of the counterweight, rb the length of the crank supporting Mb, then the centripetal force Fb due to this rotating mass is given by:

Fb = Mb * rb * w * w

This force has 2 components, one parallel to the line of stroke and
one across the line of stroke. These are in turn:

Fparallel = Fb * COS(t)
Facross = Fb * SIN(t)

To cancel out Frecip we want to use the countervailing force Fparallel, as these are oppositely directed. Thus we have full primary balance when:

Frecip = Fparallel

Substituting the above equations yields:

Mb * rb = Mp * r

This is fine, but we still have F across acting without any countervailing force. Things keep on shaking just the same, but in a different direction! The introduction of the rotating balance mass merely served to change the direction of the disturbing force from parallel to the line stroke to across the line of stroke!
It is preferable then to only partially balance the primary force.
Thus we set:

Mb * rb = c * Mp * r with c < 1

The number c is chosen arbitrarily, but the unbalanced force on the
engine mount is least when c = .5. Note that we have not considered the
unbalance due to the weight of the conrod. It turns out that a counterbalance for the rod must spin at twice the engine RPM, something of a nuisance, I think you will agree !

Now reconsider that unbalanced prop set opposite top dead centre. If we like , this can be considered an additional weight added to the counterbalance. It will therefore have the same characteristics, altering the primary partial balance. If the engine manufacturer has carefully set c = .5, then c will no longer have this value and force at the engine mount will be greater. According then to this theory, perhaps using unbalanced props may not be so smart: unless, of course, the manufacturer screwed up anyway.

This may well be the case. Graham points out that Metkemeyer and Flores of FMV T/R fame had to go to great lengths with tungsten counterweights to achieve c = .5 However, there is more to this story. At least the counterweight is almost in line with the reciprocating mass of the piston, and is thus slightly dynamically unbalanced on the shaft axis. But the propeller unbalance weight is well forward of the piston, by the length of the shaft, so there is a couple formed between the piston and the prop unbalance.

This couple introduces a rocking mode of vibration, and I think we
don't really want to add new modes of unbalanced vibrations ! Indeed,
if we want to improve the piston/counterweight dynamic balance, the heavy prop tip should be on the same side as TDC !Perhaps one could conclude, for prop imbalance opposite TDC, that primary balance may be improved for engines with c somewhat less than .5, but possibly at some small expense of dynamic balance , which loads the front and rear bearings. It may well be worth a try !

To finish off,I will dwell briefly on the 3 modes a propeller must be balanced. Firstly, if you set your prop horizontally on the balancer and file the tips to get balance, you have achieved radial static balance. My feeling is that this is the most important balance mode, despite the Internet ravings. Secondly, you may set the prop vertically on the balancer and remove material from the sides of the hub, so that the prop stays vertical. This achieves lateral static balance.
Thirdly, you may spin the prop and check the tracking of the tips. By removing facing material from the hub, you can get the tips to track true. You have then (hopefully !) achieved dynamic balance. I know Merv Bell, with his superb propellers, took great pains with this tracking.

Well I hope you are feeling better now Graham, those Internet viruses can be hard to shake off! Let me know what you would like as a prize to the value of $30 of Supercool props or my book Propeller Dynamics. So readers do send in your questions, give the Prop Doctor a call, maybe you could win ! 

Reference: Machine Design 2, Volume 2, P. Weir, 1983.

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