Once you open the subject of can formed propellers you open a can of worms at the same time. In the simple approach the maths is not very accurate (and the propeller often isn't either) but if you try to improve the propeller with such things as cone shaped cans then the maths move to an area where most people don't care to go. However there are a lot of models flying around quite successfully where the can formed propellers follow the simple principles of sloping the blade at 15 degrees on the can and cutting away the root of the blade and mounting it on a spar. Following this simple approach we can get a ball park figure for your query about the can diameter in relation to the propeller diameter.
Most of the twist in a helical propeller occurs near the root. If the inner 20% of the blade is cut away then the twist over the remainder of the blade is close to 40 degrees for a wide range of P/D ratios. Let us assume that a can formed blade has a length of 40% of the full propeller diameter (i.e. 0,4D) and is twisted through 40 degrees (even though this twist will be linear and not helical. A look at the attached sketch will allow the following two equations for L to be written down:
L = 0.4D x sin15
L = (C/2) x (40/57.3) the 57.3 is required to change the degrees to radians.
We have two expression for L so these can be equated and rearranged to find C.
0.4D x sin15 = (C/2) x (40/57.3)
C = 0.297D
So typically the Can diameter needs to be nearly a third of the Propeller diameter.
However although that answers the basic question I would strongly recommend that you forget can forming and calculate a proper mould for a helical blade. It is actually much simpler than trying to make mathematical sense of can forming. Think of the embarrassment of trying to explain can forming to the students!
John Barker - England
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Received on Sun Jan 17 2010 - 13:01:12 CET