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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.


Pitch comparison between propellers of different makes


In the February issue of VCLN, I noticed in Bendix Tales a reference to APC, Bolley and assorted unmentionable other brands of propellers.
This set in train a thought process that said:
" Can one compare propellers by their pitch ?"

Reaching for a bucket .. (relax, John) .. of broken propellers, I scraped the paint off them, then sliced through them at the 70% radius. This revealed all sorts of airfoil sections, some flat bottomed, some undercambered, some almost symmetrical. If one is to compare propellers by their pitch, then surely this polyglot of sections must confuse the issue: after all, if the performance of a propeller does not depend on its airfoil section, then what on Earth does it depend on ?

Furthering this spirit of enquiry, I measured the pitch at the 70% radius. Not entirely to my surprise, this pitch bore little resemblance in some cases to the manufacturers stated value. One 14 X 12 was a 14 X 14, and a 10 X 6 was a 9.7 X 7. If the manufacturer can't even state the correct value, what hope for the modeller ?

Clearly you need your own pitch gauge. The Prather is well known, and a similar unit is available from:
Edmunds Engineering in the US for US$50 (Fax: 0011 1 301-702-2136)
Then at least you can decide what the pitch is for yourself. In "Propeller Tips" last month I covered "face pitch", which is the pitch measured to the bottom of the airfoil at the 70% radius. Its a useful concept, especially if the blade is flat on the bottom, but gets confusing if the section is semi-symmetrical. Did you spot the deliberate error in that article. " slipstream was 34%" should have been "slipstream was 24%".

Slightly more useful is the "geometric pitch", which is the same as face pitch but measured to the airfoil chord-line, rather than the bottom. The chord-line joins the extreme trailing edge to the extreme leading edge. It has the advantage that it can always be measured, irrespective of the airfoil shape. Since nothing comes for free, it has the disadvantage that you have to eyeball just where you think these extreme points are: the TE is not so bad, but the leading edge is often round, making the chordline position there a bit of a guess.

Still, any guess is better than no guess.

But we still have not answered the question, which, in case you've glazed over, was "Can one compare propellers by their pitch ?". Unfortunately the geometric pitch doesn't help either, as the dependence on airfoil shape has still not been accounted for, yet.

This leaves "experimental pitch", which is the pitch (rough enough) measured this time to the zero-lift line of the airfoil. This time we've hit the jackpot .. propellers with the same experimental pitch will behave the same with respect to pitch, irrespective of the airfoil shape. This is because all airfoils produce about the same amount of lift for each increment in angle of attack: since we're starting at zero lift, they compare directly. Hence if you have more experimental pitch, that propeller will want to go faster.

Now if you thought measuring geometric pitch was a bitch, how on earth can you measure to the zero-lift line, when you have no idea where that is? It turns out that the zero-lift angle, measured relative to the chordline, can be easily calculated.

The formula for airfoil zero-lift angle is given by:
Zero-lift angle = arctan ( m /( 1 - p )) * 1.07

The symbol m is the airfoil camber, and is a number like .04 for a flat bottomed section, and zero for a symmetrical section. The camber line, like the chord-line, joins the extreme leading and trailing edge points, but not with a straight line. Rather, with a curved line that splits the airfoil neatly in twain. The maximum height of the camber line above the chord-line is the camber, and must be divided by the chord to get m. The symbol p is the distance of the camber maximum point from the leading edge, divided by the chord. It has a value like .3 or .4.

The value 1.07 is a fiddle factor to adjust roughly for variation of the formula between airfoils. Consider the famous Clark Y airfoil, often used for propellers, even to this day. Clark Y has camber .0355 and high point of .35 (near enough).

Zero-lift angle = arctan ( .0355 /( 1- .35)) * 1.07
= arctan ( .0546 ) * 1.07
= 3.126 * 1.07
= 3.34 degrees 

This agrees with Soartech 8 data, at a Reynolds number of 150000, which is useful for us modellers.

I leave it to you to relate this angle to the geometric pitch angle, and thereby derive the experimental pitch. Just remember that pitch is advance per revolution, you'll figure it out OK. Be careful with the above calculations, sometimes you get the answer in radians and have to multiply by 180/pi to get degrees, where pi = 4 * atn(1) or 3.141592.

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