Just how much pitch
is required for a given engine/model combination is always
a bit of a puzzle. In Goodyear, props range in pitch from
4.5 to 6 inches, which is pretty wild for a standard model
class. Since pitch is the advance per revolution, ie, inches
moved forward in one turn of the prop, it seems likely pitch
may be related to airspeed and engine RPM. Recently New Zealander
Bill Sayer was kind enough to send me some data on propeller
wind tunnel tests performed in 1934, at the National Physical
Laboratory in England. This data was comprehensive, and suggestive
of a simple formula for pitch.
Since I cannot pass up a formula without sticking it in my
computer, I thought I might share it with readers of VCLN.
Given a velocity V in metres per second, and revolutions per
second n, then the face pitch P in metres (face pitch is measured
to the flat on the bottom of the airfoil at 70% radius) is
given by:
P = V / (.9 X n)
Consider a stunter doing 60 MPH with an inflight RPM of 10000.
Then:
V = 60 * .453 = 27.2 metres per second
n = 10000 / 60 = 166.6 revs per second
P = 27.2/(.9 X 166.6) = .181 metres
and:
P = .181 / .0254 = 7 inches
This seems a little high, but the test propeller at NPL was
only 10% thick at the 70% radius. Since thin propellers behave
as though they had less pitch, this is probably OK. I recall
Steve Rothwell telling me that his props behaved as if there
was no slip. That is , the speed could be calculated directly
from the face pitch . Professor Larrabee also made a similar
comment, in that sections typical of model propellers, being
about 13% thick, had a lift coefficient of .5 when the blade
was set at zero degrees to the bottom of the airfoil.
Thus Steves formula would be:
P = V / n
and, for the above example,
P = 27.2/ 166.6 = .163 metres
and:
P = .163 / .0254 = 6.4 inches
which also seems reasonable !
Also in the article was an expression for the speed at which
zero thrust is generated. This is useful because it gives
the maximum possible speed the propeller can provide at a
given RPM. If some competitor claims to be going faster than
this, you can make with some confidence uncouth suggestions
to him.
The formula is bit messy, but if D is the prop diameter in
metres then the maximum velocity Vo is given by:
Vo = n X D X (P/D + .151) / (1  .042 X (P/D))
If the prop in the example above had a diameter of 11" (.279
metres) then:
P/D = .163 / .279 = .584
P/D + .151 = .753
1 .042 X .584 = .9755
and:
Vo = 166.6 X .279 X .753 / .9755 = 35.88 metres per second
or 79 MPH.
The data also revealed a maximum efficiency of this propeller
for the above normal flight conditions of 76%. That is,the
engine power lost to kinetic energy of the slipstream was
24% of the total. Nothing can be done to improve this, no
matter how carefully the propeller is shaped. Thrust is generated
by increasing the velocity of the airstream passing through
the propeller disc, and as soon as you do this you have lost
energy to the slipstream , a real Catch 22 situation !
The data also revealed a very surprising (to me, anyway) situation
with respect to the highest efficiency obtainable. The propulsive
efficiency of a propeller depends as much on the conditions
under which it operates as it does on its actual shape. It
appears that the highest efficiency with the pitchadjustable
propeller tested was 86%, and this occurred at the staggering
P/D of 2.5 ! So for the 11 X 6.4, you may really want a 4.4
X 6.4 !
Not really, but at higher speeds there is no fundamental reason
why the pitch cannot exceed the diameter by a factor of 2
or more: this was certainly the case with the later Schneider
trophy racers, and I suggest you look at photos of Rare Bear
, or bear Bear (Tu 95), at speed, the pitch is colossal. Do
give Steves formula a shot; maybe for your thickness props
you may need to do a bit more adjusting. I'm sure readers
of VCLN would like to know how you get on.
