On 8 May Rob wrote: -- >>Good concept, but I think you have
made it more complicated than
it needs to be. Rather than calculating a moment arm from the prop
center to the wheel and then correcting the scale force to this moment
arm, you could simply use the moment arm between the scales and the
direct scale readings.
Thus: T = (dR + dL) * d/2 where "T" is in lb ft, "dR" and "dL"
are in lb and "d" is in ft.
HP is then simply T * rpm / 5252.
The answer should be the same either way.<<
(Rob was referring to a method given by Paul Lipps in a pdf
document attached to his 5 May LML posting.)
Rob, the answer would be the same only if the prop shaft were at
the same vertical level as the scales, an impractical situation. The
problem is that the force vector at the scale due to the engine torque
is normal to a line between the prop shaft and the scale, whereas the
scale is reading only the vertical component of that vector. And torque
being a force times a distance, the distance of importance in this case
is that between the scale and the prop shaft rather than its horizontal
component. As the thrust line goes higher, or the gear tread gets
smaller, the difference between the two can be substantial. Calculating
the actual vector and distance was the purpose of Paul's calculations
(complications?). Using the figures in Paul's sample calculation in his
attached pdf he calculated 159.4 hp. Your equations give 102.8 hp for
the same figures, for an error of 35.5 per cent. The theoretical error
between the two methods is 36.1 for his prop height and gear tread.
Actually, Paul's calculations aren't that complicated. Even the
mickey mouse calculator I got from my insurance broker does square
roots.
Charles Keller
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