Thread: Discussion Efficiency of a ducted fan
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Old Feb 01, 2008, 03:27 PM
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Edina, MN, USA
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Thrust Power Derivation

Thrust time velocity is all that's needed; doesn't even matter what units you use!

Since you're primarily making comparisons, and made via the same tools and techniques a simply "scaling" (multiplier) is good enough to get it into a resonalbe range.

Here's some info from one of the other posters here:

"For thrust measurement it's enough to hang the plane from the ceiling of your garage with two wires. The deflection from the vertical will give you the thrust, you don't need a scale (In any case upside down placement on a kitchen scale will only work if the there is no front intake).

For efflux speed measurements we use a $2 electric motor hooked up to an ordinary voltmeter. It needs to be calibrated, otherwise it will give you only relative speed measurements:

It's accurate enough to measure small deviations from uniform speed throughout the fan diameter.

Thrust=weight * tan (angle). So 45 degrees deflection -> thrust = weight etc.

(rpm of sensor probe microfan) proportional to (efflux speed) ;
also (voltage out) proportional to (rpm of sensor probe).

Thus measured voltage is lclose to linear in efflux speed. Static thrust can also be measured locally, it is proportional to the rpm^2 or measured voltage^2 .


And, I've posted this in the past:

"Thrust Power Derivation

Fundamentally, thrust is proportional to rpm squared times diameter squared >> T = rpm^2 * D^2. There’s a few constants that need to come along though: rho ()/density (temp & pressure effects), pi (), a prop constant, etc.

Most often the prop constant gets determined empirically, and is usually expressed in terms of Pitch and Diameter. The most common form for thrust though doesn’t use pitch, but rather diameter squared.

Using R as rpm from hence forth.

And then, most folks don’t talk about the fundamentals so what you’ll find written is >> T = k*D^4*R^2. A few folks write as suggested above T = k*P*D^3*R^2; not much difference when P and D are close in value, like a “square” prop 5x5.

Power is actually more important in understanding a prop’s performance in E-Flight, and is the parameter that the various Calc programs use to predict a configuration’s performance. Again, it is rarely shown in its fundamental form, being written typically as Watts = k*P*D^4*R^3.

By 1st principles power is velocity times thrust. Maybe you’ve noticed the real fundamental parameter by now – Velocity!

Thrust for any propulsion system (i.e. EDF, or rocket) written from 1st principles is k*rho*V^2*A^2 – velocity (e-flux) squared applied over an area squared.

A prop turns R into V >> V = k*P*R which leads to all of the above.

Pitch speed (velocity) is commonly calculated as P*R/1000 using pitch in inches; this is an approximation that neither applies a “k”, nor use the proper constants for unit conversion."
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