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Faulty Rule Of Thumb

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About a year ago, a thread began whose topic was “Rules of Thumb”. The RoT stating that as far as the B206 is concerned, 1% torque equals about 30 or 32 pounds of thrust. This is incorrect. The following is in the interests of safety.


Two textbooks on helicopter aerodynamics, one by W. Johnson and the other by J.G. Leishman, as well as a Wikipedia article (Disk Actuator Theory, show that the power required to produce any given thrust is proportional to the thrust and the density of the air in a manner similar to the relationship between lift and airspeed. Lift is proportional to the square of the airspeed. Power is proportional to thrust raised to the 3/2 power and inversely proportional to the square root of the air density.


Power (is proportional to) (Thrust ^(3/2)) / (Density ^(1/2))


As with most things aeronautical it is a bit more complicated than that. In order to compute the absolute power required by a helicopter engine to produce a given thrust at the main rotor in an out-of-ground-effect hover, other quantities are required, amongst which are the areas of the main rotor and tail rotor discs, the figures of merit for the main and tail rotor (different for every machine), the density of the air and the distance between the main rotor drive shaft and the tail rotor drive shaft.


If the power required to produce a given thrust is known, then the power required to produce a greater or lesser thrust can be computed, not precisely, but more accurately than the answer provided by the erroneous rule of thumb.


When the ratio two power requirements are compared with the ratio of the thrusts they produce, most of the variables cancel out, providing the only things that change are the power and the thrust


If the gross weight of the helicopter is accurately known (standard passenger weights do not work) and the torque required to hover out-of-ground-effect is known, then the power required to hover out-of-ground-effect at a higher gross weight is almost equal to the ratio of the two thrusts raised to the power of 3/2. The reason it is not more accurate is that a greater gross weight requires the tail rotor to produce more thrust and the power requirement for this is subject to the same relationship as the thrust-power relationship of the main rotor.


If a B206 hovers OGE at 85% and 3000 pounds then at 3350 pounds 100% torque is required, not including some small additional amount to account for increased tail rotor power. When tail rotor power is included, the torque required might be as high as 105%. The faulty rule of thumb would have us believe this could be done at about 96% torque.


If the density altitude changes as well as the gross weight the differences can be more dramatic.


The point is that the rule of thumb is unreliable and disk actuator theory is complicated, and neither is a substitute for the HOGE charts published in helicopter flight manuals.

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In my opinion Fred, you're not an (edited by twinnie), thanks for the detailed info. For most bush operations though you should have a pretty good idea if you can comfortably take off before you pull pitch. Your rough calculations should have more to do with all up gross weight and power required to hover IGE than worrying about any calculations with powers involved. Hovering IGE at 90% in a 206? You better have a runway or unobstructed departure ahead of you. Don't commit unless you know you can do it within limits. Avoid flying over gross as much as you can, cause it's your a$$ on the line.



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