#46




Incidentally, the imperial unit of force that would produce an acceleration of 1 ft/sec˛ on 1 pound of mass is called the poundal.
It predates the SI unit of force but is rarely used. 
#47




Thank you Chuck, the converter is really neat. I have actually been using it for some time but it doesn't have spring rates. Do you think that Dino's suggestion of something like 60 lb/inch is right? As I said it sounds rather low to me.
Thank you Javier, the value I had was 1073 so the conversion seems ok, the remaining question being whether the trim springs used on a Bensen are that stiff. I calculated the value on the assumption that the back flapping of the rotor due to a gust should be compensated by a tilt of the no feathering plane. Last edited by kolibri282; 01082017 at 12:53 PM. 
#48




It seems that one error in my calculation has now been eliminated. I had used derivative values divided by rotor solidity, but the thrust factor was based on disc area, so my result would have to be multiplied by rotor solidity which for the Bensen is 0.0326 and now I end up with a spring rate of 35 N/mm or 200 lb/inch.

#49




In terms of total force at the trim spring attachment point at the rear of the torque bar, it is in the range of 10 lbs.
It is highly dependent upon pitching moment coefficient of the rotor blade airfoil. Bensen wooden rotor blades had excess reflex and seldom needed any sort of trim spring for “hands off” flight at 50 mph. There are some metal rotor blades with a negative pitching moment so high as to require a reduction of offset between spindle axis and pitch axis to be manageable with a reasonable trim spring. 
#50




Here is my calculus of the angular movement for an Bensen's head, balanced by a spring. It assumes, like any calculation of derivatives, that the tip path plane does not have time to change between F1 and F0:
Then, the result gived by my spreadsheet Excel on a Bensen B8, with and without this movement: Fix stick gives almost neutral stability. Free stick gives a good stability between 0 and 100 mN/rd of stiffness (difference are small) Do not forget, Juergen, that the spring should not interfere too much the movements given by the pilot (about 10°), hence k < 100 mN / rd Last edited by Jean Claude; 01192017 at 06:41 AM. 
#51




Thank you for posting your very thorough analysis, JeanClaude! I converted my value of 35 N/mm to Nm/rad for the dimensions of the Ken Brock rotor head and ended up with about 1000 Nm/rad. This is consistent with Dino's statement that my initial value was too large by two orders of magnitude so the revised value is greater by one order of magnitude. I assume that the value actually used by Ken Brock is a compromise found through experiment. There is one slight difference in our approaches: while you considered a vertical gust I considered the case of a horizontal gust, which would cause a rotor without a spring to flap backwards. I understand that one of the main goals of entering the spring was to reduce back flapping if the aircraft flew into a horizontal gust. I had started to implement the trim spring in my model but got stuck at one point and am now waiting for the dust to settle to the point where I can see the solution. This worked quite well on numerous occasions in the past and if it doesn't this indicates that I still know to little about the problem.
I wonder, JeanClaude, what equation you used to plug your results into and obtain the time history. This would have to be some sort of partial differential equation, yes? Currently I am clarifying a few details regarding the stability equations since my stability derivatives start to look quite good for the best models I have right now. 
#52




Quote:
A sudden increase in the load produces an angular movement of the head which limits overloading by reducing the angle of attack of the disc. But a horizontal overspeed increases the longitudinal flapping, which somewhat attenuates the change in a.o.A mentionned above. However, this effect is beneficial to improve the stability of the forward speed on long period: The movement of the head changes the slope of the flight and so restores the initial speed. Quote:
 Tail moment around GC (included damping)  Rotor thrust moment around GC (included damping)  Pod moment around GC  Prop. thrust moment around GC  Angular acceleration of pod  Angular velocity of pod  Angular speed of Disc  Angular position of disc (A.o.A)  Rotor thrust  Acceleration of the rrpm  Rotor rpm  apparent g  Vz  Acc in X  Vx Each line using the precedent line results. So, 50 lines gives 5 first seconds Last edited by Jean Claude; 01212017 at 11:56 AM. 
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