kolibri282
Super Member
Ken Wallis has time and again demonstrated hands (and feet) off flying of his designs. He sometimes swung his legs to one side and took pictures with a camera (holding it in both hands) while his aircraft kept flying straight and level and, from what could be seen from outside, perfectly stable. Since he used the usual Bensen style H-stab, which, compared to today's designs, has a rediculously small tail volume, the stability must have come from another design feature of his machines. It struck me lately that Ken always used the same type of wooden rotor blades with a small nose weight to balance the blade chord wise at the t/4 line. The nose weight is offset from the CoG of the blade and thus it develops a moment about the longitudinal axis of the blade as it flaps up and down. In the attached program I have tried to calculate that moment and the blade torsion that results from it. The physics is IMO that, as the blade has flapped down to half its flapping angle (midway between max upper and lower position), the aerodynamic forces decelerate the blade until is stops at the lowest flapping angle but the nose weight is not decelerated by aerodynamic forces and thus tries to keep going downwards, twisting the blade nose down until the moment equilibrium is reached. This nose down attitude of the blade is maintained for some time as the blade is accelerated upwards. The acceleration becomes zero when the blade passes the midpoint between max positive and negative flapping angle and now the blade is again decelerated only that the nose weight now twists the blade such that the angle of attack is increased until the blade returns from the upper endpoint of its flapping arc to the midpoint once more.
It is well known that the aerodynamic properties of a blade section are altered quite a bit if the blade undergoes a rapid cyclic change in angle of attack. My idea is that this cyclic torsion of wooden blades somehow contributes to rotor stability. I must admit though that I currently have no idea what the physics behind that added stability might be.
My argument goes something like this:
- Ken Wallis' gyros exhibited great stability in straight and level flight without an H-stab
- Ken always used wooden blades of the same design
- The small program I attached shows that wooden blades, having a nose weight, undergo considerable
...twist, with the assumptions I made the value is 2.7°
I would very much appreciate if all of you could carefully check my calculation for mayor gaffes (e.g. order of magnitude error) and also on the general validity of the idea.
Looking forward to you comments.
Cheers
Juergen
PS: you can run the program in octave, the free Matlab(TM) clone. To do so you have to rename it to Wood_Blade_Tors.m
I have used the following properties:
I have represented the blade by a single wooden spar 40x140 mm.
nRot = 380; % 1/min rotational speed
R = 10*f2m; % blade radius 10 feet converted to SI (m)
btm = deg2rad(10); % maximum flapping amplitude angle converted to rad
l = 0.8*R; % station of nose weight
Gw = 176; % [N/mm^2] shear modulus wood
d= 0.08; % [m]distance from t/4 line to CoG of balancing weight 80 mm (about three inches)
mbw= 0.35*lbMass; % balancing weight= 0.35lb converted to kg
It is well known that the aerodynamic properties of a blade section are altered quite a bit if the blade undergoes a rapid cyclic change in angle of attack. My idea is that this cyclic torsion of wooden blades somehow contributes to rotor stability. I must admit though that I currently have no idea what the physics behind that added stability might be.
My argument goes something like this:
- Ken Wallis' gyros exhibited great stability in straight and level flight without an H-stab
- Ken always used wooden blades of the same design
- The small program I attached shows that wooden blades, having a nose weight, undergo considerable
...twist, with the assumptions I made the value is 2.7°
I would very much appreciate if all of you could carefully check my calculation for mayor gaffes (e.g. order of magnitude error) and also on the general validity of the idea.
Looking forward to you comments.
Cheers
Juergen
PS: you can run the program in octave, the free Matlab(TM) clone. To do so you have to rename it to Wood_Blade_Tors.m
I have used the following properties:
I have represented the blade by a single wooden spar 40x140 mm.
nRot = 380; % 1/min rotational speed
R = 10*f2m; % blade radius 10 feet converted to SI (m)
btm = deg2rad(10); % maximum flapping amplitude angle converted to rad
l = 0.8*R; % station of nose weight
Gw = 176; % [N/mm^2] shear modulus wood
d= 0.08; % [m]distance from t/4 line to CoG of balancing weight 80 mm (about three inches)
mbw= 0.35*lbMass; % balancing weight= 0.35lb converted to kg
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