# Wooden Blades and the Stability of Ken Wallis' gyros

#### kolibri282

##### Super Member
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.

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)
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

#### Attachments

1.3 KB · Views: 9
Last edited:

#### Tyger

##### Super Member
I find Magni's solid/composite blades to be very stable. I can also easily fly hands and feet off in level flight (unlike Wallis, though, I've got a large stabilizer in back). I wonder how their blades would look in your analysis program.

#### C. Beaty

##### Gold Supporter
A nose heavy rotorblade behaves no differently than a nose heavy airplane where the center of lift trails the CG. It tends to hold its position with respect to the relative wind for the same reason.
With sufficient torsional flexibility and nose heaviness, a rotor won’t respond to hub tilt at all.

Last edited:

#### kolibri282

##### Super Member
If you could provide the mass and location of the balancing weight plus the shear modulus of the material and the wall thickness along the blade it would be technically possible to calculate the torsion of the Magni blades, Tyler, but since modern blades are specifically designed to have as little torsional twist as possible that would not be of great use and my program actually is not suited for the job. You'd need a Finite Element Program for that. What is peculiar about Ken's blades is the large distance (=lever arm) of the balancing weight combined with the very low shear modulus of wood. Both elements are missing in the Magni blades.

Last edited:

#### kolibri282

##### Super Member
Quote: A nose heavy rotor blade behaves no differently than a nose heavy airplane where the center of lift trails the CG. It tends to hold its position with respect to the relative wind for the same reason. /Quote
What makes things difficult, Chuck, is that, if my idea is correct, the angle of attack would be reduced by the blade torsion when the blade is traveling towards and away from the lower max angle and increased while traveling towards and away from the upper max flapping angle. I currently have no idea how to assess the combined effect of the two on rotor and flight stability. The best way would be to have a highly instrumented Bensen and test fly it extensively with both wood and metal blades (but that has to wait until I win in a lottery big time...;-)

Last edited:

#### C. Beaty

##### Gold Supporter
Cyclic flapping produces constant lift via angle of attack variation upwind vs downwind. If it didn’t, we’d be in a heap of trouble.

#### kolibri282

##### Super Member
The question is, whether the additional cyclic angle of attack variation brought about by the torsion due to the nose weight does in some way increase rotor damping or in some other way increases aircraft stability. One indication could be gleaned from the analysis of accident data. If for Bensen type gyros certain types of accidents, e.g. PIO, would occur significantly less frequently with wood blades than with metal blades that would support my idea.

Last edited:

#### Jean Claude

##### Junior Member
The stability of the rotation plane in space is due to the gyroscopic effect of the rotating masses.
The change of the tip plane is obtained by the cyclic control of the angle of attack of the effective zones (say > 3/4 R)
But this control is gived from the root of the blades.
Thus, torsionally flexible blades increase the damping.

The positive Cm of the blades produces an increased longitudinal flapping angle, for a given forward speed, due to the torsion of the blades.
Starting from a well-trimmed gyro, a small increase in forward speed will then greatly pitch the hub up by itself (free stick) and to return to the initial speed
Thus, blades with Cm>0 increase the forward speed stability

#### Jean Claude

##### Junior Member
Juergen,
Of course, the distance from the nose weight to the leading edge front increase the angular delay relatively to the cyclic plate due to the lack torsional stiffness of the blades. But:

Quote: "I have represented the blade by a single wooden spar 40x140 mm."
An equivalent spar of 17 x 100 mm seems to me more realistic, since the thick is 20 mm and the chord is 170 mm.
So, that's 15 times less stiffness isn't it?

Quote: "Gw = 176; % [N/mm^2] shear modulus wood"
The Young's modulus of wood is about 15 times less than steel. So, that's more like 13000 N/mm2, instead 175 N/mm2, isn't it?

Last edited:

#### kolibri282

##### Super Member
Thank you for your input, JC. To calculate the angle of torsion you need the shear modulus of the material, not Young's modulus. The shear modulus of pine wood depends upon the orientation of the wood grain. If you apply a torsional moment about the longitudinal axis, i.e. the axis along the grain, Table 1 of the paper below gives a value of 0.28 Gpa = 280 N/mm^2. The value of 176 N/mm^2 is valid for relatively soft pine wood and was one that I had used when I built a little test rig and applied a moment to a small batten of 7x20x400 mm and this value gave a reasonably close agreement with the torsional angle I measured. Since Ken Wallis' blades are not from natural wood but some sort of compressed wood (Hydulignum) you are right and the value of 176 N/mm^2 is quite likely too low indeed but I had plugged in these values just to see whether that would get me in the ballpark. The cross section of 40x140 was selected to be on the safe side, I was aware that it was probably way too much.

The values for shear modulus in the two other directions of pine wood are 1340 N/mm^2 and 1480 N/mm^2 according to Table 1 of the report.
If we assume that the rotor material has the highest of these values, 1480 N/mm^2, and take an equivalent spar of 20x110 mm the angle becomes 3.0° and with the cross section values you proposed (17x100) I get 5.3°. Thus my result of 2.7° is a fairly good ball park figure albeit one brought about by, what my mechanics teacher at university described as, a case of "Two times wrong gives a right in California" (Sorry to all Californians...;-)

Your example of a wing section with cm > 0 is helpful but there is a difference here. With a cm greater than zero the maximum torsion will occur at the highest flow speed ( i.e. on the advancing side of the rotor) and because the rotor is a second order system in resonance the maximum flapping angle will occur with a 90° phase lag, i.e. over the nose of the aircraft. The maximum angle of torsion from the nose weight occurs over the nose of the aircraft (from longitudinal flapping), so the rotor will tilt to the right (for a CCW rotor). As I said I have no idea how that behaviour relates to aircraft stability.

PS: the value for the mass of the nose weight 0.35lb is probably also too low

Last edited:

#### C. Beaty

##### Gold Supporter
As I recall, Wallis rotor blades were over balanced; they were fully balanced about their aerodynamic centers by internal balance weight and the external nose weights provided over balance, supplying increased stability at the cost of diminished agility.
A cutaway view of Wallis rotor blades was published on this forum several years ago.

#### kolibri282

##### Super Member
As you say, Chuck, the cutaway view of the Wallis blade shows an internal balancing weight, but that does, IMO, support my idea. If Ken Wallis was able to neutrally balance his blades internally it would have been much simpler to overbalance them by just adding a bit more mass, so why did he use an external weight? There is a fundamental difference between internal and external balancing. The internal mass is rigidly connected to the blade, thus the aerodynamic forces that move the blade up and down act directly on the balancing mass incrementally all along the blade plus the lever arm to the aerodynamic center is much smaller and so the moment by the internal balancing mass is quite small. As I pointed out in #1 negligible aerodynamic forces act on an external balancing mass and so it exerts a considerable moment which induces a noticeable cyclic twist. I would conclude that, if he used an external mass, he wanted to generate that effect. Finally I still feel that I have not completely understood the physics involved, because there is also the centrifugal force that ultimately keeps the blade from flapping up any further and that one, as is well known, actually exerts a moment on the blade that reduces blade twist. It remains an interesting problem.

Last edited:

#### Jean Claude

##### Junior Member
With a Cm greater than zero the maximum torsion will occur at the highest flow speed ( i.e. on the advancing side of the rotor) and because the rotor is a second order system in resonance the maximum flapping angle will occur with a 90° phase lag, i.e. over the nose of the aircraft. The maximum angle of torsion from the nose weight occurs over the nose of the aircraft (from longitudinal flapping), so the rotor will tilt to the right (for a CCW rotor).
The torsional resonance frequency of the blades cannot be confused with the rotation frequency of the rotor, Juergen.
Therefore, your conclusion about the maximum position of the torsion angle above the nose of the aircraft seems to me to be wrong

#### kolibri282

##### Super Member
Quote: The torsional resonance frequency of the blades cannot be confused with the rotation frequency of the rotor, Juergen.
Therefore, your conclusion about the maximum position of the torsion angle above the nose of the aircraft seems to me to be wrong /Quote

Perhaps something has gone pretty astray with the translation, JC. I didn’t say that the resonance frequency of the blade depends on the rotational frequency of the rotor. What I said is, that with a rotor the reaction always follows the applied force or moment by a phase lag of 90° since the rotor is a second order system in resonance, so maximum flapping occurs over the nose since the maximum moment from cm is applied at the point of maximum flow velocity, i.e. at psi=90°, where psi is the angular blade position and psi=0 is over the tail of the aircraft.

As for the position of maximum angle of torsion, if you refer to the case of the external weight (not the case of maximum moment due to cm) then I’ll stick by my guns. The maximum torsion of the blade due to the external weight takes place at the point of maximum acceleration due to rotor flapping, which is over the nose of the aircraft.

Last edited:

#### Vance

##### Gyroplane CFI
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°
In my opinion it is a mistake to equate hands off flying with stability.

Wallis WA-117 Autogyro G-AXAR: Written off (destroyed) 11/9/1970 when crashed whilst performing a demonstration flight at the 1970 Farnborough Air Show. The pilot, John W. Charles "Pee Wee" Judge (aged 48, at the time the Chief Test Pilot of Beagle Aircraft) was killed.

"The aircraft was being demonstrated at the Society of British Aerospace Companies (SBAC) air show at Farnborough. After a high speed downwind run parallel to the runway the aircraft first pitched rapidly nose-up, then nose-down, and went out of control, the rotor blades striking the propeller, fin and rudder as it fell to the ground. The pilot was killed instantly."

Last edited:

#### kolibri282

##### Super Member
I seem to remember that the pilot demonstrated some pretty advanced aerobatics. Perhaps this is the difference between static and dynamic stability? Of course Ken Wallis was an outstandingly gifted pilot but that is partly why I have opened this thread. How many members of the forum have been flying a Bensen type gyro hands off sitting side saddle?

#### Vance

##### Gyroplane CFI
I seem to remember that the pilot demonstrated some pretty advanced aerobatics. Perhaps this is the difference between static and dynamic stability? Of course Ken Wallis was an outstandingly gifted pilot but that is partly why I have opened this thread. How many members of the forum have been flying a Bensen type gyro hands off sitting side saddle?
I included the description of the event to show that Mr. Judge was not doing anything that could be described as aerobatics by the FAA.

He was an experienced test pilot.

Ken Brock among many others demonstrated hands off flying in a Bensen style gyroplane that some would suggest were not stable gyroplanes.

As experienced test pilot Jim Mayfield would say: “stability is not an opinion.”

#### kolibri282

##### Super Member
1. G-AXAR just before the accident was flying at some 92 knots EAS and at that speed a relatively small relaxation of the push force required to maintain level flight such as to allow the control column to move aft one inch, could account for the last steep portion of the climb. To recover, the aircraft could have been flown out of this manoeuvre by increasing the bank angle and executing a “wing over” to maintain positive “g”. In the event the pilot moved the control column rapidly forward.

2. Once full forward control had been applied and sustained for approximately one second the aircraft was pitched rapidly nose-down the pilot would expect to try to counteract the motion as soon as the aircraft appeared to him to have recovered from the steep nose-up attitude which had caused him to move the control column forward in the first place. Some 4.76 seconds before impact the rotor head did, in fact, tilt fully back indicating that the pilot had moved the control column fully aft. However, the rotor rpm had by this time started to fall, negative “g” having unloaded the rotor, and as a result of the consequent reduction in control effectiveness the aircraft did not respond, continued to pitch nose-down until it reached the vertical and the rotor blades came into contact with the aircraft structure.

Quote: Mr. Judge was not doing anything that could be described as aerobatics by the FAA /Quote
From the description above it seems that the pilot was flying the aircraft at the very limit of the flight envelope and instead of opting for a safe wing over manoeuvre tried to force the aircraft forward entering negative g so this seems a case of "don't do this at home, kids".

https://aviation-safety.net/wikibase/19511

#### Vance

##### Gyroplane CFI
1. G-AXAR just before the accident was flying at some 92 knots EAS and at that speed a relatively small relaxation of the push force required to maintain level flight such as to allow the control column to move aft one inch, could account for the last steep portion of the climb. To recover, the aircraft could have been flown out of this manoeuvre by increasing the bank angle and executing a “wing over” to maintain positive “g”. In the event the pilot moved the control column rapidly forward.

2. Once full forward control had been applied and sustained for approximately one second the aircraft was pitched rapidly nose-down the pilot would expect to try to counteract the motion as soon as the aircraft appeared to him to have recovered from the steep nose-up attitude which had caused him to move the control column forward in the first place. Some 4.76 seconds before impact the rotor head did, in fact, tilt fully back indicating that the pilot had moved the control column fully aft. However, the rotor rpm had by this time started to fall, negative “g” having unloaded the rotor, and as a result of the consequent reduction in control effectiveness the aircraft did not respond, continued to pitch nose-down until it reached the vertical and the rotor blades came into contact with the aircraft structure.

Quote: Mr. Judge was not doing anything that could be described as aerobatics by the FAA /Quote
From the description above it seems that the pilot was flying the aircraft at the very limit of the flight envelope and instead of opting for a safe wing over manoeuvre tried to force the aircraft forward entering negative g so this seems a case of "don't do this at home, kids".

https://aviation-safety.net/wikibase/19511
It is amazing that the person writing that description imagines he knows what was in Mr. Judge’s head and knew what he was doing with his control inputs.

Even if that is what Mr. Judge did that would still not be considered aerobatic by the FAA for rotorcraft.

I don’t know what you point is Jurgen.

It appears to me that Wallis WA-117 Autogyro G-AXAR was not dynamically stable despite being able to fly it hands off and feet off.

I can tell you that changing the rotor blades on a gyroplane will change the handling.

I don't pretend to know why.

#### kolibri282

##### Super Member
Nor do I, as I have pointed out several times in this thread. I just made an observation which I thought might lead to some new insight if all the knowledgable members of the forum contribute, even if it turns out in the end that the idea was wrong. Good science comes from asking good questions, the Nobel prize comes for finding good answers. Unfortunately I have not yet arrived at the "good answers" stage...;-)

Last edited:

Replies
29
Views
855
Replies
15
Views
1K
Replies
8
Views
1K
Replies
1
Views
146
Replies
45
Views
2K