Don, I've wanted to know for some time, which puts more stresses on the motor/gearbox, doing aerobatics with a non-folding prop, or with a folding prop?

From your description , I would think that the forces (not the stresses) on the prop would be higher for the more rigid non-folding prop.

From : Don Stackhouse

Neil, at first glance this one looks pretty easy, until we start looking at the details. (Right now most of you are thinking "OH NO, here he goes again!", and are hiding under your keyboards!)

In the case of the "rigid" prop, both blades generate centrifugal force, but that force in each blade is balanced by the opposite blade (you DID balance your prop before flying, didn't you??!!). In addition, angled airflow coming into the disc causes changes in the lift and drag of each blade at different sections of its rotation. These cause sideways loads and bending loads on the motor mounts, as I discussed in my earlier post about vectors and thrust lines. BTW, we're going to use vectors again in this discussion, so if you've forgotten the basics, you might want to go back and re-read that post.

Lets say the nose has just been pulled up at the beginning of a loop. As an individual blade starts downward on the right side of the disc (assuming this is a right-handed prop), it's moving both forward and down. It sees a slightly higher angle of attack, and a slightly higher airspeed. This results in a slightly higher thrust and a slightly higher drag for that blade. As it continues across the bottom of the disc, its angle of attack and airspeed decrease to normal, along with thrust and drag. As it goes upward on the left side of the disc, its angle of attack, thrust and drag decrease below normal, and they all return to normal again as the blade goes across the top of the disc. Since the changes in drag are in the plane of the prop disc, they cause a sideways force (upward in this case) on the prop hub. Because the trust is centered 3/4 of the way out on the blade (the aerodynamic center of a propeller blade is normally at the 75% radius, the blade C/G is usually at about the 30% radius), it has a moment arm, and therefore creates a bending moment on the hub and propshaft.

If the prop had an infinite number of blades, then the propshaft would see a once-per-rev bending moment and sideways load, and the motor mounts would see a steady bending moment and sideways load. Unfortunately, life isn't always that simple! We don't use props with an infinite number of blades, although in some regards some of the high solidity ducted fans with lots of blades might come close. With a typical 2-bladed prop, these sideways forces and moments exist when the blades are 90 degrees to the plane of the skewed airflow (horizontal in this example), but these forces and moments go away when the blades are in the plane of the skewed airflow (vertical in this example). Since this happens twice (once for each blade) during each revolution, the blades and the propshaft see a one-per-rev vibration, but the engine mounts see a two-per-rev vibration. The variations in drag forces also cause a bending stress in the prop hub due to torque variations, but because the blades are doing nearly equal and opposite things at all times, that normally does not cause any significant torsional vibrations in the propshaft.

Because the prop is essentially rigid for the purposes of this discussion, the entire amount of sideways forces and bending moments are transmitted from the blades to the prop hub, and from there the ones that don't cancel each other out are transmitted from the hub to the propshaft and airframe. However, because the prop is rigid, the thrust line doesn't change angle. It moves laterally a little because of the greater thrust on one side of the disc than the other (the true thrust line is the centroid of the total thrust of the prop), but it stays parallel to the propshaft.

In addition to all this there are gyroscopic loads whenever the plane of the prop disc is rotating in space, such as during rotation on takeoff, or during a loop. When the attitude of the disc is constant, such as during a stable, constant pitch attitude climb, there are no gyroscopic forces to speak of. This is true even when the prop disc is tilted relative to the incoming airflow and making the aerodynamics related forces I discussed above. I won't go into the gyroscopic forces in detail here, because the low mass of most model prop blades keeps these forces very small in most cases. The armature of an electric motor could in some cases add to the gyroscopic forces, but even then they are still likely to be negligible.

Full scale aircraft are another matter entirely, which is why they can do Lomcevaks and other gyroscopically driven maneuvers, that models can normally only pretend to do. That's right, in general the vast majority of models find it difficult or impossible to do true Lomcevaks because their props aren't heavy enough (For those of you not familiar with the Lomcevak family of maneuvers, I recommend you find a copy of Neil Williams' book "Aerobatics". Besides being my all-time favorite of all aerobatics books, it has an entire chapter on Lomcevaks). This is also why snap rolls and Lomcevaks have a well-deserved reputation on full scale aircraft for damaging prop hubs, fatiguing and snapping hardened alloy steel crankshafts, and occasionally ripping entire engines right off of their mounts! Let's just all be thankful that here in the modelling world it's usually safe to ignore these forces.

This pretty well covers the forces involved on so-called "rigid", non-folding props. Now we can look at the more complex (OH NO!!) situation of a folding prop.

With a folder, we generally have to consider three possibilities:

Case 1. The blades have stops that limit their travel, and the forces that act on the blades in flight are always holding the blades firmly against the stops. This is the easy one, it acts just like a rigid prop. See above,'nuff said. (That was almost TOO easy!) To borrow from an old Clint Eastwood "spaghetti western", this one's the "Good".

Case 2. The blades don't have stops, or at least they don't ride on them in flight. This one's the "Bad"; this is where it starts getting complicated.

If the blades are free to "flap" (the term used in the helicopter world for blade motion perpendicular to the prop disc; "lead-lag" is motion in the plane of the prop disc), then (assuming friction in the pivots is negligible) they can't transmit bending moments through the hinges in their roots.

Now for the tricky part: just because the blades can't transmit bending moments through the hinges in their roots doesn't necessarily mean that they can't transmit bending moments to the hub!

The hinge doesn't transmit MOMENTS through it (other than via friction, which we will ignore for this analysis), but it does transmit any and all side FORCES, such as centrifugal force ("CF") and forces in the flapping direction (such as thrust). In addition, the typical hinge on a folder behaves like a rigid joint for forces in the lead-lag direction, such as the torque reactions of the blades.

If the hinge pin goes through the center of the prop shaft, then the blade can't transmit any moments to the propshaft either. Unfortunately, most (if not all) folders aren't made that way. Each hinge pin is normally on the end of an arm, out near the rim of the spinner. When the blade on one side of the disc sees its angle of attack and airspeed increase, it starts moving forward. The forward motion reduces the angle of attack, and at the same time moves the blade's C/G forward. This causes the CF of the blade to have a rearward component. When the blade has tilted far enough that the CF moment exactly cancels the forward moment due to thrust, the blade is in equilibrium. On the other side of the disc, where the thrust would normally be reduced, the blade starts tilting back, reducing the moment due to CF exactly enough to keep the blade in equilibrium. The net effect is to tilt the entire prop disc away from the initial angle of attack of the disc. For example, if we pull the nose up at the beginning of the loop I described above, the prop disc will tilt "nose-up" at an even greater angle.

This tilting causes two side effects. Since thrust is perpendicular to the prop disc, and the prop disc is no longer in the same plane as the prop shaft and hub, then the thrust line is not parallel to the prop shaft anymore. The perpendicular distance between this new thrust line and the C/G of the aircraft is not the same as before, and may cause some truly wierd changes in the trim of the aircraft. For a tractor aircraft, this will tend to be de-stabilizing, while for a pusher they will tend to increase stability. If you have a free-floating folder like this on a tractor aerobatic model, things like spin recovery could get VERY interesting to say the least!

The second side effect is because the CF of each blade is parallel to the prop disc. Since the disc is now no longer parallel to the plane of the prop hub, the CF of the blade is now pulling at an angle on its arm of the hub. This means that even though no moments are transmitted through the hinge itself, this angled force on the hinge is transmitting a bending moment into the hub arm and prop shaft. Whether this is larger or smaller than the moment for a rigid prop will depend on the design of the prop. In general, the longer the offset distance between the prop shaft and the hinge, the greater this moment will be. BTW, this hinge offset and the resulting moment is typically a key parameter in the stability and control response of helicopters and autogiros that use fully articulated main rotor hubs.

This flapping-induced bending moment follows the same general rules as the 2-per-rev vibrations I discussed above for the "rigid" prop.

Case 3. The blades have stops, but they ride on the stops for part of their rotation, and float aft during the other part. This one's the "Ugly"!

During the part of its rotation that the blade is on its stop, it behaves like a rigid prop. During the other part of its rotation it floats on its hinge pin like the prop in Case 2. This means that the blades on one side of the disc are not following the same pattern as the blades on the other side, and therefore the torques, differential thrusts and CF's no longer balance each other. The CF on one side is pulling at a different angle than the other, the distance from the propshaft to the blade C/G is oscillating non-linearly in the fore-and-aft and the diameter directions, the moments of inertia of the blades are oscillating back and forth, creating torque oscillations, and the effective thrust line is wiggling all over the place! The prop acts like it's badly out of both static and dynamic balance. In addition, the blade flaps smoothly off of its stop on one side, but impacts when coming back onto the stop on the other side of the disc. This could create very dangerous stresses in the blades and hub. Next time you look at a Graupner folder, note how the blades are still angled quite far back when they are fully open, specifically to avoid this situation. By tilting them back, you actually have to get the blades on one side into a negative thrust situation to get the blades to come off their stops. It would take a very violent maneuver indeed to cause this while the blades on the other side were still making positive thrust!

In general, a Case 1 prop would have the same loads on the motor and airframe as a rigid prop, while a Case 2 folder would have different (probably lower in most cases) loads on the motor, but might be higher, and in most cases would probably have more profound effects on stability and trim than a rigid prop. A Case 3 prop is something to avoid, period.

One final comment on a related subject: A recent post commented that a slightly bent motor shaft could cause higher vibratory stresses in the prop. This is not directly true. An out-of-balance condition does not cause vibratory stresses in the prop, only a steady load in the direction of the unbalance. From the prop's point of view it's a "zero-per-rev" disturbance. The motor and airframe (which are not spinning with the propeller) see it as a one-per-rev vibration. The only vibratory stresses the prop would see are due to the vibratory responses of the motor and airframe feeding back into the hub through the propshaft. Still, I strongly recommend that you balance your props, and keep your shafts as straight as possible!

Don Stackhouse
DJ Aerotech