Last month, we looked at gyroplane flying qualities and considered the case of a gyro with no horizontal tail. Such a machine has some unusual characteristics, as shown in Figure 1, which is repeated here from last month. In order for the machine to be in trim, the rotor thrust vector (RTV) has to pass through the CG, and this is only the case at one rotor incidence. This means that the gyro will be neutrally stable in pitch and only in trim with the stick at one position.
In flight, the pilot will be moving the stick continuously in a series of small inputs, first one way and then the other, to keep the pitch rate near zero and hold attitude. Since the gyro is neutrally stable, pitch rates will not die off by themselves, and the pilot will be called on to actively augment pitch stability at all times. The pilot cannot simply trim for a different airspeed by changing the stick position and letting the aircraft’s stability cause it to settle at a new trimmed condition, as is the case for a stable fixed-wing airplane.
History has proven that such a vehicle is flyable, but it also has a very high pilot workload, which is undesirable. The situation gets worse as speed increases. A given stick movement commands more moment the faster the machine is flying, so the pilot will feel pitch control getting ever more sensitive as speed increases. It’s likely that this increase in pitch sensitivity with speed is why the gyro “pitch-porpoise” type of mishap became more common as gyroplane performance increased.
Figure 1: With 7.13 degrees rotor incidence, this tailless gyro is in trim. When the incidence is 9.13, the nose is pointed up, and with an incidence of 5.13, the nose is down.
It’s highly desirable for an aircraft to have enough positive pitch stability that the pilot can command an angle of attack or airspeed by moving the stick to a trim position and holding it there. A horizontal tail can provide this stabilizing effect.
As we saw last month, the rotor thrust vector always acts normal to the plane of rotation of the rotor. Accordingly, it cannot simultaneously trim and stabilize. For trim, the RTV must pass though the CG. In this condition, changing angle of attack of the vehicle changes the rotor lift, but does not produce any change in pitching moment.
If we add a horizontal tail aft of the CG, the lift of the tail changes with angle of attack of the vehicle. Increasing angle of attack increases the lift of the tail, which lifts the aft end of the fuselage, producing a nose-down moment that opposes the increasing angle of attack. If the angle of attack decreases, the opposite happens, and the tail produces a nose-up moment that tends to drive the vehicle back to its original trimmed angle of attack. In forward flight, a horizontal tail on a gyroplane has the same type of stabilizing effect that it would on a fixed-wing airplane.
The effect of adding a horizontal tail to our example gyroplane from Figure 1 is shown in Figure 2. This gyro is still using rotor tilt to control pitch, but now it has a fixed horizontal tail, set to trim the gyro at zero angle of attack at the same rotor incidence that the original gyro trimmed at.
Figure 2: adding a fixed horizontal tail to the gyro in Figure 1. It still uses rotor tilt to control pitch, but the horizontal tail is set to trim the gyro at zero angle of attack at the same rotor incidence that the gyro is trimmed at.
If we look first at the blue curve for 7.13 degrees rotor incidence, we can see a marked difference from the tailless gyro. The machine is in trim at zero body angle of attack, but now it is stable rather than neutral in pitch. If the angle of attack increases, there is a net nose-down pitching moment, and if it decreases, there is a net nose-up pitching moment. With the stick held fixed, the gyro will respond to perturbations by returning to its trimmed angle of attack.
Looking now at the other two curves, we can see the effect of moving the stick to change rotor incidence. The orange curve shows what happens if the pilot tilts the rotor back 2 degrees from the original position. The trimmed angle of attack moves from zero to about 9 degrees. The gyro is still positively stable, but the effect of moving the RTV forward of the CG is evident. Notice that the slope of the pitching moment vs. angle of attack curve, while stable, is shallower than the curve for the lower rotor incidence. Tilting the rotor back trims the machine to a higher angle of attack, but it also reduces pitch stability.
When we look at the bottom curve, we see the opposite effect. Tilting the rotor forward moves the RTV line of action aft of the CG. This causes a nose-down moment that leads to the gyro trimming at a lower angle of attack, but it also increases the slope of the pitching-moment curve, making the machine more stable.
The pitch stability of a gyro controlled by tilting the rotor is a nonlinear function of the position of the stick and the rotor incidence angle it commands. This means that a tail that is big enough to produce positive stability at one rotor incidence may not be big enough to maintain positive stability when the stick is pulled back to trim at a lower airspeed and higher angle of attack. The designer must take this into account when sizing the tail to produce positive stability over the entire flight envelope.
Another Way to Control Pitch
In forward flight, rotor tilt is not the only way to control a gyroplane in pitch. The early autogiros had no pilot control of the rotor. They used conventional airplane-style control surfaces on all axes. This worked well in forward flight, and contemporary pilots who have flown the few vintage Pitcairn autogiros that are still airworthy report that they fly pretty much like contemporary antique airplanes. The problem with using airplane-style control surfaces is that the rotor allows the gyro to fly so slowly that they become ineffective, and the early gyros had very little control in the last moments of the flare for a near-vertical landing. Converting to rotor control solved this low-speed control problem.
In retrospect, we can see that while using direct rotor control greatly improved the characteristics of a gyroplane in slow and near-vertical flight, it actually introduced some of the issues we have just discussed in faster, up-and-away flight.
Figure 3 shows what happens if we take our tailed gyro and use the horizontal tail to control pitch. For this example I have modeled it as an all-moving tail, but a fixed tail with an elevator would behave the same way. In this example, the rotor incidence is fixed at the angle where the RTV passes through the CG.
Looking at the three curves in Figure 3, we can see immediately that the behavior of this version of the machine is much more linear than the others.
Figure 3: the tailed gyro from Figure 2 using the horizontal tail to control pitch. This version of the machine will have more linear pitch characteristics and benign flying qualities than the other two configurations.
Two things are evident: First, the change in trimmed angle of attack with change in tail incidence is linear. Moving the tail forward by a given amount commands the same of angle of attack change nose-down as moving it aft the same amount commands nose-up.
Second, the slopes of all three curves with angle of attack are the same. Changing the tail setting changes the trimmed angle of attack, but does not change the underlying level of pitch stability.
These two characteristics mean that this machine will have more linear pitch characteristics and benign flying qualities. It will feel much more familiar to a fixed-wing pilot, and as long as the tail is properly sized, the pilot workload to control the aircraft in pitch will be similar to that of a conventional airplane.
Essentially all of the gyroplanes being made today, with the exception of a few high-performance experimental machines like the Carter Copter, rely on direct rotor control for pitch and roll control, even if they have large horizontal tails. In view of the more linear characteristics available from using elevators on the tail for pitch control in cruise, it might not be a bad idea for gyro designers to revisit the idea pioneered by Pitcairn and de la Cierva on their original machines.
Next month: thrust line.