To further commemorate R&WI's 50th anniversary this year, we are sharing again the work of perhaps our most popular writer, rotorcraft aerodynamicist Ray Prouty. His 30 years of R&WI columns shared the wealth of aerodynamic knowledge that nurtured generations of rotorcraft engineers. Each week online, we will reprint a selection from those columns. If you have a favorite that you would like to see again or thoughts to share on Ray's musings, let us know.
You might remember your first experience with a toy gyroscope and the amazing things it did in apparent disregard for the obvious laws of nature.
It displayed remarkable stability. If it was set spinning horizontally, it wanted to stay horizontal no matter how you moved the support, but if you were determined to move the axis by brute force, the gyro moving in a strange way — at right angles to the applied moment. Even if you were later exposed to the gyroscopic equations and acquired a confidence in your ability to manipulate them, you were probably still vaguely disturbed by this device’s strange behavior (I know I was).
The disc of a spinning helicopter rotor certainly looks much like a toy gyroscope. So does it act like one? Yes and no. The reason for the “no” is the existence of very large aerodynamic forces on the rotor blades. As a matter of fact, if you remove the aerodynamics by running a rotor in a vacuum, it will demonstrate gyroscopic stability.
A rotor with blades hinged at the center of ration (such as a teetering rotor) as shown in the top part of figure 7-2. In a vacuum, there are no aerodynamic forces, only centrifugal forces acting in the plane of rotation, and these can produce no moments about the flapping hinges. If the shaft is tilted, no changes in moments will be produced and the rotor disc will remain in its original position as if it were a gyroscope. (Of course, if the rotor had had offset flapping hinges, as in the bottom part of Figure 7-2, the centrifugal forces would have produced moments that would have aligned the blades perpendicular to the shaft.)
A rotor in air
In air, the aerodynamic forces will cause any rotor to align itself perpendicular to the shaft. The sequence of events is shown in figure 7-3.
First, there is the tilt of the shaft alone as the rotor disc acts as a gyroscope and remains in its original plane. However, since the blade feathering is referenced to that shaft, the angle of attack of the right-hand blade is increased and that of the left-hand blade decreased by the same amount.
This causes the rotor to flap until it is perpendicular to the shaft, where it will again be in equilibrium with a constant angle of attack around the azimuth and the moments will be balanced. This alignment is very rapid usually taking less than one revolution following a sudden tilt. Because of this, the flapping motion in hover has practically no effect on the stability of the helicopter in terms of holding a given attitude.
This was not recognized by many people in the early days of helicopters. They spoke of the rotor as a gigantic stabilization device similar to those used on ships of the day.
A rotor as a gyro
So, if a rotor does not act like a gyro trying to retain its position in space, when does it act like gyro? This answer has to do with how the rotor moves if you put an unbalanced aerodynamic lit on the disc. It will respond by moving at right angles to the unbalance just as the toy gyro does, and it does so in exact compliance with the gyroscopic laws that say the angular rate of motion — the “precession rate”’ — will be proportional to the applied moment.
This is in apparent contrast to Newton’s Law that states that an angular acceleration should be the result of an applied moment. (The rotor/gyro is actually obeying Newton’s Law but its high rate of rotation is producing this overwhelming side effect.)
The unbalanced lift distribution can come either from external sources such as a gust or from control inputs using cyclic pitch. For example, right stick will lower the angle of attack of the blade over the tail and raise it on the blade over the nose. This noseup unbalance on the disc will cause it to precess down to the right and the rest of the helicopter will soon follow. For a given helicopter, the resulting right roll rate will be directly proportional to the change of cyclic pitch from trim. Not all helicopters, however, will roll at the same rate for the same cyclic pitch. In response to the gyroscopic laws, the rate will be higher for those helicopters whose rotors are lighter or turning faster.
Thus, it may be seen that the rotor is like the mysterious toy gyro as it responds to applied moments but it has practically none of the toy’s inherent stability. If required, this last drawback can be compensated. Early Bell helicopters used a stabilizer bar that acted like a gyro and controlled cyclic pitch in a way that transferred some of the gyro stability to the rotor. The Lockheed rotor and gyro system did the same thing. Nowadays, the designer can use a hidden black box containing a small, rapidly turning gyro with appropriate connections to the control system to make the helicopter achieve as much stability as desired.