Designers pay strict attention to the effects of propulsion on the stability and control of an airplane. For propeller-driven airplanes, the primary concerns are thrust line and the effects of the prop slipstream. But there is another set of propeller effects that is sometimes important, and often ignored. A rotating prop acts as a gyroscope. In certain situations, its gyroscopic effects produce unexpected behavior.
Propeller Moment of Inertia
Any rotating mass acts as a gyroscope. The magnitude of the gyroscopic effects is dependent on three factors: the rate of rotation, the mass of the rotating object and the moment of inertia of the rotating object about the axis of rotation.
Inertially, a propeller behaves like a slender rod. The moment of inertia about its center is proportional to the mass of the rod and the length squared. The mass of the prop is approximately proportional to its length (diameter). Combining these two effects, we find that, to the first order, the moment of inertia is proportional to the diameter of the propeller cubed (D3).
Doubling a prop’s diameter increases its moment of inertia by a factor of eight. In practical terms, this means that as the diameter of the propeller increases, its moment of inertia also increases rapidly, and it will tend to produce more gyroscopic effects.
Gyroscopes and Precession
Before discussing how the propeller gyroscope affects the airplane, we must first look at gyroscopes in general. This could get a little more technical than is usual in this column, but bear with me and I will try not to make your heads spin like our example propeller.
The phenomenon that causes the effects we normally call gyroscopic is called precession. Precession arises from the law of conservation of momentum, which says that the total momentum of a mass remains unchanged unless an outside force acts on it. In the case of a rotating mass, we are concerned with conservation of angular momentum, which is proportional to the moment of inertia of the object and the rotation rate.
One example of conserving angular momentum is the way figure skaters use the position of their arms to control the rotation rate of a spin. The spin starts with the arms extended. Pulling the arms into the chest, or placing them overhead causes the spin to accelerate dramatically. The reason for this is conservation of angular momentum, combined with the effect of arm position on the skater’s moment of inertia. By pulling in their arms, skaters reduce their moment of inertia by decreasing the length of the “rod.” To conserve angular momentum, the spin rate increases to compensate.
A more subtle characteristic of conservation of angular momentum is that angular momentum is a vector quantity, which means the orientation of the axis of rotation is as significant as the rotation rate. This fact causes precession. If we could take a rotating gyroscope and tip it, some angular momentum about the original axis of rotation would be lost. Conservation of momentum prohibits this unless an outside moment is applied to kill some of the angular momentum about the original spin axis. To actually tip the gyroscope, we must apply a moment not only in the direction we want to rotate the spin axis, but also a moment about the original spin axis to change the angular momentum of the gyro. If the second moment is not applied, the gyroscope will change orientation, but it will continue to spin about the original axis of rotation, appearing to wobble about its new apparent spin axis. This is precession.
For a propeller, the airplane applies the moments necessary to change the prop’s axis of rotation. The force (or moment) of the airplane on the prop is equal and opposite to the force (or moment) of the prop on the airplane. To the airplane, it appears the prop is responding to a moment in pitch or yaw with a reaction moment acting about an axis rotated 90˚ in the direction of the prop rotation from the axis of the original moment.
To the pilot, the airplane will appear to want to yaw in response to a pitch input and pitch in response to a yaw input. The gyroscopic action of the propeller is causing coupled motion about two axes, even though the pilot is applying a control input on only a single axis. Rolling the airplane does not cause prop precession because the airplane is rotating parallel to the prop axis of rotation.
The strength of the gyroscopic moment is proportional to the propeller inertia, the prop rpm and the pitch or yaw rate of the airplane. The table shows the gyroscopic moment, which arises from pitching or yawing, for an airplane with a normal (for the U.S.) right-hand rotation propeller:
This gyroscopically induced cross-coupling is not usually apparent to the pilot of a trigear light airplane because the pitch and yaw rates used in normal flight are relatively small, as is the mass of the prop compared to the airplane’s mass. There are some situations in which these effects can become significant, usually involving a combination of high pitch and/or yaw rates, low airspeed and high power setting. The high angular rates give rise to larger gyroscopic moments, and the low airspeed means the aerodynamic forces available to oppose the gyroscopic effects are smaller.
During takeoff in a taildragger, gyroscopic moments can surprise a pilot as the tail lifts. The nose-down pitch rate used to raise the tail can be large, particularly if the pilot is abrupt on the stick. The engine is at full power, so the rpm of the prop is high. When the tail is raised, the gyroscopic effect of the prop causes a left yaw, which can be exacerbated by the inherent directional instability of the taildragger landing gear. The plane will tend to dart toward the left side of the runway unless right rudder input accompanies the forward stick applied to bring the tail up.
In normal flight, most airplanes don’t experience significant prop gyroscopic effects. This was not true in the days of rotary engines, common on WW-I fighters like the Sopwith Camel. In a rotary, the whole engine spins with the prop. The mass of the engine/prop gyroscope is much greater than if the prop alone was spinning, and the gyroscopic effects are also large. Sometimes the gyroscopic moments produced by rotary engines were so large that they could overpower the aerodynamic controls of the airplane.
It was considered extremely dangerous to make a right turn in a Camel, or other high-powered rotary-engine fighters, right after takeoff. In a steady, banked right turn, the airplane is yawing to the right, and pitching up relative to its flight path. The nose-up pitch produced by the elevator backpressure required in the turn causes a gyroscopic right yawing moment, which tends to tighten the turn. The right yaw of the turn causes a nose-down gyroscopic moment.
The airplane would respond to a right-turn entry by nosing down and tightening its turn. At low speed, the pilot might not be able to recover before arriving at the ground. The bright side of this bizarre characteristic is that the good fighter pilots (the ones who survived learning to fly the airplane) learned how to use the gyroscopic moments to drive the airplane through abrupt turns, which proved useful in combat, or to rapidly point the nose for a snap shot at an opponent.
In the modern world, two classes of airplane experience significant prop gyroscopic effects in flight. The first are ultralights and other very light planes. These aircraft are typically powered by fast-turning engines, which drive relatively large props through gearboxes or other prop-speed reduction units. Because of their low wing loadings and slow flying speeds, this class of airplane has a small turning radius, which causes them to have relatively high pitch and yaw rates during the turn. The combination of a large (high-inertia) prop and a large pitch and/or yaw rate makes the gyroscopic moment from the prop large enough, relative to the aerodynamic moments the control can generate at such low airspeeds, that they become noticeable. While the effect is nowhere near as pronounced as on rotary-engine airplanes, it is noticeable. In a turn in the direction of the prop rotation, the nose tends to drop, and the turn will tighten, particularly if it is steep to begin with. When turning opposite to the prop rotation, the pilot will have to hold extra rudder to coordinate the turn.
The other place where prop gyroscopic effects are significant is in aerobatics, which involve much higher pitch and yaw rates than normal flying, so pilots must compensate for gyroscopic effects to perform clean maneuvers. For example, in a loop, particularly near the top where the airspeed is low, rudder is needed to keep the airplane straight. This is amplified by the fact that aerobatic airplanes typically have a lot of power for their size and large propellers to efficiently convert that power into thrust. This combination leads to large gyroscopic moments.
To an aerobatic pilot, prop gyroscopic effects are not all bad. In fact, they are used to make some dramatic-looking maneuvers possible. The simplest of these is a flat spin. In a spin, the yaw rate is high. When the airplane is spun power-on, it tends to nose up due to propeller precession when the spin is opposite to the direction of prop rotation. By deliberately keeping the prop rpm up and spinning in the proper direction, an aerobatic pilot can force the airplane to spin flat.
More spectacular maneuvers are performed by inducing large pitch and yaw rates with the elevators and rudder, causing the prop gyroscopic moments to drive the airplane into maneuvers the aerodynamic controls alone could not produce. The most famous of these tumbling maneuvers is the Lomcovak. More recently, as aerobatic airplanes’ power-to-weight ratio has increased, maneuvers with more than one tumbling rotation, including the knife-edge spin and the shoulder roll, have appeared.
The pilot places the airplane in a 0 G trajectory to unload the wings so that the plane can develop high rates without excessive G-load onset. A combination of control inputs is made to produce a large pitch and yaw rate, which in turn gives rise to the prop precession, which drives the airplane through the maneuver.
Gyroscopic moments from the propeller have one other effect, which can be significant to the airplane designer. Propeller precession causes bending moments on the propeller shaft. If these loads are repeated often enough, they wear bearings and can lead to fatigue failures of the prop-mounting flange and crankshaft. Some aerobatic airplanes have experienced prop-mount flange failures or cracking as a result.
Barnaby Wainfan is a principal aerodynamics engineer for Northrop Grumman’s Advanced Design organization. A private pilot with single engine and glider ratings, Barnaby has been involved in the design of unconventional airplanes including canards, joined wings, flying wings and some too strange to fall into any known category.