Inertia coupling

In aeronautics, inertia coupling is a potentially catastrophic phenomenon of high-speed flight in which the inertia of the heavier fuselage overpowers the aerodynamic stabilizing forces of the wing and empennage. The problem became apparent as single-engine jet fighter aircraft were developed with narrow wingspans, that had relatively low roll inertia relative to the pitch and yaw inertia dominated by the long slender high-density fuselage.^[1]

Description

Inertia coupling occurs when an aircraft such as that described above is quickly put into a roll, resulting in violent pitching and yawing, and loss of control as the aircraft rotates on all three axes.

The phenomenon itself is not aerodynamic; it is caused by general conservation of angular momentum acting on mass whose radial distribution is not symmetric about the axis of rotation. It can be visualized by imagining a uniform long rod, at each end of which is a perpendicular extension, each pointing opposite the other. (If the rod is horizontal, one points up and the other points down.) At the end of each extension is a weight. The extensions and weights are identical, so the center of mass and the axis of rotation along the length of the rod are unaffected by the weights. If the rod is then spun about its axis, the centrifugal forces on the two weights will cause the entire assembly to tilt relative to its initial axis of rotation.

Although a typical jet aircraft has most of its mass distributed close to its centerline, and the aerodynamics in planes designed to be stable (such that small fluctuations in control tend to return it to attitude equilibrium) provide some stabilization, it is important to remember that aircraft realistically always fly with a small non-zero random rate of yawing and pitching. Inertia coupling on an aircraft usually manifests itself as a downward pitching; rolling causes the tail mass to be flung upward and thus the nose to tip down. The pitching can in turn cause gyroscopic yawing.

Early history

Inertia coupling was essentially unknown before the introduction of high-speed jet aircraft. Prior to this time, aircraft tended to be wider than long, and their mass was generally distributed closer to the center of mass. This was especially true for propeller aircraft, but equally true for early jet fighters as well. It was only when the aircraft began to sacrifice aerodynamic surface area in order to lower drag, and use longer fineness ratios that lowered supersonic drag, that the effect became obvious. In these cases the aircraft was generally much more tail-heavy, allowing its gyroscopic effect to overwhelm the small control surfaces.

Inertia coupling at Mach 3.2 killed pilot Captain Mel Apt in his first flight in the rocket-powered Bell X-2 on 27 September 1956, and had nearly killed Chuck Yeager in the X-1A three years earlier.^[2] It was also extremely obvious in the X-3 Stiletto (first flown in 1952), and flight test data on this aircraft were used to examine the problem. The first two production aircraft to overtly experience this phenomenon, the F-100 Super Sabre and F-102 Delta Dagger (both first flown in 1953), were modified to increase wing and tail areas and were fitted with augmented control systems. To enable pilot control during dynamic motion maneuvers, for instance, the tail area of the F-102A was increased 40%. In the case of the F-101 Voodoo (first flown in 1954), a stability augmentation system was retrofitted to the A models to help combat this problem. The Lockheed F-104 Starfighter (first flown in 1956) had its stabilator (horizontal tail surface) mounted atop its vertical rudder fin to reduce inertia coupling.

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