Inertia coupling
Encyclopedia
Inertia coupling is a potentially lethal 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 wing spans that had relatively low roll inertia, relative to the pitch and yaw inertia dominated by the long slender high-density fuselage
.
The phenomenon itself is not aerodynamic, and 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.
. 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 ratio
s 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 killed pilot Mel Apt in the Bell X-2
and nearly killed Chuck Yeager
in the X-1A
. It was also extremely obvious in the X-3 Stiletto
, and flight tests 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
, were modified to increase wing and tail area 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
, a stability augmentation system was retrofitted to the A models to help combat this problem.
High-speed flight
In high-speed flight the assumptions of incompressibility of the air used in low-speed aerodynamics no longer apply. In subsonic aerodynamics, the theory of lift is based upon the forces generated on a body and a moving gas in which it is immersed...
in which the inertia
Inertia
Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...
of the heavier fuselage
Fuselage
The fuselage is an aircraft's main body section that holds crew and passengers or cargo. In single-engine aircraft it will usually contain an engine, although in some amphibious aircraft the single engine is mounted on a pylon attached to the fuselage which in turn is used as a floating hull...
overpowers the aerodynamic stabilizing forces
Flight dynamics
Flight dynamics is the science of air vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of mass, known as pitch, roll and yaw .Aerospace engineers develop control systems for...
of the wing
Wing
A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...
and empennage
Empennage
The empennage , also known as the tail or tail assembly, of most aircraft gives stability to the aircraft, in a similar way to the feathers on an arrow...
. The problem became apparent as single-engine jet fighter aircraft
Fighter aircraft
A fighter aircraft is a military aircraft designed primarily for air-to-air combat with other aircraft, as opposed to a bomber, which is designed primarily to attack ground targets...
were developed with narrow wing spans that had relatively low roll inertia, relative to the pitch and yaw inertia dominated by the long slender high-density fuselage
Fuselage
The fuselage is an aircraft's main body section that holds crew and passengers or cargo. In single-engine aircraft it will usually contain an engine, although in some amphibious aircraft the single engine is mounted on a pylon attached to the fuselage which in turn is used as a floating hull...
.
Description
Inertial 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, and is caused by general conservation of angular momentum acting on mass whose radial
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
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 massCenter of mass
In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...
. 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 ratio
Fineness ratio
Fineness ratio is a term used in naval architecture and aerospace engineering to describe the overall shape of a streamlined body. Specifically, it is the ratio of the length of a body to its maximum width; shapes that are "short and fat" have a low fineness ratio, those that are "long and skinny"...
s 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 killed pilot Mel Apt in the Bell X-2
Bell X-2
-Popular culture:* The 1956 film Toward the Unknown starred the X-2, William Holden, Lloyd Nolan and Virginia Leith. A brainwashed former POW tries to return to test flying; co-starring the Martin XB-51 and the Edwards AFB flight line....
and nearly killed Chuck Yeager
Chuck Yeager
Charles Elwood "Chuck" Yeager is a retired major general in the United States Air Force and noted test pilot. He was the first pilot to travel faster than sound...
in the X-1A
Bell X-1
The Bell X-1, originally designated XS-1, was a joint NACA-U.S. Army/US Air Force supersonic research project built by Bell Aircraft. Conceived in 1944 and designed and built over 1945, it eventually reached nearly 1,000 mph in 1948...
. It was also extremely obvious in the X-3 Stiletto
X-3 Stiletto
The Douglas X-3 Stiletto was a 1950s United States experimental jet aircraft with a slender fuselage and a long tapered nose, manufactured by the Douglas Aircraft Company. Its primary mission was to investigate the design features of an aircraft suitable for sustained supersonic speeds, which...
, and flight tests on this aircraft were used to examine the problem. The first two production aircraft to overtly experience this phenomenon, the F-100 Super Sabre
F-100 Super Sabre
The North American F-100 Super Sabre was a supersonic jet fighter aircraft that served with the United States Air Force from 1954 to 1971 and with the Air National Guard until 1979. The first of the Century Series collection of USAF jet fighters, it was the first USAF fighter capable of...
and F-102 Delta Dagger
F-102 Delta Dagger
The Convair F-102 Delta Dagger was a US interceptor aircraft built as part of the backbone of the United States Air Force's air defenses in the late 1950s. Entering service in 1956, its main purpose was to intercept invading Soviet bomber fleets...
, were modified to increase wing and tail area 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
F-101 Voodoo
The McDonnell F-101 Voodoo was a supersonic military jet fighter which served the United States Air Force and the Royal Canadian Air Force...
, a stability augmentation system was retrofitted to the A models to help combat this problem.