Hinge Moments Explained

“Just give me a place to stand,” Archimedes said.

“Hinge moment” is the technical name for the force required to deflect a control surface. In small, relatively slow airplanes, hinge moments are not very large; pilots move the controls with ease. But as control surfaces get larger and speeds get higher, hinge moments grow rapidly. They increase with the chord length of the control surface, with the square of speed and with the cube of the linear dimensions. Thus, if you double the speed, the hinge moments grow four times greater; if you double the size of an airplane, keeping all of its proportions unchanged, they become eight times greater. If you double both size and speed, hinge moments increase by a factor of 32.

From Kitty Hawk onward, airplanes got bigger and faster, but pilots didn’t get any stronger. Obviously, this couldn’t go on forever. There is, furthermore, only so much you can accomplish with leverage between cockpit and control surface. In principle, a wheel-type control could have a large mechanical advantage, if you didn’t mind having to turn it 10 or 20 times to roll into a bank, but that would not make for a very agile airplane. A stick was at an even worse handicap, its movement limited by the space between the pilot’s knees.

Now, it was well-known from the world of boats that hinge moments could be reduced by putting a portion of a surface, like a rudder, ahead of the axis of rotation, or “hinge line.” Some early airplanes had completely balanced rudders and no fixed fin at all. Many also had a balancing area projecting ahead of the ailerons at the wingtips. But for really large airplanes, like the multiengine bombers that came into being during the First World War, keeping control forces within comfortable limits with aerodynamic balance was very difficult.

During that war, however, a German engineer named Anton Flettner had an ingeniously simple idea for applying leverage in a new way.

The force of moving air on a control surface such as an aileron is centered approximately a third of the way back from the hinge line. Flettner proposed attaching a small additional surface behind the trailing edge of the main surface. The main surface was allowed to float freely; the pilot’s stick was connected to the auxiliary surface. Air pressure on the auxiliary surface would have a lever arm more than three times greater than that of the force on the main surface, while the effort needed to deflect it would be much smaller because the surface itself was small. The pilot could now move a large main surface using only the effort required to move a small one.

Flettner tabs allowed pilots to control very large airplanes manually, and remained in use for decades. The DC-6 and B-29 had Flettner-equipped control surfaces, as did the Douglas DC-9, I believe the last large transport to forgo hydraulically boosted controls.

Flettner’s invention is now called a tab, and it survives in aviation in many varieties. The most familiar is the trim tab, which modifies the neutral or “floating” position of a surface, such as an elevator or rudder, by pushing on its trailing edge. A trim tab is a stationary tab: You set it and it remains in that position as the main surface moves.

Some moving tabs, called servo tabs, are used for reducing control forces. A servo tab is identical in appearance to a trim tab, but is linked, in the case of an aileron, to a fixed point on the wing. If the link is attached to the bottom of the tab, it’s also attached to the bottom of the wing. Thus, if the aileron is deflected upward, the link — usually a simple hollow rod — pulls the tab downward, helping the aileron along by reducing its hinge moment.

Something interesting happens if you attach the link to opposite sides of the tab and the main surface. When the main surface goes up, the tab, which is now called an anti-servo tab, comes down. Rather than reduce the control forces, it increases them.

But why would you want it to do that?

The answer is found on the tails of many a Piper, at least one Cessna — the Cardinal — and plenty of other types as well. It’s the all-flying tail, or stabilator.

To understand how a stabilator works, go back to the all-flying rudders of early days. Enough of the rudder was placed ahead of the hinge line to balance what was behind it, eliminating control forces altogether. It happens that aerodynamic pressures are concentrated near the nose of an airfoil, such that the lift force on the front quarter of a wing is equal to that on the back three-quarters. Therefore, if you take a rectangular wing, such as the stabilator of a Cherokee or Seneca, and pivot it one-quarter of the way from the leading to the trailing edge, it’s fully aerodynamically balanced and you can move it in flight without any effort.

Completely effortless controls are not a good thing, however, because they don’t have a home base to which they want to return. They just float in any position. Early airplanes with balanced rudders and no fin flew in a sideslip just as willingly as straight ahead.

For stability, a control surface needs a position to which it returns of its own accord, hands-off. A hinged elevator aligns itself with the stabilizer in front of it. The anti-servo tab provides the same service for an all-flying tail. When it’s aligned with the stabilator, it’s at home; when it’s deflected, it pushes the stabilator back toward its home position. Trim is adjusted by moving the anchor point at the front end of the tab link, usually with some sort of screw apparatus that has the effect of changing the stabilator incidence at which the anti-servo tab aligns with it.

Stabilators have a number of advantages over the more conventional stabilizer with hinged elevator. They are structurally simpler, lighter and cheaper to build. They are aerodynamically more effective, and so can be smaller. Control forces can be easily tailored to any desired level. The only bad thing you can say about them is that they are subject to certain flutter modes that conventional empennages lack, and so for high-speed airplanes — over 200 knots, say — manufacturers tend to make the more cautious choice. To be sure, many very fast airplanes — supersonic fighters, for example — have all-flying tails. But they are not stabilators, and they have no tabs; they are simply streamlined slabs, hydraulically driven, with no will of their own.


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