# Why isn't it possible to locate the rudder in front of an airplane's center of gravity?

Why isn't it possible to locate the rudder in front of an airplane's center of gravity?

Specifically how does this relate to the stability derivative?

• I'm not convinced this is a direct duplicate - the rudder doesn't necessarily have to be attached to the vertical stabilizer. The linked answer is PART of the answer to this question, but not an entire answer in itself. – Jon Story Jan 27 '15 at 16:34
• The Rutan Defiant push-pull canard has a ventral, starboard offset, forward mounted rudder. And, adding support to @JonStory 's comment, it is separate from the fins, which are mounted on the wingtips. – sdenham Sep 7 '16 at 2:40

## Effect on Aerodynamic Coefficients

It is possible to locate a vertical fin, as well as a control surface, ahead of the center of gravity. $c_{n_r}$ (yaw-induced yawing moment or yaw damping) will not likely change much, all other things being equal. $c_{n_\beta}$ (sideslip-induced yawing moment or directional stability), on the other hand, will be reduced, perhaps becoming negative. Any sideslip will therefore result in a yaw moment which increases the sideslip. Expressed in linear control theory terms, this will be a pole in right hand plane when you plot the complex solution of the equations of motion. It is an unstable configuration.

## Active Control

As Peter mentioned, it is possible to remain in control in this configuration by means of active control. Active control tends to be somewhat tiring for a human operator if it is possible at all. Incidentally, this kind of instability existed in the lateral axis of the 1903 Wright Flyer, which was configured with a canard of considerable proportion. It was reportedly quite tiring to keep stable.

There are advantages to having a center of pressure ahead of the center of gravity, the chief being agility. Back in control terms, the farther you move poles to the right, toward instability, the faster or "twitchy-er" the response. The F-16 is configured this way and has been the standard of maneuverability for quite some time, requiring computers and fly-by wire for stability augmentation.

## Control surfaces ahead of CG

It is also advantageous for maneuverability to have control surfaces ahead of the CG. In this case it is for avoiding a feature of control termed "non-minimum phase" response. For a conventional, tail-configured aircraft, when a climb is commanded, the tail is forced down, leading to a net reduction in lift until an increase of angle of attack is developed. This is non-minimum phase response. It was necessary to initially go the opposite direction from that which was desired. In canard configurations, this is not the case, first the nose climbs, then everything climbs.

## Put them together...

Forward control surfaces, forward center of pressure and a stability augmentation system with adequate dynamic pressure make for one heck of a maneuverable package. This is a common recipie for tactical missiles.

• Nice answer, I learned a bunch! – zeta-band Oct 6 '16 at 15:38

Well, it is. It has been done since maybe 160 Million years.

The Pterodactyloidea branch of flying saurians had long beaks, in most cases balanced by a large bony structure at the back of their heads, which provided lateral control. This is their only body part with noticeable side area, so no other part of their bodies could serve a similar purpose. Controlling direction like this helps to immediately change course to whatever the animal looks at.

Pterodactylus antiquus (picture source)

Since the head was ahead of their center of gravity, the configuration is statically unstable and needs continuous control corrections. On the other hand, it provides very quick responses. This works and has been proven several times by pterosaur-shaped flying models.

Another branch, the Rhamphorhynchoidea, had a tail which provided additional lateral and longitudinal control. Palaeobiologists are still arguing, however, whether the tip of the tail was oriented horizontally or vertically in flight.

In modern times weight and drag savings were the motivation for placing the fin at the tip of an airplane. The British space plane proposal HOTOL had such an actively controlled fin just on top of the fuselage nose. Also, many air-to-air missiles have their moveable control surfaces close to the tip, and those are balanced by bigger fins at the back. Both together make them canards in lateral and longitudinal control.

• A plane whose control surfaces were ahead of the COG would very easily find itself in a situation where its heading and direction of motion differed so much that its control surfaces could no longer generate torque in the proper direction to set things right. I would think that might also happen to a winged creature, but creatures could have a trick up their sleeve: a bird which found itself "flying" sideways through the air for whatever reason could likely change its attitude fairly quickly by drawing in its wings and shifting its mass around (something like a cat righting itself in midair). – supercat Feb 3 '15 at 19:26
• I wonder to what extent flying creatures do or did that, and to what extent such abilities may lessen problems caused by control-system runaway? – supercat Feb 3 '15 at 19:27
• @supercat: The flying models of Pterodactyls demonstrate how those animals might have flown, but will certainly fall short of the animal's possibilities of maneuverability by changing wing shape. But it is safe to assume that they were perfectly able to control their heading, quite like modern unstable and actively controlled systems. – Peter Kämpf Feb 3 '15 at 20:56
• It could also have used its feet as drag rudders :D – ymb1 May 25 '18 at 23:10