Plane & Pilot
Sunday, January 1, 2006

Balancing Act

Understanding the center of gravity

Balancing ActSometime back in the dark ages, I was getting ready to take my instrument instructor check ride, and the examiner, who was an actual FAA type from the FAA headquarters, asked me if I had done a weight-and-balance for the flight. Two thoughts flashed through my mind, the first being the obvious question: What has a weight-and-balance calculation got to do with an instrument check ride? The second was a little panicky thinking while I tried to remember how to do the calculations.

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There are lots of situations where you can be out of either side of the envelope, but still far from being either heavy or light, however. This tendency varies greatly from airplane to airplane. So, what makes the difference?

One of the parameters that defines the CG envelope is the mission for which the airplane was designed in the first place. For instance, if an airplane is designed to carry a lot of load and have as wide an envelope as possible, the makers know that everything a user puts in the airplane is likely to shift the CG back. Therefore, they intentionally set it up so that when it’s empty, the CG is as far forward as it can possibly be and still have enough tail authority to land it. Or, as was the case with my Cherokee 140 during the check ride, the combination of additional equipment and weight (fuel) pull the CG forward enough that it’s out of the envelope.

A lot of heavy-haulers, like Cherokee Sixes, Lances and other true six-place airplanes, sit right on the front of the envelope when empty, so as the seats fill up, the CG shifts back, but not so far that it’s out of the envelope. Quite often, when additional equipment, like radios, are added to an airplane that already has a far-forward CG, it’s pushed well out of the envelope in certain configurations, such as full-flap landings with only a pilot onboard.

Then why does it matter that we keep an airplane in its envelope? Are there bogeymen standing around the perimeter of the envelope ready to bite us if we put a toe outside the line? The answer to that is a resounding yes, especially if you go out of the back of the envelope where that particular bogeyman can bury you.

There are several interacting aeronautical factors that come into play when considering what happens outside either side of the envelope. One of these is the relationship between the center of lift (where the big “lift” arrow is acting on the wing) and the CG of the airplane.

First, a basic fact of physics: Aerodynamics notwithstanding, a mass rotates around its centroid, which is another way of saying an airplane will always try to rotate around its CG. If the center of lift isn’t right on the CG, which it seldom is, then that big lift arrow is going to try to rotate the airplane about the CG. If it’s forward of the CG, it will try to pull the nose up. If it’s behind the CG, it’s just the opposite.

If the airplane expects to maintain controlled flight, the tendency of the lift to rotate the airplane about the CG has to be counterbalanced, and that’s what the horizontal tail is for. If the center of lift is ahead of the CG and is trying to pull the nose up, it’s trying to push the tail down. So you push a little forward stick, which puts the elevator down and increases the camber of the tail airfoil, generating more lift and balancing the nose-up tendency. If the wing’s lift is behind the CG, it’s trying to pick up the tail, and some back stick is required, so the tail is lifting down, not up.

What can really complicate this is that as an airplane slows down and the angle of attack goes up, the center of lift moves around, which changes the relationship of the CG and the lift arrow, generating a pitching moment of its own. And then, of course, as fuel burns off, the CG changes position and, depending on the airplane, may try to raise or lower the nose.


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