In Search of the Neutral Point
By Peter Garrison
November 2008
 Four of us were invited to a friend's house in Northern California, a 10-hour drive from Los Angeles. "Could we all go up in your plane?" Carl asked. Two hours and 15 minutes sounded a lot better.
I had to say no.
What was the problem? My homebuilt, Melmoth 2, is a four-seater. It was originally designed to carry four full-sized people, plus a modest amount -- say 40 pounds -- of baggage. But I had never determined whether it really could. I always meant to, but never got around to it. I don't have that many friends.
It all had to do with the CG range. I had flown with a person in one of the back seats, and also with a couple of hundred pounds of cargo back there. That put the CG at 29 percent of the mean aerodynamic chord. Typical CG ranges are from, say, 10 or 15 percent of the MAC to 35 percent. Adding a fourth person and a couple of bags in back would push the CG back to 40 percent. That's an unusual number. It would need to be verified.
Naturally, I had done all of the necessary calculations. Back in the 1980s I wrote a computer program using some equations that I picked up from an aerodynamics textbook. It said that the neutral point -- the CG location at which the airplane would have no longitudinal stability at all -- would be around 40 percent. Now, you don't want to fly with the CG at the neutral point; the aft limit of the CG range is always put a few percent ahead of the neutral point. It's those few percent -- called the "minimum static margin" -- that ensure that if you pull the nose up and let go, it comes back down. That's what longitudinal stability is: the airplane's tendency to return to a trimmed attitude and speed. Airplanes can be flown without longitudinal stability, but they require constant attention and can do horrible things near the stall.
Later I got into the aeronautical software business, and my partner, Dave Pinella, wrote a program called Digital Wind Tunnel (DWT) that calculates longitudinal stability by analyzing the changing air pressure over the entire surface of the airplane at two or more different angles of attack and CG positions. DWT said that Melmoth 2 's neutral point was at 60 percent of MAC -- 129.96 inches aft of the datum.
Sixty percent? Say again?
DWT had performed billions of mathematical operations to arrive at its answer, but it seemed scarcely plausible nevertheless. I had never heard of an airplane whose neutral point was at 60 percent of chord.
Before going farther into this tale, I need to clarify the peculiar way that the neutral point's location is expressed, namely, as a percentage of "mean aerodynamic chord." The mean aerodynamic chord, or MAC, is a sort of average chord of the wing, and serves as a shorthand representation of the complete wing. The use of percentage of MAC to express both neutral point location and static margin is conventional, even though (like the use of wing area as the basis for the drag coefficient) it doesn't make perfect sense.
The wing chord itself has little role in stability; you could replace a wing with one of half the chord and twice the span, and stability would scarcely be affected. Yet the neutral point location and the static margin would appear to have been doubled, because they are being expressed in terms of the chord.
In reality the neutral point is located at a certain physical point on the airplane, and the static margin is the distance from it to another physical point, the center of gravity. They could -- should -- be measured in inches. The problem is that desirable values are proportional to the size of the airplane; a 5-inch static margin may be ample for a Cessna single, but would not do for an A380. So that's why we end up putting these numbers in terms of wing chord, even though different airplanes of roughly the same size can have quite different MACs.
Now, Melmoth 2 has an aspect ratio of 12 and a MAC of less than 36 inches. So maybe 60 percent wasn't such an outlandish number after all. But how would I be absolutely certain?
I could just keep adding weight in back until the plane started to feel squirrelly, and call that the aft limit. (The aft limit of the CG range, remember, is some little distance -- the minimum static margin -- ahead of the neutral point.) But there's a more systematic way, and it allows you to identify not just an aft limit defined in units of squirreliness (nuts, maybe?), but the neutral point itself. It involves measuring the stick force necessary to hold speeds other than the trimmed speed. You record these forces over a range of speeds and at several CG locations, and that allows you to extrapolate the CG location at which the force would be zero and the airplane would maintain any speed with no change in stick force. That is the neutral point.
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