# In Search of the Neutral Point

###### Peter Garrison

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.

What had held me up for so long -- apart from the fact that there always seemed to be more important things to do -- was the lack of a convenient way to measure stick force. I don't fish, and did not have a spring scale handy. The solution finally came in the form of a stick grip equipped with an electronic load cell. A friend bought this for some testing he wanted to do, and he lent it to me to try out. I mounted it on Melmoth 2 's sidestick in lieu of the usual stick grip, bought four 50-pound sandbags and a \$15 digital voltmeter, and I was ready to be a test pilot. (I should note that my investment in this process, \$27, was dwarfed by my friend's in the stick-force-measuring gadget -- \$2,000.)

The first test was with the empty airplane. The CG was at 12.4 percent of MAC. I set a moderate cruising power -- 24/2,400 at 6,500 feet -- and trimmed hands-off at 120 kias. I turned on the autopilot to maintain heading, and noted down the stick forces -- millivolts, actually; nothing would have been gained by the additional step of converting these to pounds and ounces -- at 10-knot intervals from 90 to 160 kias. Upon landing, I plotted the results and was gratified to find that they formed a nice straight line with very little scatter.

For the second test, I loaded 100 pounds of ballast into the baggage compartment and repeated the procedure. Again, the data lay on a nice straight line and, as expected, the line was at a shallower angle than the previous one.

The answer I was looking for lay in those angles. They represented the rate of change of stick force with speed: the more forward the CG, the larger the static margin, the greater the forces and the steeper the slope of the line. At the neutral point, the slope would be zero; there would be no change in stick force at different speeds. So to ascertain the location of the neutral point I just had to extrapolate from two pairs of numbers: the two CG locations and their respective stick-force slopes.

My jaw just about dropped when I saw the answer. It was 130.2 inches aft of the datum -- identical, given the limited precision of my methods, to the figure of 129.96 inches that Digital Wind Tunnel had arrived at by calculation.

It was profoundly gratifying to have the result of the test coincide so closely with that of the computer's analysis. On the other hand, it was unsettling. It was too good; such celestial harmony can only be accidental.

Accordingly, I repeated the test two more times, with weights of 150 and 200 pounds in the baggage compartment. I then fitted a straight line to the four slopes (using both eyeball and least-squares fits -- they agreed). The neutral point stubbornly remained at 60 percent of MAC -- the equivalent of putting 375 pounds into the baggage compartment. Digital Wind Tunnel really had gotten it right.

Knowing this, where would I put the aft limit?

This is a more slippery question than that of the location of the neutral point. It's a matter of flying qualities, not numbers. I had not been exposed to turbulence or icing during my CG tests. I had not done stalls. I had also not investigated the destabilizing effects of power at high angles of attack, a critical aspect of longitudinal stability that gives a lot of airplanes trouble.

On the other hand, I knew that typical values of static margin are in the range of 5 to 7 percent of MAC. Since Melmoth 2's MAC is unusually short for an airplane of its capacity, I somewhat arbitrarily decided to put the aft limit at 45 percent of chord. This provides a 5-inch, 14 percent-of-MAC static margin, and allows carrying four passengers (the old 170-pound kind though, not the new supersized 190-pounders) and 80 pounds of baggage.

As far as flying qualities were concerned, I had found nothing troubling. The reduction of stick forces with increasing aft loading was palpable, but the airplane remained comfortable to fly and its speed stability on approach and in the flare were good.

I did become aware of a couple of practical issues. With 100 pounds of ballast or more the nose strut extended completely and the airplane assumed a three-degree nose-high attitude on the ground. Because of the design of the steering system, this meant that I had to rely on differential braking to steer while taxiing -- an annoyance, though a minor one. Takeoff with aft CG calls for a much more forward trim setting than I'm used to; there is no trim indicator, and so I have to guess at it (of course, it's a small airplane, and the stick forces are low enough that you can just hold attitude while retrimming). With 200 pounds of ballast, however, I ran out of nose-down trim at around 125 kias. The elevator has two trim tabs, but at the moment I'm using only one of them; I clearly need to hook up the other as well.

I may also need to get a new steady date. When I started talking about all the tests I was doing to ensure that the airplane could safely carry four people, my partner, Nancy, explained that her claustrophobia would make it impossible for her to be in such a crowd.

Sorry, Carl and Sue -- the airplane's okay, but you'll still have to drive.

Peter Garrison taught himself to use a slide rule and tin snips, built an airplane in his backyard, and flew it to Japan. He began contributing to FLYING in 1968, and he continues to share his columns, "Technicalities" and "Aftermath," with FLYING readers.
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