How to Compute the MAC Position of the CG

How to Compute the MAC Position of the CG
by
Stan Hall
Chapter 62 Technical Advisor

Comments Regarding Procedure Shown above

Note that the datum line, which is commonly located at the prop spinner is, in this procedure, located at the front wheel center, at the scale(s). This greatly simplifies matters, making it unnecessary to add or subtract distances from a remote point - which can change if the size of the engine and/or the spinner is subsequently changed. The location of the landing gear is likely to remain more permanent. The procedure also minimizes bookkeeping by eliminating the need to keep track of moment.
The most practical procedure in small airplanes is to weigh the aircraft with everything aboard; the pilot, fuel, baggage, everything. If not, the calculation of the c.g. position gets more complicated because the centers of gravity of each of those elements and their location in the aircraft need be accurately known and accounted for in the calculation. The work then becomes considerably more arduous, particularly when considering the pilot's c.g.
In small and thus light airplanes the weight of the pilot is a large percentage of the all-up weight, and so has a stronger influence on c.g. movement than in a heavier vehicle. It is difficult to accurately predict the c.g. position of the pilot since it depends largely on his seating attitude. If, for example, he sits near the floor and his legs extend well forward, his c.g. will be forward of where it would were he seated more upright like, say, in a Cessna. It is thus considered more accurate to weigh small aircraft with all the heavy weights or their substitutes already in place.
If this is not feasible the effect of adding, moving or removing weight items can be determined by applying the following principle. The aircraft c.g. will move in the ratio of the item's weight to the vehicle's new total weight. An example. if the item represents 10% of the new total weight the c.g. will move 10% of an inch per inch of item movement - in the same direction as the item's movement. If the item is added the vehicle c.g. will move toward it, if removed it will move away from it.
Unless you pay close attention during this process, this can get a little hairy, computation-wise, which is another reason the aircraft should if at all possible be weighed with everything aboard. If you'd prefer not weighing the aircraft with full fuel tanks, empty them and substitute the weight with, say, containers of equivalent-weight water placed strategically to simulate the original fuel c.g. weight and location.
Now this is vital. The position the c.g. in relation to the mean aerodynamic chord (m.a.c.) lies at the heart of the whole weighing process. This is why you weigh the aircraft in the first place. The details of this relationship are likely to be only vaguely understood by non-technical persons because they involve the stability of the aircraft, the calculation of which involves a complicated mathematical process which these same persons would probably prefer not getting into.
But fundamentally the c.g. should always be kept forward of the aircraft's Neutral Point by at least ' 5 percent of the m.a.c. The neutral point can be likened to the c.g. of all the aerodynamic forces acting on the aircraft. The aerodynamic center of the win is almost invariably located at a point 2596 of the m.a.c. aft of its leading edge. If the aircraft had no tail, it's neutral point would be close to 2596 and to assure stability the c.g. would need be held to a point at least 5_ forward of that. However, the tail brings the neutral point aft, commonly to around 35%. Thus for tailed aircraft the c.g. should be located no farther aft than 30%. That yields a Static Margin of 5% (35 - 30 = 5).
As to the forward c.g. Limit, this is largely a matter involving elevator power, you need enough to get the nose up in landing. At low speeds this could be of concern. Unfortunately, determining what this c.g. position needs to be involves another complicated engineering procedure and, since the farther forward the c.g. (the higher the static margin) the more stable the aircraft, this calculation is not often undertaken if adequate elevator power is available. Keep in mind, though, that the more stable the aircraft the higher the stick forces. This is why aerobatic aircraft characteristically have low built-in static margins. Translation: the more the stability, the less the control with acceptable stick forces.