A quick review: aircraft stability rests on the location of two data points: Center of Gravity (CG) and aircraft Aerodynamic Center (AC). The relative position of these two crucial points determines whether aircraft will want to recover from pitch excursions (“stable”) or not (“unstable”).
Provided the CG is forward of the AC, aircraft act much like arrows and darts, turning and facing into the relative wind the way you want them to. Move the points too close together and self-correction becomes unreliable, then non-existent.
The AC doesn’t shift; the CG does, so determining its position on any given flight is critical to flight safety.
COMPUTATION AND THE DATUM
As I stated last month, every empty airplane has a measured CG location. If you add weight on either side, its added moment upsets the status quo, slightly moving the CG.
It is this shifting nature of CG location that tends to complicate things. Each new weight moves the CG and thus the effect of each subsequent weight; if you were to re-compute CG location with every addition, balance computations would be lengthy and very tedious.
In a stroke of minor brilliance, someone figured out that the easiest way to resolve this shifting situation is to create a phantom pivot point (the “datum”) somewhere toward the front of the aircraft and then treat the entire structure as a weight trying to twist around that point.
This approach eliminates the need to compute the effect of each new added weight against an ever-changing CG location: the datum remains stationary, and each new weight simply adds to the total moment trying to twist around that point. Later, this total moment magically leads to computation of the actual CG location.
MEASUREMENT
The process starts with knowing the empty weight of the plane and the actual location of its CG, both of which were originally determined by somebody with a set of scales and a typewriter. Keep in mind that this CG is the very real place where the total weight of the empty aircraft appears to be concentrated.
Next up: re-express the CG in terms of its position relative to the datum, the phantom Pivot point. This is done by measuring the CG distance from the datum, thus creating a phantom Arm. If you then multiply the total weight by this arm, you arrive at a phantom Moment, a numeric expression of how much twisting force the entire empty airplane is exerting on the datum.
And there you have it: empty weight and empty weight moment, the starting points for all subsequent computations.
Before charging into the details of what comes next, take a moment to look at a typical empty weight/moment pairing: 1600 pounds and 66,000 inch pounds (a 1984 C-172, with the datum at the firewall). The numbers mean that the 1600 pound empty airplane exerts a twisting force of 66,000 inch pounds around the datum, a figure arrived at by multiplying the empty weight by its CG distance from that datum.
Although the information would have little value, you could re-find the CG at this point by reversing the math: divide the moment by the weight to discover the empty aircraft CG: 39.2 inches aft of the datum (firewall).
Once empty weight and empty weight moment are known, the process of adding people, fuel and baggage is reduced to simple math. Each addition has a known distance from the datum, so new weights contribute to two totals: total weight and total moment. Weight totals require simple addition, while moment add-ons require multiplication, then addition. Most manufacturers provide line graphs to simplify the multiplication steps.
The valuable final product of all this work is total weight/total moment.
ALMOST THERE
Although the total moment is still only an abstract, this final pairing provides easy access to the real location of the loaded aircraft CG: simple division of the total moment by the total weight reveals the magic number. In this one quick math step, you abandon the phantom pivot point and find the real one.
Interestingly, you may never perform this last step. In the opinion of most manufacturers, it is less important to know the actual location of the CG than it is to know whether the weight/moment pairing falls into the allowable loading envelope. A simple graph that plots gross weight against total moment is all that is needed.
TODAY’S PILOTS
While line graphs and weight/moment envelopes have reduced the tedium of weight and balance computations, the simplification has come with a price: the time-saving steps tend to conceal the nuts and bolts of the process, to the point that few modern student pilots understand what they are doing as they follow the dance steps. This general fog has a predictable result: it becomes difficult to recognize and troubleshoot mistakes. I hope that this and the preceding five columns have brought clarity. I’ll finish next month with a look at how CG location affects stall and spin recovery.
