Common error in center of gravity calculation

I thought I should highlight an error that is being made in
calculating CG that appears to be widespread, and that can lead to a
miscalculation in center of gravity by up to 10% (or possibly more) of
the allowable CG range.

The problem arises from a difference in the way Europeans and
Americans calculate the CG.

In the US, we commonly use the formula: Center of gravity = total
moments / Total mass. So for an empty glider CG calculation, that
would be (datum to main wheel * main wheel weight) + (Datum to tail
wheel * tail wheel weight) / Total weight. This is the method taught
in the FAA “Glider Flying Handbook” (Sec 5-13)

In many European glider manuals (ASW20B and ASG29E, for example), the
formula given for the glider CG = ((Horizontal distance between the
wheels * tail wheel weight) / Total weight) + (datum to main wheel).

BOTH formulas are correct, but the problem arises when the tail wheel
datum is confused with the distance between the tail wheel and main
wheel. So far I have seen three or four examples of this. Once the
error was even made on a written weight and balance sheet done by a
repair facility.

I noticed the pattern when users of the weight and balance calculator
“SeeG” would inquire as to why the program did not yield the same
results as their own calculations, only to discover that they had made
this error in their own calculations long ago, and the SeeG result was
the correct one.

The resulting error is not obvious because it is not wildly off of
expectations, and therefore often goes undetected. For a Ventus C,
using the “main to tail” distance rather than the “datum to tail”
distance for an empty glider weighing results in the CG being placed
too far forward by 5%. For a Discus B, the same error places the CG
too far forward by 9% of the allowable range.

Whatever method is used; the SeeG program, a spreadsheet, or a pencil,
it might be worth double checking that the tail wheel distance being
used is appropriate for the CG formula being employed. If you think
your CG is at 80% aft, you might actually be flying at 90% aft or
more.

Thanks,

Matt Herron (Jr)
http://www.glideplan.com