Definitions and Calculations — Page 44, Lesson 63

Right, let's pick this up with the moment calculations. We've got the mass and balance sheet in front of us, and we're dealing with the take-off and landing centre of gravity positions. First, a practical point about the numbers themselves. Moments are often large numbers containing more than six digits, and that can be an extra source of difficulty. In the SEP example we're using, the moments have been divided by one hundred to reduce the number of digits and make them more manageable. Take care if you use this procedure, because you must remember at the end of any calculations to multiply the final answers by one hundred to arrive at the correct total moment. So if you see a moment written as 3102.9, that's actually 310,290 lb in — the abbreviated form is less accurate but easier to cope with. Now, the fuel load. It may be given as a quantity — in Imperial or American gallons — rather than as a mass. You must convert it to mass before you can complete the load sheet. That's where Figure 2.7, the quantity mass conversion chart, comes in. Fuel mass and distribution may also be given in tabular form, as in our example, where the fuel mass and moment have been taken from the SEP1 fuel chart, Figure 2.3, of the CAP 696 Mass and Balance Manual. Now let's walk through the take-off CG procedure step by step. First, sum the vertical 'MASS' column to determine, in turn, the ZFM, the Ramp Mass, and the TOM. ZFM is the Zero Fuel Mass, Ramp Mass is the mass of the aircraft before engine start, and TOM is the Take-Off Mass. In our example: ZFM = 3295 lb; Ramp Mass = 3655 lb; and TOM = Ramp Mass minus Start/Taxi fuel = 3655 minus 13 = 3642 lb. Second, check the Operating Manual to ensure that the limiting masses of MZFM, MSTM, and Regulated TOM have not been exceeded. MZFM is the Maximum Zero Fuel Mass, MSTM is the Maximum Structural Taxi Mass, and Regulated TOM is the Regulated Take-Off Mass — these are the structural and regulatory limits you must not exceed. Third, sum the vertical 'MOMENTS' column to determine the total moment for ZFM, Ramp Mass moment, and TOM. In our example: ZFM moment = 284,286 lb in; Ramp Mass moment = 284,286 + 27,000 = 311,286 lb in; TOM moment = 311,286 minus 1000 = 310,286 lb in. Remember, these are shown in the abbreviated form, e.g. 310,286 divided by 100 = 3102.9. Fourth, divide the moment of the TOM by the TOM to determine the CG position at take-off. TOM CG position = 310,290 divided by 3642 = 85.2 inches aft of the datum. The datum is the reference point from which all arms are measured. Fifth, check the Operating Manual to ensure that the CG is within limits at both the ZFM and TOM situations. If this is the case, then the CG will remain within the limits throughout the flight and should not go out of limits during the journey, provided the fuel is used in the correct sequence. Now for the landing CG. First, determine the moment of the fuel used in flight — the trip fuel — by multiplying its mass by the fuel arm. In light aircraft, the fuel arm will usually be the same as the one used previously to calculate the take-off CG position. However, caution is required, because in some large aircraft the balance arm of the fuel may change with the quantity of fuel consumed. And here's a critical point about signs. The fuel consumed will give a negative mass in the mass column, and this will change the moment sign. For example, if the fuel arm is positive, the fuel moment will become negative. So when you subtract the trip fuel, you're not just reducing the mass — you're also reducing the moment, and that shifts the CG in a specific direction. That's why you must track the sign carefully. So the key takeaway: the take-off CG is found by dividing the TOM moment by the TOM, and the landing CG is found by accounting for the trip fuel's negative mass and moment. Both must be checked against the Operating Manual limits. That's the complete procedure.