Definitions and Calculations — Page 44, Lesson 63

Let’s pick this up right where the load sheet work gets interesting. You’ve got your masses and moments, and now I want to walk you through the real skill: turning those big numbers into a take-off and landing centre of gravity position, and doing it without tripping over the arithmetic. First, a practical warning about moments. Moments are often large numbers — more than six digits — and that can be an extra source of difficulty. In the single-engine piston example we’re using, the moments have been divided by one hundred to reduce the number of digits and make them more manageable. Here’s the catch: if you use that abbreviated procedure, you must remember at the end of any calculations to multiply the final answers by one hundred to arrive at the correct total moment. Forget that step and your CG position will be wrong by a factor of a hundred. Now, before you can even complete the load sheet, you may be given the fuel load as a quantity — in Imperial or American gallons — rather than as a mass. You must convert it to mass before you can proceed. That’s exactly what Figure 2.7, the quantity mass conversion chart, is for. Fuel mass and distribution may also be given in tabular form, as in the 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. So the fuel data can come to you either as a volume to convert, or already tabulated as mass and moment. Let me show you the take-off CG procedure step by step, because it’s a sequence you’ll use every single time. Step one: sum the vertical MASS column to determine, in turn, the ZFM, the Ramp Mass, and the TOM. ZFM is zero fuel mass — that’s the aircraft fully loaded but with no usable fuel. Ramp Mass is the mass at the ramp, before engine start. TOM is take-off mass. In our example: ZFM equals 3295 pounds, Ramp Mass equals 3655 pounds, and TOM equals Ramp Mass minus the start and taxi fuel — that’s 3655 minus 13, giving 3642 pounds. So the start and taxi fuel is the fuel you burn before you even line up for take-off, and it comes off the ramp mass to give you the take-off mass. Step two: check the Operating Manual to ensure that the limiting masses — MZFM, MSTM, and Regulated TOM — have not been exceeded. MZFM is maximum zero fuel mass, MSTM is maximum structural taxi mass, and Regulated TOM is the regulated take-off mass limit. You’re comparing your calculated values against these published limits. Step three: sum the vertical MOMENTS column to determine the total moment for ZFM, for Ramp Mass, and for TOM. In the example: ZFM moment is 284,286 pound-inches. Ramp Mass moment is that plus 27,000, giving 311,286 pound-inches. TOM moment is 311,286 minus 1000, giving 310,286 pound-inches. Notice the note: the figures in the table are shown in abbreviated form — for example, 310,286 divided by 100 is 3102.9. That’s less accurate but easier to cope with. So you’re working with the divided-by-one-hundred numbers, and you must remember to multiply back by one hundred at the end. Step four: divide the moment of the TOM by the TOM to determine the CG position at take-off. TOM CG position equals 310,290 divided by 3642, which gives 85.2 inches aft of the datum. The datum is the reference point from which all arms are measured, and the CG position is expressed as a distance aft of that datum. Step five: check the Operating Manual to ensure the CG is within limits at both the ZFM and TOM situations. If it is within limits at both, then the CG will remain within limits throughout the flight, and it should not go out of limits during the journey — provided the fuel is used in the correct sequence. That’s a key operational point: fuel burn order matters for keeping the CG in envelope. Now the landing CG. Here’s the procedure. First, determine the moment of the fuel used in flight — that’s the trip fuel — by multiplying its mass by the fuel arm. In light aircraft, the fuel arm will usually be the same one used previously to calculate the take-off CG position. But caution is required, because in some large aircraft the balance arm of the fuel may change with the quantity of fuel consumed. So you can’t always assume a constant fuel arm. And here’s the critical sign convention, and I want you to really lock this in. 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 mass, you’re adding a negative mass, and that flips the sign of its moment contribution. That’s how the landing CG shifts relative to the take-off CG. So the whole picture is: you build up masses and moments, you check limits, you divide moment by mass to get the CG position in inches aft of the datum, and you watch the sign of the fuel moment when you compute the landing condition. That’s the complete take-off and landing CG determination procedure.