Definitions and Calculations — Page 44, Lesson 61

Let’s start with the big picture. When we load an aircraft, we don’t just care about how heavy it is — we care about where that weight sits, because that determines the centre of gravity, the CG. For a light aircraft, we work this out by tabulating three things for every item we put on board: the mass, the arm, and the moment. Let me define those precisely, because they’re the backbone of everything here. The mass is simply the weight of the item, in pounds. The arm is the horizontal distance from a reference point called the datum to the centre of gravity of that item, measured in inches. The moment is the product of the two — mass multiplied by arm — and it’s the measure of the turning effect that item has about the datum. Now, the procedure. We take the mass, arm, and moment of the passengers, baggage, cargo, fuel, and oil, and we tabulate them. We add all the masses to the BEM — that’s the Basic Empty Mass, the aircraft as it sits with standard equipment and unusable fuel and oil, but no payload. Adding the payload masses to the BEM gives us the TOM, the Take-Off Mass. And we add all the moments together to get the Total Moment. Then the CG position is found by dividing the Total Moment by the Total Mass. So the formula is: CG = Total Moment ÷ Total Mass. That gives you the CG location in inches from the datum. Then we go one step further for the LM, the Landing Mass. We find the LM by subtracting the fuel and oil consumed during the flight from the TOM. And to find the CG position of the LM, we take moments again — we divide the LM Moment by the LM. For simplicity and standardisation, all this mass, arm, and moment data is laid out on a Load Manifest or Load Sheet. That’s the document we’re going to work through. Now, let’s work a real example. We’re using a single-engine piston aircraft called SEP1. Here are the values we start with. The Basic Empty Mass is 2415 lb. Front seat occupants — 340 lb. 3rd and 4th seat passengers — another 340 lb. Baggage zone B — 200 lb. Fuel at engine start — 60 US gallons. And trip fuel, the calculated fuel burn for the flight — 40 US gallons. Now look at the completed load sheet, which is Figure 2.9. Let me walk you down it row by row, because this is where it all comes together. First row: Basic Empty Mass — mass 2415 lb, arm 77.7 inches, and the moment is entered as 1876.46. Notice the column header says MOMENT/100. That’s a standardisation trick — the moment is divided by 100 to keep the numbers manageable. So the actual moment is 187,646 pound-inches, but we record 1876.46. Next, Front seat occupants — 340 lb, arm 79 inches, moment/100 of 268.6. Then 3rd and 4th seat pax — 340 lb, arm 117 inches, moment/100 397.8. Then we have rows for Baggage zone A — nil, arm 108; 5th and 6th seat pax — nil, arm 152; Baggage zone B — 200 lb, arm 150, moment/100 300; and Baggage zone C — nil, arm 180. Now, here’s an important point. The subtotal of all these items — everything except fuel — is called the ZERO FUEL MASS, the ZFM. That’s the mass of the aircraft with all payload but no usable fuel. In our example, the ZFM is 3295 lb, and the total moment/100 is 2842.86. Then we add the fuel. Fuel loading 60 US gallons — that’s 360 lb, at an arm of 75 inches, giving a moment/100 of 270. Adding that to the ZFM gives us the RAMP MASS — 3655 lb, with a total moment/100 of 3112.86. The ramp mass is the mass of the aircraft with all fuel on board, before we start the engines. Now, a note here. Fuel for start, taxi, and run-up is normally 13 lb, and it’s entered at an average arm of 10 inches in the moment/100 column. So we subtract 13 lb and 10 from the moment column. That gives us the TAKE-OFF MASS — 3642 lb, with a moment/100 of 3102.9. Then we subtract the trip fuel — 240 lb at an arm of 75 inches, moment/100 of 180. That gives us the LANDING MASS — 3402 lb, moment/100 2922.9. So you can see the full chain: ZFM → RAMP MASS → TAKE-OFF MASS → LANDING MASS, each step adding or subtracting fuel. Now, how are those individual moments calculated? The arm data is entered on the load sheet in the appropriate columns, and each moment is found by multiplying the mass of an item by its balance arm from the datum, then entering that figure in the moment column. So for the front seat occupants: 340 lb × 79 inches = 26,860 pound-inches, divided by 100 gives 268.6. That’s exactly what we see. Finally, once the load sheet is complete, we use it to check that the limiting values have not been exceeded. Those limits are MZFM — the Maximum Zero Fuel Mass, RAMP MASS — the maximum ramp mass, MSTOM — the Maximum Structural Take-Off Mass, and MSLM — the Maximum Structural Landing Mass. The mass and CG limits are presented graphically, and we check our calculated values against that graph. So the whole process is: tabulate mass, arm, and moment for every item, sum them to get the total mass and total moment, divide to find the CG, and then verify you’re inside the limits. That’s the complete method for calculating the loaded mass and CG position for a light aircraft.