Definitions and Calculations — Page 44, Lesson 61

Let's get straight into it. We're going to calculate the loaded mass and centre of gravity for a light aircraft, and I want you to think of this as the core arithmetic of every flight you'll ever plan. The whole method rests on one idea: we tabulate the mass, the arm, and the moment of every item we load. Mass is the weight of the item in pounds. The arm is its distance from the datum — the reference point all measurements are taken from — in inches. And the moment is the product of those two, mass times arm. We'll actually record it as moment divided by 100, just to keep the numbers manageable, but the principle is exactly that multiplication. Here's the sequence. We start with the Basic Empty Mass, the BEM — that's the aircraft's mass with no passengers, baggage, fuel, or oil. To that we add the masses of the passengers, baggage, cargo, fuel, and oil. Adding all those masses to the BEM gives us the TOM, the Take-Off Mass. And we add all the individual moments together to get the Total Moment. The centre of gravity, the CG, is then simply the Total Moment divided by the Total Mass. That's the formula: CG equals Total Moment divided by Total Mass. Now, the Landing Mass, the LM, is found 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 standardization, all this mass, arm, and moment data is laid out on a Load Manifest or Load Sheet. That's the document we'll be working through. Let me give you the actual numbers we'll use for a single-engine piston aircraft we'll call SEP1. The Basic Empty Mass is 2415 pounds. Front seat occupants, 340 pounds. Third and fourth seat passengers, 340 pounds. Baggage zone B, 200 pounds. Fuel at engine start, 60 US gallons. And trip fuel — the calculated fuel burn for the flight — is 40 US gallons. Now let's walk through the completed load sheet, because that's where it all comes together. I'll read it line by line. First, the Basic Empty Mass: 2415 pounds, with an arm of 77.7 inches, giving a moment divided by 100 of 1876.46. Front seat occupants: 340 pounds, arm 79 inches, moment 268.6. Third and fourth seat passengers: 340 pounds, arm 117 inches, moment 397.8. Baggage zone A is nil — no load there — but its arm is 108 inches. Fifth and sixth seat passengers, nil, arm 152. Baggage zone B: 200 pounds, arm 150 inches, moment 300. Baggage zone C, nil, arm 180. Now, the subtotal of all those items is the Zero Fuel Mass, the ZFM. That's 3295 pounds, with a total moment of 2842.86. Next we add the fuel loading: 60 US gallons. Now, 60 US gallons of fuel weighs 360 pounds — that's the mass we enter. Its arm is 75 inches, giving a moment of 270. Adding that to the ZFM gives us the Ramp Mass: 3655 pounds, moment 3112.86. But before take-off we burn fuel for start, taxi, and run-up. The note tells us that's normally 13 pounds, at an average arm entry of 10 in the moment-divided-by-100 column. So we subtract 13 pounds of mass and 10 from the moment. That brings us to the Take-Off Mass: 3642 pounds, moment 3102.9. Then we subtract the trip fuel — the 40 US gallons we calculated as the burn. That's 240 pounds of fuel, at arm 75, so a moment of 180. Subtracting that gives us the Landing Mass: 3402 pounds, moment 2922.9. So you see the full chain: ZFM, then Ramp Mass, then Take-Off Mass, then Landing Mass. Each one is a subtotal in the load sheet. The arm data is entered in the appropriate columns, and each individual moment is calculated by multiplying the mass of an item by its balance arm from the datum, then entering that figure in the moment column. Once the load sheet is complete, we can use it to check that the limiting values haven't been exceeded — the MZFM, the maximum zero fuel mass; the Ramp Mass limit; the MSTOM, the maximum structural take-off mass; and the 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 find the take-off mass and its CG; then subtract the fuel burn to find the landing mass and its CG. That's the complete calculation for a light aircraft.