Definitions and Calculations — Page 50, Lesson 65

Let’s pick this up right where the calculation leaves off. We’ve just worked out the Landing Mass and the Landing Moment, and now I want to show you the final step — finding the landing CG position — and then the graphical shortcut that ties the whole thing together. First, the arithmetic we already have. The Take-Off Mass, the TOM, was 3642 pounds. We subtracted the fuel used during the flight, 240 pounds, and got a Landing Mass of 3402 pounds. That’s the mass column. Then in the moments column, we took the TOM moment of 310,286 pound-inches, and we had to decide the sign of the fuel moment. Fuel is being removed, so its moment is negative — we subtract it. The fuel moment is the fuel mass times its arm: 240 pounds times 75 inches, which is 18,000 pound-inches. So the Landing Moment is 310,286 minus 18,000, giving 292,286 pound-inches. And you’ll often see that abbreviated as 2922.9 pound-inches in the shorthand form where the moment is divided by 100. Now, the key point about whether you even need to compute the landing CG. For a large aircraft, if the CG is within limits at the Zero Fuel Mass — the ZFM — then it is not normally necessary to calculate the landing CG position at all. Why? Because, as we stated earlier, the CG will remain within limits throughout the entire flight. The fuel burn doesn’t push it out of the envelope. But for a light aircraft, it is usual to determine the landing CG position, because the margins are tighter and you want to confirm it explicitly. And that calculation is simply the landing moment divided by the landing mass. So we take 292,286 pound-inches and divide by 3402 pounds, and that gives us 85.92 inches aft of the datum. Notice the sign — it’s positive, so it’s aft of the datum. That’s the landing CG position. Now, there’s a second way to find the CG, and that’s the graphical method using the Centre of Gravity Envelope for the SEP1. Let me explain what this envelope actually is. It’s a graphical representation of the mass and centre of gravity limits — the two things we’ve been juggling all along. The vertical axis is the mass in pounds. The horizontal axis is the CG position in inches aft of the datum. And the slanted lines that run across the plot represent the moment divided by 100 — that’s the abbreviated moment form we saw earlier, the 2922.9 figure. So what you’re doing with this graph is plotting your mass against your CG position, and you check that the point falls inside the envelope — inside the limits. If it does, you’re within the certified mass and CG limits. The slanted lines let you read off the moment/100 value directly, which is why we bothered to express moments in that abbreviated form. That figure shows you the SEP1 CG Envelope itself — the vertical mass axis, the horizontal CG position axis, and those slanted moment/100 lines. So you have two tools for the same job: the arithmetic division of moment by mass, and the graphical envelope check. Both give you the CG position, and both confirm you’re within limits.