Let’s pick this up right where the numbers start doing the real work — Page 44, Lesson 59

Let’s pick this up right where the numbers start doing the real work. We’ve got a worked example in front of us, and I want you to see exactly how the Basic Empty Mass and the Centre of Gravity come out of the weighing scales. Look at the top line: +60 000. That’s the moment from one of the main wheels. Below it we have BEM = 4500 lb, and the Total Moment = +110 000 lb in. Then the CG is calculated as: CG = Total Moment ÷ Total Mass = +110 000 lb in ÷ 4500 lb = +24.4 inches. So the Basic Empty Mass of this aeroplane is 4500 lb, and the CG is 24.4 inches behind the datum — that’s what the positive sign tells us. Positive means behind the datum; negative would mean in front. Now, where does that 4500 lb come from? The Basic Empty Mass is found by adding together the readings on the scales. Simple addition of the three wheel loads. But to find the CG position, we don’t just add — we need to take moments about the datum. And here’s the key definition: in Mass & Balance terms, a moment is a mass multiplied by a balance arm. The arm is the distance from the datum to where that mass acts. Remember the sign convention: arms forward of the datum are negative, and a negative multiplied by a positive gives a negative value. That’s why the nose wheel line shows a negative moment. Look at the table under the example. We have three entries above the line: - Nose wheel: weight 500, arm −20, moment −10 000. - L. Main wheel: 2000, arm +30, moment +60 000. - R. Main wheel: 2000, arm +30, moment +60 000. Each entry is a mass multiplied by an arm to give a moment. Add the moments: −10 000 + 60 000 + 60 000 = +110 000 lb in. Add the masses: 500 + 2000 + 2000 = 4500 lb. That’s your BEM. Now notice something important: the entry below the line — the CG — consists of a mass and a moment but no balance arm. The missing arm is exactly the CG position. So to find it, you divide the total moment by the total mass. That’s the whole trick: CG = Total Moment ÷ Total Mass. And the sign of the answer tells you the location: if the CG value is negative, the CG is in front of the datum; otherwise it’s behind the datum. Now, I have to stop here and make a critical distinction — mass versus weight. This is a classic trap. Mass is the amount of matter in a body, measured in kilograms. Weight is the force that the matter exerts on the earth’s surface, measured in Newtons. They are not the same thing. So if the weighing scales give you readings in Newtons, but the question asks for the BEM and CG position, you must convert weight into mass before you can get the right answer. Look at the second version of the example. The table now shows weights in Newtons: - Nose wheel: 500 N, arm −20, moment −10 000 N in. - L. Main wheel: 2000 N, arm +30, moment +60 000 N in. - R. Main wheel: 2000 N, arm +30, moment +60 000 N in. The total weight is 4500 N, and the total moment is +110 000 N in. Dividing gives CG = +24.4 inches — same position, because the arms haven’t changed. But here’s the catch: the weight of the aeroplane is 4500 N, yet to find the Basic Empty Mass we must divide the weight by the acceleration due to gravity, 9.81 m/s². So: 4500 N ÷ 9.81 m/s² = 458.7 kg. That’s the BEM — 458.7 kg — and the CG is still 24.4 inches behind the datum. So the rule is: whenever your scale readings are in Newtons, convert to mass by dividing by 9.81 before you call it the Basic Empty Mass. The moment calculation itself works the same way — you just carry the units through. Now, the excerpt gives you three practice problems to try yourself. Let me walk you through what each one is asking, because they each test a slightly different skill. Problem 1: An aeroplane with a two-wheel nose gear and four main wheels rests on the ground with a single nose wheel load of 725 kg and a single main wheel load of 6000 kg. The distance between the nose wheels and the main wheels is 10 metres. You’re asked for the BEM and how far the centre of gravity is in front of the main wheels. Notice — here the datum isn’t given directly; you’re working relative to the main wheels. So you’ll need to set your arms accordingly. Problem 2: A tail wheel aeroplane has readings of 2000 lb and 2010 lb for the main wheels and 510 lb for the tail wheel. The tail wheel is 16 feet from the main wheels. You’re asked for the BEM and CG position, and you’re given the conversion 1 foot = 12 inches. So you’ll need to convert feet to inches to keep your arms consistent with the moment units. Problem 3: A light aircraft has the datum 20 inches behind the nose wheel and 70 inches forward of the main wheels. The readings are 255 N on the nose wheel and 1010 N on each main wheel. Here you’ve got Newtons again, so remember to convert to mass by dividing by 9.81 for the BEM. And you’ve got to work out the arms from the datum — the nose wheel is 20 inches forward of the datum, so its arm is negative; the main wheels are 70 inches behind the datum, so their arms are positive. The answers are shown on page 92, so you can check your work. One more thing I want to make sure you carry forward: the moment sign convention. Forward of the datum is negative, behind is positive. That single rule drives everything — the nose wheel moment is negative, the main wheel moments are positive, and the final CG sign tells you which side of the datum you’re on. So the complete picture: weigh the aeroplane on scales, add the readings for BEM, multiply each load by its arm for moments, sum the moments, divide by total mass for the CG, and if your scales read in Newtons, divide by 9.81 to get mass in kilograms. That’s the whole procedure in one breath.