So that's +110 000 lb inches divided by 4500 lb, which gives us +24.4 inches — Page 44, Lesson 59

Right, let's pick this up with the worked example we've got in front of us. We've got an aeroplane with a Basic Empty Mass of 4500 lb, and the total moment is +110 000 lb inches. To find the centre of gravity, we divide that total moment by the total mass. So that's +110 000 lb inches divided by 4500 lb, which gives us +24.4 inches. That positive sign tells us the CG is 24.4 inches behind the datum. Now, where does that 4500 lb come from? The Basic Empty Mass is found by simply adding together the readings on the scales. In this example, we've got three weighing points: the nose wheel and the left and right main wheels. Each of those three entries above the line is a mass multiplied by an arm to give a moment. The nose wheel is 500 lb at an arm of -20 inches, giving -10 000 lb inches. The left and right main wheels are each 2000 lb at an arm of +30 inches, each giving +60 000 lb inches. Add those three moments together and you get the total moment of +110 000 lb inches. Here's the key idea I want you to hold onto. In Mass and Balance terms, a moment is a mass multiplied by a balance arm. And remember, arms forward of the datum are negative. A negative multiplied by a positive gives a negative value — that's why the nose wheel moment comes out negative. The entry below the line consists of a mass and a moment but no balance arm. That missing arm is exactly what we're solving for — the CG position. So to find the CG, we divide the total moment by the total mass. If the CG value comes out negative, the CG is in front of the datum; otherwise it's behind it. Now, I need to make a careful distinction here between mass and weight, because it's easy to slip up. 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. Let me show you why that matters. The next example in front of us uses the same aeroplane, but this time the scale readings are given in Newtons. The nose wheel is 500 N at -20 inches, giving -10 000 N inches. The main wheels are each 2000 N at +30 inches, each giving +60 000 N inches. The total moment is +110 000 N inches, and dividing by the total weight of 4500 N gives us the same +24.4 inches for the CG position. But here's the trap. The weight of the aeroplane is 4500 N, but to find the Basic Empty Mass, we must convert that weight into mass. We divide the weight by the acceleration due to gravity, 9.81 metres per second squared. So 4500 N divided by 9.81 m/s² gives us 458.7 kg. That's the BEM — 458.7 kg — and the CG is still 24.4 inches behind the datum. So if the question asks for BEM and CG, and the scale readings are in Newtons, you must convert weight into mass first, or you'll get the wrong answer. Now, I want you to try a few of these yourself. There are three examples here. The first is an aeroplane with a two-wheel nose gear and four main wheels, resting 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 need to find the BEM and how far the centre of gravity is in front of the main wheels. The second is a tail wheel aeroplane with 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. Find the BEM and CG position — and remember, 1 foot equals 12 inches. The third is a light aircraft with the datum 20 inches behind the nose wheel and 70 inches forward of the main wheels. The scale readings are 255 N on the nose wheel and 1010 N on each main wheel. Find the BEM and CG position. The answers are on page 92, so work through them and check yourself. The key steps to remember: add up the scale readings for the BEM, take moments about the datum to find the total moment, divide total moment by total mass to get the CG, and if your readings are in Newtons, convert to mass by dividing by 9.81 before you state the BEM.