So, question 7 — Page 58, Lesson 77

I want to walk you through the rest of that worked example first, because it ties together the fuel-loading calculation we've been doing, and then we'll move into the graphical presentation of mass and CG, and finally into cargo handling. So, question 7. We have an aeroplane with a zero fuel mass of 47,800 kg and a performance-limited take-off mass of 62,600 kg. The leading edge of the mean aerodynamic chord, the MAC, is 16 m from the datum, and the trailing edge is 19.5 m from the datum. We need to find how much fuel, in imperial gallons, must be taken on board to move the CG from 30% MAC to 23% MAC. The tank arm is 16 m aft of the datum, and the fuel specific gravity, the SG, is 0.72. Let's break this down. First, the MAC length is the trailing edge minus the leading edge: 19.5 minus 16, which is 3.5 m. The CG is moving from 30% to 23% of the MAC, so that's a shift of 7% of the MAC. Seven percent of 3.5 m is 0.245 m. So the CG moves forward by 0.245 m. Now, the mass change. We're adding fuel, so the total mass increases. The new mass is the zero fuel mass plus the fuel mass we add. The CG shift formula relates the change in CG position to the mass added and the arm of that added mass. The fuel tank arm is 16 m aft of the datum, and the original CG is at 30% MAC. The CG position from the datum is the leading edge plus 30% of the MAC: 16 plus 0.3 times 3.5, which is 16 plus 1.05, so 17.05 m. The new CG at 23% MAC is 16 plus 0.23 times 3.5, which is 16 plus 0.805, so 16.805 m. The shift is the difference: 17.05 minus 16.805, which is 0.245 m, matching what we calculated. Now, the formula for CG shift when adding mass is: the shift equals the mass added times the distance between the added mass arm and the new CG, divided by the new total mass. But we can also use the moment method. The moment about the datum before adding fuel is the zero fuel mass times the original CG arm: 47,800 times 17.05. After adding fuel, the total mass is 47,800 plus the fuel mass, and the new CG arm is 16.805 m. The moment after is the total mass times 16.805. The difference in moment is the fuel mass times its arm, 16 m. So we set up: (47,800 + fuel) times 16.805 equals 47,800 times 17.05 plus fuel times 16. Let's solve. The left side is 47,800 times 16.805 plus fuel times 16.805. The right side is 47,800 times 17.05 plus fuel times 16. Subtract 47,800 times 16.805 from both sides: fuel times 16.805 minus fuel times 16 equals 47,800 times 17.05 minus 47,800 times 16.805. The right side is 47,800 times 0.245, which is 11,711. The left side is fuel times 0.805. So fuel equals 11,711 divided by 0.805, which is 14,548 kg approximately. Now, we need imperial gallons. The fuel SG is 0.72, meaning the density is 0.72 times the density of water. One imperial gallon of water weighs 10 pounds, or about 4.546 kg. So one imperial gallon of fuel weighs 0.72 times 4.546 kg, which is about 3.273 kg. So the fuel mass in kg divided by the weight per gallon gives the volume in gallons: 14,548 divided by 3.273, which is approximately 4,445 imperial gallons. That's the answer. Now, let's move to the graphical presentation. In practice, we don't always do these calculations by hand. We use graphs. The key point is that any mass and CG envelope graph has two things in common. First, the CG must be within the envelope or on the line of the envelope. Second, the mass of the aeroplane is always shown on the vertical scale. The horizontal scale can vary. It might use the CG position in inches, metres, or centimetres. It might use the moment of the CG in kg inches, kg metres, or kg centimetres. Or it might use the percentage of the CG along the mean aerodynamic chord. Different aircraft types use different presentations. For example, the SEP1 envelope in CAP 696 uses both mass and moments on the vertical scale, which is unusual. The MEP1 envelope uses CG position on the horizontal scale, and the MRJT envelope uses the MAC percentage. So when you're using these graphs, you plot the mass on the vertical axis and the CG position or moment on the horizontal axis, and you check that the point falls within the envelope. Now, let's look at cargo handling. This is about how we physically load the aeroplane. We have cargo compartments in the lower deck that accommodate baggage and cargo. These compartments have fire-resistant sidewalls, ceilings, and walkways. They're usually pressurized and heated, and they typically have fire detection and protection equipment. Each compartment has a maximum floor loading, measured in kg per square metre, and a maximum running load value, measured in kg per metre. The floor loading tells you how much weight per unit area the floor can support, and the running load tells you how much weight per unit length along the floor. There are three main types of cargo. Containerized cargo is loaded into standard-size containers that fit and lock into the compartment. Each container has an individual maximum mass limit and an individual floor loading limit, which is the mass per unit area. Palletized cargo is loaded onto standard-size pallets and restrained with cargo nets or strops. Typically, the forward area of the forward cargo compartment is configured to take palletized freight. Bulk cargo is loosely loaded in the area at the aft of the rear cargo compartment, separated from the containers by a restraining net attached to the floor, ceiling, and sidewalls. Finally, the cargo handling systems. The forward and aft cargo compartments typically have separate cargo power drive systems to move containers and cargo pallets. The power drive system is operated by a control panel at the door area of each compartment, and it's capable of loading and unloading fully loaded containers or pallets in wet or dry conditions. A typical panel is shown in Figure 2.17. So to summarize: we've done the fuel calculation, we understand the graphical envelope, and we know how cargo is physically loaded and restrained. Each of these is part of the mass and balance picture — the calculation, the graphical check, and the physical loading all have to work together to keep the CG within limits.