Definitions and Calculations — Page 73, Lesson 96

Let’s pick up right where the calculation left off. We had just worked out the underload for the MRJT1: maximum traffic load minus actual traffic load, which came to 12,800 kg minus 12,400 kg, giving us 400 kg of underload. That’s the spare payload capacity you have left after loading the aeroplane. Now I want to walk you through the full example calculation, because this is where the definitions and calculations chapter really comes together. We’re going to use two methods: the Loading Manifest, which is a data sheet, and the Load and Trim Sheet. Both are in CAP 696, Chapter 4, for the MRJT1. Let me give you the input values first, because everything hangs off these. The Dry Operating Mass, or DOM, is 34,300 kg, and its centre of gravity position is 15% MAC. MAC stands for Mean Aerodynamic Chord — that’s the reference line for the CG position, expressed as a percentage of the chord length. The passengers: total 116, at a standard weight of 84 kg each. They’re distributed across zones: 10 each in zones A and G, 12 each in zones B and F, and 24 each in zones C, D, and E. So that’s the passenger distribution across the cabin. Cargo: 600 kg in hold 1, and 1,500 kg in hold 4, and that hold 4 figure includes checked baggage. Fuel: 15,000 kg at take-off, 260 kg for start and taxi, and 10,000 kg trip fuel. So the trip fuel is what you burn en route, and the start and taxi fuel is what you burn before take-off. Now, the key technique here: you use the CAP 696 MRJT1 data sheets to find the balance arm for the MAC, and vice versa. The moment divided by 1,000 is calculated from the arm divided by 1,000. And the balance arm itself is calculated by dividing the total moment by the total weight. The fuel balance arm and the quantity in each tank also come from the data sheets. One important note: the centre fuel tank content is used before the wing tank fuel content, and the centre tank includes 24 kg of unusable fuel. Unusable fuel is fuel you can’t actually burn — it stays trapped in the tank. Let me walk you through the first calculation. If the DOM CG position is 15% MAC, and the MAC is 134.5 inches, then 15% of 134.5 inches is 20.175 inches. That makes the CG balance arm 20.175 plus 625.6, which equals 645.8 inches aft of the datum. The datum is the reference point from which all arms are measured. The fuel load balance arm can be extracted from the loading manual figures. For example, the maximum contents of tanks one and two is 9,084 kg, with a balance arm of 650.7 inches. Now, a practical note from me: in my worked answer, I estimated changes to the fuel tank CG position and accounted for the unusable fuel in the centre tank. But in the EASA exams, the fuel CG position will be fixed, and there will be no unusable fuel to account for. So don’t worry about that complication for exam purposes. If you want to check your mass values and CG positions using the Load and Trim Sheet for the MRJT1, you use a DOI of 40.5. DOI stands for Dry Operating Index — it’s a way of expressing the DOM CG position as an index number, which makes the trim sheet calculations easier. Finally, the maximum permissible aeroplane mass values you need to check against are: taxi mass, zero fuel mass, and take-off mass. Taxi mass is the mass at the start of taxiing, before take-off. Zero fuel mass is the mass of the aeroplane with all payload and cargo but no usable fuel. Take-off mass is the mass at the moment of take-off. You check each of these against the CG envelope to make sure you haven’t exceeded any limits. So the whole process is: fill in the Loading Manifest with these values, calculate the moments, find the balance arm by dividing total moment by total weight, then check the CG position and the three mass limits against the CG envelope. That’s the complete method.