Definitions and Calculations — Page 80, Lesson 103

Let's pick this up right where the load sheet leaves off. We've just finished filling in the traffic load on the sheet, and now we're moving into the heart of the trim sheet — the graphical part where we actually see the centre of gravity move. I want to walk you through Part B of the load sheet, which is the load and trim calculation diagram. This is the graph you see in Figure 2.24. We enter it at the top, and we work our way down. Here's the procedure. We start with the DOM index — that's the Dry Operating Mass index, a number that represents the position of the aircraft's empty and fixed equipment mass. In our example, that index is 45. So we draw a vertical line down from the DOM index of 45 at the top of the graph, and we bring it into the row for cargo compartment 1. Now, here's the clever bit. That row for cargo compartment 1 is split into sections by heavy lines. Each heavy line represents 1000 kg of mass. And each of those sections is split again into 10 smaller divisions, so each small line represents 100 kg. So as you move along that row, you're effectively moving the centre of gravity by a known amount for every 100 kg you load into that compartment. There's an arrow in the box, and that arrow tells you the direction to move along the row to adjust for that mass. So if you're loading mass into compartment 1, you move in the direction the arrow points, by the number of divisions that corresponds to the mass you've loaded. We follow exactly the same procedure for each cargo compartment or seating compartment — one row at a time, moving along each row by the appropriate amount for the mass in that compartment. We keep doing this until we've adjusted for all of the traffic load. Traffic load, remember, is everything that earns revenue — passengers, baggage, cargo, mail. Now, before we adjust for the fuel load, we do something important. We draw the line down to intersect with the zero fuel mass — the ZFM. That intersection gives us the ZFM CG position. The zero fuel mass is the mass of the aircraft with all traffic loaded but no usable fuel, and its centre of gravity position is a critical check — it tells us where the CG sits before fuel is added. Then, and only then, do we adjust for the fuel index. That fuel index is taken from the data sheets — specifically, page 30 of the manual. We adjust for that fuel, and then draw the line vertically down to identify the take-off CG position. That's the final position of the centre of gravity at the moment of take-off, with all traffic and all fuel on board. So the sequence is: DOM index down, adjust for each compartment, down to ZFM, check the ZFM CG, adjust for fuel, down to take-off CG. That's the whole graphical procedure. Now, let me show you how this all ties together with a worked example — a typical exam question. This is a scheduled flight of three hours estimated time, within Europe. We're given a set of data, and we're asked to calculate the maximum mass of freight that may be loaded. Here's the data. The performance limited take-off mass is 67 900 kg. That's the maximum mass the aircraft may have at take-off, limited by runway length, obstacle clearance, or climb performance. The performance limited landing mass is 56 200 kg — the maximum mass at landing, again performance-limited. The MZFM — the Maximum Zero Fuel Mass — is 51 300 kg. The DOM — Dry Operating Mass — is 34 960 kg. The fuel on board at ramp is 15 800 kg. And the taxi fuel is 450 kg — that's the fuel burned during taxi from the ramp to the runway. Now, the question asks for the maximum freight. To work this out, you can use either the load sheet method we've just described, or the calculation method. Let's think about what limits us. The take-off mass is limited by the performance limited take-off mass of 67 900 kg. But we have fuel on board at ramp of 15 800 kg, and we'll burn 450 kg of that in taxi. So the take-off mass will be the ramp mass minus the taxi fuel. The ramp mass is DOM plus traffic load plus fuel on board at ramp. The landing mass is limited by the performance limited landing mass of 56 200 kg. At landing, we'll have burned the trip fuel — the three hours of fuel — so the landing mass is the take-off mass minus the trip fuel. And the zero fuel mass is limited by the MZFM of 51 300 kg. The ZFM is DOM plus traffic load — no fuel. So the maximum freight is the smallest of the masses allowed by these three limits, after we account for the fuel. The freight is part of the traffic load. So we work out the maximum traffic load allowed by each limit, and the freight is the traffic load minus the passenger and baggage mass — but in this question, we're told to calculate the maximum freight, so we treat the traffic load as freight. Let me walk you through the calculation. First, the take-off limit. The take-off mass must not exceed 67 900 kg. The take-off mass is ramp mass minus taxi fuel. Ramp mass is DOM plus traffic plus fuel on board at ramp. So: 34 960 plus traffic plus 15 800, minus 450, must be less than or equal to 67 900. That gives us a maximum traffic load of 17 590 kg from the take-off limit. Second, the landing limit. The landing mass must not exceed 56 200 kg. The landing mass is take-off mass minus trip fuel. The trip fuel is the fuel on board at ramp minus taxi fuel, which is 15 800 minus 450, giving 15 350 kg of fuel at take-off. But we need to know the trip fuel for three hours. In this question, we're told the fuel on board at ramp is 15 800 kg, and taxi fuel is 450 kg, so the fuel at take-off is 15 350 kg. The trip fuel is what's burned during the three-hour flight. For the landing limit, we need to know that trip fuel. In the CAP 696 MRJT1 data, the trip fuel for three hours would be given. But from the data we have, we can work it out: the landing mass is take-off mass minus trip fuel, and the take-off mass is limited to 67 900, so the landing mass is 67 900 minus trip fuel, which must be less than or equal to 56 200. That gives us a trip fuel of at least 11 700 kg. So the trip fuel for three hours must be at least 11 700 kg. Third, the zero fuel limit. The ZFM must not exceed 51 300 kg. The ZFM is DOM plus traffic load. So 34 960 plus traffic must be less than or equal to 51 300. That gives us a maximum traffic load of 16 340 kg from the zero fuel limit. Now, the take-off limit gave us 17 590 kg of traffic, but the zero fuel limit gives us only 16 340 kg. The landing limit depends on the trip fuel. If the trip fuel is 11 700 kg, then the landing limit gives us the same as the take-off limit: 67 900 minus 11 700 is 56 200, so the traffic would be 17 590 kg as well. But the zero fuel limit is the binding one here — it gives us the smallest traffic load of 16 340 kg. So the maximum mass of freight that may be loaded is 16 340 kg, limited by the Maximum Zero Fuel Mass. That's the whole picture. The load sheet method on page 71 and the calculation method on page 64 should give you the same answer — the ZFM limit is the one that binds in this case.