Definitions and Calculations — Page 80, Lesson 103

Let's pick this up right where the load sheet leaves off. We've just finished the traffic load in Part A, and now I want to walk you through Part B — the load and trim calculation itself. In Part B, we enter the graph at the top. You draw a vertical line down from the DOM index of 45, and that line goes into the row for cargo compartment 1. Now, this row is split into sections by heavy lines, and each heavy line represents 1000 kg. Each of those sections is split again into 10 smaller divisions, and each of those smaller lines represents 100 kg. So you've got a scale that reads in hundreds of kilograms, with the heavy marks at every thousand. There's also an arrow in the box, and that arrow tells you the direction to move along the row to adjust for that mass. So the arrow is your sign convention — it tells you whether adding mass to that compartment shifts the CG index up or down the scale. You follow the same procedure for each cargo compartment and each seating compartment, until you've adjusted for all of the traffic load. That's the key discipline here — you work through every compartment in sequence, one at a time, using the same vertical-line entry and the same arrow direction for each. Now, before you adjust for the fuel load, you draw the line down to intersect with the zero fuel mass. That intersection identifies the ZFM CG position — the zero fuel mass centre of gravity. That's your CG with all the traffic on board but before any fuel is added. Then you adjust for the fuel index, which you take from the data sheets on page 30. You apply that fuel index adjustment, and then draw the line vertically down again to identify the take-off CG position. So the sequence is: traffic load first, then capture the ZFM CG, then fuel, then capture the take-off CG. Now let's look at the worked example that follows. This is a typical exam question for Part A — calculating the traffic load or underload. The question gives you a scheduled flight of three hours estimated time, within Europe, and asks you to calculate the maximum mass of freight that may be loaded. You're told to work it out using both the load sheet method from page 71 and the calculation method from page 64. Here's the data. The performance limited take-off mass is 67 900 kg. The performance limited landing mass is 56 200 kg. The MZFM — maximum zero fuel mass — is 51 300 kg. The DOM — dry operating mass — is 34 960 kg. Fuel on board at ramp is 15 800 kg, and taxi fuel is 450 kg. So let's think about what this question is really asking. You've got a three-hour flight within Europe, so you need enough fuel for that trip. The maximum freight you can load is constrained by three separate limits: the take-off mass limit, the landing mass limit, and the zero fuel mass limit. The freight is the traffic load, and you have to find the smallest of the three constraints — that's the one that binds. The take-off limit: take-off mass is DOM plus traffic load plus fuel on board. The landing limit: landing mass is take-off mass minus the fuel burned on the trip. And the zero fuel limit: ZFM is DOM plus traffic load, and that must not exceed the MZFM of 51 300 kg. So you work through each constraint, find the maximum traffic load each one permits, and the answer is the lowest of those three values. That's the maximum freight you can carry without exceeding any of the certified limits. Now, I want to be clear about the fuel figures here. The fuel on board at ramp is 15 800 kg — that's what's in the tanks when you're at the ramp, before taxi. The taxi fuel is 450 kg, which is burned during taxi-out. So the fuel available for the flight itself is the ramp fuel minus the taxi fuel. And the fuel burned during the three-hour flight is what reduces your mass from take-off to landing. Let me walk you through the take-off constraint first. Take-off mass equals DOM plus traffic load plus fuel on board at ramp. So 34 960 plus traffic load plus 15 800 must not exceed 67 900. That gives you one ceiling on the freight. Now the landing constraint. Landing mass equals take-off mass minus fuel burned. The fuel burned is the ramp fuel minus the taxi fuel, so 15 800 minus 450 gives you 15 350 kg of fuel available for the flight. But the landing mass limit is 56 200, and that's the take-off mass minus the fuel burned. So you need to work out what take-off mass would give you a landing mass of 56 200, and that constrains your freight differently. And the zero fuel constraint: ZFM equals DOM plus traffic load, and that must not exceed 51 300. So 34 960 plus traffic load must stay at or below 51 300. The maximum freight you can load is the smallest of these three ceilings. That's the whole point of the exercise — you're finding the binding constraint, the one limit that actually governs how much cargo you can carry on this particular flight. Now, I want to point you to the figures here. Figure 2.24 shows the load and trim calculation diagrams — that's the graph you're working with in Part B, with the cargo compartment rows and the fuel index adjustment. And Figure 2.25 shows a completed trim sheet, so you can see what the finished product looks like when all the lines are drawn and the CG positions are identified. Let me also make sure you understand the distinction between the two methods you're asked to use. The load sheet method from page 71 is the graphical approach — you're drawing lines on the load sheet and reading off values. The calculation method from page 64 is the arithmetic approach — you're computing the masses and moments directly. Both should give you the same answer, and that's why the question asks you to do both: it's a check on your understanding. So the key takeaways from this excerpt: Part B is the load and trim calculation, where you enter at the DOM index of 45, work through each cargo and seating compartment using the 1000 kg heavy lines and 100 kg subdivisions, capture the ZFM CG before fuel, then apply the fuel index and capture the take-off CG. And the example shows you how to find the maximum freight by testing all three limits — take-off, landing, and zero fuel — and taking the lowest result.