Definitions and Calculations — Page 73, Lesson 101

Let’s pick this up right where the load sheet procedure gets concrete. We’ve already walked through the early steps of the loading manifest — the rows of boxes for each compartment, the index calculations, and how you drop a vertical line down to bisect a mass on the envelope. Now I want to take you through the final steps of that procedure, and then into the worked example that ties the whole thing together. So, step 4: you repeat operations 1 to 3 for each subsequent row of boxes, all the way down to and including row 0g. That’s the last row — the one labelled 0g. After you’ve completed the index calculation for row 0g, you drop a line vertically down until it bisects a mass on the vertical scale of the envelope corresponding to the Zero Fuel Mass. And here’s the critical check: that point of bisection must occur within the MZFM envelope. MZFM, by the way, is Maximum Structural Zero Fuel Mass — the maximum mass the aeroplane may be at with no usable fuel in the tanks. If your bisection point falls outside that envelope, you’re not within limits. Step 5: you go to the horizontal row of boxes marked ‘Fuel index’ and add the take-off fuel index. That’s the index value for the fuel you’ll have on board at take-off. Step 6: after completing that fuel index calculation, you drop a line vertically down from it until it bisects a mass on the vertical scale of the envelope corresponding to the Take-off Mass. And again, the point of bisection must occur within the TOM envelope — the Take-off Mass envelope. Step 7: providing both the ZFM and the TOM are within their respective envelopes as described, the aircraft is safe for the intended flight — including any permitted diversions. That’s the whole point of the exercise: two envelope checks, one for zero fuel mass, one for take-off mass, and if both bisections fall inside, you’re cleared. Now let’s make this real with the worked example. The data given is: DOM equals 34,300 kg. DOM is Dry Operating Mass — the mass of the aeroplane ready for service, including crew, catering, and everything except traffic load and fuel. DOI is 45.0 — that’s the Dry Operating Index, the index value for the dry operating mass. RTOM is 62,800 kg — that’s the Regulated Take-off Mass, the maximum take-off mass permitted for the existing airfield conditions. MZFM is 51,300 kg, the Maximum Structural Zero Fuel Mass. And RLM is 54,900 kg — Regulated Landing Mass, the maximum landing mass permitted. Then we have the traffic load. Passengers: 130, at an average mass of 84 kg each. Baggage: 130 pieces, at 14 kg per piece. Cargo: 630 kg. Take-off fuel: 14,500 kg. Trip fuel: 8,500 kg. Now, the limitations for this EASA Medium Range Twin Jet. Maximum Structural Taxi Mass: 63,060 kg. Maximum Structural Take-off Mass: 62,800 kg. Maximum Structural Landing Mass: 54,900 kg. Maximum Structural Zero Fuel Mass: 51,300 kg. Maximum number of passengers: 141. Then the cargo holds. Hold 1: max volume 607 cubic feet, max load 3,305 kg. Hold 2: max volume 766 cubic feet, max load 4,187 kg. And the standard crew, which is already allowed for in the DOM: flight deck, 2; cabin crew forward, 2; cabin crew aft, 1. Now here’s the key concept for Section 1 of the load sheet. Section 1 is completed first, and its purpose is to find the three potential take-off masses — labelled (a), (b), and (c). Let me explain each one carefully. Value (a) is the take-off mass you would achieve if you loaded the aeroplane to the MZFM — that is, right up to the maximum structural zero fuel mass — and then added your intended fuel load. So it’s MZFM plus the fuel you plan to carry. Value (b) is the regulated take-off mass for the take-off airfield conditions as existing. That’s the RTOM — the mass the regulations allow you to take off at, given the runway length, temperature, pressure altitude, and so on at the departure airfield. Value (c) is the take-off mass you would achieve if you were to land at the regulated landing mass — the RLM — and then added back the mass of the trip fuel. So it’s RLM plus trip fuel. Now, the lowest of (a), (b), and (c) is the limiting take-off mass for traffic load calculations. That’s the governing value — the one that constrains how much traffic load you can carry. The maximum allowable traffic load for the trip is then determined by subtracting the operating mass from that limiting take-off mass. Operating mass here is the DOM — the dry operating mass. So allowable traffic load equals limiting take-off mass minus DOM. Then, any underload can be calculated by subtracting the actual traffic load from the allowable traffic load. And the example gives you the numbers: 14,000 minus 13,370 equals 630. So the allowable traffic load is 14,000 kg, the actual traffic load is 13,370 kg, and the underload is 630 kg. That underload sets the limiting mass for any last minute changes — LMC. In other words, if you need to add or move load at the last minute, the underload is the margin you have to play with. Finally, Sections 2 and 3 of the load sheet detail the mass and distribution of the traffic load, and give the actual values of take-off and landing masses. So Section 1 finds the limiting take-off mass and the allowable traffic load; Sections 2 and 3 then show how that traffic load is actually distributed across the holds and cabins, and give you the real take-off and landing masses for the flight. Let me just make sure the arithmetic hangs together for you. The actual traffic load is 13,370 kg. Let’s check that: 130 passengers at 84 kg each is 10,920 kg. 130 baggage pieces at 14 kg each is 1,820 kg. Cargo is 630 kg. Add those together: 10,920 plus 1,820 is 12,740, plus 630 is 13,370. Yes — that matches the actual traffic load in the example. And the allowable traffic load of 14,000 kg comes from the limiting take-off mass minus the DOM. The difference between them, 630 kg, is your underload — your LMC margin. So the whole logic of Section 1 is: find the three candidate take-off masses, take the lowest as the limiter, subtract the operating mass to get the allowable traffic load, and compare that with what you actually plan to carry to find your underload. That underload is your safety margin for last-minute changes.