In this example the performance limitation is not stated and could be anything — Page 117, Lesson 137

Let’s pick this up right where the worked example left off. We’ve just finished calculating the traffic load for a landing below the maximum structural landing mass, and now I want to walk you through the reasoning that sits behind that calculation — because in the exam, and in real operations, you need to understand why we do each step. First, a key point about the performance limitation in this example. Notice that the performance limitation is not stated — it could be anything. It might be a runway length restriction, a sloping runway, an obstruction limitation, and/or altitude and temperature limitations. That’s important because the performance limit is the one that governs how much we can actually take off with, and here we’re told it’s unspecified. So we work with the structural limits we do have. Now, why does landing below the maximum structural landing mass matter? Because when we land heavy, we have to brake hard. And heavy braking can cause a burst tyre, brake fade, and/or brake fire. Even if the tyres don’t burst, the tyre temperatures might exceed limits — and that can delay the take-off time, because you can’t just turn around and go again if the tyres are overheated. Also, the climb slope for obstacle clearance during a go-around might be reduced — that’s the gradient the aeroplane can achieve when it aborts the landing and climbs away. If we’re heavy, that slope is shallower, so obstacle clearance becomes marginal. But here’s the reassuring part: because the landing is below the MSLM — that’s the Maximum Structural Landing Mass — the structure itself should not suffer direct damage, providing the aeroplane comes to a stop without hitting anything. So the structural integrity is protected as long as we stop cleanly. Now let’s move to the actual calculation method. The golden rule for this sort of question is: work out the fuel states first. Once you know the fuel states, you can simply use the three formulae to determine the answer. Let me walk you through the numbers. We have: - TOF = 9700 + 1200 + 1400 = 12 300 kg. That’s the Take-Off Fuel — the total fuel on board at take-off. - FR = 1200 + 1400 = 2600 kg. That’s the Fuel Reserve — the fuel that must remain at landing. - DOM = 34 900 kg. That’s the Dry Operating Mass — the mass of the aeroplane ready for service but without traffic load and without fuel. - MZFM = 53 000 kg. Maximum Zero Fuel Mass — the maximum mass of the aeroplane with no usable fuel. - RTOM = 62 800 kg. Regulated Take-Off Mass — the maximum mass at which take-off is permitted. - RLM = 54 900 kg. Regulated Landing Mass — the maximum mass at which landing is permitted. Now, the three formulae. Each one gives us a candidate for the allowable traffic load — the mass of passengers, baggage and cargo we can carry. Formula 1: MZFM – DOM = 53 000 – 34 900 = 18 100 kg. This is the traffic load allowed by the zero fuel mass limit. Formula 2: RTOM – DOM – TOF = 62 800 – 34 900 – 12 300 = 15 600 kg. This is the traffic load allowed by the take-off mass limit, after subtracting the take-off fuel. Formula 3: RLM – DOM – FR = 54 900 – 34 900 – 2600 = 17 480 kg. This is the traffic load allowed by the landing mass limit, after subtracting the fuel reserve. Now, the allowable traffic load is the lowest of these three — because the most restrictive limit governs. So we take 15 600 kg. Next, we calculate the actual traffic load. That’s PAX plus baggage. We have 130 passengers, each at 84 kg, plus 130 bags at 14 kg each. So: Actual TL = (130 × 84) + (130 × 14) = 10 920 + 1820 = 12 740 kg. Now, the difference between the allowed traffic load and the actual traffic load is the underload — the spare capacity we have. And that underload is exactly the cargo that can be taken. Cargo = 15 600 – 12 740 = 2860 kg. So the answer is 2860 kg of cargo can be carried. One more thing — a practical note about fuel jettisoning. If we ever need to reduce mass to a safe level at or below the RLM, the pilot calculates the amount of fuel to jettison. And before jettisoning, the pilot should attempt to declare an emergency if time permits, and advise Air Traffic Control of his intentions. That’s a real operational procedure, not just an exam point. So the whole logic is: fuel states first, then three formulae, take the lowest, subtract the actual load, and the remainder is your cargo capacity. That’s the complete method.