General Principles - Cruise — Page 263, Lesson 318

Let’s pick this up right where the cruise picture starts to get interesting — the optimum altitude. This is one of the most important ideas in jet cruise performance, so I want you to really get it. First, look at Figure 5.25. There’s a left-hand blue line on that graph, and it shows you something crucial: for a jet aeroplane at a given weight and speed, there is one particular altitude where the specific range is greatest. In the example on that figure, that altitude sits just below 33,000 feet. That altitude is what we call the optimum altitude. Now, let me define that precisely, because the definition matters for your exams and for how you fly. The optimum altitude is defined as the pressure altitude which provides the greatest specific range, or fuel mileage, at a given weight and speed. So it’s not just “the best height to fly” — it’s the pressure altitude that gives you the most miles per unit of fuel, for a specific weight and a specific speed. If you fly higher than that altitude, or lower than that altitude, the range of the aeroplane will decrease. So there’s a sweet spot, and deviating from it in either direction costs you range. Now here’s the key thing you must understand: the optimum altitude is not fixed. It changes as the flight progresses. Let me walk you through why. You’ll recall that as the aeroplane burns fuel, its weight decreases. And when weight decreases, the drag curve moves down and to the left. That has two consequences. First, the best range speed — which for a jet is 1.32 VMD, that is 1.32 times the speed for minimum drag — falls. Second, the total drag decreases. So with decreasing weight, the aeroplane needs to slow down to maintain that best range speed. Now, as the aeroplane slows down, the Mach number also decreases. That means the aeroplane is no longer limited by the high Mach number and the corresponding high drag that comes with it. Because that Mach limit has eased off, the aeroplane is allowed to climb a little. As it climbs, the Mach number increases again back up to its previous limiting value, and the drag increases back to its previous value as well. But here’s the important part: the higher altitude has decreased the specific fuel consumption. That’s the fuel consumed per unit of thrust per unit of time — and at higher altitude, it goes down. So during that little climb, the specific air range increases. Specific air range is the distance flown per unit of fuel, so if it increases, you’re getting more miles for the same fuel. So the chain of logic is this: weight decreases with fuel burn → the aeroplane can climb a little → the higher altitude lowers specific fuel consumption → the specific air range increases during that climb. And that means, over time, as weight keeps decreasing, the optimum altitude keeps increasing. You can see this in Figure 5.25 by comparing the specific range line for high weight versus low weight. Notice too that as the optimum altitude increases, the specific range also increases. Now, if you plot how the optimum altitude changes over time, you get Figure 5.26. That graph shows the optimum altitude increasing with a reduction in weight as the flight progresses, for a typical jet aeroplane. And here’s the operational takeaway. In order for the aeroplane to maximize the specific range, it must stay with the optimum altitude as that altitude slowly increases. In other words, the aeroplane must climb along the green line shown in Figure 5.26. Climbing in this way — following the rising optimum altitude — is sometimes called a… well, the excerpt cuts off right there, but you can already see the idea: it’s a gradual climb that tracks the optimum as weight burns off. So the whole picture is: optimum altitude is the pressure altitude giving greatest specific range at a given weight and speed; it rises as weight falls; and to get the best fuel mileage, you climb along that rising optimum. That’s the core of jet cruise performance.