General Principles - Climb — Page 175, Lesson 203

Let’s pick this up right where the climb picture gets serious: what happens when you lose an engine, and then how flaps change the climb, and finally how we actually measure the climb angle. First, the engine failure case. Look at Figure 3.10. If you lose 50% of your Thrust Available, your Excess Thrust drops by roughly 75%. Why so much? Because the same aerodynamic Drag still has to be balanced. Think of it this way: thrust has to overcome drag just to hold level, and only what’s left over—the Excess Thrust—is what actually pulls you uphill. Cut thrust in half, and you’ve eaten away almost all of that leftover margin. Figure 3.11 drives the point home: a two-engine aeroplane with one engine inoperative has a severely reduced ability to climb. That’s the core safety reality of asymmetric flight. Now, flaps. High lift devices—flaps—increase aerodynamic Drag. From Principles of Flight you’ll recall the purpose of flaps is to reduce the take-off and landing run. But here’s the trade-off, shown in Figures 3.12 and 3.13: because flaps add drag, they reduce the climb angle. More drag means less Excess Thrust, so the climb gets shallower. The figures label it clearly: “Flaps reduce climb angle” and “Flaps reduce excess thrust—more drag from flaps.” So whenever you extend flaps, you’re buying a shorter ground run but paying for it with a weaker climb. Now the climb angle itself. Figure 3.14 introduces the symbol: the Greek letter GAMMA, γ. The climb angle is the angle between the horizontal and the flight path. And here’s a neat geometric fact: that angle is exactly the same as the angle between the Weight vector and the transposed Lift vector. We’ll be using climb angle for the free air climb. When an aeroplane is in a steady climb, there’s a gain in height after a given horizontal distance travelled. That relationship is the % climb gradient. The calculation on page 48 gave 15.7% climb gradient, all engines. From Figure 3.14 you can visualize it: for 100 units of horizontal travel, the aeroplane will be 15.7 units higher. That’s a fundamental concept. Let me make it concrete with the example. An aircraft with a climb gradient of 15.7% all engines operating will be 314 ft higher after travelling 2000 ft horizontally. But the one-engine-inoperative climb gradient of 3.7% will only give a height gain of 74 ft in the same distance. Here’s the arithmetic: horizontal distance is 2000 ft. Divide by 100, that’s 20. Multiply 20 by 15.7 ft, you get 314 ft for all engines. For one engine inoperative, 20 times 3.7 ft gives you 74 ft. So the gradient literally tells you how many feet you climb per 100 feet forward—15.7 feet per 100, or 3.7 feet per 100 when you’ve lost an engine. That’s the whole climb story in one sweep: engine failure crushes your excess thrust, flaps add drag and shallow the climb, and the climb gradient quantifies exactly how much height you gain per horizontal distance.