General Principles - Climb — Page 175, Lesson 203

Let’s pick this up right where the climb performance story gets serious: what happens to your climb when an engine quits. I want you to picture the force balance we’ve been building. In a climb, you have Thrust acting forward, Drag acting backward, Weight acting straight down, and Lift acting perpendicular to the flight path. The climb is only possible because Thrust exceeds Drag — that surplus is called Excess Thrust, and it’s what actually pulls the aeroplane up the slope. Now, the moment one engine fails on a twin, you lose 50% of the Thrust Available. But here’s the kicker: your Excess Thrust doesn’t just drop by half. It drops by approximately 75%. Why? Because the same value of aerodynamic Drag still has to be balanced. Think of it this way — Drag doesn’t care how many engines you have; it still demands the same amount of thrust just to hold level. So when you halve the thrust, the first half of what’s left goes purely to fighting that unchanged Drag, and only the remainder is left over as Excess Thrust. That remainder is a fraction of what you had before. That’s why the book stresses that a two-engine aeroplane with one engine inoperative has a severely reduced ability to climb. It’s not a proportional loss — it’s a dramatic collapse. Now let’s talk about flaps, because they change the same picture. High lift devices — flaps — increase aerodynamic Drag. From Principles of Flight you learned their purpose: they reduce the take-off and landing run by giving you more lift at low speed. But that benefit comes at a cost. Because flaps add Drag, they eat into your Excess Thrust. And since Excess Thrust is what drives the climb, flaps reduce the climb angle. The figures make it obvious: with flaps down, you have more Drag, less Excess Thrust, and therefore a shallower climb. So in the climb phase, you want those flaps up — you only use them for the low-speed phases where their lift benefit outweighs the drag penalty. Now let’s get precise about the climb angle itself. The symbol for climb angle is the Greek letter GAMMA, written γ. Look at the geometry: the angle between the horizontal and the flight path — that’s your climb angle — is exactly the same as the angle between the Weight vector and the transposed Lift vector. That’s a neat geometric identity, and we’ll use this climb angle for what the book calls the FREE AIR climb — that’s the climb in undisturbed air, not the climb relative to the ground. Here’s the key relationship. 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 us 15.7% climb gradient, all engines. What does that mean physically? From the figure, for every 100 units of horizontal travel, the aeroplane will be 15.7 units higher. That’s a fundamental concept — the gradient is literally the vertical gain per 100 units of horizontal distance. Let me make that concrete with the example from the book. Take an aircraft with a climb gradient of 15.7% all engines operating. After travelling 2000 ft horizontally, how high is it? Divide 2000 ft by 100 — that gives you 20. Multiply 20 by 15.7 ft, and you get 314 ft. So all engines, you gain 314 ft in that distance. Now the same aircraft with one engine inoperative has a climb gradient of only 3.7%. Same 2000 ft horizontal distance — still 20 units of 100 ft. Multiply 20 by 3.7 ft, and you get only 74 ft of height gain. Same distance, same aeroplane, but the engine failure cuts your height gain from 314 ft down to 74 ft. That’s the practical, brutal consequence of that 75% loss of Excess Thrust — your climb gradient collapses from 15.7% to 3.7%, and your obstacle clearance margin shrinks accordingly. So hold onto these three numbers: the 50% thrust loss producing a 75% Excess Thrust reduction, the 15.7% all-engine gradient versus 3.7% one-engine-inoperative, and the 314 ft versus 74 ft height gain over 2000 ft. That’s the whole story of why engine failure transforms your climb performance.