General Principles - Climb — Page 195, Lesson 227

Let’s pick this up right where the climb-gradient calculation gets practical. We’ve already worked out that our Class B aeroplane has a 10.15% ground gradient, and now we’re going to turn that percentage into an actual distance — the horizontal distance the aircraft travels to climb from the screen height up to 2000 ft above Reference Zero. First, remember what a gradient percentage means. A 10.15% gradient simply means the aircraft gains 10.15 units of height for every 100 units of horizontal travel. So if we know how much height we still need to gain, we can find out how much horizontal distance that takes. Here’s the key setup. For a Class B aeroplane, the screen height is 50 ft. The climb segment begins at that screen height, which is measured above Reference Zero. So if our target is 2000 ft above Reference Zero, the aircraft doesn’t need to climb the full 2000 ft — it only needs to gain an additional 1950 ft, because it already starts 50 ft up. Now, to find the horizontal distance, we ask: how many times does 10.15 divide into 1950 ft? That’s 1950 divided by 10.15, which gives 192.12. What does that number mean? It means the required vertical height gain is 192.12 times greater than the 10.15 units in our gradient. And because the gradient is a ratio — 10.15 up for every 100 along — the horizontal distance will also be 192.12 times greater than the 100 units. So we multiply 100 by 192.12, and that gives us the horizontal distance in feet: 19,212 ft. So the logic is: height gain divided by the gradient percentage gives you the multiplier, and then you multiply that by 100 to get the horizontal distance. That’s the whole trick. Now let’s look at Example 6, which applies the same idea but from a slightly different angle. Here we have a light twin-engine aeroplane with a 10% climb gradient after take-off. There’s a 900 m high obstacle situated 9740 m from the end of the Take-off Distance Available — that’s the TODA. The question asks: by how much will the aeroplane clear the obstacle? Again, remember the definition: percentage gradient is merely the vertical height for a horizontal distance travelled of 100 units. So a 10% gradient gives 10 units up for every 100 units along. To find out how much height the aircraft gains after covering 9740 m horizontally, we set up the same ratio. For every 100 m along, it climbs 10 m. So over 9740 m, the height gain is 9740 divided by 100, times 10 — that’s 974 m of height gained. Now, the obstacle is 900 m high, and both the obstacle height and the start of the climb segment are measured above Reference Zero. So the aircraft gains 974 m, and the obstacle is 900 m. The clearance is the difference: 974 minus 900, which is 74 m. That’s how much the aeroplane clears the obstacle by. One practical note here: for practical purposes, a screen height of 50 ft is taken as 15 m. So in this example, the climb segment effectively starts 15 m above Reference Zero, and the obstacle is 900 m above Reference Zero — both measured from the same datum, which is why we can compare them directly. And that’s the core of climb-gradient work: convert the gradient percentage into a height gain over a given horizontal distance, then compare that height gain against the obstacle or target height, remembering to account for the screen height at the start.