General Principles - Climb — Page 195, Lesson 225

Let's pick up right where the climb gradient leaves off — we've got the air gradient, and now I want to show you how to turn that into a ground gradient, because that's what actually matters when you're clearing obstacles on the ground. First, the definition you need to hold onto: any gradient is the vertical distance divided by the horizontal distance. That's the core of it. So when we talk about an air gradient, that's the climb angle relative to the body of air the aeroplane is flying through. But the ground doesn't move with the air — so if there's wind, the path over the ground is different from the path through the air. That's why we need a wind factor to correct the air gradient for wind. Let me walk you through the headwind case first, because that's Example 1. We have an aeroplane with an air gradient of 12%, a TAS of 100 knots, and a headwind of 20 knots. Now here's the key rule that I want you to remember — and it's a rule we'll come back to: when we apply wind for gradient work, we use 50% of the headwind. So 50% of that 20-knot headwind is 10 knots. That makes the ground speed 90 knots — 100 minus 10. The ground speed is the TAS corrected for wind, so with a headwind it's slower. Then we compute the wind factor. The wind factor is TAS divided by GS. So 100 knots TAS divided by 90 knots GS gives us a wind factor of 1.11. Now we multiply the air gradient by that wind factor: 12% times 1.11 gives us a ground gradient of 13.32%. Notice the headwind made the ground gradient steeper than the air gradient — because the aeroplane is moving forward over the ground more slowly, it climbs more steeply relative to the ground. Let me give you Example 2 to reinforce that. Same air gradient of 12%, but now TAS is 160 knots and the headwind is still 20 knots. Applying 50% of the headwind — 10 knots — gives a ground speed of 150 knots. The wind factor is 160 divided by 150, which is 1.07. Multiply 12% by 1.07 and you get a ground gradient of 12.8%. Same idea, just a different TAS. Now let's flip it to the tailwind case, Example 3. Same air gradient of 12%, TAS of 100 knots, but now a tailwind of 20 knots. Here's where the rule changes — and this is critical. For a tailwind, we apply 150% of the wind, not 50%. So 150% of 20 knots is 30 knots. That makes the ground speed 130 knots — 100 plus 30. The wind factor is TAS divided by GS: 100 divided by 130 gives 0.77. Multiply 12% by 0.77 and you get a ground gradient of 9.24%. The tailwind made the ground gradient shallower — the aeroplane moves forward over the ground faster, so it climbs less steeply relative to the ground. Example 4, just to lock it in: air gradient 12%, TAS 160 knots, tailwind 20 knots. Applying 150% of the tailwind — 30 knots — gives a ground speed of 190 knots. Wind factor is 160 divided by 190, which is 0.84. 12% times 0.84 gives 10.1%. Now, that note in the text is worth its weight in gold, so I want to stress it: if the ground gradient is going to be used for obstacle clearance calculations, the application of headwinds and tailwinds must include the 50% headwind and 150% tailwind rule. That's not optional — that's the rule you apply when obstacle clearance is on the line. Now let's move to a typical climb gradient question, Example 5. We're asked to determine the ground distance for a Class B aeroplane to reach a height of 2000 feet above Reference Zero. The conditions are: OAT 25°C, pressure altitude 1000 feet, gradient 9.4%, speed 100 KIAS, and a wind component of 15 knots headwind. Before we do anything, we need to know what Reference Zero is. Reference Zero is the point on the runway or clearway plane at the end of the Take-off Distance Required — the TODR. It's the reference point for locating the start point of the take-off flight path. So when we say "2000 feet above Reference Zero," we mean 2000 feet above that point at the end of the take-off distance required. That's the datum from which we measure the climb. Now, the question gives us a gradient of 9.4% — that's the air gradient. We have a 15-knot headwind, and per our rule we apply 50% of that headwind, which is 7.5 knots. So the ground speed is 100 KIAS minus 7.5, giving 92.5 knots. The wind factor is TAS divided by GS — 100 divided by 92.5, which is about 1.08. Multiply the air gradient of 9.4% by that wind factor, and you get a ground gradient of roughly 10.15%. Then, to find the ground distance to climb 2000 feet, you take the height — 2000 feet — and divide by the ground gradient expressed as a decimal. 2000 divided by 0.1015 gives you approximately 19,700 feet of ground distance. That's the distance over the ground the aeroplane needs to reach 2000 feet above Reference Zero, given that headwind. So the whole process is: correct the air gradient for wind using the 50% headwind / 150% tailwind rule, get the ground gradient, then divide the required height by that ground gradient to get the ground distance. That's the climb gradient calculation in a nutshell.