The Navigation Computer - Slide Rule Face — Page 84, Lesson 83

We're going to work through a rate-and-ratio problem on the slide rule face of the navigation computer. This is the same division process we've been using, but now we're putting it into an aviation situation. Here's the scenario. An aircraft has an average rate of climb of 700 feet per minute. How long will it take to climb from 3,000 feet to 20,000 feet? First, let's find the height we need to climb. From 3,000 up to 20,000 is a climb of 17,000 feet. So the question becomes: at 700 feet per minute, how many minutes to climb 17,000 feet? That's straightforward division — 17,000 divided by 700. Before we touch the computer, let's do a rough mental check of the order of magnitude. If we climb 700 feet in one minute, then 7,000 feet takes ten minutes, and 14,000 feet takes twenty minutes. So 17,000 feet will take a few minutes more than twenty. Another way to estimate: 700 feet per minute is not far from 1,000 feet per minute. So 17,000 divided by 1,000 is 17, and since we're actually climbing slower than 1,000 fpm, the answer will be a bit more than 17 — somewhere in the low twenties. That's our sanity check. Now let's set it up on the computer. Hold the instrument with the 17,000 — shown as 17 on the outer scale — at the top. Then rotate the disc to bring the 700 — shown as 7 on the inner scale — immediately opposite that outer-scale 17. Now turn the instrument the shortest way, which is clockwise in this case, to bring the 10 of the inner scale to the top. Opposite that 10, read off from the outer scale the answer digits: 243. Since our rough check told us the answer is in the low twenties, we place the decimal point to get 24.3 minutes. Now, there's a second way to approach this — solving by proportion rather than by direct division. Let's restate the problem. The aircraft climbs 700 feet in one minute. It will climb 17,000 feet in t minutes, where t is the answer we want. We can write this as a ratio: 700 over 1 equals 17,000 over t. Here's the key idea. If you arrange this equation on the circular slide rule with the numerators — 700 and 17,000 — on the outer scale, set respectively above the denominators — 1 and t — on the inner scale, the problem is solved. Let me show you how that looks. Align the 700 — shown as 70 on the outer scale — exactly over the 1 — shown as 10 on the inner scale. That sets up the left-hand side of the equation: 700 over 1. Now turn the instrument clockwise and look for the right-hand side of the equation. Look for 17,000 — shown as 17 — on the outer scale. Immediately under it, read off 24.3 from the inner scale. That's your t. Same answer as before: 24.3 minutes. And notice — even with this proportion method, you still have to do that rough mental calculation first, to position the decimal point correctly. The slide rule gives you the digits; your brain gives you the order of magnitude. This proportioning, or ratio, technique is important. It's the basis of all distance, speed, and time calculations, and of fuel consumption calculations. We'll return to it in the next lesson.