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

I want to walk you through a practical example that reinforces the division process on the navigation computer, this time in an aviation context. We’ll look at rates and ratios. Here’s the scenario: the average rate of climb of a particular aircraft is given as 700 feet per minute. How long will it take to climb from 3000 to 20 000 feet? First, let’s work out the climb height. The aircraft is climbing from 3000 to 20 000 feet, so it needs to climb through 17 000 feet. At 700 feet per minute, straightforward division of 17 000 by 700 will determine the number of minutes for the climb. Before we touch the computer, let’s do a rough mental estimate to get the order of magnitude. If the aircraft climbs 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 more minutes than twenty. Alternatively, 700 fpm is not too far from 1000 fpm, so the sum is approximately 17 000 divided by 1000, which is a bit more than 17 — somewhere in the low twenties. That’s our sanity check. Now let’s set up the computer. Hold it so that 17 000 — shown as 17 on the outer scale — is at the top. Then rotate the disc to bring 700 — shown as 7 on the inner scale — immediately opposite the outer scale 17. Next, turn the instrument the shortest way — clockwise in this case — to bring 10 of the inner scale to the top. Opposite that ‘10’, read off from the outer scale the answer digits 243. That gives us a final answer of 24.3 minutes. Now, you might prefer a slightly different approach — solving in terms of proportion rather than 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. This can be written as a ratio: 700 over 1 equals 17 000 over t. That’s the equation: 700/1 = 17 000/t. If you arrange this equation on your 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. As shown in Figure 4.17, 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. Then 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 the same answer we had before — 24.3 minutes. One important note: even if you solve the problem this way, you still have to perform a rough mental calculation, as before, to position the decimal point correctly. The computer gives you the digits; you decide where the decimal goes. This proportioning, or ratio, technique is important. It is the basis of all distance, speed, and time calculations, and of fuel consumption calculations. We will return to it in the next lesson.