The Navigation Computer - Slide Rule Face — Page 71, Lesson 81

Let’s start with the heart of the Navigation Computer—the slide rule face. Before we multiply or divide anything, we have to understand the scale itself, because it doesn’t work like a normal calculator. Look at the scale on the face. From Figure 4.12, you can see there is no number smaller than 10 and no number larger than 99.9 printed on it. That’s a deliberate design. The slide rule only gives you the digits—it doesn’t tell you where the decimal point goes. So we have to mentally insert the decimal point ourselves. For instance, the number 12 printed on the scale can represent 0.12, 12, 120, 1200, and so on. We put the decimal point in after we finish the Navigation Computer operation. That means you must carry out a rough calculation in your head first, just to know what order of magnitude your solution will be. Order of magnitude means roughly how big the answer is—is it around 25, or 250, or 2.5? The slide rule gives you the digits, but only your rough mental check tells you where the decimal belongs. Let me walk you through a multiplication example to make this concrete. Suppose you have to multiply 11.5 by 2.54. First, do the approximate calculation. 11.5 is approximately 10, and 2.54 is approximately 2½. So 10 times 2½ is about 25. The answer will be approximately 25. It will not be 2½, and it will not be 250. That rough check tells us the order of magnitude. Now we use the slide rule. Against 11.5 on the outer scale, we line up 10 on the inner scale—and here, 10 represents 1.0. That’s the key setup: the inner scale’s 10 is standing in for 1.0. So we align 11.5 on the outer scale with 1.0 on the inner scale, as in Figure 4.13. Next, find 2.54 on the inner scale. On the printed scale, 2.54 is shown as 25.4—remember, the decimal point is not printed. Align the cursor over that 25.4 on the inner scale, as in Figure 4.14. Then read off the answer on the outer scale, which gives you 29.2. Now the critical question: is this the correct order of magnitude? Is the answer 2.92, 29.2, or 292? We know from our rough calculation that the answer is about 25. So 29.2 is the correct order of magnitude. The slide rule gave us the digits 2, 9, 2—our mental check told us the decimal goes after the 9. Now let’s do division. Divide 3050 by 3.28. Again, start with the rough calculation. 3050 is approximately 3000, and 3.28 is approximately 3. So 3000 divided by 3 is 1000. The answer will be just under 1000—about nine hundred and something. That’s our order of magnitude. Now set up the slide rule. Find 3050 on the outer scale and align the cursor over it. Then find 3.28 on the inner scale and align it with the cursor. That’s the setup for division, as in Figure 4.15. Now, to read the answer, find 10 on the inner scale and read off against the outer scale, as in Figure 4.16. The initial answer you read is 93.0. Is that the right order of magnitude? We know from our rough calculation that it should be about 900. So the correct answer must be 930, not 93.0. The digits are 9, 3, 0—our mental check places the decimal to give 930. So the whole principle is this: the slide rule face only gives you the significant digits, never the decimal point. You always do a rough mental calculation first to fix the order of magnitude, then you use the slide rule for the precise digits, and finally you place the decimal point according to your rough check. That’s the foundation for everything else on the Navigation Computer.