The Navigation Computer - Slide Rule Face — Page 71, Lesson 77

I want to walk you through the slide rule face of the Navigation Computer, and I’m going to start with the big picture before we touch a single dial. The Navigation Computer is an analogue computer. That means it solves problems using physical scales and movement, not digital electronics. It’s built to solve navigation and flight planning problems quickly and easily. And here’s a key fact for your exam strategy: the EASA regulations allow you to take the analogue computer of your choice into the General Navigation examination. Several manufacturers make suitable products. The diagrams in these notes are based on the Pooley CRP-5. If you choose to buy a different computer, it’s your own responsibility to adapt the examples to your own instrument. Now, why should you care about this device? Because Navigation Computer calculations form a large part of the General Navigation EASA ATPL examination. Almost 25% of the exam comprises direct Navigation Computer questions. That’s a quarter of the paper, straight off. And many of the other questions can often be solved faster with a Navigation Computer than with a calculator. Rapid operation of the Navigation Computer is also fundamental to Flight Planning. So it is essential that you learn to operate it quickly and accurately. Those who don’t make the effort to master it completely lose marks unnecessarily in exams. I want you to take that seriously — this is a marks-grabber, and it’s also a time-saver. Let me describe the instrument itself. The Navigation Computer has two faces. One is a circular slide rule face. The other is a wind face. This chapter deals with the slide rule face only. We’ll get to the wind face later. Now, the theory. I want you to understand the slide rule theory behind the computer, rather than just learning the operations parrot-fashion. Here’s why that matters: the advent of digital calculators over the last 30 years means that few students have experience of the old-fashioned engineer’s slide rule. But the Navigation Computer uses the same slide rule theory, except that instead of the scales being presented on a straight ruler, they are on two circular discs. So let’s start the explanation by imagining a problem of addition, not multiplication. Imagine you had to add two numbers, but you had never learnt how to do simple addition. One way to solve the problem would be to use two rulers. Here’s the idea. Take two straight linear rulers, each with a scale marked on them. To add 3 plus 2, you align the zero of one ruler with the 3 on the other ruler, and then you read off the number on the first ruler that lines up with the 2 on the second ruler. That gives you the sum. The key insight is that addition on a linear scale is just aligning the starting point and reading the offset. Now, here’s the beautiful part. The slide rule face does exactly the same thing, but for multiplication. Instead of linear scales, it uses logarithmic scales. And instead of straight rulers, the scales are on two circular discs that rotate relative to each other. When you rotate one disc to align a number on the inner scale with a number on the outer scale, you’re effectively adding the logarithms of those numbers. And adding logarithms is the same as multiplying the numbers themselves. That’s the whole trick of the slide rule. So the theory you need to hold onto is this: the slide rule face is an analogue device that performs multiplication by adding logarithms, using two circular discs instead of straight rulers. And the reason we started with the addition example is that the physical action — aligning one scale against another — is identical. Once you understand that alignment principle, the slide rule operations will make sense instead of being a set of memorised moves. Let me show you the two rulers in the figure. There they are — two straight linear rulers. That’s our starting point. In the next step, I’ll walk you through exactly how the alignment works for 3 plus 2, and then we’ll extend that same logic to the circular slide rule face.