The Navigation Computer - Distance, Speed, Time and Conversions — Page 94, Lesson 99

Let’s pick this up right where the fuel conversions get interesting. We’ve just converted 300 US gallons into imperial gallons and litres, and now I want to walk you through the rest of that example, because it introduces two scales you haven’t touched yet — the pounds weight scale and the specific gravity scale. So, the problem: convert 300 US gallons into four things — imperial gallons, litres, pounds weight, and kilograms — using a Specific Gravity of 0.80. We already did the first two. Let me remind you of the method, because it’s the same principle every time: set what you know, then read off what you need. For the first conversion, we aligned 300 on the inner scale against the US gallon index on the outer scale. Then we read off against the imperial gallon index, and that gave us 250 imperial gallons. Notice the relationship — 300 US gallons is 250 imperial gallons. That’s because the imperial gallon is larger than the US gallon, so fewer of them hold the same volume. Then we kept that same setting — 300 on the inner scale still aligned with the US gallon index — and we read off against the litres index. That gave us 1135 litres. So the same alignment gives you all the volume conversions at once. That’s the beauty of the circular slide rule: one setting, multiple readings. Now here’s where it gets new. The next two conversions — pounds weight and kilograms — are not volume conversions. They’re weight conversions. And weight depends on density, which is where Specific Gravity comes in. Specific Gravity, or SG, is the ratio of the density of a substance to the density of water. Water has an SG of 1.00. If a fuel has an SG of 0.80, it means it’s 80% as dense as water — so a given volume of that fuel weighs less than the same volume of water. So to convert a volume into a weight, you can’t just use the volume scales. You need the specific gravity scales. Look at Figure 5.22 — that shows the SG scales. These are the two scales I want you to focus on now. They let you bring density into the calculation. Here’s how it works. You still have 300 on the inner scale aligned with the US gallon index. Now, to get pounds weight, you read off against the pounds index on the outer scale — but you must first set the specific gravity. You align the SG value of 0.80 on the specific gravity scale against the appropriate index. Once the SG is set, the pounds weight reading is taken directly from the scale. The same setting gives you kilograms. You read off against the kilograms index, and because you’ve already set the SG at 0.80, the weight in kilograms comes straight off the scale. So the key idea here: volume conversions — US gallons, imperial gallons, litres — are done with the volume indices alone. Weight conversions — pounds and kilograms — require you to set the Specific Gravity first, because weight depends on density. The SG scales are the bridge between volume and weight. Let me show you the figures so you can see exactly what I mean. shows the fuel consumption setup, and shows the SG scales in detail. Look at how the SG scale sits alongside the main scales — that’s your density input. One thing to keep straight: the specific gravity is a ratio, so it has no units. It’s just a number — 0.80 in this case. And it’s always relative to water. So when you set 0.80 on the SG scale, you’re telling the computer, “this fuel is 80% as dense as water,” and the computer then does the weight calculation for you. So to summarise the whole example: 300 US gallons converts to 250 imperial gallons, 1135 litres, and then — using an SG of 0.80 — to a weight in pounds and a weight in kilograms. The first two are pure volume conversions. The last two need the specific gravity set first, because weight is volume times density. That’s the complete picture for this example. The method is always the same: set what you know, read off what you need. And when weight is involved, remember the SG scales are your density key.