Definitions and Calculations — Page 38, Lesson 57

Let’s pick this up right where the fuel density question lives, because that’s the heart of what we’re doing now. We’ve just established that the refuelling operator gives you the specific gravity of the fuel taken on board. But here’s the operational reality: if, for some unforeseen reason, the actual fuel density is not known, then you must use a standard fuel density — and that standard value is specified by the operator in the Operations Manual. So you’re never guessing; you have a fallback number that’s approved for your operation. Now, let’s nail the definitions, because these are exam-critical and they’re precise. Density is defined as mass per unit volume. That’s the fundamental relationship — how much mass is packed into a given volume. Then we have relative density, which is also called specific gravity, often abbreviated SG. Specific gravity is simply a comparison between the mass of a certain volume of a substance and the mass of an equal volume of pure water. So it’s a ratio — it has no units, it’s just a number that tells you how heavy that fuel is compared to water. Water has an SG of 1.0; AVGAS at 0.72 is lighter than water. Now, the practical problem: you often know the volume of fuel you’ve taken, but you need the mass — because mass is what matters for weight and balance and for performance. So I want to walk you through a conversion chart that’s a handy method of converting volume to mass. And I want you to remember this chart and how to use it, because it will not be provided in the exams. You have to carry it in your head. Here’s the structure. The chart links pounds, kilograms, and volumes. Let me give you the key conversion factors that sit above the lines between the units. Between kilograms and pounds, the factor is 2.205 — that’s the number of pounds in one kilogram. Between US gallons and litres, the factor is 3.785 — that’s the number of litres in one US gallon. And between imperial gallons and pounds, the factor is 10 — that’s the number of pounds of water in one imperial gallon. There’s also a factor of 0.4536, which is the number of kilograms in one pound — that’s the reciprocal of 2.205. Now, the rule for using the chart: when you move in the direction of the arrows, you multiply by the number above the line. When you move against the direction of the arrows, you divide by the number above the line. And there’s an important note: the conversion factors have been rounded for simplicity, so small errors might occur. That’s acceptable in these calculations, but you should be aware of it. Let me show you how this works with the worked examples, because that’s where it all comes together. Worked Example 1, part (a): Find the mass of 50 imperial gallons of AVGAS with a specific gravity of 0.72. The calculation is: Mass = 50 × 10 × 0.72 = 360 lb. Let’s break that down. The 50 is the volume in imperial gallons. The 10 is the conversion factor — the mass of one imperial gallon of water in pounds. And the 0.72 is the specific gravity of the AVGAS. So you’re taking the volume, converting it to the mass of water, then scaling by the specific gravity to get the mass of the fuel. The result is 360 pounds. Part (b): For 50 US gallons, this would be: Mass = 50 × 3.785 × 0.72 = 136.26 lb. Notice the difference — the US gallon is smaller than the imperial gallon, so the conversion factor is 3.785 instead of 10. Same logic: 50 US gallons, times 3.785 to get litres, times the specific gravity 0.72, gives 136.26 pounds. Worked Example 2: Find the mass of 2250 litres of fuel with a density of 0.82. The calculation is: Mass = 2250 × 0.82 = 1845 kg. Here, the density is given directly as 0.82 — that’s the mass per unit volume in kilograms per litre. So you just multiply the volume in litres by the density to get the mass in kilograms. 2250 litres times 0.82 gives 1845 kilograms. So the key takeaway: when you have specific gravity, you’re comparing to water and you need the conversion factor for the volume unit you’re using. When you have density directly, you can multiply volume by density straight away. And remember — if you don’t know the actual density, use the standard fuel density from the Operations Manual. I’ve got a diagram here that shows the definitions and the flow of these calculations — it’s Figure 2.4, the definitions and flow diagram. Take a look at that on your screen, it ties all of this together visually.