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’re converting fuel volume into mass, and the whole thing hinges on density. First, the definition you must lock in: density is mass per unit volume. That’s the formal definition. So if I tell you a fuel has a density of 0.82, that means each litre of that fuel has a mass of 0.82 kilograms. Mass per unit volume — mass divided by volume. Now, the refuelling operator gives you the specific gravity, or SG, of the fuel taken up. Specific gravity is also called relative density. Here’s the precise meaning: it’s a comparison between the mass of a certain volume of a substance and the mass of an equal volume of pure water. So if a fuel has an SG of 0.72, that fuel is 0.72 times as heavy as the same volume of water. Water itself has an SG of 1.0 by definition. But here’s the operational catch: if, for some unforeseen reason, the actual fuel density is not known, you must use a standard fuel density — the one specified by the operator in the Operations Manual. You don’t guess. You don’t invent a number. The Operations Manual is the authority for that fallback value. Now, the practical problem: fuel is delivered in volume — gallons or litres — but mass and balance work needs mass. So we need a conversion method. I want you to remember this chart, because it will not be provided in the exams. You must carry it in your head. Here’s the chart. We have three units: lb, kg, and US gallons. Between lb and kg, the conversion factor is 2.205. Between kg and US gallons, the factor is 3.785. And there’s a factor of 10 that connects imperial gallons to lb — that’s the AVGAS-specific conversion. 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 that number. Let me walk you through the worked examples so you see exactly how this works. Worked Example 1a: Find the mass of 50 imperial gallons of AVGAS with a specific gravity of 0.72. The calculation is: 50 × 10 × 0.72 = 360 lb. So the 10 converts imperial gallons to pounds for AVGAS, and then the 0.72 SG scales it down because AVGAS is lighter than water. Worked Example 1b: For 50 US gallons, the calculation changes: 50 × 3.785 × 0.72 = 136.26 lb. Notice the factor changed from 10 to 3.785 — that’s because US gallons are a different volume than imperial gallons. The 3.785 converts US gallons to pounds, and again we multiply by the SG. Worked Example 2: Find the mass of 2250 litres of fuel with a density of 0.82. Here we’re working in metric, so it’s simply: 2250 × 0.82 = 1845 kg. No conversion factor needed because litres and kilograms are already in the same system — density in kg per litre directly gives you mass. One important note: the conversion factors have been rounded for simplicity, so small errors might occur. That’s acceptable in these calculations — you’re not chasing laboratory precision, you’re getting a working mass for balance purposes. So the complete picture: density is mass per unit volume, SG is the comparison to water, the Operations Manual provides the standard density when actual density is unknown, and the chart lets you move between lb, kg, and gallons — multiplying with the arrows, dividing against them. Now, there’s a figure I want to show you that ties all of this together — it’s the quantity mass conversion chart we just discussed. Let me bring that up for you.