Questions from the Cockpit: Fake weight

Becky, a student pilot in Florida, writes: I’m fully caffeinated and working my way through Chapter 10 of the Pilot’s Handbook of Aeronautical Knowledge to get my head around this weight and balance stuff. I just encountered “standard weights.” The good book says that standard weights are “established weights” and “should be used if actual weights are not available.” Then the first thing on the list is gasoline at 6 pounds per gallon. Huh? How can the weight of gas be a mystery? It weighs what it weighs…right?

Good eye, aviator. Most student pilots don’t catch that subtlety.

And you are correct that the weight of gas is no mystery — but it is, in fact, a variable.

Here’s the thing: The weight of a given unit of dispensed fuel changes with temperature. This is because the molecules, when they are cold, huddle close to each other just like humans do when they are cold.

Fluids contract when cold and expand when hot, which changes their volume. As a thought experiment, let’s assume I put one gallon of fuel in a two-gallon jerry can, and let’s say I do this on a 20℃ day, and that the fuel is at ambient temperature. If I take the fuel somewhere else, say to where the temperature is 30℃, it will expand, rising up in the container to beyond the one gallon mark. Next, flying through a cold front, let’s say the temperature then drops to 10℃. Now my “gallon” of gas shrinks and, if I were a cynical person, I might suspect the gas pump had cheated me.

As a historical side note on fuel contraction, for the 1946 Bendix air race, Paul Mantz, the future King of Hollywood stunt flying, famously added dry ice to his fuel truck right before the race to “shrink” the fuel, allowing him to squeeze the absolute maximum into the wet wing of his modified P-51 Mustang.

He won first place.

Now, to be clear, whatever the fuel weighs when first pumped in stays the same as the gas expands and contracts. The load doesn’t get lighter or heavier, it just gets bigger or smaller. Only the volume changes.

Still, a gallon pumped on a hot day will, in fact, weigh less than a gallon pumped on a cold day — and in GA, as we buy fuel by the gallon, not by the pound, we need a way to figure out the poundage of our pumping for weight and balance purposes.

In theory, it should be a simple unit conversion to go from gallons to pounds, but if the weight of each gallon of fuel you buy changes with temperature, the math becomes… well… not so simple.

I’ll run through all the complications involved in that in a bit, but to make our lives easier, the industry uses an agreed-upon “standard” weight, instead of having pilots adjust for temperature with each fuel purchase. This standard weight is 6 pounds per gallon, which in itself is an interesting choice. That’s the rounded-to-the-nearest whole number weight of avgas at a standard temperature (and pressure — yet another variable).

You’ll notice that I didn’t say at “the” standard temp. That’s because, while in aviation our standard temperature for almost everything is 59℉, for fuel the standard is 60℉, a temperature adopted from the petroleum industry.

How much does this standard weight vary from the actual weight? Not a hell of a lot.

Filling a Cessna 172 with 53 gallons, using the standard weight, gives us 318 pounds. But the real weight, at our aviation standard temperature, is 318.53 pounds.

Meanwhile, filling the same Cessna up at 32℉, the denser fuel now weighs in at 325.42 pounds — not quite seven pounds more.

Naturally, on the other end of the spectrum, if it was warmer, your fuel load would be lighter, but again, only by a handful of pounds.

And with lower volume fuel loads, the differences get rather paltry — although it’s interesting to note that when it comes to wholesale delivery of large amounts of fuel from refineries, two different pricing systems are deployed, depending on the temperature difference between the supplier and the customer.

OK, you say, but if we know what fuel weighs at various temperatures, and the Pilot’s Handbook of Aeronautical Knowledge says of standard weights that “these weights should not be used if actual weights are available,” shouldn’t we do a weight and balance with actual fuel weight?

Well, let’s see what that would involve.

First, you’d need to drain all the fuel out of the airplane. Next you’d tank whatever amount you want, measure the temperature, then crunch the math. Each time you added fuel, you’d need to measure the temperature coming out of the nozzle, crunch that fuel weight, then add it to the existing fuel load, which of course you’d need to reduce — very precisely — by the amount of the previous weight fuel that was consumed.

And after all that work, the difference is probably less than the impact of wardrobe and breakfast on pilot weight. You use your naked-on-the-bathroom-scale weight for weight and balance, not your flight jacket and headset weight, right?

So standard fuel weight is a time and frustration saver. The difference between standard and actual — for the small tanks of GA airplanes — is such that it is safe. In fact, probably safer than the potentially error-ridden mathematical gymnastics required to calculate and update actual fuel weights.

All of that said, while it’s acceptable and safe to use standard weights for fuel, I would caution against using the standard weights for passengers and baggage. Those standards were developed in a bygone era when people were lighter, and were intended for bigger aircraft where the margins aren’t so slim.

A gallon or two of gas weight won’t matter, but the impact of a 145 pound passenger vs. the impact of a 210 pound passenger in a light airplane? That’s some math worth doing!