Aviation Fuel Weight vs Temperature and Load Sheet

What a quantity of aviation fuel actually weighs at its actual temperature, and what the standard-density figure gets wrong. The conversion is a multiplication and the trap is WHICH DENSITY. Published densities are quoted at a reference temperature, and fuel drawn from an above-ground tank on a hot day is materially less dense than that -- so a given number of gallons weighs less than the table says. The consequence runs in two directions and they are not the same kind of error. Loading to a WEIGHT by counting gallons at standard density puts LESS fuel aboard than intended, which is not a safety problem but shows up as shorter range than planned. Computing a load sheet with an overstated fuel weight understates the payload available, which is conservative. Computing one with an UNDERSTATED fuel weight -- which is what using the standard density on cold fuel does -- reports less weight aboard than there is, and that is the direction that matters. The temperature difference is computed from two entered temperatures here rather than taken as a figure, because that subtraction is exactly where this goes wrong. A fuel weight error moves the centre of gravity as well as the gross weight, which is why the moment is reported when an arm is entered: an aircraft can be within gross weight and outside its centre of gravity envelope, and fuel is usually a large moment at a fixed arm. Densities and the temperature coefficient are ENTERED because they vary by fuel and by batch: Jet A and 100LL differ substantially, the coefficient is an approximation to a real density curve, and a fuel receipt or a refueller's densitometer reading is better than any table. This computes a weight and a moment; it does not perform weight and balance, check the centre of gravity envelope, account for unusable fuel, tank geometry or attitude, address fuel expansion in the tank and the ullage it needs, or convert between mass and volume bases used in different countries. The aircraft flight manual, the operator's load sheet procedure, and the fuel supplier's density data govern.

weight = gallons x the density at the ACTUAL fuel temperature, where that density is the reference-temperature value reduced by the entered change rate over the computed temperature difference; gallons for a target weight is that relation inverted, and the moment is the weight times the arm.

Fuel weight at the actual temperature rather than at the reference, with the temperature DIFFERENCE computed from two entered temperatures. Densities and the coefficient are ENTERED because they vary by fuel and batch, and a fuel receipt or a refueller's densitometer beats any table. It does not perform weight and balance, check the centre of gravity envelope, account for unusable fuel, tank geometry or attitude, address expansion and ullage, or convert between the mass and volume bases used in different countries.

One multiplication and one linear temperature correction.

Estimate. AHJ and licensed professional govern.

Field names used by the API: gallons, standard_density_lb_gal, reference_temp_f, fuel_temp_f, density_change_pct_per_10f, arm_in, required_weight_lb, temp_difference_f, actual_density_lb_gal, standard_weight_lb, actual_weight_lb, weight_difference_lb, gallons_for_weight

• Density and coefficient are entered they vary by fuel and by batchthe fuel supplier's density data
• A linear correction the real density curve is not exactly linearthe fuel specification
• Not weight and balance the centre of gravity envelope is checked elsewherethe aircraft flight manual