How many gallons?
:big(A):ccording to the F.A.A., the total number of passenger trips is 1.1 billion per year. This same source gives us 1.6 trillion revenue passenger miles per year.
The C.D.C. tells us that adults had 40.3% obesity from August 2021 to August 2023. They also tell us an average adult has a BMI of 26.5.
ThrustFlight tells us the average cruise speed is around 520 miles per hour.
We can find on Wikipedia that Jet A/A-1 density is around 6.71 pounds per gallon, or 3.04 kilograms per gallon.
Cost of weight is a bit trickier to find, but OpenAirlines gives us a rule of thumb of 3.5% per flight hour, and I.C.A.O. gives us a range of 2.5% to 4.5%. So we can estimate 0.035 kilograms of fuel per kilogram carried per flight-hour.
\[\text{Average miles per passenger}= \frac{1.6 \text{ trillion revenue passenger miles}}{1.1 \text{ billion passengers}}\approx 1455 \text{ miles per passenger}\] \[\text{Flight time}= \frac{1455 \text{ miles}}{520 \text{ miles per hour}}\approx 2.80 \text{ hours}\]Now, this is ambitious, but assuming weight loss drugs improve, get cheaper, and see mass adoption, I claim the obese population will drop by 80%.
\[\text{Successful GLP-1 share of all passengers}= 40.3\% \times80\%=32.24\%\] \[1.1\text { billion passengers}\times 32.24\%\approx 354.6\text{ million passenger trips losing weight}\]This is also a generalization, but for the sake of simplicity of the math, we can claim that the average obese BMI is 35. Now using the BMI formula, and using CDC average adult heights (66 inches), roughly averaging men and women:
\[\text{BMI drop} = 35 - 26.5 = 8.5\] \[\text{Weight drop}\approx53\text{ pounds}\approx24\text{ kilograms}\] \[354.6\text{ million trips}\times 24\text{ kilograms}\times 2.80\text{ hours}\approx23.8\text{ billion kilogram hours of passenger weight removed}\] \[23.8\text{ billion kilogram hours}\times 0.035=835\text{ million kilograms of fuel saved}\] \[\text{Gallons of fuel saved annually}=\frac{835\text{ million kilograms}}{3.04 \text{ kilograms per gallon}}\approx 274\text{ million gallons per year}\]So, if we shrink the obese population to a fifth of what it currently is (as well as assume obese people go on flights at roughly the same rate as non-obese people), U.S. commercial passenger aviation saves around 274 million gallons of fuel per year.