23 May 2012

A back of the envelope calculation

I was watching my budgies the other day, and had a thought which led to a brief online investigation, followed by the following back-of-envelope calculation:

According to a Boeing presentation on airline fuel efficiency that I found on the Internet, a 1% reduction in landing weight gives about a 1% reduction in trip fuel.

A Boeing 747’s operational empty weight (with equipment, flight crew etc) is 390,700lbs. Subtracting that from its Maximum Zero Fuel Weight (max weight allowed before fuel is loaded) gives a maximum value for passengers and cargo of 144,300lbs. (Apologies for not citing all my sources for all these figures; most of them were found on flight sim enthusiast forums. If someone wants to do a more precise calculation with better data from a real aircraft flight manual, please go right ahead.)

Let’s assume the airline is incredibly efficient, packs in the maximum weight it can, and only carries the absolute minimum fuel necessary. At landing, the 747 will weigh 390,700 + 144,300 = 535000 lbs.

1% of that is 5350lbs.

747 fuel consumption = 5.5 gallons per mile

NYC to SF is 2905 miles = 15977.5 gallons of fuel

1% of that is 159.775 gallons.

So if we can save 535lbs of weight, we can save 160 gallons of fuel.

Current cost of jet fuel is $3.09 per gallon.

So by saving 535lbs of weight, we can save $494. This is fact number one.

Now for fact number two: According to a study I found, mean daily stool weight for an adult human is 349g, which is 0.76941lbs.

Conclusion: If you’re taking a long haul trip, the airline should maybe give you a discount of 71 cents if you take a really big poo before takeoff.

© mathew 2017