Evaluating the "half-tank" suggestion

A recent article here suggested that if a car weighed more, it would have less fuel efficiency. This seems intuitive, but then it also included a suggestion that fueling only half-tank at a time would be beneficial. Now it's time to see whether it is actually worth it for the time.

The article states that 100 pounds of reduced weight increases the mileage by 1-2%.

Assume that:
- the vehicle can hold 20 gallons (a minivan)
- has 25 mpg on average under normal circumstances; so every 500 miles, it requires refueling.
- the vehicle travels 10000 miles per year (i.e. 20 refuelings)
- in the "half-tank" situation, we only fuel 10 gallons at a time. Thus the vehicle will be 10 gallons, or around 70 pounds lighter. We'll say that this increases the mileage by 1%.
- gas costs $3 per gallon
- it takes 5 minutes to get fuel

However, this benefit of lower weight will only be applicable half the time. Right after refueling, the "full-tank" and "half-tank" vans hold 20 and 10 gallons. 10 gallons later, it's 10 and 0 gallons. The half tank van must refuel now, so we actually have 10 and 10 gallons. The benefit is gone!

Because the 1% works half the time, mathematically we can approximate it as .5% better mileage. So the half-tank vehicle will have an average of 25.13 mpg; it will travel 251.3 miles per tank, requiring 39.8 refuelings per year.

Now let's compare the costs:
Full tank:
- 20 times, 20 gallons each time, $3/gal = $1200

Half tank:
- 39.8 times, 10 gallons each time, $3/gal = $1194.

So you save $6 per year. Meanwhile, you needed
- 19.8 extra refuelings, 5 minutes each = 99 minutes = 1.65 hours.

Or, $3.64 per hour. Not exactly productive. Go full tank.