Or get gas on the way home.
That would have been too logical.
Like many of us here on this forum, I spent many HS and college years working at the local full service gas station. I was working the 3-11 shift one night. The 12-8 guy had gotten off half an hour earlier and came walking back to the station and grabbed a gas can. He ran out of gas on his way home. Not coming to work, on his way home.
This guy worked at a place that sells gas, and ran out driving away from there. Not the brightest guy around.
Unlike your BIL, I always fill the tanks on my vehiclesā¦ Having been assigned overseas in various third world countries, you never know when a strike, riot, or even an insurrection will take place and you never want to be low on gasā¦
However, I too run a Harley (1984 Ironhead Sportsterā¦) with a Peanut Tank and mine holds 2-1/2 gallons and I like to run my baby richā¦ but Not āPig Richā¦ā
I average only about 40-45 MPG on the highway, so when I travel, I carry four 1-liter fuel grade jugs (picked them up in the UKā¦), filled with gas (for an extra gallon-plusā¦), in the saddle bagsā¦ The small tool bag on the front forks carries my bottle of āLead Additiveā¦ā
Iāve heard all the arguments that lead additive is not needed, but I cannot argue with 90,000 miles of trouble free performanceā¦ The average H-D Ironhead needed a top-end overhaul every 50,000 to 60,000 miles but I am still running 90% of the factory cranking compression pressure of roughly 125 PSI.
My question was for @Cavell .
Big difference buying a $1.00 or $2.00 worth of gas when it was $0.36 a gallon when a dollar would have gotten you 2.78 gallons of gas or for $2.00 would have gotten you 5.56 gallons, nowadays on smaller vehicles that is a 1/2 tank of gasā¦
In 2008 when gas was over $4.00 a gallon in my area, (2022 even higher) customers were only putting in enough to maybe get 1 gallon of gas, it was ridiculesā¦ Granted most modern vehicles get better fuel mileageā¦ lol
Customer: $4 on pump #5.
Cashier: Just enough to get to the next gas station, huh?
Customer: Whateverā¦
Also back around this time I had a car come in, driver stated that gas gauge didnāt work and she kept running out of gas even though she put in $20 at a time. I gave her the estimate for $400 to fix gas gauge and she said she had no choice because she kept running out.
I explained to her, that if she filled the car till the nozzle shut off, the tank would be full. Reset the trip odometer, and at 200 miles fill the tank all the way full again, and she would never run out of gas.
She said she couldnāt afford a full tank every time she got gas, so go ahead and fix the gauge. 
That reminds me when our standard brakes had a lifetime pad warranty and 12/12 labor warranty and the labor price was $110.00, well we often ran $99.99 sales on standard brakes at the time, well a Lady came in and wanted (needed) her brakes warrantied out, yes ma-am, your price will be $110.00 + tax, she said to go ahead, I said OK and got started, then said ma-am just to let you know we have our brakes on sale for $99.99 right now and it will save you $10.00, I just have to wright it up a different way, same exact job and warranty, just saves you $10.00, she got upset and said NO I want me brakes warrantied and was adamant about it, so after 3 times trying to explain, even showed her in the computer how it would save her money, I said WTH and charged her the $110.00 for the warranty job and she was happyā¦
As dad used to say, you canāt argue with stupidā¦ lol
And yes, I tried to explain that filling up the tank could save you money by not having to stop at the gas station everydayā¦ You can lead a horse to water but you canāt make it drinkā¦ I am so glad I donāt have to deal with people that much anymoreā¦ 
After work a group of us went to a local watering hole. After several drinks my supervisor wanted to order wings, they were running a happy hour special $0.25 wings, but he insisted on ordering from the menu, menu pricing worked out to about $0.75/wing.
I too am glad I no longer have to deal with people. Was at a continuing ed program, at the lunch break several of us went to a chain restaurant owned by Pepsi, one woman insisted on a Coke with her order, waiter explained several times they served Pepsi, finally gave up, brought her a Pepsi, she, of course, could not tell that is was not Coke.
Back to cars, yes, had a 67 Pontiac with a non working fuel gauge, with the driving I did, filling twice a week was fine.
And, when you have to deal with the public, itās part of the jobā¦ unfortunately. When I was working part-time for a large chain department store, back in the late '70s, there was a TV news story about some small businesses that had decided to provide a small discount for cash-paying customers.
I lost count of how many of my customers would flash a credit card, and would then inform me that, āYou have to give me a discount because Iām paying with cashā. I triedāpatientlyāexplaining that this was an optional policy with some small businesses, and that Federated Department Stores did not choose to do business that way. They would swear that I was trying to cheat them.
Similarly, in the '80s, a few school districts decided to allow out-of-district students to attend, albeit for a fairly-large tuition fee. That resulted in a number of parents who attempted to register their children in our schoolāwhich did not have that type of policy. Of course, this would produce verbal abuse from the misinformed parents when I informed them that our district didnāt have that policy.
In both the case of the department store and the school, I politely provided the phone number of the people who were in charge, so that they would complain to the powers-that-be, instead of complaining to a person who did not establish the rules.
Putting only a dollar of gas in my car (1966 to 1970ish) saved me moneyā¦ When I had gas in the car, I drove it and I only had to have enough in the tank the following morning to buy another dollarās worth on the way to schoolā¦ If I put in more, I drove it out. And when I filled it up, I often skipped school with my friends and it was āRoad Tripā¦ā
The weight argument is real but barely matters for daily driving. A full tank on most cars is 80-110 lbs. On a 3,500 lb car thatās about 3% of total weight. Youād burn maybe 1-2% more fuel running full vs half.
The stronger argument for keeping it full is actually about the fuel pump. On most modern cars the fuel pump sits inside the tank and uses the surrounding gasoline as a coolant. Running it low constantly means the pump runs hotter, which can shorten its life. Not a huge deal if you fill up at a quarter tank, but habitually running near empty isnāt great for it.
Also condensation. Half-empty tanks have more air space, more moisture can condense on the tank walls, especially with temperature swings. Old steel tanks this mattered more. Modern plastic tanks, less so.
Appears Cavell is not going to provide his rationale for not filling his tank.
My truck has a 35 gallon fuel tank, I used 10 gallon/year.
If the gasoline in my car is more than 6 months old, I add 5 gallons when the tank is low, this removes more of the old fuel before the next fillup.
Using the calculation from Page 8 I calculated that the additional power to travel @ 30 mph with 20 additional gallons of fuel in a 2-ton pickup is 0.6%; accelerating requires 4% more.
Whoops! I used the wrong density for gasoline, 8 pounds/gallon instead of 6 (the right number), which drops the additional power saved to 0.46%, the additional acceleration to 3%. Sorry.
I did not use your linked calculator, but the 4% figure is really too high to accelerate an additional 20-gallons of gas (approximately 120 poundsā¦) as there would only be enough energy left to accelerate 3,000 additional pounds, not the reported 2-ton (4,000 pound) pick upā¦
Itās an easy calculation: mass Ć acceleration. 20 gallons is 120 pounds, which is 3% of 4,000. I mistakenly used 8 pounds/gallon (waterās density), thus the 4%. I didnāt think to look it up.
Further expanding on the energy calculation I calculated that it would take 57 minutes of traveling at 30 mph with 120 pounds less fuel to compensate for the extra period of acceleration to 30 mph that an extra stop would entail.
I do not know what you are trying to prove with your ācalculationsā but I believe it is āBad Mathā¦ā
The Calculations of your carās speed or acceleration that are mathematically sound but in reality are physically meaninglessā¦ Mostly by ignoring physical constraints (traction, engine power, time, wind resistance, and so much moreā¦), especially since you are treating acceleration as an instantaneous change rather than a rate over time.
Driving a car at 60 mph requires roughly four times the aerodynamic power to overcome wind resistance compared to driving at 30 mph. Because air drag increases with the square of speed, doubling your speed from 30 to 60 mph causes drag force to quadruple, significantly increasing fuel consumption, typically by 15% or more.
Less tire spin on the muscle cars of the sixtiesā. Or, if your Little Deuce Coupe gets rubber in all four gears.