Fill your gas tank before it warms up. Here's why

Sure, the polar vortex is hard to love. But it can help you save at least a few coins on gasoline.

The arctic air blast over the last few days sent Michigan and the rest of the Midwest into a deep freeze, with Detroit reaching a record-low temperature of minus 13 on Wednesday.

It will be warming up to a high of about 17 on Friday, but then a big "heat wave" rolls in, with temperatures expected to reach 48 by Monday — a whopping 61-degree swing from Wednesday's low.

If your car needs a tank of gas, bundle up, clench your teeth and go get a fill-up before that big temperature rise: You'll get slightly more fuel for the money than you would filling up after the warm-up. Consider it a scientific cheat code.

The volume of liquid fuel expands and contracts with changes in temperature — quite a bit, actually — more than four times temperature's influence on water volume. After filling up the tank amid our arctic chill, that gas will expand a little as it warms up. Gasoline's volume changes approximately 1 percent for every 15-degree temperature change, according to the U.S. Government Accounting Office.

Andre Boehman is a professor of mechanical engineering at the University of Michigan and director of its W.E. Lay Automotive Laboratory.

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"This is not trivial science at all — I asked it to a group of 160 seniors in a mechanical engineering class just two weeks ago," he said.

In Boehman's test question, he uses a crazy winter weather day in Ann Arbor's recent past: Feb. 20, 2015, when the temperature swung from minus 26 in the morning to the high 20s within a 24-hour period.

"In a remarkably bad coincidence, that day we had potential doctoral students coming to campus to visit — people from California, Florida and Texas," he said. "I don't think we had good retention that year."

Boehman asked students whether it would have been better to fill up early that bone-chilling morning, or in the warmer afternoon, and why. The answer is the morning, he said, when the gasoline's density was about 3.6 percent higher.

It's an even bigger temperature swing from Wednesday's low to Monday's high. If the gasoline was actually as cold as that frigid Wednesday air (we'll get back to that), it would be about 4 percent more dense than at nearly 50 degrees on Monday. If gas costs $2 a gallon, that's about 8 cents of free, additional gasoline per gallon, Boehman said.

At the wholesale level, where huge volumes of gasoline are involved, that amount of variation is intolerable. In the U.S. and elsewhere in the world, temperature compensation factors are applied, formulating the volume of fuel sold, and its temperature, to what it would be at 60 degrees Fahrenheit. Canada also allows retail gas stations to have temperature compensators on their pumps. This, says the website for Measurement Canada, the nation's weights and measures regulator, "benefits consumers and retailers by removing the effects of temperature variation when purchasing and selling fuel."

Those temperature compensators, however, aren't allowed on gasoline pumps in Michigan, said Craig VanBuren, director of the Michigan Department of Agriculture and Rural Development laboratory that includes the state's weights and measures regulation.

Eddie Osman, who owns a Marathon gas station in Wixom, confirmed it.

"There is nothing like that — the pump is the pump," he said.

So let's all go fill up cold and get that 8-cents-per-gallon bonus when it warms up.

Unfortunately, it's a little too good to be true. There are caveats.

"If we think about how fuel is stored at a gas station, it's underground in a big tank," Boehman said. "Depending on how deep that tank is underground, that tank temperature isn't going to vary a lot, even when it's really cold aboveground."

On the other hand, many gas stations have such busy fuel sales, the gasoline transported to the station's underground tanks doesn't stay there long.

"I get a delivery of gas twice or three times per day," Osman said.

While that could help keep the fuel colder, its trip from bulk storage distribution center to tanker truck to underground station tank certainly isn't going to have the gas matching the temperature of the frigid outside air, VanBuren said.

"I think you're talking pennies with this" temperature change phenomenon, he said.

OK. Still, don't say the polar vortex never gave you anything.

Contact Keith Matheny: 313-222-5021 or [email protected]. Follow on Twitter @keithmatheny.