# Big truck fuel physics

Here’s one for all you math guys.

I have a class 8 vehicle (semi truck) with two 163 u.s. gal fuel tanks. Because the tanks are cylindrical, when filled, the fuel takes up 95% (154.85 u.s. gal) of the tank giving a combined total of 309.7 u.s. gal.
Now, I attempt to track my fuel mileage assiduously, but with summer here, and no source of cooling for the interior of the truck while stationary (e.g. when I’m sleeping), I’m forced to idle the truck - which consumes an industry average of around 1 u.s. gal per hour at idle.
To determine the exact consumption rate at idle, I filled the tanks to the aforementioned levels, and sat, at idle, for 5.5 hours. I then topped off, expecting to add no more than 5 or 6 gallons. I could only put in 2.14 u.s. gallons, which couldn’t be right - as I have said, the industry average is 1 u.s. gal per hour and I had only apparently burned .4 gal/hour.
The only parameter that changed between fill up and top off was fuel temperature - excess fuel in the engine is cycled back to the tanks. I filled up with fuel at 70 degrees f and by the time I had topped off 5.5 hours later, the fuel in the tanks had heated to 135 degrees f. So the fuel had expanded by an undetermined amount, thus skewing my readings.
I will conduct the test again factoring in this effect and will post the results, but I wanted to see if anyone could anticipate my findings. So the question is this…exactly how much fuel did I actually burn while I sat idling my truck?

One factor you may need to know; outside air temp was 95 degrees f the entire time.

If anyone wishes to amuse himself with this problem, you need to know that the standard coefficient of gasoline’s expansion/contraction equals 0.069 % per degree Fahrenheit.

The fuel temperature is what skewed the fuel consumption. Diesel fuel has a cetane rating which indicates how easily it ignites. If the diesel fuel temperature increases the diesel fuel become more volatile which increases the cetane rating and burns more efficiently.

That’s why when doing diesel engine emission tests on a dyno, the fuel tanks have to be buried and the lines insulated to the engine so the fuel stays at a constant temperature. Otherwise it skews the test results.

Also, instead of idling that diesel engine, have you looked into an Auxiliary Power Unit? This is a small diesel engine add-on that supplies power to the truck when down. It’s quiter, uses even less fuel, and produces no emissions.

Tester

OK, so your truck idles more efficiently than the industry average, so?

Let’s see how the math works:

Assume all 135 gallons of fuel rose from 70F to 135F. That’s a 65 degree rise.
Diesel’s coefficient of expansion is 0.00045%/°F.
Therefore the percentage your fuel volume increased by was (65 degrees F * 0.00045%/°F = 0.0295%). Call it 0.03%.
Your volume increase in gallons was (0.00045/100 * 135 = 0.0405 gallons).

An increase in fuel volume of 0.0405 gallons is hardly enough to drive your consumption over 5.5 hours from 1 gal/hr to 0.4 gal/hr.

Discussions on the TDI forums indicate performance decreases as diesel temperature increases, which goes against earlier replies.

I suspect something else is happening.
Is there an element of experimental error at play?

Joe

I think Joe’s math is off…I have seen fuel tanks overflow with a much smaller temperature rise…Fuel coming out of an underground tank at 55 degrees warmed up to 80 degrees, a rise of only 25 degrees, caused the tank to overflow by a fair amount, and it was not filled to the brim to begin with…

But what we REALLY want to know is how much it’s costing you to sleep in air-conditioned comfort every night…Sounds like \$25-\$30 to me…not counting wear and tear on all the moving parts…

Out West, some of the big truck stops have long rows of parking spaces equipped with full plug-ins, including large air supply hoses so engines can be turned off…

Thanks Caddyman. I do see where my math is likely off.

I took the coefficient of expansion for diesel fuel to be 0.00046%/°F, rather than just 0.00046. If it isn’t “percent”, that would mean my math for the amount of expansion is off by 100, and the amount of increased fuel is 4.05 gallons (rather than 0.0405 gallons).

That sounds better…

0.046%/°F makes more sense for diesel, especially if gasoline is 0.069%/°F

I’m seeing the coefficient written both ways, with and out being noted as a percent. I need to look it up further when I have time. Somehow an increase in volume of over 4 gallons sounds a bit much.

Sounds like in reality the emissions tests are inaccurate

For any scientific experiment, you can usually not base a conclusion on one event. The experiment must be verified and you can guess as well as I can as to how many repeats will lead to a firm conclusion. In addition to what is already known, repeats may lead to unanticipated variables.

I know little or nothing about a semi truck but will ask if you filled at the same pump with your truck parked in exactly the same place, are the fill ports at the middle or toward one end of the tanks making an air bubble a possible source of filling repeat inconsistency and do you fill each tank or is that not necessary due to the presence of a crossover pipe that permits both tanks to be filled at one port?

It is also possible that the tank capacity may have changed due to the heat expansion of the tank metal although that would be contrary to what happened regarding the refill.

Ok…lets see, i have dual fill ups and made sure both were at the max fill up without overfilling. The fillups are at the ends of the tanks. I did stay in the same spot. I am working on an anti-idling solution but the options are rather expensive at the moment - sabing up for it.

One thing i just thought about…the initial fill up was 156 gallons, so i had roughly 153 gallons ALREADY at 135 degrees f then added 156 gallons at 70 degrees f. I wonder how you combine the two to figure the initial fuel temp at beggining of test?