June 25th, 2009 - Lighten Up

I'm blatantly stealing my friend Buthidae's green valve cap photo here, because: 1) I like the picture, 2) I like to give her blog some PR, 3) I don't have a green valve cap, however, I do have some purple valve caps, but they're on my bike tires, and 4) I can't think of any photos I already have that have anything to do with today's topic, and today's topic is probably too stupid to go out and specifically photograph something for anyway, especially when I like this one so much.

So with that rather dubious introduction, let's proceed to the chalkboard...

Okay. Sharon was engrossed in a blog for awhile about these guys that try to maximize their driving habits and cars to induce maximum fuel efficiency. They go to some pretty extreme measures, but have definitely influenced their fuel consumption. Some things worked, some things didn't, but it was interesting to hear all the thought that was put into the topic.

I've had an idea along these lines for awhile, and I finally sat down and crunched some numbers just to see if my theory had any justification at all. Unfortunately, doing so brings up one of those "story problems," you know the ones... those that I hated so much in math class: "If a train full of passengers leaves the station going east at 8 A.M., and another train..." my eyes begin rolling back in my head at the thought. However, since there may be an actual practical application for it this time (who knew?) I will attempt the calculation AND, I'm probably doing it wrong since I was so bad at these in school, so speak up and get ready to whack my hand with a ruler if you see an error.

Here's the premise:
I have heard that if you carry a certain amount of weight in your car, it will take a certain amount of gasoline to move it. For example, if I filled my trunk with lead weights and left them in the car, my gas mileage would go down as opposed to my car without the lead weights.
What about the weight of the gasoline itself? Gas is lighter than water, they used to use it in submarines as anti-ballast if I remember correctly, but a full tank of gas must be heavier than an empty tank. So IN THEORY, I should be getting better gas mileage as my tank goes dry, because I have less weight.
My question is, how much difference does this make...? dot dot dot... question mark.
Before we go into the math, (I'm putting that off as long as possible) I'm reminded of the days when I used to race bicycles:

With them, it was all about weight. You wanted the lightest bike you could get without it falling to pieces after hitting the first bump. If you had the cash, you would replace all the aluminum parts with titanium parts to save those precious ounces. Grams really. And they WERE precious. At one point, I think we figured out that most machined titanium bike parts came out to something like $100 an ounce, average, so the joke was that you could dump half the water out of your water bottle and save $500. Conversely, those grams and ounces saved DID add up to calories burned over an 80 mile road race or stoking up the side of a ski hill on a mountain bike. Part of it is psychological ("psycho" for short) and part is reality. Especially when you start taking grams and ounces off of your wheels, which go round and round with every pedal stroke you suffer through.
If you have ever watched a bicycle road race, if a rider is lucky enough to have extra water on the last lap, they will usually chuck all their bottles somewhere before the finishing sprint or the last big hill. No reason to drag around a half pound of water at this point, there's plenty at the finish (we hope) and we want every advantage we can get. My dad was a tailgunner in a B-17 in WWII, and when they were down to one engine and unable to fly the plane above the mountain tops any longer, they threw out everything that wasn't bolted down: guns, ammunition, tools, fuel, maybe their St. Christopher medals, I don't know, they wanted to make it to Switzerland. The point is: less weight, less fuel needed to move it.
Alright, to the chalkboard. This time for real:

Q: How much does a gallon of gasoline weigh?
A: 2.69 to 2.91 kg (5.93 to 6.42 lbs), depending on temperature, type and blend (e.g. with methanol, water, benzene etc.)
We'll call it 6 lbs., US.
By the weigh, water ways in at about 8.35 lbs. per gallon ("pint's a pound, the world a 'round", that would be 8 lbs., but close enough).

Let's say my 2000 Ford Focus Wagon has a 13 gallon gas tank:
13 gallons of gas = ~ 78 lbs. (that's a little surprising. It's like having an extra passenger, albeit a small one)

Q: How much MPG loss is there if I put weight in my car?
A: The best answer I could find on the web for this came up with:
A loss of 2% MPG for every 100 lbs. in vehicle.

78/100 = 0.78, times 2(%) = 1.56 % loss of MPG for the weight of a full tank...
0.078 % loss of MPG for the weight of a 1/2 tank...
0.039 % loss of MPG for the weight of a 1/4 tank...

So if I normally get 30 MPG with my car:
30 MPG x 0.078 % = 2.34 (it would actually be better than that, because as you drive your tank is getting lighter, so let's call it 2.5 conservatively) of added MPG, driving on 1/2 tank (and less) compared to driving on a full tank.

Say I get 390 miles out of a full tank (at 30MPG)...
I would get 211.25 mi on 1/2 tank (at 32.5 MPG)...

That means I would save about 0.52 gallons per tankful by filling it to 1/2 full compared to filling it completely full of gas.

Based on that, if I fill my tank 25 times to only 1/2 full, I will have saved about 1 full tank of gas.

Hmmm. 13 gallons of gas = $32.50 (at $2.50 a gallon). Is it worth it stopping twice as often...? Is my theory correct?
More research must be done in a more empirical fashion, me thinks...


TC said...

Remember, you don't drive a full tank of gas with a full tank of gas...

Less confusingly, I usually fill up at about 1/4 tank - so for that tank of gas, I *average* about 5/8s of a tank. Assuming you want the same safety buffer, you'd average about 3/8s of a tank. Thus the difference would be on average about 1/4 of a tank - by your math about 1.17 MPG - half the savings.

This is still oversimplified - to do it right you'd need some greek symbols and scotch whiskey.

By this math, you'd also be filling up 3 times as often, rather than 2x, and your added slushie expenses would more than eat any savings.

buthidae said...

I agree with greek symbols and scotch whiskey for a really geeky result, but the basic logic looks sound. What happens if Hap the dog sticks his head out the window between miles 147 and 238 while your speed is varying between 45MPH and 65MPH?

dignature said...

Agreed, it's not a perfect thereom. There may be too many variables to even make it worth trying to prove. I am however going to try and put it to some "practical" testing. Since I drive nearly the same commute every day, (Oy, let's not get into that) and my weekend mileage is negligable (unless I take a trip up north or such) my plan is to fill up to 7 gallons and refill when my warning light comes on, or close thereafter. After a few fills I should see some change if any is going to happen. Sharon should really be doing it with her car because I carry around a lot of camera gear, catapults, animal food (bait) and other weirdness at times. But, I'm assuming all that evens out in the long run.
Wish me luck, place your bets... I can't carry an extra can of gas or that would screw it up.
- T.

buthidae said...

How much does a AAA card weigh?

I am just back from walking to the grocery store. As I approached the store, a fellow opened the tailgate of his black Lincoln Navigator with the 20 inch wheels remotely. I could not help but notice that the car was already idling, for as I walked by the now-open tailgate I was blasted with cold air. The fellow had not yet arrived at his car, and I peered inside to see if anyone had been awaiting him. Nope, he was alone. Apparently, he'd left the car idling with the AC on for the duration of his shopping trip. Judging by the stuff in his cart, that must have been at least 20-25 minutes.

For every ounce of gas you manage to save thru some careful experimentation, jerks like this will burn up 40 gallons cooling a parking lot with nary a thought about it.

I wished I'd remembered to recharge my Navigator blasting laser.

(Oh, nice pic BTW. I opened it and thought I was having deja vu all over again)

dignature said...

Ahh yes, the Lincoln Earth-negator. Well I just have to bite my tongue and live by the principles I respect and believe I'm making a difference. Sharon has a great book about nuclear power called "Nuclear Choices," which quite objectively looks at nuclear power generation. The thing I love about the book is that it breaks down power as an analogy of how much work human slaves would have to do to equal a person leaving a light bulb on in the bathroom while they were at work, or run a television, etc. If we had to generate our own power, our feelings about conservation would be quite different.
The best I can hope for is that if there is reincarnation, the guy comes back as a midge, lives for a day and becomes a petroleum product.
We do have AAA, BTW, so that weight is already accounted for. I feel better.