[Nikita Strauss]

Nikita Strauss asked the Naked Scientists:
   
Hi Chris

I'm curious, is there a difference in fuel consumption on a full or empty tank of gas?

Would appreciate your answer!

Thanks

Nikita Strauss

What do you think?

[Geezer]

The amount of fuel in the tank has no effect on the efficiency of the engine. The mass of the fuel in the tank does have an effect on the fuel consumption of the vehicle, but not very much.

Also, it's really the average amount of fuel in the tank that matters. If you always completely fill it then only refill when it's almost empty, the effect is about the same as trying to keep it half full with frequent fuel stops, except that you'll waste more fuel with all the stopping and and starting.

[damocles]

In the motor racing game, the weight of the fuel on board makes a tiny, but significant difference to lap times -- maybe tenths of a second.

Same power driving a lighter weight means faster speeds possible.

Only other consideration is that during the lifetime of a vehicle heavier impurities, condensation (=water), and sludge in the fuel can accumulate at the bottom of the tank. So with older cars that have done a lot of running, it is probably a wise idea to avoid running on the last 2 litres in the tank.

[Geezer]

Same power driving a lighter weight means faster speeds possible.

Not necessarily faster speeds, but higher average speeds because of greater acceleration.

[Dr.Abdullah]

A full tank would have slightly lower fuel efficiency due to the added mass of the liquid itself. Although you would not notice a difference.

[Don_1]

As has been said, there is a difference, but it is not significant, unless you have a particularly large fuel tank. For most cars a full tank will weigh about the same as a slim woman. So you can run on a tank virtually empty and be able to pick up a hitch hiking piece of totty without having an adverse effect on your fuel consumption. Trouble is, the piece of totty might not be too keen on pushing the car to the next filling station when you run out of petrol (gas). Also, if the Mrs finds out you've been picking up totty in the car, you may discover how far and fast she can run and kick you up the butt at the same time.

[techmind]

I'm curious, is there a difference in fuel consumption on a full or empty tank of gas?

The only difference will be the exrra "deadweight" of a full tank. For longer journeys at near constant-speed this will make very little difference, but if you're driving about town with lots of stopping and starting at lights/junctions, pulling inbetween parked cars to let other pass etc then the added mass that you keep accelerating will detriment the full economy to some extent. Similarly if you're doing a lot of driving in hilly areas so you're lifing that deadweight up the hills.

A typical UK car has a tank of 10 gallons (45 litres). If petrol has a density of 0.7kg/litre, thats just over 30kg of fuel.
If a small car + one occupant (driver) weighs say 1200kg, thats an additional 2.5% on the weight of the car. If we do a simplification and a worst case scenario that you spend all your time accelerating and braking (and never travelling at constant speed where energy is required merely to overcome friction, rolling resistance, wind resistance etc), then (since energy required to accelerate = (1/2)*m*v^2 ) this might worsen your fuel consumption by roughly 2.5%. Similarly for potential energy (hills) potential energy (m*g*h) scales with mass, so the deadweight makes a difference.

This is a simplified worst-case analysis. For normal driving the difference is probably quite a bit less, although if you drive particularly hard on the accelerator (where the engine efficiency probably drops anyway) the economy-impact of carrying extra deadweight could be disproportionate.

Much the same reasoning explains why the motoring organisations will exhort drivers not to habitually carry all the accumulated junk everywhere with them in the boot!

[Geezer]

A typical UK car has a tank of 10 gallons (45 litres). If petrol has a density of 0.7kg/litre, thats just over 30kg of fuel.
If a small car + one occupant (driver) weighs say 1200kg, thats an additional 2.5% on the weight of the car. If we do a simplification and a worst case scenario that you spend all your time accelerating and braking (and never travelling at constant speed where energy is required merely to overcome friction, rolling resistance, wind resistance etc), then (since energy required to accelerate = (1/2)*m*v^2 ) this might worsen your fuel consumption by roughly 2.5%. Similarly for potential energy (hills) potential energy (m*g*h) scales with mass, so the deadweight makes a difference.

Yes, but you are overlooking an important detail. The amount of fuel is not constant. The calculation should be based on the average amount of fuel in the tank, which is probably more like 55% of the tank capacity in the case of vehicles that are fueled to capacity.

The other problem with frequent refueling is that you waste a lot of fuel (and time) at every refueling stop.

[wolfekeeper]

Rolling friction of a car dominates up to about 50 miles per hour or so; and is the main place that the power of the engine ends up (up to that speed).

Rolling friction is proportional to the mass of the car, including the fuel, so adding a gallon of fuel is the same as adding roughly 4 kg to a tonne vehicle (less in America, due to their smaller gallons); so ten gallons is about 4% of the weight of the vehicle and adds 4% to your fuel bill (if you spend most of the time below 50, less if you spend more time cruising at high speed, since the extra weight doesn't affect the aerodynamic drag).

There's also losses during acceleration; if you accelerate to a given speed, you need to use proportionately more fuel to do that, because the weight of the fuel slows you down, and you have to accelerate for longer, with the same, higher, throttle setting.

[Geezer]

Rolling friction of a car dominates up to about 50 miles per hour or so; and is the main place that the power of the engine ends up (up to that speed).

Not really. See FIGURE 3-1. http://onlinepubs.trb.org/onlinepubs/sr/sr286.pdf

At lower speeds, rolling resistance only accounts for about 4% of the fuel consumed.

[wolfekeeper]

Careful here, that's 4% of the 13% of energy from the original fuel that makes it through to drivetrain.

The other bigger part is the 6% you lose in braking (which will depend on how you drive), so that's 10% of 13% or 77% of the propulsive energy that is affected by greater vehicle weight.

[Geezer]

Careful here, that's 4% of the 13% of energy from the original fuel that makes it through to drivetrain.

The other bigger part is the 6% you lose in braking (which will depend on how you drive), so that's 10% of 13% or 77% of the propulsive energy that is affected by greater vehicle weight.

Er, no it ain't []

It's 4% of the total energy from the fuel, and it's not 4% of 13%.

Even if you completely eliminated rolling resistance, you would only reduce the fuel consumption by 4.1%, so it's a bit unlikely that adding a few kilograms in weight will increase your fuel bill by 4%.

The coefficient of resistance for a rolling tire is only around 0.01

[wolfekeeper]

No, the diagram is showing that of the original energy in the original fuel only 13% makes it to the back wheels.

Of that:

4 parts out of 13 is lost in rolling energy
6 parts out of 13 go into the brakes
3 pars out of 13 go into airdrag

Making 13%.

If you were to get rid of all rolling friction you would save 4/13 of your fuel bill, because that 13% is the reason you are burning the fuel in the first place (neglecting the energy to run subsidiary components, lights etc.) So if that energy goes up by a percentage, you need that much more enegy in general.

So if you had twice as much of rolling losses, braking and airdrag, you would (nearly) double your fuel bill.

[Geezer]

If you were to get rid of all rolling friction you would save 4/13 of your fuel bill, because that 13% is the reason you are burning the fuel in the first place (neglecting the energy to run subsidiary components, lights etc.) So if that energy goes up by a percentage, you need that much more enegy in general.

So if you had twice as much of rolling losses, braking and airdrag, you would (nearly) double your fuel bill.

Erm, he he, I'm sorry, but have you considered a career in politics? ([] [])

You are calculating it as if you didn't have to pay for the gigantic amount of energy that simply goes into heating the atmosphere. Relative to that, the loss to rolling friction is peanuts.

To affect the fuel consumption by 4% by changing the weight as you suggest, you would have to double the weight of the vehicle. By eliminating rolling friction entirely, the best you could hope for would be a 4.2% improvement (100/96*100 = 104.2%)

[wolfekeeper]

No, sorry, you've got it wrong.

The 13% is the useful bit. In other words for every kilojoule you get at the back wheels, you need 7.7 kjoules of petrol.

For example if the rolling friction is 0.02, and the car mass is about a tonne and weighs 10000 N, then for every meter you roll you need 200 joules. For every kilometer that's 200 kJ, and hence that's 1.54MJ of energy. The energy density of petrol is about 35 MJ/L, so that's 22km/l; over 100km to the gallon. You only normally get under a third of that, because of air drag and brakes, they're all very, very roughly equal.

So it's not 4% of the energy, it's 4 out of 13 parts of the USEFUL energy; it's completely not negligible.

So if you increase the weight of the car by X%, you increase the fuel consumption by about 10/13 X%, because the air drag is unaffected, but both the braking energy and rolling energy are increased proportionately.

[Geezer]

The 13% is the useful bit. In other words for every kilojoule you get at the back wheels, you need 7.7 kjoules of petrol.

Wolfekeeper, you are probably going to hate this, but it doesn't matter which bit is "useful". The fuel is consumed whether it does useful work or not. If we measured vehicle fuel consumption in miles per useful gallon, your approach might work, but some poor schmuck would still have to cough up the money to cover the cost of the non-useful part.

I think you are getting mixed up between mechanical efficiency and thermal efficiency. Miles per gallon is a measure of mechanical and thermal efficiency combined. You can't simply toss away the thermal bit.

[wolfekeeper]

No, I'm not tossing anything away, you're assuming that the thermal bit gets spent whether or not the useful bit gets spent.

That makes no sense at all.

The thermal and other losses are percentages of a gallon of fuel that is used for some purpose. If you don't use part of a gallon for any purpose then you don't get the associated thermal losses for that fraction, because it simply wasn't burnt; you don't press the throttle down so hard, and the fuel doesn't get injected, or if those bits go up you press the throttle harder and burn more fuel.

You press the throttle harder or less hard depending on what you want the car to do.

Actually, what you're describing has been a problem with one type of engine; jet engines and gas turbines use more or less the same amount of energy irrespective of how much useful power is being made (not completely but there's fairly heavy consumption the whole time they're spinning). That's why jet engines and gas turbines aren't used much on cars!!! They're much better for aircraft, where you need much more constant power from takeoff to touchdown.

[Geezer]

No, I'm not tossing anything away, you're assuming that the thermal bit gets spent whether or not the useful bit gets spent.

That makes no sense at all.

Let's start at the beginning.

You burn a gallon of gasoline to make your car go. 4% of the thermal energy in the gasoline is used in overcoming rolling friction. (True/False)

Let's say we increase the total weight of the vehicle by 10%. We have increased the rolling friction by 10%. (True/False)

How much of the thermal energy in the gallon of gasoline is now used in overcoming rolling friction?

a) More than 15%
b) About 4.5%
c) At least 8%

[wolfekeeper]

No, I'm not tossing anything away, you're assuming that the thermal bit gets spent whether or not the useful bit gets spent.

That makes no sense at all.

Let's start at the beginning.

You burn a gallon of gasoline to make your car go. 4% of the thermal energy in the gasoline is used in overcoming rolling friction. (True/False)

FALSE!!!!

Just about 4/13 of the energy in the gasoline is spent overcoming rolling friction!

There's big losses that are specific and necessary parts of generating the force to overcome rolling friction, there's 6% losses in the drive train (of which rolling friction is 4/13ths), and the 60% losses in the unrecovered heat in the exhaust, (of which rolling friction is responsible for 4/13ths).

If the rolling friction magically went away; these energy fractions would drop to zero! If the rolling friction doubles, they double too! (The other parts of the thermal fraction and drive trains losses could in theory be completely unaffected).

[Geezer]

FALSE!!!!

Just about 4/13 of the energy in the gasoline is spent overcoming rolling friction!

I'm afraid not. That's almost 31% of the thermal energy in the gas, which is impossible because the engine only delivers 19% of the energy in the gas to the drive-line. It's quite clear that only 4% of the energy in the gas is overcoming rolling friction.

You might want to study that diagram an awful lot a bit more carefully.

Tell you what, why don't you start with the thermal energy in a gallon of gasoline and show us your budget of where all the energy ends up. I think you'll be quite surprised (and at least we'll get a good giggle).