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Physics question - fuel used per kg of weight?

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After emptying 8kg of junk out of my car the other day, I wondered how much fuel might be used per kg per mile during “average” motoring...however you define that.

If you’re dead brainy and can work out things like this I’d be very interested/grateful.

In reply to Frank the Husky:

mv^2/2 is the energy required to take a mass m up to velocity v. Without regenerative braking, this will be lost as heat when stopping or slowing. Then there's friction whilst running, which will depend on the mass, plus a lot of other factors not so easy to quantify.

Significant energy is used to overcome wind resistance, especially at higher speeds.

 lowersharpnose 06 Aug 2022
In reply to Frank the Husky:

Get a order of magnitude...

Assume car is 1000Kg, you have just reduced the mass by 0.8%. 

Good fuel consumption 6L / 100 km

6000ml / 100 km

Usage : 0.8% x 6000 = 48ml / 100 km

More useful to think that you will save 1L every ~2000km or 1300 miles.

Estimates, obs.

1
 wintertree 06 Aug 2022
In reply to lowersharpnose:

I always appreciate the OOM approach - a good way of showing it’s pretty insignificant here.

Rolling resistance is normally a fair bit smaller than air resistance so you can probably chuck a zero on the end of those miles.

I suspect loading has more effect on economy through the effect on the tyres and so changing the drag coefficient…?  But still, small changes.  

In reply to captain paranoia:

> Without regenerative braking, this will be lost as heat when stopping or slowing.

It also increases the inertia of the car, so you can access that energy stored in the mass; when slowing down you can back off the throttle a little bit earlier as the car is going to decelerate more slowly.  I see regeneration as a way of accessing that economy without frustrating the impatient driver behind who wants to hit the next queue sooner.    Edit: it’s also handy for descending big hills where you can’t store the energy kinetically without speeding…

Post edited at 11:57
In reply to lowersharpnose:

Interested with your approximation. I have noticed how often we are advised to remove junk from our cars and have guessed that not many people have enough junk to make a worthwhile difference. Frank’s 8kg is probably typical and even I can work out that that is only a tenth of the weight of an extra adult male in your car. How you drive and if you keep a roof rack on your car are much more significant. 
my guess is that the extra weight only has an effect when accelerating or driving up hills. As far as the latter is concerned if you look at mpg setting on your car’s computer you may be surprised how much of the fuel economy you lose, say, going up to Shap summit on the M6 you regain on the descent to Carlisle.

 jimtitt 06 Aug 2022
In reply to Frank the Husky:

For an HGV a good rule of thumb is 1l/100km for every 2 tons load. They measure it for obvious reasons.

 montyjohn 06 Aug 2022
In reply to Frank the Husky:

If you do a lot of motorway miles the answer will pretty much 0. Wind resistance is the dominant loss here.

If you do a lot of stop start driving the answer will be a "bit" under 0.5% (assuming you have a 1600kg car). I say a bit as you're not impacting engine friction losses, engine parasitic losses, wind resistance etc. But with urban driving, accelerating is the dominant loss. I would guess 0.4% on balance.

Now assume you do a mix of driving, I'd call it 0.2% saving (half way between the two)

Now assume your car does 40mpg (0.11 lites per mile) then you have saved 

That's 0.22ml per 8kg per mile.

It 0.03ml per kg per mile.

Or a million pounds per kg per mile today. 

I'll let someone else check the maths, it's lunch time.

 Stichtplate 06 Aug 2022
In reply to wintertree:

> In reply to captain paranoia:

> > Without regenerative braking, this will be lost as heat when stopping or slowing.

> It also increases the inertia of the car, so you can access that energy stored in the mass; when slowing down you can back off the throttle a little bit earlier as the car is going to decelerate more slowly.  I see regeneration as a way of accessing that economy without frustrating the impatient driver behind who wants to hit the next queue sooner.    Edit: it’s also handy for descending big hills where you can’t store the energy kinetically without speeding…

I hate braking and drive according. Partly for fuel efficiency and partly for a smoother ride / less wear.

The boy racer in me also likes accelerating hard on occasion. I’m hoping the two sort of cancel each other out.

 wbo2 06 Aug 2022
In reply to Frank the Husky:  Do you live somewhere flat or hilly.  The ideal of course would be to only drive downhill.

I once emptied the back of a local 'characters' Renault 12 (upside down saucepan style) and found two enormous plate steel tool boxes full of tools (probably 15kilos a piece) and circa 200 loose shotgun cartridges.. apparently it vastly improved the performance and reduced his crash/explosion danger to boot!

 Maggot 06 Aug 2022
In reply to lowersharpnose:

> More useful to think that you will save 1L every ~2000km or 1300 miles.

> Estimates, obs.

In 2020, about 210 billion miles we're driven by cars and taxis, so your figures would give a saving of 162 million litres of fuel!

In reply to Frank the Husky:

I can give you a real world example. My old van used to average 34 mpg. I put it on a weigh bridge and found with just my daily carry I was 150kg overloaded and that didn't include myself as driver nore my passenger so I put the van on a 450kg diet.

I do probably a 50/25/25 mix of motorway, country road, town driving. The new average was a whole 35 mpg.

Not exactly a fair test though, because it was lighter it performed better and I probably sped up a bit. 

In reply to Dax H:

Well that is a 3% improvement in fuel economy. Not a lot, but better than nothing. Not quite sure how that translates to Frank’s example.

 tlouth7 10:27 Sun
In reply to Frank the Husky:

Relevant xkcd: https://what-if.xkcd.com/22/

The headline is a 0.5% hit for 50lb (23kg) of stuff, the source for which appears to be a post on a random forum referencing an unnamed article.

 mike123 11:23 Sun
In reply to tlouth7: Brilliant . I always forget about xcd until somebody links to it on here and then I fall down the hole ……

In reply to Frank the Husky:

The best answer is "it depends"...

On long journeys as more or less constant high speeds the majority unavoidable waste* loss (hence fuel consumption) is spent on friction / air resistance. A small amount of this will be attributable to the weight of the car since air resistance will dominate.  A small weight saving might not be noticeable. Typically frictional losses (due to weight) are less than a few percent of the total and a 1% weight saving probably leads to a <0.1% loss saving since the air resistance is dominant and unaffected. You will be better off checking your tyre pressures.

On short journeys it's different - you speed up and use brakes to slow down.  The energy used is 1/2 mv^2 so proportional to "m" so if all your fuel goes into acceleration (not air resistance or other losses) and you drive at the same speeds then you will get an "8Kg/mass of car" saving (0.8% as est above).

This is an over estimate (the assumption as "all") because there are other losses but the proportions depend on many assumptions (eg regenerative braking, you keeping to the same speeds / acceleration, other loses) you'll probably not notice.

Now try this again with and extra person (80Kg) and it starts to become measurable at slow speeds. Add 800Kg (van load of crap) and it's noticeable. Add a roof-rack, open your windows, drive with soft tyres etc etc and it makes a difference.

If these things worry you (and they should) keep a well maintained vehicle and drive 10% more slowly, don't race, keep your distance, drive calmly, remove crap from your car and ride a bike - you will make substantial gains. If you can afford it drive a modest small modern vehicle, preferably electric or hybrid.

* here we'll ignore the thermodynamic losses inevitable in a fuel/heat engine


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