My family and I often drive 180 miles between St Albans and Huddersfield to visit the in-laws, most of which is just going along the M1. It’s common knowledge that the faster you go the higher your fuel consumption, so I was wondering what speed I should go at to get the optimal balance between time taken and money spent on fuel?

Speed vs. Fuel Consumption

We have a 2008 Ford Focus (1.8 litre petrol engine, for reference). A rather nice feature it has is a little fuel consumption computer. You can reset it by pressing a button on the indicator stalk and after a few miles see what your average consumption has been, as well as your average speed. So over several journeys I tried doing a succession of 10-20 mile stints where I would try to go at a steady speed, and record my average speed and fuel consumption. Below are some graphs which shows the results, in imperial and metric units. (The bits around 50mph were some roadworks.)

When fuel consumption is expressed the metric way this looks pleasingly neat – the faster you go the higher the fuel consumption, and it looks like the trend line would hit the y-axis at zero. (It wouldn’t really, of course, but that’s moot given that it would be impractical to drive in 5th gear at low speeds.) So if we go at 70mph* (=113kph) the fuel consumption will be 7.4 litres per 100km (=38 miles per gallon), and for every 10% increase in speed the fuel consumption will also go up by 10%.

(This is actually quite surprising – at high speeds like these the reason for the increase in fuel consumption is wind resistance, and wind resistance goes up proportionally to the square of the speed. For every 10% increase in speed you hit 10% more air molecules AND the relative speed difference between the car and the air molecules is 10% higher. Might be something to do with the efficiency of the engine in the range of speeds I’ve measured.)

(* – The charts above are based on the actual speed rather than what the car’s speedometer says. Most cars I’ve ever driven have overstated the speed by 5%, although I once had one which overstated it by 10%!)

Hills vs Fuel Consumption

There’s a fair bit of variation around the trend, probably because of inclines. To get a handle on how big an effect hills make, I used the fact that on the M1 there’s a very long hill either side of the exit for Coalville. Here the elevation goes up by 500 feet over the course of 5 miles, then down again over the following 5 miles – that’s a sustained incline of 2%. The graphs show these observations, from which I estimate that a 2% incline results in a 20-25% increase/decrease in fuel consumption (when you’re going at 80mph).

This is why you should ideally do a fuel consumption measurement over 20 miles or more to get an accurate measurement. Over 5 or even 10 miles you could easily be thrown out quite a long way by a long hill. The tricky bit is trying to stay at a consistent speed over the whole distance!

Speed vs Cost

So now we need to assemble all the factors that contribute to the cost of driving. The only one that has any impact on consideration of the optimal speed is fuel consumption, but it’s good to get them all together…

**Fuel**: So, at 70mph in 5th gear this works out around 15p per mile if petrol costs £1.25 per litre, which it does at the time of writing (January 2011). As described above, every 10% increase in speed gives a 10% increase in fuel cost for a given distance.**Servicing costs**: Our car requires a service every 10,000 miles, and typically costs £150, but will sometimes cost more when things need fixing. If we double the basic service cost that’s 3p per mile.**Tyres**: On our car, a full set of decent tyres costs £500 and lasts about 25,000 miles. That’s another 2p per mile.**Depreciation**: Tricky one this, and one I plan to expand on in another article. Over the course of the first 3 years of owning our car we’ll probably do 36,000 miles, and it will have lost about £5k of its value. That works out as 14p per mile. However, if we’d bought it and just kept it parked on the drive the whole time it would still lose a fair bit of its value: low-mileage cars do hold their value better, but it would probably still lose £3½k. The marginal cost of making an extra journey is what matters when thinking about the cost of any journey, so for now I’ll assume a cost of 4p per mile.

To get a handle on the question, I’m going to work with an example journey: 200 miles on the motorway. The table below shows the speeds, times and costs for a variety of speeds on this 200 mile journey…

Speed (mph) |
Time (mins) |
Cost | Cost Diff (£) |
Time Diff (mins) |
Marginal time value (£/hr) |
---|---|---|---|---|---|

50 | 240 | £39 | – | – | – |

60 | 200 | £44 | £4.27 | 40 | £6 |

70 | 171 | £48 | £4.27 | 29 | £9 |

80 | 150 | £52 | £4.27 | 21 | £12 |

90 | 133 | £56 | £4.27 | 17 | £15 |

100 | 120 | £61 | £4.27 | 13 | £19 |

110 | 109 | £65 | £4.27 | 11 | £23 |

120 | 100 | £69 | £4.27 | 9 | £28 |

Every extra 10mph you go faster costs you an extra £4.27 over the course of the journey, but the amount of time saved gets less and less, so the cost per minute saved increases from around £9/hour at the official speed limit, and up to £30/hour at outrageously illegal speeds.

Choosing your journey

Here’s another way of thinking about it. If you went on this journey at a sedate 67mph (=70mph according to the typical speedometer), it would take you exactly 3 hours, and would cost you £46.50. If someone said you could trim the cost down to £42.38 by taking an extra half hour, would you? If you would, that means you value your time at less than £8/hour. (You’d be going at 60mph on the dial if you chose this option)

On the other hand, if someone said you could reduce the journey time by half an hour by paying £52.13 (= an extra £5.70), would you pay it? I probably would, especially if the whole family was in the car. This would implicitly value your time at more than £11/hour. (You’d need to go at 80mph, or 84 on the dial, to achieve this.)

And if you were in a real hurry you could go for the ‘express’ upgrade and take the journey in a mere 2 hours. This would involve going at 100mph the whole way, and would cost you £60.66, implicitly valuing your time at more than £17/hour. To say nothing of your willingness to risk being done for speeding!

So ask yourself – when you’re driving on a motorway, do you drive at a speed that correctly reflects how you value your time? Because every extra mph costs you money…

Very interesting. I’ve done similar experiments myself in the past without actually writing (or typing) anything down. Certainly Friday nights on the M1 were always surprising good for fuel consumption as long as the traffic generally slowed your progress rather than being the much worse stop-start variety. I came to the satisfying conclusion that the best compromise between time and cost was to drive at the national speed limit!

A grammatical error in the first word of an article is a very neat touch!

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Thanks Robin! One thing I’ve sometimes wondered is how best to handle hills: whether to let the car slow down on the way up and speed up on the way down (ie. to approximately equalise fuel consumption) or just to keep going at the same speed (and burn up fuel on the way up but get the savings on the way down). I previously reasoned that if consumption is proportional to the square of speed then the average consumption would be lower at a constant speed, but in reality it looks like that’s not significant enough to bother worrying about!

Quite right – “Me and my family often drive”… *blush*. Fixed now. Me must try harder.

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You don’t mention the fact that engines will be more efficient at some speeds than others. Is increased air resistance at higher speeds sufficiently significant to negate that?

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I guess the way to find out would be to collect a couple of data points at 100mph. Not sure I’m foolish enough to try! Come to think of it, gathering more data on performance in 4th gear would shed light on that, as one can go into the top-end of the range of revs that the engine can deliver without going indecently fast.

A chap who serviced my car once told me that one of the things about modern electronic fuel-injected engine management systems is that they’re great at achieving good efficiency at a constant level of strain, which is partly why they can be so much more efficient at high speeds than in urban driving. Other than that I believe they exhibit a pretty linear relationship between fuel consumption and power delivered – the fact that the engine power/torque maxes out at high revs limits your speed, but also limits the extra fuel consumption to an equivalent extent.

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Very interesting, and something I’ve often wondered about. Nice to see real-world considerations included like wear and tear. I would like to see a final graph of the cost vs speed, when you get a minute 😉

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I know this blog has been quiet for a while – nonetheless very interesting data!

About the quadratic increase of consumption vs. speed:

You are plotting consumption/distance vs. distance/time and this looks pretty linear.

However the air resistance is basically energy lost per unit of time (and energy = consumption). So if you plot liters/hour instead of liters/100km you get a non-linear relation (sort of quadratic). You get this by doing liters/hour=liters/100km * km/h. So at 50km/h you get ~8 l/100km * 50 km/h = 4 l/h. At 110km/h -> 7.7 l/h, at 120 -> 9.6 l/h and at 140 -> 12.4 l/h. Of course at a higher speed your trip will also be over in a shorter time, so consumption/distance indeed only grows linearly with speed (- and that is of course the relevant quantity for travelers).

Hope this clarifies that conundrum. 😉

Cheers!

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