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.)

Fuel consumption for Ford Focus 1.8 (petrol) - imperial units

Fuel consumption for Ford Focus 1.8 (petrol) - metric units

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…

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…

I saw it the other day and felt inclined to agree – it is really excellent. After mentioning this on Facebook and getting some good counter-suggestions from friends (Bourne, Indiana Jones, Back to the Future), I thought I’d find out if he’s right with some hard-core analysis…

I used two main sources:

• IMDB, which has average scores (on a 1-10 scale) from tens of thousands of punters.
  This is not ideal in some ways because the viewers of films are self-selecting – people can only rate the things they’ve seen, and they’ll only watch the things they like the sound of. On the other hand, you could argue that that’s fair enough anyway, especially of genre films. The other problem with IMDB is that it will be biased towards the kind of people that can be bothered to record their opinion about films on an internet site, so is likely to be nerdier and more male in its profile than the viewing public.
  I’ve used two measures:
  • Weighted Average Score: where IMDB try to adjust weightings of reviews to make it as representative and fair as possible.
  • Top 1000 Average Score: the scores from the 1000 individuals who have reviewed the most films – these guys have seen a lot of films so should be less susceptible to the ‘viewing only films I like the sound of’ factor.
• Rotten Tomatoes, which collates results from hundreds of movie reviews in reputable publications.
  Being professional reviewers these people shouldn’t suffer so much from self-selection bias, but probably tend to be more considered and more impressed by artistry rather than simple entertainment. The main problem with film reviews is that they are not rated on a consistent numerical scale (many use a 5-star scale, but some use percentages, or letters), so combining them together to give a consistent rating is not trivial. Again, there are two measures I used:
  • ‘Fresh’ score: the percentage of reviewers who, on balance, liked it. (The simplicity of this is a good way of dealing with the problem of putting the reviews on a consistent scale.) This is a good indicator of whether you’re likely to enjoy a film.
  • Average score on 1-10 scale: this is done by each review being re-coded by Rotten Tomatoes onto a 10-point scale then averaging them together. This is arguably a better indicator of ‘greatness’.

So I collected these scores on all the films in 34 movie trilogies/series, including the 30 most popular movie series of all time (according to Box Office Mojo), but also a couple of others that the critics often talk about (including Godfather and 3 Colours). I also included Police Academy, which is the perfect example of what normally happens with movie sequels.

The results – the punters

First of all, here are all the results from IMDB. In each case they are sorted by the average across the trilogy. (In other words, when there are more than three films only the first 3 are used to calculate the ‘overall’ score, although all films in the series are shown)

Clearly, the punters like a bit of sci-fi / fantasy, with either Lord of the Rings or Star Wars taking the top slot. The Godfather is pretty close (let down by film number 3), and Toy Story does pretty well with the best 3rd film of all time according to the masses. Indiana Jones does well too.

It’s amusing to see how many film series start out with one good first film (all those red dots at the top of the charts), then produce an endless succession of ever-worse ones. Think Rocky, The Matrix, Lethal Weapon, Batman, Superman, Jaws, etc. Notable exceptions are Star Trek (with the famously good even-numbered ones), Harry Potter (they’re all good), and Bourne (the final one was a corker).

I thought Police Academy would be the worst film series of all time. But numbers 4 to 7 were truly appalling, and if you base it just on the first 3 then the (highly popular) Twilight series comes bottom. This feels overly harsh. I hate them, but a lot of people really like them. This is probably partly because they are very clearly aimed at young girls, and this group is probably least likely to bother telling IMDB what they thought of a film!

The results – the critics

So what about the critics? Remember, ‘Percent Fresh’ is how many recommended the film, and ‘Average Score’ is their rating of how good it is.

Well, that’s pretty conclusive – not only has Toy Story 3 got the best 3rd film ever, but it’s actually the best trilogy of all time too according to the critics. It’s that amazingly rare thing – a trilogy where all of the films were universally seen as excellent.

And it looks like Mark Kermode was pretty representative of other critics in considering Trois Couleurs a contender for crown of ‘best trilogy’. I’ve never seen any of them, but I now think maybe I should!

—–

Combined rating (from IMDB weighted average and Rotten Tomatoes average rating). * - Foreign-language film

UPDATE: 28th July 2010

Thanks to the various commenters and other suggestions I’ve received, I’ve realised that there are plenty of other trilogies that I really ought to have included. Among them are some little-known foreign-language trilogies that some people rate very highly (Ozu, Apu, Vengeance), some real classics (The Man With No Name, Frankenstein, Evil Dead) but also some other popular ones that I missed (in order of increasing rubbishness: Hannibal Lecter, X-Men, Mad Max, the Star Wars prequels, Scream, Mission Impossible, Blade, Rush Hour, Poltergeist, Robocop, Underworld, High School Musical).

I’ve also adjusted the ‘trilogy’ rating of Star Trek so it’s based on films II to IV, which all thread together. I’ve also decided to completely ignore the Next Generation Star Trek films because I can’t decide which set to put Generations into!

To keep things simple, I’ve tried to settle on a single definitive result, and have used the combination of the IMDB weighted score and the Rotten Tomatoes average rating score.

The final result is that Toy Story is actually the 3rd-best trilogy of all time, behind Star Wars and the (little-known, Japanese, 1950s) Noriko trilogy by Yasujirō Ozu. Another 1950s trilogy I’d never heard of comes fourth, the Indian Apu trilogy, and then the usual suspects of Lord of the Rings and The Godfather come in 5th and 6th.

Click on the picture to view it at full size.

Apparently, the explanation is that the Gulf Stream (which keeps Europe much warmer than other places that far north) allowed for the growth of cereals (wheat, etc.) starting about 5,000-13,000 years ago, and the widespread adoption of cereals in Europeans’ diets caused a significant shift in our skin colour – it’s all to do with vitamin D and folates. And the shift in skin colour in turn caused the incidence of blond hair and blue eyes which is so unique to northern Europeans.

Read the article to find out more.

My new daughter is currently too young to learn her alphabet (10 months), but it won’t be long and I was thinking about putting one of those alphabets up in her room where there’s a little picture of something for each letter.

My brother-in-law (Iain Anderson) and has been collecting the basis for a nonsense alphabet – a set of words for a children’s alphabet board that would really mess up my daughter’s education if I pinned them up in her room! Below is my slightly improved set [EDIT March 2011: now including some commenters' suggestions]

• A for Aitch *
• B for Bdellium †
• C for Cue * / Czar †
• D for Double-U *
• E for Ewe *
• F for Ghoti ◊ [thanks Greg!] / Fillip §  [thanks Nobf!] / Vescent ¤ [thanks David!]
• G for Gnome †
• H for Hour †
• I for One ‡
• J for Juan ◊
• K for Knight †  (or even the double-meaning “K as in Knew” †*)
• L for Llandudno ◊ / Fifty ‡
• M for Mnemonic † / Thousand ‡
• N for Entropy ¤
• O for Ouija ◊
• P for Psalm †
• Q for Quay ◊
• R for C Clark ¤ [thanks David!] / Arson ¤ [thanks Seven!]
• S for Sea *
• T for Tchaikovsky †
• U for Youth ¤  [thanks Seven!]
• V for Five ‡
• W for Why *
• X for Ten ‡ / Xylophone/Xanadu ◊
• Y for You *
• Z for Zori §  [thanks Nobf!]

I’ve indicated why it’s in with a category, as shown below in decreasing order of how much I prefer them…

* – sounds like or is another letter word
† – silent initial letter
‡ – roman number
◊ – unusual initial sound
§ – sounds like another (more common) word with similar pronunciation
¤ – word starts with the sound of the letter word

If you can think of any better ones (ideally using one of the same tricks this list uses) please post a comment with your suggestion!

Anyway, below is a chart I produced at one point which I think is rather nice, based on the 2001 census. It shows the distribution of the population of the UK where each point is the population-weighted centroid of a ward. Britain  is split up into 408 Local Authorities (average size 140,000, the largest being Birmingham with 977k, with the smallest generally being no smaller than about 25,000 apart from islands like the Scillies), and each of those split into 10,000 Wards which are the units used for election of local government officials (average size 6,000, varying from 100 to 35,000).

(Click on the image to open a larger version in a new window)

I actually produced this particular display in humble Excel. So adding the outline of the country can’t easily be done, though you can see the shape of Britain quite easily really because humans like to live by the sea.

Some things I think are interesting to see on this view:

• It’s amazing to see quite how ‘empty’ Scotland is apart from the ribbon of population between Glasgow and Edinburgh.
• The gap of the Pennines between Manchester and Yorkshire is clear to see.
• The North-East (Newcastle, etc.) is quite separated, which probably explains why they have such a strong regional identity.
• London and its surrounding towns is the dominant feature of the whole of the southern half of England.
• Wales is very sparsely (but evenly) populated apart from Swansea and Cardiff in the South.
• This isn’t quite as clear on this chart, but the population in the South is mostly in lots of towns and villages (lots of small/medium wards), whereas the population in the North (Yorkshire/Lancashire/Derbyshire/Humberside) is much more densely packed in large urban wards. This is mainly a reflection of history – the rapid urban development due to the industrial revolution. Although I think geography (those dramatic landscapes) probably matters too.
• There’s a surprising amount of population run along the South Coast.

The chart below shows the history of UK house prices (according to The Nationwide) over the 45 years from 1964 to 2009 Q1 (i.e. this is based on figures released at the start of April 2009), and the average earnings index (according to the Office of National Statistics – more info here). Between 1964 and 2003 the average property has been almost exactly 4x the average income, so the chart actually shows incomes multiplied by 4 so that it’s easy to make this comparison.

What strikes you looking at this is how spectacular the latest house price bubble looks compared to years past. The late-80s bubble and 90s bust is also clear, but it’s hard to see anything of what went on before the 80s because inflation from the 70s and 80s means that everything is squeezed up. When it comes to things like house prices a 50% increase is just as significant whether it’s from £4,000 to £6,000 or from £100,000 to £150,000, but it doesn’t look that way on the chart.

The obvious (and extremely rarely-seen) solution is to show the same data on a log scale, in which a % change is represented by the same vertical distance whether the actual value is large or small, shown below:

This shows that incomes and prices are closely linked, and this would make sense: the chronic shortage of houses in this country means that everyone will pay as much as they can afford (or believes they can), thus defining the market price. Some have said that low interest rates mean people can afford bigger mortgages, but I would argue this is only true if it’s low real interest rates. That’s something for a later article…

It’s also clear that prices have deviated from incomes plenty of times before, including a bubble in early 70s (burst by dint of high inflation rather than actual falls in house prices), another one in the late 70s (ditto), then the notorious bubble and crash of the 80s/90s which left many households in negative equity due to the unprecedented fall in nominal prices. This was then following by a sustained period of low inflation from the early 90s onwards, and the emergence of the bubble that is now deflating.

What I think most striking from the above is how sustained the noughties bubble was – it got going in 1999, kept surging ahead until 2004, and then stayed inflated (continuing to increase in line with or ahead of incomes) for at least another 3 years, defying gravity like a carton character that’s run off a ledge. It now seems that this was only made possible by a huge expansion in the amount of credit in our economy, imported from high-saving emerging economies and made possible by such toxic inventions as CDOs and the like.

Given that prices and incomes look linked, let’s look at the ratio of the two…

This shows clearly the history of this relationship – an apparently relentless cycle of booms and busts. It also shows that despite recent falls the ratio has just reached the same level it reached at the very peak of the 70s and 80s bubbles! If this housing cycle follows the pattern of those before it then the market will stabilise when this ratio drops below 4 (which was the average between 1965 and 2003), which on current form will be some time in 2010, with prices about 20% lower than they are now, and approximately 40% below their 2007 peak. In other words, that would mean we’re only half-way through this crash! And that’s exactly what the derivatives markets think: just published by Tradition, the latest figures on housing futures show that prices are expected to drop by 19% between now and March 2010. Whether that really will happen remains to be seen, but as a potential first-time buyer I am hoping so!

Part 2 will look into regional differences, and will shed some very illuminating light on just how big the differences are between different parts of the country and what it might mean for the future.

• Predicting the path of UK House Prices
• How the different UK house price indices compare
• Whether low interest rates really make houses more affordable
• Optimum strategies playing TV game show “The Colour of Money”
• Eurovision Song Contest voting biases
• Understanding the dynamics of used car prices
• Working out the ideal locations for hospitals in the UK
• How to get the optimal return from investments on Zopa
• The impact of speed on fuel consumption when driving