updated tl;dr: fuel is a problem, so is wear - alternative fuel sources will be required, as will some serious mechanical skills to patch the cars - for a 1st world country that has mostly newer cars, expect most to break down within 2 years, with very few left after 4-6. Calculations below.
Some variables I dug up to help calculations:
all numbers are approximate and correspond to values taken for years 2009-2013 as far as I know. Also, using scientific notation to prevent zero overload. Rounding is performed on an arbitrary basis.
also fuel units are in gallons and barrels because that's the units they're reported in online - I would much prefer metric since I don't live in a country that uses imperial units, but gotta bite the bullet this time.
usage and production:
- Total number of automobiles:
- Total number of automobiles produced per year:
- Total number of barrels of gasoline produced per year:
Now we need to check distribution of these across people and cars. I'm electing to use US numbers here since they're more readily available and the US seems to have both lots of cars and consume lots of gasoline, so if the numbers work out for the US, they should work in an apocalypse - if not, we can adjust them downwards to see how far we'd have to go until it's workable.
- Total number of automobiles:
- Automobiles per capita:
800 per 1000
- Total gasoline usage in barrels per year:
- per day:
- per automobile per day:
- Total number of automobiles per year:
- Total number of barrels of gasoline per year:
Now, I know nothing about average compatibility of parts between automobiles. It might be high or low, or anything in between, so I'm not going to include it now. There are obviously other factors that influence maintenance and usage: battery lifetime and wear, makeshift solutions, alternatives used, dangers and vast numbers of cars destroyed. I'm going to assume none of these factors play a role for now.
What I am going to assume is that the world goes to hell pretty quickly - in a matter of days. Lets be generous and say that despite the bombardment, we get 2 days worth of production done before production stops abruptly. Lets also assume, all cars in the world have half their tank full and assume that this means they have about 8 gallons in there. Since major cities are completely obliterated, we have to find out what percentage of people and cars are left. Lets say 20% of people and cars are outside city centers. Of that 20%, we'll assume 5% survives the bombardment, since most of the surface is destroyed. That leaves:
edit - I originally had calculated that fuel availability would last
an outrageous 20 thousand years, which is horribly wrong. Brian
Drummond in the comments caught the error and with the proper
calculations (aka, calculating for all cars not just one) it turns
out that with the amount of cars left and the daily consumption of
fuel for a city car today (which is about 10 miles per day), there's
about 6 days of fuel left (again, lol).
This scarcity is further compounded by my original estimate of how far
cars would travel daily, which I placed in the range of 60-125 miles,
since the daily consumption was equal to about 10 miles, which is too
low for a post-apocalyptic world (you want to save fuel so you either
don't use a car or use it to travel long distances). If we assume
about 100 miles average use whenever you move a car, we're left with
about about 15 hours of continuous driving (this assumes the tank has
enough fuel for ~150 miles plus its share of fuel from what has been
produce in 2 days within the country). That means, if
every one of those cars where to travel on the first day, trying to
escape or find safety, they'd be out within the day. There'd be no
usable fuel left, not even in refineries, gas stations etc. - so the
calculations about how long it would take for cars to break down must
assume an alternative source of fuel, which of course, if not ideal
for the car's engine, will cause it to fail sooner. Cut the amount of
cars to a fourth per year! Unless you have statistics on how many
older cars exist - if there's lots of them, you might have more cars
left. See vsz's comment for more details.
Also, as the numbers stand, we have 3.8 (lets say 4) people per car
which leaves no room to say "yeah but what if less cars are used?".
Even if less cars where used, we're obviously in the range of days
rather than hours - not a big improvement. If you add the weight of
equipment and provisions to the estimate, it's even more bleak.
If you want to see the original text, just see the edit history
Now how long can we expect a car to work until it breaks down? Lets assume cars last for
100e3 miles on average (half of what they're expected to if maintenance is available) and they're already half-way there, so about
50e3 miles left on each car on average. Based on the average daily consumption of gasoline and the average fuel efficiency we get about
10 miles per day which is very low, so lets assume a highest bound of
125 miles per day. That gives us about
400 days average life for each car, a bit over a year. If the average usage is half that much, we get
800 days, which is a bit over 2 years.
Obviously, people skilled with car maintenance, with available parts or scrap to turn into parts and a bit of creativity will get them working for longer, but I doubt you'll get cars older than 5-6 years still in working condition. Of course, that's speculation.
So I'd say, as a rule of thumb, halve the amount of working cars every 2 years after the apocalypse. After a decade, you're left with about
40e3 cars in the US, most of them hosts to parts of their fallen brethren. In 20 years, you have about a thousand cars left. This further removes fuel as an issue - it will never run out by car usage alone, but the cars will run out pretty soon.