TVR pub crawl maths
Discussion
WARNING: the following thread includes light-hearted maths content. Those of a pedantic disposition may wish to stop reading now...
Late last night, a friend on a WhatsApp group shared this article about mathematicians who had calculated the most efficient route for a pub crawl involving all 24,727 pubs in the UK. This morning, having time to kill while waiting for a delayed train from London to Southampton, I found myself wondering how long it would take in the Tuscan... here follows the results of my idle musings:
First off, the more observant among you may have noticed that the article was published last year, and undoubtedly the number of pubs will have changed since then. However, it apparently took the researchers two years to solve the problem, and I don't have the time or inclination to come up with a new solution taking into account pub openings/closures in the past year. After all, I'm only after an estimate...
The article gives the total distance as "over 28,000 miles" - let's assume 28,500. The total number of pubs is given as 24,727, which means 24,726 journeys between pubs (the fencepost problem). Dividing the total distance by the number of trips (24,726) gives an average distance between pubs of 1.15 miles. The Tuscan can apparently cover a 1/4 mile in 12.9 seconds, at which point it is travelling at 118 mph (data from www.torquestats.com). Assuming that it continues at 118 mph for the next 0.8 miles and then brakes from 118 mph to 0 mph over the remaining 0.1 miles (roughly 160 metres). The top speed of the Tuscan is around 180 to 190 mph (depending on who you believe), and so covering the majority of the 28,500-mile crawl at 118 mph should avoid unduly stressing the engine and drivetrain, hopefully minimising the number of engine rebuilds that will be needed over the course of the crawl.
Assuming constant deceleration over a time 'x', integrating under the velocity-time curve (in this case, a straight line) gives the total distance 'd' travelled during braking, i.e. ((118-0)*x)/2=d. Since d=0.1, solving for x gives a braking time of 0.00169 hours, or 6.1 seconds. Wikipedia quotes a 100-0 mph time of 4.15 seconds, so a 118-0 mph time of 6.1 seconds seems reasonable and ought to be safely achievable.
Putting all this together gives us a total travel time per leg of:
12.9 + (3600*0.8/118) + 6.1 = 43.4 seconds
The world record for downing a pint is apparently a scarcely believable 0.45 seconds. For mere mortals, let's assume a more conservative estimate of 15 seconds. Added to the driving time, this gives a theoretical minimum time per pub of just under 1 minute.
If we phone ahead to place our drinks order and impress upon the bar staff the urgency of our mission, then the usual time spent queuing to get served could in theory be reduced to zero. However, in reality we will still need to travel on foot from the car park to the bar, as the UK doesn't have any official drive-through pubs. Let's assume a typical car/bar separation of 20 metres, giving a round trip on foot of 40 metres per pub. At a leisurely walking pace of 3 mph (this is a pub crawl after all, not the Olympics), the time taken in seconds to complete the 40 metres would be (60*60*40/(3*1609)) = 29.8 seconds. Added to our earlier estimate of 1 minute, this gives a more 'realistic' estimate of 1.5 minutes per pub.
Assuming that the pub crawl starts at the first pub, we only need to allow a time of 15 seconds for the first stop on the crawl, plus the time to walk to the car (29.8/2=14.9 seconds), i.e. roughly 30 seconds in total, or 0.5 minutes. We can now calculate the total time to compete the crawl, in days, as:
(0.5 + (24726*1.5))/(60*24) = 25.75 days
By coincidence, my annual holiday allowance is 25 days. To quote Morpheus from the Matrix (technically from the Matrix Reloaded, in case any pedants have made it this far): "I do not see coincidence, I see providence. I see purpose."
So... when do we start?
lucido grigio said:
Your train must've been REALLY late......
You have no idea... although even if it was on time I'd probably have done the same thing, I'm a geek for this sort of thing 
Oh, and re. the new clutch - don't forget the new tyres, brake pads, oil checks etc. Plus half an hour at the start of the damn thing trying to explain to my passenger how the doors work, and why everything smells vaguely of glue...
I can see that you have overlooked a few major considerations:
1. What is the capacity of your bladder and how often will it require emptying?
2. A substantial number of pubs are located in built-up areas and the good ole boys in blue will want a few words with you about your 118 mph in a 30 limit.
And having intercepted you as you arrive at the next pub, there is a high probability that they will catch a whiff of your breath and possibly, just possibly, commence the drawn out and tedious "Would you mind blowing into this, Sir?", somewhat delaying your urgent mission.
3. The resultant readings on their clever device would inevitably show that it would be inadvisable to let you proceed anywhere except accompanying them to the local nick for a further period which could jeopardise your chances of adhering to your carefully planned schedule.
4. Have you taken into account the respective pub opening and closing times? I mean, it's no good turning up after a lock-in has commenced and you can't get in.. Or indeed getting locked in in the 15 seconds it takes to down your 24,000th pint! That would scupper your timetable after putting in all that effort
Also consider that some rural pubs can be closed for one day out of seven, often a Monday or a Tuesday. Have you accounted for that in your route plan? I don't think so!
I therefore feel that your estimate is unrealistic and needs a further application of man-maths.
Good idea though OP. Cheers!
1. What is the capacity of your bladder and how often will it require emptying?
2. A substantial number of pubs are located in built-up areas and the good ole boys in blue will want a few words with you about your 118 mph in a 30 limit.
And having intercepted you as you arrive at the next pub, there is a high probability that they will catch a whiff of your breath and possibly, just possibly, commence the drawn out and tedious "Would you mind blowing into this, Sir?", somewhat delaying your urgent mission.
3. The resultant readings on their clever device would inevitably show that it would be inadvisable to let you proceed anywhere except accompanying them to the local nick for a further period which could jeopardise your chances of adhering to your carefully planned schedule.
4. Have you taken into account the respective pub opening and closing times? I mean, it's no good turning up after a lock-in has commenced and you can't get in.. Or indeed getting locked in in the 15 seconds it takes to down your 24,000th pint! That would scupper your timetable after putting in all that effort
Also consider that some rural pubs can be closed for one day out of seven, often a Monday or a Tuesday. Have you accounted for that in your route plan? I don't think so!
I therefore feel that your estimate is unrealistic and needs a further application of man-maths.
Good idea though OP. Cheers!
Edited by glenrobbo on Saturday 29th July 11:42
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