A while ago there was a proposal to increase the UK's motorway speed limit from 70 mph to 80 mph, and a group of us were discussing the pros and cons over a pint in the Jolly Quizmaster.
The discussion was ended by someone at the bar stating that "It will make no difference as you get the highest number of cars per hour along a motorway at 30 mph, because of the gaps between the cars!"
Not wishing to have an argument with someone who looked quite belligerent we changed the subject; however, one of our colleagues raised this with us over another pint in the Jolly Quizmaster. So we decided to work it out.
Assuming a two-second gap between cars (as recommended) and a car length of 14 and a half feet (the UK average), does 30 mph give the highest number of cars per hour along a motorway? If not, what speed does?
Starting with 30 mph, which is 44 feet per second, a car that is 14.5 feet long will pass in about 0.33 seconds. With the two-second gap, one car passes every 2.33 seconds, which gives about 1545 cars per hour in one lane.
At 60 mph, which is 88 feet per second, a car the is 14.5 feet long will pass in about 0.16 seconds. With the two-second gap, one car passes every 2.16 seconds, which gives about 1663 cars per hour in one lane.
It can be seen quite easily that the faster the cars are travelling, the shorter time they take to pass, and the more cars that pass in one hour. So, increasing the speed limit from 70 mph to 80 mph would get more cars along the motorways. Don't listen to belligerent drunks in bars!