It was recently suggested that we should raise the speed limit to 80mph to ‘increase productivity’. I think we need to be honest about this. Frankly hearing my engine growl just that little bit more (without incurring the wrath of the traffic police) is reason enough - and productivity is a slightly lame distraction.

Increasing the speed limit is a bit of fun. It's a fantastic idea on an empty motorway in the middle of the night. It'll make a few petrol heads smile. But it's absolutely definitely not going to increase productivity. In fact it's going to decrease the number of cars you can get on the motorway. Sounds mad?

The issue is that raising the speed limit is actually going to reduce the capacity of motorways. Why? Because maths (and physics). I always knew that being a maths fan wouldn't win me any friends, but here goes...

As everyone knows, the faster cars are driven, the more spaced out they should be because they need longer to stop (that’s the physics). And honestly, all those nose to bumper people in the fast lane seriously need to have a word with themselves.

The stopping distance for the average car increases from 53m at 50 miles per hour to 96m at 70 miles per hour (and even the fanciest modern brakes aren't going to shave an awful lot off that). Follow this logic, and at 50 miles per hour you can fit just shy of 28 cars per mile of motorway whereas at 70 mph the number of cars per mile (on a single lane) is not quite 16 per mile.

What about speed though? Surely the fact that the cars at 70 mph are going faster means that they’ll clear the lane more quickly?

Well, yes, this does make a difference, but not big enough to compensate for the increased stopping distance required.

So a car travelling at 50mph takes 1 minute 12 seconds (1.2 minutes) to clear a mile. You can work out how many of the 27.83 cars will have cleared the mile in a minute by dividing 27.83 by 1.2. This gives you 23.19 cars per minute at 50mph or 1,391 cars per hour.

At 70 mph the cars will clear a mile in less than a minute – in 51.4 seconds to be precise (0.85 of a minute). So if you divide the 15.92 cars per mile by 0.85 you get 18.511 cars clearing the mile every minute. Or 1,111 cars per hour.

So basically, at a steady 50mph the capacity of a mile of motorway lane is 280 more cars per hour than at a steady 70 mph.

The trend is not better at 80mph. At 80mph the stopping distance increases to 122m. Add in a car length of 4.5m (so each car requires 126.5m of lane to travel safely) and you can fit 12.65 cars per mile of motorway. Although these cars clear a mile in 45 seconds the capacity of a mile per minute is still only 16.87 cars per minute – or 1,012 cars per mile per hour.

This reduces the maximum capacity of the lane by just short of 100 cars per mile per hour. And this is at a steady speed. Which is very difficult to achieve - and varied speeds introduce another mathematical problem entirely. And not a helpful one.

If you’ve ever been in a traffic jam which seems to have been caused by nothing in particular you’ve probably been a victim of the maths of turbulent systems.

Here the problem is bunching. The maths of bunching is a slightly crazy branch of fluid dynamics which is used to model all sorts of systems. It shows how you can end up with cars creating snarl ups just because someone braked sharply. This slows the traffic behind even more precipitously and can create a solid mass of stopped cars which don’t start moving again fast enough for the jam to disperse (basically more cars add to the jam more quickly than the cars at the front start moving).

Here’s a great explanation…

So, whilst you can cut nearly half an hour off a journey of 240 miles on motorway if you can maintain a steady 80 mph as compared with 70mph the key is in the ‘maintain a steady 80mph’. Both you and everyone around you has to do this for it to work (and the fuller the motorway is, the less likely this is to happen – especially as the faster you are travelling the less capacity the lanes have).

The reality of most motorway traffic is that it’s far from steady anything. I recently had to drive from Yorkshire to Coventry and 120 miles took a round 4 hours at peak rush hour – an average speed of 30 miles per hour. The truth is that many sections of motorway are at capacity - and raising the speed limit is pretty much irrelevant to most of the journeys we make.

I guess raising the speed limit on motorways isn't as politically acceptable if it's 'just for the hell of it'. But that's the truth (and frankly, it's better to be honest).

By Beate Kubitz at 4 Nov 2018, 00:00 AM