I was trying to work out mentally and then on a back of an envelope and then on a spreadsheet what the actual journey time impact of changing a speed limit from 30mph to 20mph on a given stretch of road would actually be. Specifically I had the 1.6mile rat run in Holyrood Park from the Commonwealth Pool gate to Meadowbank gate in mind.
I was of course aware that it's not just a simple 1/3 increase in time as the limits (and having to pass through a number of roundabouts) mean it's not a case of a journey of a constant 20mph vs. a constant 30mph.
Without a car to actually test these things out for myself I got reading and found out something called the "Time Saving Bias" which is a sort of collision of maths and psychology about peoples' perception of journey times when it comes to changing the speed they are driving at.
I read a couple of the papers that I could actually access without a university journal subscription and the Wikipedia article seems largely lifted from these; https://en.wikipedia.org/wiki/Time-saving_bias
Anyway it's quite interesting and there's a formula in there to calculated the actual change in journey time when the speed is changed;
t=cD (1/V1 – 1/V2),
where c is a constant for converting between units, D is the distance, V1 is the original speed and V2 is the new speed.
This formula shows that the relationship between increasing speed and journey time is curvilinear: a similar speed increase would result in more time saved when increasing from a low speed compared to a higher speed.
So to put it simply, the faster you go the less effect on your journey time you are having.
Now one of the consequences of this all is;
Drivers who underestimated the time saved when increasing from a low speed or overestimated the time lost when decreasing from a high speed, overestimated the speed required for arriving on a specific time and chose unduly high speeds, sometimes even exceeding the stated speed limits.
So at lower speeds, people are over-estimating how fast they need to go and end up driving faster than they need to.
Of course, I haven't yet worked out how to realistically model the effect on actual (and not just straight line, theoretical) journey times, accounting for slowing down for roundabouts and acceleration time again.
But the answer isn't 96 seconds different as the simple formula suggests.