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Blog: What's in a number?
How our lives are dominated by numbers yet we somehow get it wrong

1. How high is a bridge?

The "immaculate bridge" in Earley, Berkshire, UK, which is a slightly different size depending on whether you use metric or Imperial measurements.

Britain is a confused place for units, with Imperial units and metric units mixed up on the same notices or signs. I live near a suburban railway line and there are a number of bridges nearby. Each of these has a sign indicating the clearance height both in metric and Imperial but they are subject to different rules. While out running I noticed that the metric measurement was usually slightly less than the Imperial measurement, so I started to wonder whether that was due to the measurement being made in one system or another.

I was intrigued by the idea that if a bridge was marked as 3.5 m and a lorry was exactly 3.55 m tall (i.e. 5 cm taller) could the lorry get under the bridge? You could imagine a well-educated lorry driver puzzling over this dilemma for a few minutes. In fact he could indeed get under the bridge!

Here are the rules for measurement. (i) Make the measurement in metric and truncate down to the nearest 10 cm. (ii) Take off another 10 cm for "luck". Engineers always seem to like to do this, I don't know why. Apparently it annoyed Feynman during the investigation into the Challenger explosion. The process should then be repeated in Imperial with the truncation being 3". The fact that the truncation is slightly larger in the metric case leads to the aspect I had noticed: that the metric measurement seemed to be lower than the Imperial as far as I could tell. However, one can turn this process around and get the actual height of the bridges and the numbers for a few bridges locally are given next. for each bridge, I give first the Imperial measurement on the sign, the exact metric equivalent in brackets, followed by the metric measurement on the sign.

Bridge 1: marked as 11' 3", 3.4 m
Actual Height (Imperial): 11' 6" - 11' 9" = 3.51 - 3.58 m
Actual Height (metric): 3.50 - 3.60 m
Combined: 3.51 - 3.58 m

Bridge 2: marked as 13' 0", 3.9 m
Actual height (Imperial): 13' 3" - 13' 6" = 4.04 - 4.12 m
Actual height (metric): 4.00 - 4.10 m
Combined: 4.04 - 4.10

Bridge 3: marked as 12' 3", 3.8 m
Actual height (Imperial): 12' 6" - 12' 9" = 3.81 - 3.89 m
Actual height (metric): 3.90 - 4.00 m
Combined: None

Bridge 4: marked as 16' 3", 4.9 m
Actual height (Imperial): 16' 6" - 16' 9" = 5.03 - 5.11 m
Actual height (metric): 5.00 - 5.10 m
Combined: 5.03 - 5.10 m

So in three of the four cases the metric and Imperial measurements are consistent with each other. However, in the case of bridge 3, the measurements are not. It makes you wonder which measurement if any to trust. Overall, this is a terribly wasteful process: you have to measure each bridge twice to be strict when one measurement should be sufficient. Then why post the Imperial height when Britain is officially metric anyway? It just adds to the confusion. For more reasons to use the metric system, see my book, Measuring the World: Making complicated problems simpler by really going metric.

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Website revised by John Austin, 29/1/2015. © Enigma Scientific Publishing, 2015.