1434 : Measuring slow speeds with a tachymeter: step-by-step

Thu, 07 September 2000 03:38

Several people have told me that they found my method for measuring slow speed on a standard tachymeter scale (TZ Classic 1433) confusing, and would benefit from step-by-step instructions with some examples.

The ordinary use of a tachymeter scale is to run the chronograph for some number of seconds as a unit distance (such as 1 mile or 1 kilometer) is traversed, and then to read the speed in units per hour directly from the tachymeter scale. For example, if it takes 30 seconds to traverse 1 mile, then you can read on the tachymeter scale opposite the 30 seconds position on the dial that you are traveling at 120 miles per hour. Similarly, if it takes 45 seconds to traverse 1 kilometer, then you can read on the tachymeter scale opposite the 45 seconds position on the dial that you are traveling at 80 kilometers per hour.

If, however, it takes longer than 60 seconds to traverse the unit distance, then it is impossible to read speed directly from the tachymeter scale. Mathematically, what the tachymeter scale actually provides is the divisors of 3600, the number of seconds in one hour. It can therefore be used as a handy reference for reciprocals to allow measuring slow speeds.

For example, if it takes 80 seconds to traverse 1 mile, then you can look at the tachymeter scale -- not the seconds dial as you ordinarily would -- to find that 80 is opposite 45 on the dial, which implies that you are traveling at 45 miles per hour. Similarly, if it takes 120 seconds to traverse 1 kilometer, you can look up 120 on the tachymeter scale and see that it is opposite 30 on the dial, which implies that you are traveling 30 kilometers per hour.

It is not intuitive to use the tachymeter scale in this way because there will, in all likelihood, not be any hands pointing to the important places on it. Unlike the conventional use of the tachymeter scale to measure things which take 60 seconds or less to traverse the unit distance, you must mentally move from the number of seconds measured on the chronograph to the same number on the tachymeter scale, and only then read the number opposite on the dial.

The ability of the tachymeter scale to be used "backwards" like this, freely interchanging time and rate, is a direct consequence of the fact that it is created as a table of reciprocals in the first place. The limit of resolution will occur when the time to traverse the unit distance is so large, much above 300 seconds (5 minutes), that the relevant numbers are bunched up together on the tachymeter scale. At 300 seconds to traverse a unit distance, you are down to 12 units per hour. Useful accuracy is probably achievable down to about 5-6 units per hour if you are willing to accept a large tolerance.