A tachymeter

Tachymeter

A tachymeter or tacheometer is a type of theodolite used for rapid measurements and determines, electronically or electro-optically, the distance to target, and is highly automated in its operations. Such tachymeters are often used in surveying...

 scale is a scale sometimes inscribed around the rim of an analog watch

Analog watch

Analogue watch is an example of a retronym. It was coined to distinguish analogue watches, which had simply been called "watches", from newer digital watches; see watch and clock....

. It can be used to compute a speed based on travel time or measure distance based on speed.

For example, if one were driving on the highway and timed how long it took to travel 1 mile, the tachymeter scale allows one to determine at a glance the speed in miles per hour. The typical tachymeter scale on a watch converts between the number of seconds it takes for an event to happen and the number of times that event will occur in one hour. The formula used to create this type of tachymeter scale is


where T is the tachymeter scale value; t is the time in seconds that it takes for the event to occur; and 3600 is the number of seconds in an hour.

As a sample calculation

Calculation

A calculation is a deliberate process for transforming one or more inputs into one or more results, with variable change.The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm to the vague heuristics of calculating a strategy in a competition...

, if it takes 45 seconds to travel 1 miles (1.6 km), then the average speed is 80 mi/h. On the watch, 45 seconds gives scale value 80. Note that the tachymeter scale only calculates the average

Average

In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....

speed.
As a second example, if it takes 20 seconds to travel 1 km (0.621372736649807 mi), then the average speed is 180 kilometre per hour (examine the picture of the watch).

For events that happen either very quickly or slowly, one needs to adjust the sixty-second tachymeter scale commonly found on watches. The scale on a watch is only valid for things that happen in 60 seconds or fewer, and the scale is also difficult to resolve for events that take fewer than 10 seconds or so to occur. As an example, if it takes 100 seconds to eat an apple, cutting that number in half allows one to say that it takes 50 seconds to eat half an apple. Using the tachymeter scale one can calculate that 72 half apples (36 whole apples) could be eaten in one hour.

The scale can also be used to measure distance if you travel at a constant speed.
For example, if you travel at a constant 80 mph (or at 80 km/h), then the distance traveled while the second hand sweeps to "80" (45 seconds) will be exactly 1 mile (or 1 kilometer at 80 km/h).