Definitions

subtense

Tachymeter

[ta-kim-i-ter, tuh-]
A tachymeter or tacheometer is a kind of theodolite used for rapid measurements and determines, electronically or electro-optically, the distance to target, and is highly automated in its operations. A tachymeter is also used as the name of the scale sometimes inscribed around the rim of an analog watch, useful in converting time intervals to speed or other rates of events.

Tachymetry or tacheometry is the process of measuring distance indirectly. This can be done by measuring time and speed in a moving vehicle or by sighting through small angle a distant scale transverse to the line of sight.

Surveying

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

Stadia measurements

Other forms of tacheometry in surveying include the use of stadia rods with theodolites or plane-table alidades. These use stadia marks on the instrument's reticle to measure the distance between two points on the stadia rod (the stadia interval). This is converted to distance from the instrument to the stadia rod by multiplying the stadia interval by the stadia interval factor. If the stadia rod is not at the same elevation as the instrument, the value must be corrected for the angle of elevation between the instrument and the rod.

Subtense bars

Another device used in tacheometry is the subtense bar. This is a rigid rod, usually of a material insensitive to changes in temperature and humidity such as invar, that is of fixed length (typically two metres). This bar is mounted on a tripod over the station to which the distance is desired. It is brought to level and a small telescope on the bar allows the bar to be oriented perpendicular to the line of sight to an angle measuring station.

At the angle measuring station, a theodolite is used to measure the angle between indicators on the two ends of the subtense bar. The distance is determined with simple geometry to be the altitude of a triangle with the theodolite at the upper vertex and the subtense bar length at its base.

On watches

A tachymeter is the name of the scale sometimes inscribed around the rim of an analog watch. It can be used to compute speed based on travel time or measure distance based on speed. The function performed by a tachymeter is independent of the unit of distance (e.g. statute miles, nautical miles, kilometres, metres etc.) as long as the same unit of length is used for all calculations. It can also be used to measure an industrial production process in units per hour. A tachymeter is simply a means of converting elapsed time in seconds per X to X per hour.

Measuring speed

To use a tachymeter-equipped watch for measuring speed, start the chronograph at a starting marker of a known distance. At the next marker, the point on the scale adjacent to the second hand indicates the speed (in distance between markers per hour) of travel between the two.

A standard tachymeter will only determine speeds greater than 60 units per hour using this method; slower speeds can be measured by decreasing the unit of measurement. Rarely, a tachymeter function is implemented in a fully digital watch, with digital display. Some watch sellers will use the term tachymeter incorrectly for a non-calculating seconds bezel.

The speed of an object is defined by the equation

speed=frac{distance}{time}

The tachymeter scale computes the function

Tachymeter dial =frac{3600}{Elapsed time}.

The spacings between the marks on the tachymeter dial are therefore proportional to 1/t where t is the elapsed time, or -log(t), and hence the tachymeter scale is sometimes also described as logarithmic.

The scale is generally only accurate for elapsed times over approximately 7 seconds. Some watches, not common, have 'wraparound' or 'scroll' scales, which extend the readings to lower speeds, typically 45 mph.

Some tachymeter scales are on a rotating, indexed bezel. This allows two additional modes of use: The tachymeter bezel can be aligned with a free running second hand, and, more subtly, can be used to average speed over longer times/distances. Set the rotary bezel index opposite the position of the minute hand, note the mileage. Glance at the tachymeter scale 60 units later, and average speed will be indicated. A little mental math allows interim averages, easiest at 1/4 (15 unit) and other integer values.

Measuring distance

A tachymeter-equipped watch can be used to measure distance by timing the travel over the distance while the speed is held constant. The tachymeter scale is rotated to align with the second hand at the start of the length to be measured. When the second hand reaches the point on the scale where the speed indicated equals the speed of the vehicle, one unit of distance (miles if speed is miles per hour, kilometres if kilometres per hour, etc.) has been covered.

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