Over the last few years several watches with chronograph functions from different watch brands were released. We believe it is important to explain the main types of graduated scales displayed on the inner or outer bezel of the watch case. These scales are used in sports, recreational activities or even for technical purposes.

In this article we will comment on the meaning and use of four types of graduated scale used in chronograph watches, namely:

- tachymetric: the average performance per hour of a machine, equipment, the average speed of a vehicle or an object in motion etc
- pulsometric: average number of pulsations or heart beats per minute.
- telemetric: the distance from the occurrence of an event which caused a sound and the observer who heard the sound after an elapsed time.
- asthmometer: average number of breaths per minute.

A graduated scale is a very useful device and it works like a slide rule. Its construction is very simple.

**Tachymeter**

The average speed of a moving object is given by the division of distance by time, that is:

average speed = distance/time.

**Omega Speedmaster Grey Side of the Moon**

The tachymetric scale does not depend on the distance unit to measure the average speed. It does not matter if the distance can be fixed in kilometers or in miles or in any other unit length, because the result will be always expressed in that unit. It is assumed that the object or the vehicle in motion traveled the distance without interruption and at a constant speed.

**TAG Heuer Carrera Calibre 16**

In order to determine the average speed, it is worth mentioning that the distance between two points must be previously known by the observer.

If the object in motion has reduced or increased the speed during the course, the tachymeter scale will not capture this change.

Lets imagine the following numerical example for a one kilometer course: in the first 500 meters the vehicle speed was 60 km/hour and in the remaining 500 meters the speed was reduced to 50 km/hour. The average speed for all the route was not (60 + 50)/2 or 55 km/h as one may imagine, because the time in the first half was shorter than in the second half. The correct, in this case, is to use the harmonic mean criteria and the calculus is as follows: 2/(1/50 + 1/60) = 3,000/(50+60) ~ 54 km/h.

Proceeding, if the length of the route was completed in 30 seconds, which is vehicle average speed expressed in km?

The result will be given by the following simple equation:

d/t = v/3,600

d = distance. It can be expressed in one quilometer, one mile etc

t = number of seconds the car or vehicle has taken to complete the route

v = average speed of the vehicle

Since one hour corresponds to 3,600 seconds, the printed figures on the tachymetric scale are obtained by the division of 3,600 by the time in seconds the vehicle spent to complete the distance, as shown by the formula below:

v = 3,600/t

A numerical example with the distance (d) expressed in one kilometer: as the vehicle crosses the initial point of the distance, the chronograph is started. As soon as the vehicle completes the route, the chronograph function is suspended. Let’s suppose t = 30 seconds. Which is the vehicle average speed?

v = 3,600/30, or 120 km per hour.

The central seconds hand of the watch will indicate the number 120 printed on the tachymetric scale and such number is near of 6 o’clock.

If, by hypothesis, the distance is expressed in miles, instead of kilometers and the vehicle spent the same period of 30 seconds to cover one mile, the average speed will be 120 miles/h. Note that in this hypothesis, the average speed of 120 miles/h is much greater than 120 km/h, since 1 mile = 1.60934 kilometer.

The shorter the time period, the higher the average speed. In general, the tachymetric scale is numbered between 60 and 500.

The tachymetric scale is based on a simple rule of proportionality and it can be used for other purposes. For example:a machine produces steel plates. If a steel plate is produced in 18 seconds and if this machine operates without interruption and at a constant efficiency, how many steel plates such machine will produce in one hour? The central seconds hand will indicate the number 200 printed on the tachymetric scale and the answer is 200 steel plates per hour. Another example: an equipment harvests 1 tonne of soy grains in 53 seconds. How many tonnes of soy grains are expected to be harvested by the equipment operating with the same efficiency and without interruption? The central seconds hand of the chronograph will show the number 68, that is, aproximately 68 tonnes (3,600/53 ~68).

**Pulsometric**

The pulsometric scale can be adjusted to 15 or 30 pulsations. The large majority of chronograph watches with this type of scale uses 30 pulsations as basis for measurement. This figure is printed on the dial and in the French language: “Gradué pour 30 pulsations” or “Gradué pour 15 pulsations”. The watch chronograph with pulsometric scale is in general used by doctors.

**Longines Heritage**

Similar to the tachymetric scale, the pulsometric scale is also based on a simple rule of proportionality. We are interested in determining the number of pulsations per minute, which is a *proxy* for the average number of heart beats per minute. It is given by the following formula:.

“Gradué pour 30 pulsations”:

p = number of pulsations per minute

t = elapsed time in seconds for 30 pulsations

30/t = p/60

p = 1,800/t

“Gradué pour 15 pulsations”

p = number of pulsations per minute

t = elapsed time in seconds for 15 pulsations

15/t = p/60

p = 900/t

As soon as the pulsations counting is iniated, the chronograph function is activated. When the number of pulsations reaches 30, for instance, the chronograph is suspended. The central seconds hand of the watch will indicate a number on the scale. This figure is the average number os pulsations per minute. Worth mentioning that such number of pulsations may change as a result of the physical or the emotional condition of the patient at the moment of counting.

**Montblanc Meisterstück Heritage Pulsograph**

**Eterna Heritage Pulsometer Chronograph**

The ** Heuer Monza Chronograph**, from TAG Heuer, for instance, has two scales, the tachymetric and the pulsometric.

In order to make easier the reading of each scale, the tachymetric scale of the *Heuer Monza Chronograph* had its extension around the inner bezel reduced and 220 as the maximum number. Such figure is located near the correspondent index to 3 o’clock.

**Telemetric **

The telemetric scale is another interesting scale, albeit its use is more restricted. It is used to measure or to estimate the distance of a physical phenomenon which was seen, but the sound provoked by the phenomenon was only heard by the observer after a elapsed time. In order to measure such distance, it is necessary the occurrence of the phenomenon provokes an audible sound up to a certain distance.

For instance, a lightning storm. The flash and the rays from the electric-static discharge in the atmosphere occur before the thunder. An observer can measure the distance he is from the lightning storm using a telemetric scale.

As the observer sees the lightnings, he starts the chronograph. As soons as he hears the sound of the thunder, the chronograph counting is suspended. The central seconds hand will indicate the estimated distance of the phenomenon expressed in kilometers.

**Baume Mercier Capeland**

**Longines Telemeter Automatic Chronograph**

The sound wave at the sea level and at the temperature of 20º C or 68º F travels at the average speed of 343 meters per second. Such speed, however, may be faster or slower, depending on both the climate and altitude conditions. Note that the telemetric scale of both watch models above is fixed in kilometers because the sound speed is expressed in meters per second (343 m/s). However, it is possible to create a telemetric scale expressed in miles per hour. Just divide 0.343 by 1.60934 and we will have the scale expressed in miles, that is, 0.213 miles per second. Of course, the figures printed on the scale expressed in miles will be different from that expressed in kilometers.

On the other hand, we know that the distance is the result of the multiplication of speed by the time:

distance = speed x time

The graduation of the telemetric scale is based on the following relation:

d = (0.343 km/s ) x time (in seconds)

For instance, the elapsed time between the occurrence of an event or phenomenon, like a cannon shot, lightning etc and instant the sound was heard by the observer is 30 seconds. Which is the estimated distance between the occurrence of this event and the observer? The central seconds hand of the chronograph will stop at number 10, below 6 o’clock. It means that the phenomenon occurred at a distance of 10 kilometers, approximately.

**Asthmometric **

This type of scale follows the same criteria of the pulsometric and it is based on the time necessary for five breaths. This figure is printed on the dial and in the French language, “Gradué pour 5 respirations”.

**Longines Asthmometer-Pulsometer Chronograph**

Therefore, we have:

r = number os breaths per minute or per 60 seconds.

t = elapsed time in seconds for five breaths

5/t = r/60

r = 300/t

For instance, after five breaths of an adult person the central seconds hand stopped in front of number 16 of the blue printed scale on the dial of the *Longines Asthmometer-Pulsometer Chronograph, *it means that such figure is inside the range of an adult person in normal health conditions, that is, between 14 and 18 breaths per minute.

In the past there were chronograph watches with decimal scale. The circunference of the dial was divided into 100 equal parts, like the watch model from Claude Meylan brand. This brand is situated at the village of L’Abbaye, Switzerland and the watch was produced in the beginning of 60’s.

This type of scale was used for a time for scientific and industrial purposes. However, the watchmaking industry advanced towards specific scales for watches with chronograph functions, which seems to be more appropriate.

Finally, a copy of the wonderful reedition of the pocket watch from Omega used during the 1932 Olympic Games, in Los Angeles.

The model, with COSC certification, is available in three versions of gold case tone: white, yellow and rose. 300 units were produced, 100 units of each variety of gold.

The movement, proprietary caliber 3889A, is a *rattaprante* integrated chronograph with double column wheels.