Using a tachymetre scale?

[RichB]

Right chaps, here's one for you; we are all familiar with the tachymetre scale around watches and I can see how this is used to calculate speed based on having fixed mile markers like on motorways etc. but could one of the more mathematically agile among you explain how you use it to calculate distance?

Wikipedia says the following:

A tachymeter 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.

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 that event that will occur in one hour. The formula used to create this type of tachymeter scale is:

,
where T is the time in seconds that it takes for the event to occur.

As a sample calculation, if it takes 45 seconds to travel 1 mile, then the speed is 80 mph. Note that the tachymeter scale only calculates the average speed.

Edited by RichB on Tuesday 29th September 18:43

[bikemonster]

If you know the distance you can calculate the speed.

Conversely, if you know your speed, you could calculate distance...but I'm not sure that the tach scale would be the way to do it.

You would need to know either speed or distance to calculate the other though.

James

[ShadownINja]

Erm... if you hold the speed constant, you just watch it go round to that speed and that's 1 mile, surely.

[RichB]

ShadownINja said:

Erm... if you hold the speed constant, you just watch it go round to that speed and that's 1 mile, surely.

Oh I see... so for example if I hold the speedo at 70 then as it passes that on the tachy I've just passsed a mile. OK not much use because all speedos have a milometer which is easier to use but interesting...

[Beards]

Rich,
Have a read of this:-
http://www.mydigitallife.info/2006/12/10/how-to-us...

[ShadownINja]

RichB said:

ShadownINja said:

Erm... if you hold the speed constant, you just watch it go round to that speed and that's 1 mile, surely.

Oh I see... so for example if I hold the speedo at 70 then as it passes that on the tachy I've just passsed a mile. OK not much use because all speedos have a milometer which is easier to use but interesting...

Well, indeed, but they're supposed to measure speed/rates rather than distances. Why you'd use a tachymetre in a car/plane/space shuttle is beyond me.