Definition of beat error - Page 4

# Thread: Definition of beat error

1. ## Re: Definition of beat error

Originally Posted by Roland Ranfft

ea = (et/2) * (la/lt)

Regards, Roland Ranfft
Aha, one point of data!

This formula is correct if you use the Witschi definition of beat error, but not if you use the Mumford definition, as in that case you would have to divide by 4.

Is this an endorsement of that particular definition? Who knows? Who knows anything? (Thanks anyway for contributing to my little thread.)

2. ## Re: Definition of beat error

Hi there,

no clue how you come to the quarter, but right, I should have defined the terms more precisely:
et: error time (disregarding beat-error definitions), i.e. time difference between both half cycles.
ea: error angle, i.e. the angle the hairspring collar is misadjusted, and needs to be turned to adjust it right.

Hopefully you don't counter that the half cycles are not really half unless the escapemnt is symmetrical (what it is never) and the beat error is zero (which is at least imaginable).

Regards, Roland Ranfft

3. ## Re: Definition of beat error

Originally Posted by Roland Ranfft
Hi there,

no clue how you come to the quarter, but right, I should have defined the terms more precisely:
et: error time (disregarding beat-error definitions), i.e. time difference between both half cycles.
ea: error angle, i.e. the angle the hairspring collar is misadjusted, and needs to be turned to adjust it right.

Hopefully you don't counter that the half cycles are not really half unless the escapemnt is symmetrical (what it is never) and the beat error is zero (which is at least imaginable).

Regards, Roland Ranfft
Dear Roland, I do believe that with these definition you should use the
fomula
ea = (et/4) * (la/lt)
so you should divide by four instead of two. But I always forget factors
of two and in such things I make horrible mistakes. I would be grateful if
you could follow my little computation here and point out where I am doing
the first mistake. Please pardon my slowness of mind, and consider that
this might be good information also for other members of this forum.

You will forgive me if I make just an example with numbers, so it's easier
to understand. Let's pick a movement that should beat every 100
milliseconds, El Primero style. From now on all numbers are milliseconds.
Assume that it has beat error, so one half oscillation is
tic-to-toc = 98
and the other is
toc-to-tic = 102
So we have
et = "time difference between both half cycles" = 102 - 98 = 4
Let's look concretely at when the movement beats. I get to choose when the
first tic happens, and I decide that the first tic is at millisecond 1.
What for the other beats?
tic toc tic toc tic toc tic toc ...
1 99 201 299 401 499 601 699 ...
Clearly beacause 1+98=99, 99+102=201, 201+98=299, etc. Now suppose that
we turn the collet (in the correct direction) by the angle that the
balance travels in one millisecond, what happens? It so happens that all
the tics advance by one millisecond, and all the tocs retard by one
millisecond.
tic toc tic toc tic toc tic toc ...
old 1 99 201 299 401 499 601 699 ...
new 0 100 200 300 400 500 600 700 ...
In beat. We can conclude that in order to bring this watch in beat we need
to turn the collet by the angle the balance covers in 1=et/4 milliseconds.
This angle is one millisecond times the angular velocity of the balance,
which is la/lt. So we have, at least in this case
ea = (et/4) * (la/lt)

4.

5. ## Re: Definition of beat error

The spacing of my example above has been completely messed up by the forum. It replaced, I think, all multiple spaces by single spaces, so the numers that should have been neatly arrangled are now placed haphazardly. And also I can not find the edit button...

6. ## Re: Definition of beat error

Originally Posted by pithy
. . . Are we going to have to go through a big rig-a-ma-row or do you just want the source code (or are you wanting us to help you attempt to write your own)? . . .
Originally Posted by contrate_wheel
. . . Ok, enough boring stuff, and someone will complain again that I am asking for help, which I am not. . . .
Originally Posted by contrate_wheel
. . . I would be grateful if you could follow my little computation here and point out where I am doing the first mistake. . . .
lol

Originally Posted by contrate_wheel
. . . consider that this might be good information also for other members of this forum. . . .
Doc, don't try do it for me.

I wrote my first timing routine as an undergrad.

lol

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