Dear Roland, your formula is certainly correct. The problem, as you can
see, is in the inputs. In my post, I made that angular velocity depend on
the amplitude, you make it depend on the lift time. You see: the amplitude
and the lift time are basically the same thing. The lift time is the time
between the first and the third sound of the escapement. It is absolutely
clear, I believe, that as soon as you have the lift time you can compute
both the amplitude and your angle quite easily. As I was trying to explain
a couple of posts ago, if the audio is bad, one can fail to detect the
three sound clearly, or mistake, say, the second sound for the first. No
sounds, no time between the first and the third sound, no lift time. When
this situation occurs, it is often still possible to get good values for
the rate and the beat error (the error time of your formula).
Yes, your formula is Apple II stuff, but, sir, could you tell me please
where the Apple II gets his lift time from?
About your mathematicians vs. engineers thing. Actually, in the head of a
mathematician, amplitude and lift time, for instance, are the same thing.
Of course they are different numbers, but related via a trivial identity.
For an engineer, I see, it is not the case. I say "I don't trust the
amplitude!", and you answer "Use the lift time!". Of course I know how to
reduce one to the other, actually it is almost an insult to me suggesting
that I don't see a linear proportion (or that I don't see that the
derivative of sine is close to one for small angles). Point is that I say
"Peasants have no bread!", and you answer "Let them eat cake!".
There is no point of presenting mathematical beat error in degrees. Mathematical beat error is only guess, but gives good idea of the symmetry.
If horological beat error is zero, when balance is at rest and roller is on the line drawn between balance wheel pivot and escape wheel pivot, mathematical beat error CAN be different than 0.
Becoming WUSF6 trained watchmaker one step at a time
Dear Ronald, I make a screenshot to better illustrate what I was attemting
to say. This is my program, as it is now, running on a watch (AS1950
movement) that yours truely has butchered countless times. The watch was
held in my hand, about five centimeters in front of my laptop. The data is
read as follows.
On the left you have a simple paper strip like diagram. On the right you
see a red sad watch, this means that the program is not picking up a watch
right now, and the data diplayed is what it was at the time the watch was
last detected (I took it away in order to make the screenshot). Then you
have the two waveforms. These waveforms are updated in real time, but they
result from a messy process of filtering and integration, which actually
adjusts its integration time dynamically, so they don't look crisp but
that is the best that I can do for now. As you can see the program detects
the waveforms very well and aligns them correctly in their windows. The
rate and beat error displays as well as the waveforms are also very
stable (but you would need an animation to see this, sorry).
The waveform windows are graduated in milliseconds and in degrees of
amplitude, so I can say that this watch has about 280 degrees of amplitude
(confirmed by the fact that both the waveform of the tic and that of the
toc suggest the same amplitude). However, as you can see, the first sound
is very very weak, possibly due to the butchering that this watch has
suffered, and no algorithm can be really expected to get a reliable number
out of this mess.
Edit: Oops, I had a phone call in between, and uploaded my post without reading your last. Of course the first noise is weak compared with the big bang at the end. And I can ony say what I did when considering to realise a cheap timing machine many years ago (pre smart phone age): I optimized the gain for every escapement noise individually for better distiction between the noise to be detected, and background noises. This allowed pretty exact trigger moments even with a poor mic.
Regards, Roland Ranfft
Last edited by Roland Ranfft; September 22nd, 2015 at 21:20.
Of course I need the lift angle to produce the amplitude graduation. Did I ever claim that I would have done without it? That is clearly not possible.
Last edited by pithy; September 22nd, 2015 at 23:04.
Dear Ronald, you are clearly free to trust what you like, and, if you have
access to professionally built hardware or software, by all means, that is
going to be better! However I will tell you now why you can trust my beat
error, and for that I need you to examine the screenshot again.
Now, you see that the two waveform appear aligned one over the other (you
have the graduations to make sure of this). The algorithm first computes
the beat error, and then uses this to "zoom in" on the two waveforms. Now,
in your mind, move one of the waveforms to the right by one millisecond:
do they still look aligned? Very definitely not. So you can tell that the
alignemnt is much more precise than one millisecond. How much? Well, move
one of the waveforms by two tenths of a millisecond: do they still look
OK? Yes, acceptably yes. So I know, almost by logical necessity, that my
beat error, in this case, can not be off by 1ms, but it might be off by
You see, this is one of the reasons why I like my approach. Suppose that
one of those smartphone apps gives you the wrong answer, can you tell
this? No, because all that they display are numbers, and maybe some dots.
(Granted these apps are possibly much better programs than mine, here I am
discussing only the approach.) Now, if my program gets its rate or its
beat error wrong, the waveforms appear immediately, in real time, either
out of aligment (if only the beat error is wrong) or completely messed up
(if also the rate is wrong). So the user doesn't have to trust it, he can
see with his very eyes how well (or badly) the algorithm is working.
Now to how I get the beat error without detecting the pulses. This is the
idea: take the tic as a whole waveform and try to match it to the toc as a
whole waveform, and then compute the delay in time that gives you the
better match. This must be the tic-to-toc time, and from now you know how
to do the math. As a toc looks much more like a tic than like a Dirac
delta, this tecnique is much less sensitive to noise than the trigger
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