The 41 second clock failure syndrome

[anorlunda]

That is one test, an enecdote. I feel uneasy about it.
How long did the inverted test run?
Did you give it a fair chance to settle down and fail at maybe 11 or 41 sec?

OK, I promised to run more tests. It took me a while to locate that weak battery. But I found it and did 20 tests. The raw data is below in the chronological order I measured them. So here's the experiment.

1. Put in the weak battery.
2. Hang the clock with a certain angle. I express that angle in terms of the hour pointing up. Angle 12 is the normal orientation for a clock, angle 3 is 90 degrees on its side, angle 6 is 180 degrees upside down ...
3. Measure how long for the second hand to get stuck. Some tests I terminated at 30 minutes. In those cases it might have continued indefinitely without sticking.

Trial	Angle	Time Until Stuck
1	12	30 seconds
2	3	> 30 minutes
3	6	> 30 minutes
4	9	1 second
5	12	100 seconds
6	9	1 second
7	11	100 seconds
8	10	40 seconds
9	8	30 seconds
10	7	30 seconds
11	6	7 seconds
12	6	1 second
13	5	20 seconds
14	4	2 seconds
15	3	40 seconds
16	2	45 seconds
17	1	45 seconds
18	12	1 second
19	9	45 seconds
20	11	45 seconds

Here is a plot, sorted by angle. I capped the maximum time to 600 seconds. Some tests were repeated, so there is more than one dot at the same angle.

Unfortunately, the data doesn't really support my theory that a flaw in the gears made it angle sensitive. There does seem to be slight angle sensitivity. However, I think the battery got weaker as I conducted the tests, and that swamped out other factors.

By the way, no matter the orientation angle of the clock. When the second hand did stick, it always did so in the 3rd quarter (180-270 degrees). That gives credence to the theory of increased torque to lift the weight of the second hand.

Note that this brand new clock started sticking on its very first day of service, so worn out parts should not be a factor.

 

[NTL2009]

Thanks for the update. Another test (if you are game), based on these results:

Add or subtract weight from the second hand so it is balanced, then try again. I'm actually surprised these hands (at least on large face clocks) are not balanced. Many styles of clock hands look like they were meant to be balanced (the short side of the hand is wide), and I think that is partially aesthetics, and partially historical. I'd bet that old large clocks had to be balanced to operate, but...

OK, I did a google image search, and it is not obvious that old, large clock hands were balanced. Some seem to be, but it's not universal, and doesn't appear to fully balance them. But that balance could also be inside the clock, behind the face.

 

[anorlunda]

Another test (if you are game), based on these results:

Add or subtract weight from the second hand so it is balanced, then try again.

I did one better. I removed the sweep second hand. Now, the clock runs indefinitely with the weak battery.

 

[Baluncore]

We have considered static balance, but not impedance and time matching through the seconds drive train. The seconds hand moves in steps. By adjusting the time constant of the seconds-hand mass system, the reflection from the hand impedance may oppose or support the next step in one second.

I would consider making the seconds hand into a balanced rotary pendulum with a period of one second. That might require the addition of a spring into the drive train to dominate the restoring force.

As the mechanism changes temperature the gear backlash may change which might change the hysteresis and reflection time.

 

[anorlunda]

I would consider making the seconds hand into a balanced rotary pendulum with a period of one second. That might require the addition of a spring into the drive train to dominate the restoring force.

I think I'm going to apply for a NSF grant to finance this research. Enough to provide for 3 grad students and a workshop. We can call it Studio 41.

 

[Baluncore]

I think I'm going to apply for a NSF grant to finance this research.

Well, I understand that the wall clock is immersed in a flow of time, in the same way that a water wheel is immersed in a river. If your research group, Studio 41, can increase the efficiency of the clock, to the point that it slows down at a lower rate than the Earth's rotation slows due to tidal drag, then it should be possible to charge the clock battery with the difference. And that does not even require PM.

 

[jedishrfu]

Perhaps this is where Douglas Adams got his answer to everything is 42 when clock stopped at 41.

https://en.wikipedia.org/wiki/42_(number)

versus 41

https://en.wikipedia.org/wiki/41_(number)

 

[Not anonymous]

I can't believe it! I thought it was only my old wall clock that was jinxed by 40-41 seconds. Now I know it is was not alone :)

 

[Baluncore]

I can't believe it! I thought it was only my old wall clock that was jinxed by 40-41 seconds. Now I know it is was not alone :)

My wall clock sped up over the last week, then two days ago, it stopped at 40 seconds. I replaced the battery, and it is now keeping time again. I think clocks are organised and stop in sympathy.

 

[sophiecentaur]

The evidence is about clocks that have run for a long time. It won't only be to do with the angle of the second hand at the time it actually stops, I'm sure. Every rev of the second hand produces a maximum load at round about the same place on the dial - say 42s. As the movement passes this point the wear of the bearings and the gears is likely to be be highest here. (the whole mechanism is built as cheap as poss) So rotating the clock by 180 degrees will change the points on all the gears where the wear is now greatest. So, if the clock then keeps going on an almost flat battery, it would not be too surprising. With a new battery, it could be that it will then carry on until it now stops at (say) 12s, when a new set of worst wear coincides with failing to drag the second hand beyond the same value of around 225degrees relative to vertical.

So the answer to the universe and everything could, in fact be 225.

 

[Baluncore]

I can accept that the answer may approach 42 asymptotically, and I can understand why in a digital system, it may fall short given insufficient observation time, but where is zero?

 

[sophiecentaur]

https://en.wikipedia.org/wiki/Fusee_(horology) can accept that the answer may approach 42 asymptotically, and I can understand why in a digital system, it may fall short given insufficient observation time, but where is zero?

It's not really relevant that the clock uses a digital system to provide pulses to to drive a motor. The same thing could happen with a mechanical clock with a spring. I would pursue this further but I don't have the time.
Or is this whole thread just a wind up?

 

[jedishrfu]

According to some sources, the meaning of 42 is rooted in the ASCII character set where 42 represents the code point for ‘*’ the asterisk which is used to reference every file or everything.

 

[anorlunda]

In any event, it's fun to separate the sf literate from illiterate using 42.

 

[gmax137]

In any event, it's fun to separate the sf literate from illiterate using 42.

Or, the musically literate:

On a slightly less technical plane, and as a person of some time on-planet, I offer a more worrisome supernatural explanation from a favored musician:

I was fortunate to see Doc Watson play a few times, just amazing. I'm not a guitar player but even I can hear how clear each note is.

The only other bit I have to add is this, normally seen in barber shops.

 

[DaveC426913]

In any event, it's fun to separate the sf literate from illiterate using 42.

I worked it out when I was a young lad:

6 x 9 does equal 42 ... In Base 13.

 

[hutchphd]

I was fortunate to see Doc Watson play a few times, just amazing.

I saw him play in the early 70's with his son Merle (at Antioch College in Ohio). What an extraordinary man.

 

[sophiecentaur]

42 represents the code point for ‘*’

If he'd used 2A then everyone would have got it!

 

[hutchphd]

Literati devotees of Kurt Vonnegut will recognize the "*" as Fundamental

Spoiler: Warning Literary Content

 

[DrGreg]

6 x 9 does equal 42 ... In Base 13.

For what it's worth, 42 days is exactly 10! seconds. (Ten factorial.)

 

[jedishrfu]

So I used simple factoring to show that 42 days has 10! seconds

42 days in seconds is 42 . 24 . 36 . 100: $2^8 . 3^4 . 5^2 . 7$

10! is 10 . 9 . 8 . 7 . 6 . 5 . 4 . 3 . 2 . 1 which is $2^8 . 3^4 . 5^2 . 7$

How did you come to learn this arcane factoid?

 

[DaveC426913]

42 days in seconds is 42 . 24 . 36 . 100: $2^8 . 3^4 . 5^2 . 7$

OK, I get this, but...

10! is 10 . 9 . 8 . 7 . 6 . 5 . 4 . 3 . 2 . 1 which is $2^8 . 3^4 . 5^2 . 7$

How do you get this? That doesn't seem to be a shortcut or anything: 256.81.25.7

 

[DrGreg]

How did you come to learn this arcane factoid?

I can't remember when I first saw this, but it stuck in my mind as another candidate for the Ultimate Question, "What is the smallest integer number of days that is an exact factorial number of seconds?"

$$\begin{align*}
&\frac
{42 \times 24 \times 60 \times 60}
{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \\
&= \frac{60}{10} \times \frac{1}{9} \times \frac{24}{8} \times \frac{42}{7 \times 6} \times \frac{60}{5 \times 4} \times \frac{1}{3 \times 2} \\
&= 6 \times \left( \frac{1}{9} \times 3 \times 1 \times 3 \right) \times \frac{1}{6} \\
&= 1
\end{align*}$$

 

[jedishrfu]

OK, I get this, but...

How do you get this? That doesn't seem to be a shortcut or anything: 256.81.25.7

I just prime factored the 10! Factors and counted up the 2s 3s 5s and 7s

2.5.3.3.2.2.2.7.2.3.5.2.2.3.2.1

You can think there are 5 even factors in 10! Hence five 2s But 8 gives you two more and 4 one more for a total of 8 2s or $2^8$ …

 

[billm]

I've not got an answer to your 41 second problem but it may be not dissimilar to the Thursday effect for grandfather clocks. This causes longcase clocks to stop on Thursdays* i.e. when the pendulum is the same length as the (hanging) weights causing a transfer of energy to the (swinging) weights if there is the slightest tendency for the clock to sway.
The standard cure is to put a match stick under the appropriate corner of the clock for which the clockmaker (or repairer) will charge five guineas.
*This, of course, is based on the normal rules of the household i.e. that the clock is wound up on a Sunday evening.

 

[DaveC426913]

So there's your answer @anorlunda : tilt your clock:

 

[berkeman]

So there's your answer @anorlunda : tilt your clock:

That'll be five guineas please...

 

[Andrea_Dubai]

my experience (about 30 years) with many clocks is that the stuck occurred at 44 seconds when the effort from 44 to 45 requires more energy and tend to increase. The effort from 45 to 46 tends to use the same energy but it moves to decreasing power needs. If the clock is able to move from 44 it is not guaranteed to achieve 45, but if it is able to move from 45, for sure it will reach a 46 and it will be able to 1 more clockwise round. However, and influencing parameter could be the threshold move of the second clock hand. I had a very 'smooth like' hand which stopped at 47 seconds in the past.