Re: The aerodynamics of lead

Harvey Moseley

Hi Bepi,
Pretty interesting!  One parameter to look at is temperature.  The expansion coefficient of lead is significantly larger than that of iron. Presumably it was in thermal equilibrium by the time you tested it, but it is a thought.

On Fri, Feb 7, 2020 at 8:30 AM Bepi <pepicima@...> wrote:

In "Circular error and my pseudo-synchronome" you can see data showing an unexpected relationship between period and amplitude over a large swing range. I was expecting the circular error to show up in all its might.

No experiment can be simpler than this, the recordings refer to winding down free-pendulum data, with the case door open and closed, I'll show those data again later on in this post. Q values of 5,000 and 8,000 respectively.

At the same time we were noticing a large instantaneous frequency shift at opening and closing of the case door, with a time dependence indicating a lack of symmetry of the air resistance, in the "tangent rule" logic. See also the "Effect of open case vs. closed case" topic.

In both experiments I couldn't think of anything else other than aerodynamic causes to explain what I was seeing.

Noticing that my synchronome bob is unexpectedly low density, 6.9 g/cm3, I thought it would have been interesting to test a more aerodynamic, denser, equal weight, bob made of lead (11.3 g/cm3).

Chatting on skype to an excellent mechanic, friend of mine and also a retiree, I asked him how difficult would have been to make a lead bob, in a soft iron skin for magnetic impulsing, and a few days later I got in the mail a very heavy box.

We designed it like a cylindrical lens, 59 x 86 x 203 mm, to make it more streamlined and to keep it another 12 mm away from the back wall. My intuition tells me that those 8-10 mm from the back wall of the conventional bob might be responsible for high speed, large turbulence, flows, which means more undesirable effects.

Repeating the free pendulum experiment mentioned earlier I got a clearly different behavior.


About the period vs amplitude dependence, with the old cylindrical bob and the door closed I was measuring this:

with the new lead bob (the first ramp is with the door closed, the second with the door open):


Quite a different picture, now the period decreases with a decreasing angle (green bottom trace, left scale), linearly instead of parabolically, but now it decreases instead of increasing. A drop of - 270 μs instead of the predicted - 400 μs (bottom red trace, right scale), an indication that there is something else lurking in the muck. The spring? Case asymmetries? Hidden degrees of freedom? There is not much else to think about.

Energy wise another big difference, Qs roughly double.

Old Q , door closed:

Lead bob Q, door closed, hr 0 to 3, door open, hr 3.5 to 7:


Data are from the same series as above where one can get the angle evolution with time. Typical old Q = 5,000 at 2.5 deg, with the new bob at the same angle Q= 13,000.

Similarly the instantaneous frequency shift when one opens and closes the case door is much reduced with the lead bob, from 80 μs to 20 μs. More experimentation is needed to understand if at case closed, the normal condition for the clock, the "tangent error" associated with this effect is already geometrically optimized or not.



Lead bob:


Traditional bob:


To summarize: the new streamlined lead bob is a lot more efficient than the old cylindrical INVAR (?) one. Not surprisingly it shows also in the power needed to run the clock in steady state at the same angle, it more than halves. With the new bob we lost our cosy flat spot in the period vs angle dependence but we gained a more conventional "circular error" behavior. Still a bad agreement with the simple picture, almost a factor of two smaller than predicted. Of the roughly factor of four reduction in the anomalous period jump at case door opening, more than a factor of two is coming from the more than doubled Q and the remaining is presumably due to a reduced interaction of the new pendulum with the case walls.

A denser bob for the same weight is certainly reducing also the buoyancy error.


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