My Clock Build Project Thread

Okay, I learned something. I would have guessed that the rate the clock runs at is dependent on the pendulum weight/length. I thought you could speed up a clock by shortening the length of the pendulum and/or reducing the weight.

Bruce

Not the weight. The weight controls the amplitude of the swing, and therefore the required power from the escapement. The (effective) length controls the period. The centering controls beat error.

The heavier the weight that the escapement can sustain, the more accurate the clock will be because it reduces circular error. This type of deadbeat escapement should be able to drive a pretty heavy weight.

Rick “amateur horologist” Denney
 
The formula above for a pendulum's period is only for a purely theoretical ideal pendulum, of which none exist in reality. Those presume a frictionless hinge, a weightless yet infinitely-stiff rod, a bob that is a point, no air resistance, etc.

As you can see from the formula, the weight of the bob doesn't even appear - it's actually irrelevant to the period of an ideal pendulum (and somewhat irrelevant to a good real one, even). The only parameters that matter are g - the local acceleration of gravity, and L, the length of the pendulum.

Actual physical pendulums are "compound" pendulums, as the rod and hinge, etc., all have mass, the bob is not a point, and all that must be taken into account.

The same formula would be approximately correct if the bob small and dense while being much heavier than the rod, the rod is quite stiff and on a near-frictionless spring, and so on. But that "approximately" is not nearly good enough for math alone to deliver a reasonably accurate clock. Clock pendulums must be hand-tuned by trial and error to get right.

Changing the position of the bob is the obvious way to control the period, usually with some sort of threaded mount for the bob, but that's usually difficult to dial in accurately enough all by itself. So then changing the relative distribution of mass along a compound pendulum by adding tiny weights (as small as fragments of aluminum foil or the like), typically to the top of the bob or to a little shelf mounted along the rod, changes the effective length of the pendulum and hence its period too.
 
The formula above for a pendulum's period is only for a purely theoretical ideal pendulum, of which none exist in reality. Those presume a frictionless hinge, a weightless yet infinitely-stiff rod, a bob that is a point, no air resistance, etc.

Changing the position of the bob is the obvious way to control the period, usually with some sort of threaded mount for the bob, but that's usually difficult to dial in accurately enough all by itself. So then changing the relative distribution of mass along a compound pendulum by adding tiny weights (as small as fragments of aluminum foil or the like), typically to the top of the bob or to a little shelf mounted along the rod, changes the effective length of the pendulum and hence its period too.
Makes sense and that was my assumption. It reminds me of our son's cub scout days and the Pinewood derby. In that case, you are converting potential energy (mass x g x height) in kinetic energy (1/2 x mass x velocity^2).

PE = KE -> m g h = 1/2 m v^2
mass cancels out and leaves:

velocity = sqrt (2 g h)

We had a bit of an unfair advantage in those days as I stored the pinewood derby track in my pole barn. We had a couple of "standard" cars built up for run comparisons (our track did not have a timer). If the cars were put on the track squarely, they'd finish about 2 car lengths apart very consistently. Theoretically mass shouldn't matter, but the slower car would win if I taped an end mill to it.

Me being my anal self, the only physical thing you can vary in the formula is the height of the car. On our son's car, we adjusted the position of the weight so the back end weighed 4.5 oz. and the front 0.5 oz. That biased the center of gravity towards the rear. The cars started at about a 45 deg. angle pointing down, the rear biasing of the weight effectively moved his height up about 2" for more potential energy.

Did it matter against our "standard" cars? Not that we could tell. The biggest benefits were from polishing the nails (axles) and test spinning them with a multitude of wheels. We'd stick a nail/axle through a wheel, chuck it in a drill motor, and spin it up to high speed. Then shut the motor off and time how long the tire spun. We'd have some that would go 10 seconds, others that went for 50 seconds. No idea what was physically different, but it made a 2-3 car length difference against the "standard" cars.

Another trick was adjusting the camber so the wheels rod on an edge. There's less rolling resistance with a skinny racing bike tires as opposed to a wide tire. You can't reshape the wheels to a knife-edge per the rules, but you can adjust the axle angle so the wheels run on an edge. I recall also adjusting one of the front wheel axles up a touch so the wheel didn't touch the track. That way we were running on 3 wheels with less resistance than 4. It really boiled down to an exercise in the elimination of friction.

Our son was very successful in the races; his first use of a metal lathe was truing his wheels and filing/polishing the nails.

Anyway, enough reminiscing; back to our regularly scheduled thread. . . .

Bruce
 
PE = KE -> m g h = 1/2 m v^2 only holds in a vacuum. Heavier Pinewood derby cars are faster. Imagine two identical cars dropped from a height. The heavier one falls faster. At the extreme, the heavier one has a higher terminal velocity.
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Changing the weight may effect the rate of the clock.

More weight applies more power to the pendulum which can cause it to swing a greater distance.

With Atmos it seems backwards, a sticky mainspring reduces the power available resulting in a smaller arc of rotation, less than 360 degrees.

But the clock runs SLOWER,.

Clean the mainspring and get everything else right and the disk rotates more, as much as 540 degrees, but now runs faster.

Sent from my SM-G781V using Tapatalk
 
Changing the weight may effect the rate of the clock.

More weight applies more power to the pendulum which can cause it to swing a greater distance.

With Atmos it seems backwards, a sticky mainspring reduces the power available resulting in a smaller arc of rotation, less than 360 degrees.

But the clock runs SLOWER,.

Clean the mainspring and get everything else right and the disk rotates more, as much as 540 degrees, but now runs faster.

Sent from my SM-G781V using Tapatalk
An Atmos, like any 400-day clock, adjusts the period in the gross sense by the spread of the weights. The polar moment of inertia is what dictates the period, against a suspension spring of a given stiffness. This is similar to a balance-wheel escapement that spins a balance against a hairspring like any wristwatch. (An Atmos is regulated in the fine sense by slightly adjusting the length and therefore the stiffness of the suspension spring. Again, wristwatches work similarly.)

But this is a conventional pendulum clock. The density of the bob does change the effective length, but that’s the only reason it affects the period. With a pendulum clock, gravity provides the resistance to the pendulum swing, and does the work of suspension and hair springs with clocks that have horizontally spinning weights like the Atmos or 400-day clocks.

But gravity only applies vertically, so the effective length changes as the pendulum departs vertical.

A heavier weight takes more power, it doesn’t give more power. The impulse from the exit pallet has to be enough to sustain enough amplitude to release the pallets indefinitely. Otherwise the clock will stop. That takes a heavier weight on a weight-driven clock like this one, or a lighter pendulum. Generally, the slower the beat and the heavier the pendulum, the heavier the weight must be.

Most tall case clock movements usually use a hollow pendulum bob, but even so the meterish-long length required for the one-second beat takes a lot of power to sustain. The weights are heavy—15-20 pounds. A 6” bob may swing through a 10” arc outside-to-outside—fairly large. Lots of furniture-grade grandfather clocks have very large and showy pendulums, but they are relatively light. They have lots of circular error because the effective length of such a large contraption changes more as it departs from vertical than a compact, heavy pendulum.

Fill that bob with lead and the amplitude reduces to something much smaller. My Gilbert jeweler’s regulator wall clock (actually a timepiece—no striking) with the dead-beat escapement has a stick maybe two feet long and a 4” bob, but it is lead-filled. The beat is 2/3-second, and the swing is about 6” outside to outside. The weight is only about five pounds, but that’s because the deadbeat tooth shape produces a strong impulse. That clock can maintain an accuracy of a few seconds per week if freshly regulated and kept in a consistent environment.

Pendulums are complex, but that’s why they are adjustable. And the adjustment is in the length only.

Rick “recently cut a custom pendulum for a century-old tall case clock movement” Denney
 
I decided to make a 24 hole plate for my dividing head since I need it to make wheels (gears) with 96 teeth. I used mild steel.

I brought the steel down to proper thickness and then used my boring head to make the odd sized hole.
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Then, I mounted on my rotary table and made the counterbored mounting holes.
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Drilling the 24 holes was next.
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After that was completed, I made an arbor to mount this on my lathe to make it round. The shoulder is 0.828" to match the plate's hole. The thread is 3/4-16 since that was the only nut I had that size.
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Almost round.
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Mounted on dividing head.
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Just finished making four 12T, Module 1 pinions for this project. I used W1 steel to be hardened later. I made multiple passes to not stress out my little mill. The import cutter seemed to work fine.

I used Mr. Pete's method of getting the gear cutter to the center of the shaft by using a feeler gauge under the parallel clamped to the top of the cutter.
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I realized I didn't have enough clearance near the footstock so I made an extender to go into the bore.
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Centered and ready to make first cuts.
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After a few shallow passes.
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Cuts done.
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Closeup.
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Cut off from holding shaft portion.
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Cut to size and ready to use.
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