9/4/22

Pendulum Physics

 Clayton,

In your written instructions for the Mantis clock you say to slow the time adjust the Bob up and to speed the clock turn the Bob down. Isn’t this backwards?

I thought to slow the clock you make the pendulum longer and shorter to speed it up. 

Thanks, Cal 

Cal, your query got me thinking that I should create a blog post explaining about the various types of pendulums and hopefully make their action simpler to understand.

There are basically three pendulum arrangements used in modern clockmaking.  These are shown in the Pendulums jpg below.  It is important to notice first that "0" is the pivot point.

Fig 31 shows a standard straight hanging "simple" pendulum with the pivot at the top.  Most of my clock designs use this type of pendulum.  It's fairly simple to understand.  If we raise the bob, it speeds the clock.  If we lower the bob, it slows the clock.  The longer the pendulum shaft, and the lower the bob, the slower this type of pendulum will oscillate.  We can also slow the oscillation of the clock by increasing the mass of the bob. With this style of pendulum, a very short pendulum shaft, or very light bob, will oscillate much faster.

Fig 32 shows a compound balance pendulum.  This is the style of pendulum used on the Mantis, Celebration, Balance, Organic and SwingTime and others.  Compound balance pendulums have the most variation, and are the most difficult to understand...but are pretty cool, because of their versatility.  For example, we could create a compound balance pendulum that is very short, say only 15 inches (38cm) tall, to take the place of a standard "simple" pendulum (Fig 31) that would need to be 42 inches (107cm) long.  Of course, we can make our compound balance pendulum shorter than 15", but the shorter we make them, the touchier, and more difficult to adjust it would become.  I saw one metal clock with a compound balance pendulum that was only three inches (7.5cm).  However, that's a bit unrealistic for our wooden mechanisms.

Fig 33 shows the pendulum arrangement used on the Toucan and Arts&Crafts clocks.  There is a stationary bob at the bottom of the pendulum shaft, and an adjustable bob between the stationary bob and the pivot.  Although it is a variant of the compound pendulum,  this type pendulum works much like the pendulum in Fig 31.  Raise the bob (or lighten it) to speed the beat, and lower the bob (or add more bob weight) to slow the clock's beat.

This morning I was sitting on the couch reading a book and it hit me how to answer your question and explain a compound balance pendulum's action.  It all has to to with what is called "Restoring Force".  The force exerted on the pendulum by gravity.

With a heavier bob on the bottom of the pendulum shaft, there is more restoring force on the bottom.  That's simple to imagine.  (we will not be concerned here with oscillations - only the effects that gravity has on the restoring force of the pendulum)

Think about a pendulum that pivots in the center, like the pendulum example that is shown in Fig 32.  But in our example here, instead of the pendulum being vertical, think of it horizontally.  (if you want a visual, simply turn the Pendulums jpg 90 degrees and look at Fig 32)

With the pendulum shaft being held horizontally, add a stationary, immovable weight at the very end of one side of the shaft, and then add a heavier, adjustable weight to the other side.  Don't let go of it yet.  Keep holding it horizontally.  If you move that heavier bob inwardly toward the pivot until it balances with the lighter, stationary bob at the other end, the pendulum has no restoring force.  You can let it go and the pendulum stays at rest horizontally.

With that same horizontal pendulum arrangement in mind, move the heavier bob down the shaft away from the pivot just a fraction of the distance so that the pendulum is no longer perfectly balanced.  Let it go and the pendulum will begin to move.  The heavier side moves down toward the floor, and the lighter side moves up toward the ceiling.  You can imagine that if the imbalance is very slight that the movement of the heavier side toward vertical is quite slow.

In a second experiment, holding the pendulum at balance horizontally, move the heavier bob all the way out to the extreme end of the pendulum shaft, and let the pendulum go.  The pendulum will now move quite fast to the vertical position (and overshoot vertical, thus the pendulum will oscillate a while.  But we are not concerned with oscillations here.  We are only concerned with the speed at which restoration takes place.)

In the first example with the heavier, adjustable bob essentially raised up (in) toward the pivot, the pendulum has little restoring force and moves slowly to a vertical position.  (thus, when lower adjustable bob is raised it causes slower restoration)

In the second example with the bob lowered toward the bottom end of the shaft, the pendulum quickly moves under the influence of gravity to the vertical position.  (thus, when we lower the adjustable bob further from the pivot it causes faster restoration).

Since Mantis has a compound balance pendulum, as shown in Fig. 32, by raising the bob up toward the pivot the motion of the pendulum is slowed.

We can also slow the Mantis pendulum another way; by lightening the lower bob.  A lighter lower adjustable bob has less restoring force.

SwingTime and Organic have compound balance pendulums also, however unlike the adjustable lower bob of the Mantis, their lower bob mass is not adjustable and stays constant.  On these clocks the upper bob is the bob used to adjust the beat.  Fortunately, the same "Restoring Force" physics apply whether you are adjusting the upper bob or the lower bob.  On a pendulum with a constant weight below the pivot, if we raise the bob that is above the pivot we slow the beat of the clock...alternatively, we could simply make the upper bob heavier.  In this case of an upper adjustable bob, both a heavier bob or raising the upper bob have the same effect on the restoring force of the pendulum.

One more, just for fun.  I created a clock that is yet another variation of Fig 33.  This clock is ALL pendulum.  The only part that is not pendulum is the wall mount.  Everything else is contained in or on the pendulum.  I call this clock "Minimalist."



Since the clockworks is integrated into the pendulum we have a compound balance pendulum that is similar to the Toucan or Arts&Crafts, except that in this case the center bob (the clockworks) is stationary, and the lower bob is the adjustment for the beat.

Because of the clock being integrated into the pendulum, the mass of the pendulum has increased and thus we need lower the bob with a longer pendulum shaft than would normally be the case.  Most of my "Simple" seconds pendulums are around 42" (107cm) from pivot to center of the bob.  The Minimalist pendulum requires about 63" (160cm) to give a seconds beat.  My purpose for this clock was to stretch out and thin down the overall appearance of the mechanism.  Integrating the clockworks into the pendulum allowed me to do just that.

Thin, slim and streamlined, Minimalist is a lovely clockworks with a unique pendulum.

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I love comments, but in order for me to have more time playing in my sawdust, I cannot respond to them here. If you have a technical question, please do not post it here, or I will have my wife answer it for me and her technical knowledge is highly suspect. For technical questions, check out the FAQ section of my website, or find my email link there. Mahalo and Aloha, Clayton