Pendulums, Springs and Timekeeping

Posted by PITHOCRATES - September 25th, 2013

Technology 101

A Swing is a Pendulum that loses Energy due to Air Resistance and Friction

Remember what it was like to swing on a swing?  You sat down on a seat supported by two chains that connected to a bar above you.  When you were real young your mom or dad may have pushed you to get you started swinging back and forth.  As we got older we didn’t need Mom or Dad anymore.  We just pushed back with our feet.  Picked up our feet.  Pulled back on the chains as we swung forward.  As our forward momentum petered out we swung backwards.  Until that backward momentum petered out.  As we swung forward again we’d pull back on those chains again.  Until we began to fly.

Well, not fly literally.  But we’d swing back and forth, getting pretty high before we started swinging back in the other direction.  Going pretty fast as we swung through the bottom.  We could do this for hours because it hardly took any effort.  Most of the work was done by gravity pulling our weight back down to the ground.  Gravity made us go faster as we swung towards the bottom.  And slowed us down after we passed through the bottom.  Which is why few kids, if any, were ever able to wrap the swing around the overhead bar like in the cartoons.  As they could never build up enough speed to escape the pull of gravity.

But we could maintain that back and forth motion almost forever.  The only thing stopping us was a bathroom break.  Stopping to eat.  Stopping to go to bed.  Or stopping because we got bored.  If we sat still on the swing the distance we swung back and forth would get smaller and smaller.  Coming to a full stop if we let it.  Why?  Because the swing loses a lot of energy.  Though kids are small they catch a lot of air.  This air resistance slows down their motion.  There is friction where the chains connect to the overhead bar.  And with two chains our pulling would be uneven and twist the swing from side to side.  Creating more friction in the chain as the links twist against each other.

A Constant Period at Small Amplitudes makes the Pendulum Ideal for Timekeeping

The pendulum is probably the closest we’ve come to achieving perpetual motion.  In ideal conditions where there was no friction or air resistance the back and forth motion (oscillation) of pendulum would go on forever.  Even in the ideal conditions it would still take an energy input to begin the oscillation.  But even though we can’t create the ideal conditions for a pendulum we can get close enough to make the pendulum do useful work for us.

The parts of a pendulum are a suspended weight (bob) and a pivot point.  The weight of the bob and the distance between the bob and the pivot determine the distance the pendulum travels (amplitude).  One swing back and forth is one period.  The greater the amplitude the greater the period and the slower the oscillation.  The smaller the amplitude the smaller the period and the faster the oscillation.  The greater the distance between the bob and the pivot the greater the period and the slower the oscillation.  The smaller the distance between the bob and the pivot the smaller the period and the faster the oscillation.

Pendulums with small swings have a very useful feature.  The period will remain the same even if the amplitude does not.  So the effects of friction and air resistance will be negligible for small swings.  Making the pendulum ideal for timekeeping.  Such as in a grandfather clock.  Where the bob is suspended on a long rod from the pivot.  That oscillates in small swings back and forth.  When this period is one second it can advance a minute hand one minute with 60 periods.  And with gears and cogs connecting the axle of the minute hand to the axle of the hour hand 60 revolutions of the minute hand will move the hour hand one hour.  Gears and cogs make the minute and hour hands move.  But it’s the pendulum that actually keeps time with its constant period.  With one other element.

Early Marine Chronometers replaced the Pendulum with a Wound Spiral Spring in the Escapement

So what actually makes the hour and minute hands move?  Gravity.  Wrapped around one of these axles is a cable.  At the end of this cable hanging down in the clock body is a weight.  Think of a fishing rod when a fish strikes.  The fish will pull the line out of the reel until you start reeling it in.  This is what gravity does.  It pulls that weight down pulling the cable off of the main drive axle causing it to spin.  But it doesn’t spin out of control.  In fact, it moves in very short, discrete steps.  Because of the escapement at the heart of a pendulum clock.

An escapement is a gear and a locking mechanism.  The locking mechanism attaches to the pendulum and looks a little like an inverted letter ‘V’.  As this rocks back and forth with the pendulum it moves two teeth (at each tip of the ‘V’) into and out of the gear.  As it rocks one way one tooth moves out of the gear.  Releasing it and allowing the gear to turn.  At the same time the other tooth moves into the gear.  Locking it and stopping the gear from turning.  When the pendulum swings the other way the locking tooth releases, allowing the gear to turn.  Until the other tooth moves into the gear and locks it again.  This happens with every swing of the pendulum, giving it that characteristic tick-tock sound.

Before the pendulum clock the existing mechanical clocks of the day were accurate to about 15 minutes a day.  The pendulum clocks, though, were accurate to within 15 seconds a day.  Making it the most accurate time piece for about 300 years until the advent of the quartz clock around 1930.  One of the drawbacks of the pendulum clock was that it needed to be stationary.  Which made it poorly suited for ships which could get tossed around in rough seas.  Which was a problem.  For telling time was crucial for navigation.  As ships traveled away from the coastline they needed to find their position on a chart.  They could use a sextant to find what line of latitude (north-south location) they were at.  But to determine what line of longitude (east-west location) they were at they needed an accurate time piece.

Early marine chronometers used an escapement.  But replaced the accurate pendulum and weight with a less-accurate wound spiral spring.  Which found their way into wristwatches.  Before there were batteries.  They weren’t as accurate as a pendulum clock.  And you had to wind them up every day whereas a grandfather clock will keep time for about a week.  But a spring allowed miniaturization.  And the ability to tell time when you didn’t have the ideal conditions a pendulum requires.  Such as on a ship navigating across rough seas.

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