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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Energy Absorption and Conversion, Vibration Isolation, Dampening, Oscillation, Advanced Building Technologies, Building Codes and Code Enforcement

Posted by PITHOCRATES - March 7th, 2012

Technology 101

Springs and Shock Absorbers on a Car provides Vibration Isolation from the Shocks of the Road

Roads aren’t perfect.  They have their bumps.  And their potholes.  Especially in the north.  Where they use salt to melt snow and ice.  Which get to the reinforcing steel within the concrete.  Causing it to corrode.  Further stressing and cracking the concrete.  Allowing water to get underneath the concrete.  Where it expands as it freezes, heaving and cracking the road.  Then there’s the normal heating and cooling.  That can buckle and crack blacktop.  Heavy truck traffic that stresses and hammers our roads.  Even sinking slightly into our asphalt roads making tire ruts.  And then there are railroad crossings.  Sewers and manholes that aren’t flush with the surface.  There’s a lot out there to make for a rough ride.  Yet in a new car you barely feel any of this.  And you can drink a cup of coffee while driving without it splashing out of the cup.  Why?

Because the shocks from the rode are isolated from the passenger compartment.  Air-inflated rubber tires smooth out much of that rough ride.  By compressing to absorb some bumps.  Then expanding back to their original shape.  Springs handle the larger bumps.  Which compress underneath the car as the tires hit a large bump.  Absorbing the energy from that impact before it reaches the passenger compartment.  By using it to compress a spring.  Then the energy in that compressed spring releases and the spring expands until it can expand no longer.  Placing the stretched spring into tension.  The stored energy in the tensioned spring compresses it again.  And this continues back and forth until the energy fully dissipates.  Or is absorbed in a shock absorber.  That dampens the oscillation of the spring.  Bringing it back to a steady-state quickly.  Further smoothing out the ride.

A car is a magnificent piece of engineering.  From converting a fuel into motive power.  To brakes slowing a car down by converting kinetic energy into heat via the friction of brake pads or shoes on rotors or drums.  To the isolation and dampening of the road forces imparted to the car.  It’s a remarkable control and conversion of energy.  That provides for a comfortable ride.  And a smooth ride.  Smooth enough to enjoy a cup of coffee while driving.  Without being too distracted from the business of driving.

Tuned Mass Dampers prevent Dangerous Oscillations in Buildings that can lead to Structural Failures

But a car moving over a road is not the only way energy transfers between the earth and something manmade.  Sometimes the earth moves.  And energy is transferred into something stationary.  Manmade structures like buildings and bridges.  During earthquakes.  And some of these stationary things get damaged.  Some even collapse.  Depending on how we constructed them.  And how similar they are to a car.

Tectonic plates are trying to move.  But the friction between these plates as they jam into each other holds them in place.  Until the pressure builds so much that the plates shift.  Causing an earthquake.  Sending seismic waves through the earth.  In active seismic regions structures need to be like cars.  They need isolation and dampening from the shockwaves caused by shifting tectonic plates.  For during a seismic event these shockwaves ‘grab’ these structures by their foundations and shake them.  This energy applying great forces on these buildings.  Energy that needs to go somewhere.  Because of the conservation of energy principle.  We can’t create it.  Nor we can destroy it.  At best we can redirect it.  Absorb it.  Or convert it.  Like converting the forward movement of a car (kinetic energy) into heat (created during braking).  Or the conversion of kinetic and potential energy of moving springs into heat (via shock absorbers). 

Waves have an amplitude and a frequency.  They oscillate.  That is, they vibrate.  And have energy.  Which is why we build buildings and bridges to move.  To bend and sway.  To dissipate this energy.  For if they were too rigid the forces could instead lead to a structural failure.  However, if they move too much and the external force is in ‘resonance’ with the building’s natural frequency of movement, this oscillation can grow.  Producing great vibrations.  (Like a car driving without any shock absorbers.)  And great forces on the structural integrity of the building.  Itself leading to a structural failure.  That’s why high rises include dampening systems.  Such as tuned mass dampers.  A great mass suspended within a building and restrained by hydraulic cylinders.  Such as the tuned mass damper atop Taipei 101 in Taiwan.  So when the building sways in one direction the mass swings in the opposite direction.  Thus dampening the oscillation of the building.

Free Market Capitalism allows a Higher Standard of Living and Creates the Kind of Wealth that can build Safe Houses and Buildings

Smaller buildings may use springs-with-damper base isolators.  Which does the same thing springs and shocks do for a car.  Isolates the structure from vibrations.  But using the proper building materials to allow a building to move or withstand destructive forces without structural failure provides most seismic protection.  And this is nothing new.  The Machu Picchu Temple of the Sun in Peru is an early example of good seismic engineering.  Peru sits on the Ring of Fire.  A highly seismic region that circles the Pacific Ocean.  The Inca were highly skilled stone cutters.  They built the Machu Picchu Temple of the Sun without mortar.  Because of this the stone can move during seismic events.  Which has let it stand through the millennia.  Today we use mortar.  And reinforcing steel to strengthen our masonry construction (these blocks can’t move but when the walls they make crack the steel inside keeps them from collapsing).  As well as other advanced building technologies.  And ever evolving building codes and code enforcement to make sure builders meet the exacting standards of these technologies.  To keep these buildings from collapsing and killing hundreds of thousands of people.  Which is why in the most modern and advanced cities in seismic regions survive some of the worst seismic events with minimal loss of life.  Where they count deaths in the hundreds instead of the hundreds of thousands.  As they did before we used these advanced building technologies.

The countries and regions sitting on the Ring of Fire (New Zealand, Indonesia, the Philippines, Japan, Alaska, California, Mexico, Peru and Chile) use some of the most advanced building technologies.  And can withstand some of the most severe earthquakes.  With little loss of life.  Now compare that to the impoverished country of Haiti.  Their 2010 earthquake was devastating, claiming 230,000 lives.  Because they have no such building codes or code enforcement.  Or advanced building technology.  Because Haiti is not a nation of free market capitalism.  Or the rule of law.  But one of political corruption.  And abject poverty.  Are they predisposed to be impoverished?  No.  Because countries can change.  If they embrace free market capitalism.  And the rule of law.

Chile was one such country at one time.  Corrupt.  And anti-capitalistic.  During the heyday of Keynesian economics.  Where nations said goodbye to the gold standard.  And ramped up their printing presses.  Igniting hyperinflation.  Including the Chileans.  But they changed.  Thanks to the Chicago Boys.  Chilean economists schooled in the Chicago school of economics.  With a little help from Milton Friedman.  Perhaps the most esteemed member of the Chicago school. Economic reforms produced solid economic growth.  A prosperous middle class.  And advanced building technologies, building codes and code enforcement.  So when Chile suffered a more powerful earthquake than Haiti did that same year Chile measured their death toll in the hundreds.  Not the hundreds of thousands as they did in Haiti.  And the major difference between these two nations?  Chile has a higher standard of living than Haiti.  And has less poverty.  Because Chile embraces free market capitalism.  Which creates the kind of wealth that can build safe houses.  And safe buildings.  For everyone.  Not just the ruling elite.

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