Heat Transfer, Conduction, Convection, Radiation and Microwave Cooking

Posted by PITHOCRATES - September 4th, 2013

Technology 101

At the Atomic Level Vibrating Atoms create Heat

We make life comfortable and livable by transferring heat.  And by preventing the transfer of heat.  In fact, once we discovered how to make fire our understanding of heat transfer began and led to the modern life we know today.

At the atomic level heat is energy.  Vibrating atoms.  With electrons swirling around and jumping from one atom to another.  The more these atoms do this the hotter something is.  There is little atomic motion in ice.  And ice is very cold.  While there is a lot of motion in a pot of boiling water.  Which is why boiling water is very hot.

How do we get a pot of water to boil?  By transferring heat from a heat source.  A gas or electric burner.  This heat source is in contract with the pot.  The heat source agitates the atoms in the pot.  They begin to vibrate.  Causing the pot to heat up.  The water is in contact with the pot.  The agitated atoms in the pot agitate the atoms in the water.  Heating them up.  Giving us boiling water to cook with.  Or to make a winter’s day pleasant indoor.

Fin-Tube Heaters create a Rising Convection Current of Warm Air to Counter a Falling Cold Draft

If you touch a single-pane window in the winter in your house it feels very cold.  Cold outside air is in contact with the glass of the window.  Which slows the movement of the atoms.  Bringing the temperature down.  This cold temperature doesn’t conduct into the house.  The heat conducts out of the house.  Because there is no such thing as cold.  As cold is just the absence of heat.

The warm air inside the house comes in contact with the cold window.  Transferring heat from the air to the window.  The atoms in the air slow down.  The air cools down.  And falls.  This is the draft you feel at a closed window.  Cold air is heavier than warm air.  Which is why hot air rises.  And cold air falls.  As the cold air falls it pulls warmer air down in a draft.  Cooling it off.  Creating a convection current.

To keep buildings comfortable in the winter engineers design hot-water fin-tube heaters under each exterior window.  Gas burners heat up water piping inside a boiler.  The heat from the fire transfers heat to the boiler tubes.  Which transfers it to the water inside the tubes.  We then pump this heating hot water throughout the building.  As it enters a fin-tube heater under a window the hot water transfers heat to the heating hot water piping.  Attached to this piping are fins.  The heat transfers from the pipe to the fins.  Which heats the air in contact with these fins.  Hot air rises up and ‘washes’ the cold windows with warm air.  As it rises it pulls colder air up from the floor and through the heated fins.  Creating a convection current of warm air rising up to counter the falling cold draft.

Microwave Cooking won’t Sear Beef or Caramelize Onions like Conductive or Radiation Cooking

If you’ve ever waited for a ride outside an airport terminal on a cold winter’s day you’ve probably appreciated another type of heat transfer.  Radiation.  Outdoor curbside is open to the elements.  So you can’t heat the space.  Because there is no space.  Just a whole lot of outdoors.  But if you stand underneath a heater you feel toasty warm.  These are radiators.  A gas-fired or electric heating element that gets very, very hot.  So hot that energy radiates off of it.  Warming anything underneath it.  But if you step out from underneath you will feel cold.  It’s the same sitting around a campfire.  If you’re cold and wet you can sit by the fire and warm up in the fire’s radiation.  Move away from the fire, though, and you’re just cold and wet.

We use all these methods of heat transfer to cook our food.  Making life livable.  And enjoyable.  When we pan-fry we use conduction heating.  Transferring the heat from the burner to the pan to the food.  When we bake we use convection heating.  Transferring the heat from the burner to heat the air in the oven.  Which heats our food.  When we use the broiler we use radiation heating.  Using electric heating elements that glow red-hot, radiating energy into the food underneath them.  A convection oven adds a fan to an oven.  To blow heated air around our food.  Decreasing cooking time.

There’s one other cooking method.  One that is very common in many restaurants.  And in most homes.  But real chefs rarely use this method.  Microwaving.  With a microwave oven.  They’re great, convenient and fast but fine cooking isn’t about speed.  It’s about layering flavors and seasoning.  Which takes time.  Which you don’t get a lot of when a microwave begins vibrating the atoms in the water molecules in your food.   Which is how microwaves cook.  Cooking by vibrating atoms in your food brings temperatures up to serving temperatures.  Unlike conduction heating such as in pan-frying where we bring much higher temperatures into contact with our food.  Allowing us to sear beef and caramelize onions.  Something you can’t do in a microwave oven.  Which is why real chefs don’t use them.



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Air Handling Unit, Outside Air, Exhaust Air, Return Air and Energy Recovery Unit

Posted by PITHOCRATES - March 27th, 2013

Technology 101

Things that Absorb Energy can Cool Things Down and Things that Radiate Energy can Warm Things Up

When two different temperatures come into contact with each other they try to reach equilibrium.  The warmer temperature cools down.  And the cooler temperature warms up.  If you drop some ice cubes into a glass of soda at room temperature the warm soda cools down.  The ice cubes warm up.  And melt.  When there is no more ice to melt the temperature of the soda rises again.  Until it reaches the ambient room temperature.  The normal unheated or un-cooled temperature in the surrounding space.  As the soda and the air in the room reach equilibrium.

When two temperatures come into contact with each other what happens depends on the available energy.  Higher temperatures have more energy.  Lower temperatures have less energy.  For heat is energy.  Things that absorb energy can cool things down.  Things that radiate energy can warm things up.  And this is the basis of our heating and cooling systems in our buildings and homes.

Boilers burn fuel to heat water.  A furnace burns fuel to heat air.  The heated water temperature and heated air temperature is warmer than the temperature you set on your thermostat.  When this very hot water/air circulates through a house or building it comes into contact with the cooler air.  As they come into contact with each other they bring the air in the space up to a comfortable room temperature.  Above the unheated ambient temperature.  But below the very hot temperature of the heating hot water or heated air temperature.

Heating and Cooling Buildings consume up to Half of all Energy on the Planet

Large buildings have air handling units (AHU) that ventilate, heat and cool the building’s air.  They’re big boxes (some big enough for grown men to walk in) with filter sections to clean the air.  Coil sections that heat or cool the air as it blows through these coils.  A supply and a return fan to blow air into the building via a network of air ducts.  And to suck air out of the building through another network of air ducts.  And a series of dampers (outside air, exhaust air and return air).

To keep the air quality suitable for humans we have to exhaust the breath we exhale from the building.  And replace it with fresh air from outside of the building.  This is what the dampers are for.  The amount they open and close adjusts the amount of outside air the AHU pulls into the building.  The amount of the air it exhausts from the building.  And the amount of air it recirculates within the building.  Elaborate computer control systems carefully adjust these damper positions.  For the amount of moving air has to balance.  If you exhaust less you have to recirculate more.  Otherwise you may have dangerous high pressures build up that can damage the system.

It takes a lot of energy to do this.  Buildings consume up to half of all energy on the planet.  And heating and cooling buildings is a big reason why.  Because it take a lot of energy to raise or lower a building’s air temperature.  And keeping the air safe for humans to breathe adds to that large energy consumption.  If you stand outside next to an exhaust air damper you can understand why.  If it’s winter time the exhausted air is toasty warm.  If it’s summer time the exhausted air is refreshingly cool.

An Energy Recovery Wheel is a Circular Honeycomb Matrix that Rotates through both the Outside & Exhaust Air Ducts

In the winter large volumes of gas fire boilers to heat water.  Electric water pumps send this water throughout the building.  Into baseboard convection heaters under exterior windows to wash this cold glass with warm air.  And into the heating coils on AHUs.  Powerful electric supply and return fans blow air through those heating coils and throughout the building.  After traveling through the supply air ductwork, out of the supply air ductwork and into the open air, back into the return air ductwork and back to the AHU much of this air exhausts out of the building.  That returning air is not as warm as the supply air coming off of the heating coil.  But it is still warm.  And exhausting it out of the building dumps a lot of energy out of the building that requires new energy to heat very cold outside air to replace it.  The more air you recirculate the less money it costs to heat the building.  But you can only recirculate air so long before you compromise the quality of indoor air.  So you eventually have to exhaust heated air and pull in more unheated outside air.

Enter the heat recovery unit.  Or energy recovery unit.  There are different names.  And different technologies.  But they do pretty much the same thing.  They recover the energy in the exhaust air BEFORE it leaves the building.  And transfers it to the outside air coming into the building.  To understand how this works think of the outside air duct and the exhaust air duct running side by side.  With the air moving in opposite directions.  Like a two-lane highway.  These sections of duct run between the AHU and the outside air and exhaust air dampers.  It is in this section of ductwork where we put an energy recovery unit.  Like an energy recovery wheel.  A circular honeycomb matrix that slowly rotates through both ducts.  Half of the wheel is in the outside air duct.  Half of the wheel is in the exhaust air duct.  As exhaust air blows through the honeycomb matrix it absorbs heat (i.e., energy) from the exhaust air stream.  As that section of the wheel rotates into the outside air duct the unheated outside air blows through the now warm honeycomb matrix.  Where the unheated air absorbs the energy from the wheel.  Warming it slightly so the AHU doesn’t have use as much energy to heat outside air.  It works similarly with air conditioned air.

Many of us no doubt heard our mother yell, “Shut the door.  You’re letting all of the heat out.”  For whenever you open a door heated air will vent out and cold air will migrate in.  Making it cooler for awhile until the furnace can bring the temperature back up.  It’s similar with commercial buildings.  Which is why a lot of them have revolving doors.  So there is always an airlock between the heated/cooled air inside and the air outside.  But engineers do something else to keep the cold/hot/humid air outside when people open doors.  They design the AHU control system to maintain a higher pressure inside the building than there is outside of the building.  So when people open doors air blows out.  Not in.  This keeps cold air from leaking into the building.  Allowing people to work comfortably near these doors without getting a cold blast of air whenever they open.  It allows people to work along exterior windows and walls without feeling any cold drafts.  And it also helps to keep any bad smells from outside getting into the building.



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Generator, Current, Voltage, Diesel Electric Locomotive, Traction Motors, Head-End Power, Jet, Refined Petroleum and Plug-in Hybrid

Posted by PITHOCRATES - June 6th, 2012

Technology 101

When the Engineer advances the Throttle to ‘Run 1’ there is a Surge of Current into the Traction Motors

Once when my father suffered a power outage at his home I helped him hook up his backup generator.  This was the first time he used it.  He had sized it to be large enough to run the air conditioner as Mom had health issues and didn’t breathe well in hot and humid weather.  This outage was in the middle of a hot, sweltering summer.  So they were eager to get the air conditioner running again.  Only one problem.  Although the generator was large enough to run the air conditioner, it was not large enough to start it.  The starting in-rush of current was too much for the generator.  The current surged and the voltage dropped as the generator was pushed beyond its operating limit.  Suffice it to say Mom suffered during that power outage.

Getting a diesel-electric locomotive moving is very similar.  The massive diesel engine turns a generator.  When the engineer advances the throttle to ‘Run 1’ (the first notch) there is a surge of current into the traction motors.  And a drop in voltage.  As the current moves through the rotor windings in the traction motors it creates an electrical field that fights with the stator electrical field.  Creating a tremendous amount of torque.  Which slowly begins to turn the wheels.  As the wheels begin to rotate less torque is required and the current decreases and voltage increases.  Then the engineer advances the throttle to ‘Run 2’ and the current to the traction motors increases again.  And the voltage falls again.  Until the train picks up more speed.  Then the current falls and the voltage rises.  And so on until the engineer advances the throttle all the way to ‘Run 8’ and the train is running at speed. 

The actual speed is controlled by the RPMs of the diesel engine and fuel flow to the cylinders. Which is what the engineer is doing by advancing the throttle.  In a passenger train there are additional power needs for the passenger cars.  Heating, cooling, lights, etc.  The locomotive typically provides this Head-End Power (HEP).  The General Electric Genesis Series I locomotive (the aerodynamic locomotive engines on the majority of Amtrak’s trains), for example, has a maximum of 800 kilowatts of HEP available.  But there is a tradeoff in traction power that moves the train towards its destination.  With a full HEP load a 4,250 horsepower rated engine can only produce 2,525 horsepower of traction power.  Or a decrease of about 41% in traction horsepower due to the heating, cooling, lighting, etc., requirements of the passenger cars.  But because passenger cars are so light they can still pull many of them with one engine.  Unlike their freight counterparts.  Where it can take a lashup of three engines or more to move a heavy freight train to its destination.  Without any HEP sapping traction horsepower.

There is so much Energy available in Refined Petroleum that we can carry Small Amounts that take us Great Distances

The largest cost of flying a passenger jet is jet fuel.  That’s why they make planes out of aluminum.  To make them light.  Airbus and Boeing are using ever more composite materials in their latest planes to reduce the weight further still.  New engine designs improve fuel economy.  Advances in engine design allow bigger and more powerful engines.  So 2 engines can do the work it took 4 engines to do a decade or more ago.  Fewer engines mean less weight.  And less fuel.  Making the plane lighter and more fuel efficient.  They measure all cargo and count people to determine the total weight of plane, cargo, passengers and fuel.  So the pilot can calculate the minimum amount of fuel to carry.  For the less fuel they carry the lighter the plane and the more fuel efficient it is.   During times of high fuel costs airlines charge extra for every extra pound you bring aboard.  To either dissuade you from bringing a lot of extra dead weight aboard.  Or to help pay the fuel cost for the extra weight when they can’t dissuade you.

It’s similar with cars.  To meet strict CAFE standards manufacturers have been aggressively trying to reduce the weight of their vehicles.  Using front-wheel drive on cars saved the excess weight of a drive shaft.  Unibody construction removed the heavy frame.  Aerodynamic designs reduced wind resistance.  Use of composite materials instead of metal reduced weight.  Shrinking the size of cars made them lighter.  Controlling the engine by a computer increased engine efficiencies and improved fuel economy.  Everywhere manufacturers can they have reduced the weight of cars and improved the efficiencies of the engine.  While still providing the creature comforts we enjoy in a car.  In particular heating and air conditioning.  All the while driving great distances on a weekend getaway to an amusement park.  Or a drive across the country on a summer vacation.  Or on a winter ski trip.

This is something trains, planes and automobiles share.  The ability to take you great distances in comfort.  And what makes this all possible?  One thing.  Refined petroleum.  There is so much energy available in refined petroleum that we can carry small amounts of it in our trains, planes and automobiles that will take us great distances.  Planes can fly halfway across the planet on one fill-up.  Trains can travel across numerous states on one fill-up.  A car can drive up to 6 hours or more doing 70 MPH on the interstate on one fill-up.  And keep you warm while doing it in the winter.  And cool in the summer.  For the engine cooling system transfers the wasted heat of the internal combustion engine to a heating core inside the passenger compartment to heat the car.  And another belt slung around an engine pulley drives an air conditioner compressor under the hood to cool the passenger compartment.  Thanks to that abundant energy in refined petroleum creating all the power under the hood we need.

The Opportunity Cost of the Plug-in Hybrid is giving up what the Car Originally gave us – Freedom 

And then there’s the plug-in hybrid car.  That shares some things in common with the train, plane and (gasoline-powered) automobile.  Only it doesn’t do anything as well.  Primarily because of the limited range of the battery.  Electric traction motors draw a lot of current.  But a battery’s storage capacity is limited.  Some batteries offer only about 20-30 miles of driving distance on a charge.  Which is great if you use a car for very, very short commutes.  But as few do manufacturers add a backup gasoline engine so the car can go almost as far as a gasoline-powered car.  It probably could go as far if it wasn’t for that heavy battery and generator it was dragging around with it.

This is but one of many tradeoffs required in a plug-in hybrid car.  Most of these cars are tiny to make them as light as possible.  For the lighter the car is the less current it takes to get it moving.  But adding a backup gasoline engine and generator only makes the car heavier.  Thus reducing its electric range.  Making it more like a conventional car for a trip longer than 20-30 miles.  Only one that gets a poorer fuel economy.  Because of the extra weight of the battery and generator.  Manufacturers have even addressed this problem by reducing the range of the car.  If people don’t drive more than 10 miles on a typical trip they don’t need such a large battery.  Which is ideal if you use your car to go no further than you normally walk.  A smaller battery means less weight due to the lesser storage capacity required to travel that lesser range.  Another tradeoff is the heating and cooling of the car.  Without a gasoline engine on all of the time these cars have to use electric heat.  And an electric motor to drive the air conditioner compressor.  (Some heating and cooling systems will operate when the car is plugged in to conserve battery charge for the initial climate adjustment).  So in the heat of summer and the cold of winter you can scratch off another 20% of your electric range (bringing that 20 miles down to 16 miles).  Not as bad as on a passenger locomotive.  But with its large tanks of diesel fuel that train can still take you across the country.

The opportunity cost of the plug-in hybrid is giving up what the car originally gave us.  Freedom.  To get out on the open road just to see where it would take us.  For if you drive a long commute or like to take long trips your hybrid is just going to be using the backup gasoline engine for most of that driving.  While dragging around a lot of excess weight.  To make up for some lost fuel economy some manufacturers use a gasoline engine with high compression.  Unfortunately, high compression engines require the more expensive premium (higher octane) gasoline.  Which costs more at the pump.  There eventually comes the point we should ask ourselves why bother?  Wouldn’t life and driving be so much simpler with a gasoline-powered car?  Get fuel economy with a range of over 300 miles?  Guess it all depends on what’s more important.  Being sensible.  Or showing others that you’re saving the planet.



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Northeasters, Convection Heating, Thunderstorms, Electricity, Electric Charge, Capacitors, Lightning and Lightning Rods

Posted by PITHOCRATES - February 8th, 2012

Technology 101

A Couple of Centuries ago when a Winter Storm Approached we Stocked Up on Wood for our Cast-Iron Heating Stoves

A study of prevailing weather conditions can predict tomorrow’s weather.  Once you’ve learned some basic weather phenomenon.  Weather generally moves from west to east.  Where cold fronts meet warm fronts we can get storms, tornados, rain, sleet, snow, etc.  And if a swirling northeaster buries a town under snow people in a town northeast of this town can expect the same.  Even though the winds are blowing in the opposite direction.

Today in the worst of winter’s weather we can stay warm and snug at work.  And at home.  Amazing when you consider some of our work places have a lot of exterior glass walls.  Glass curtain walls.  Which really transmit the cold.  Of course, even these rooms can be toasty rooms.  Ever wonder how?  Take a look at the floor under the window.  What do you see?  Fin-tube radiation heating registers.  Copper pipes with metal fins soldered to them.  We pump heating hot water through the copper pipe.  And when we do these fin-tube radiators heat the air as it moves through those fins.  As air heats it expands and gets thinner.  Becoming lighter than the cold air.  And rises.  As it moves up it pulls the cold air below through those heated fins.  Heating the cold air.  Where it, too, expands and gets thinner.  And rises.  Creating a heating convection current.  Heating the room.  And the window.  By washing it with warm air.  All without using a fan to move the air.  Heating units that do have fans and move the air are more for circulating the air to prevent the build of carbon dioxide (produced as we breathe).  While fin-tube heating does the lion’s share of heating our buildings.

So when they predict a winter storm we really don’t worry much about staying warm inside.  Of course, it wasn’t always like this.  A couple of centuries ago when we saw a winter storm was moving our way we made sure we had enough wood available.  To burn in our cast-iron heating stoves.  Where we burned our heating fuel in the room we heated.  And vented the products of combustion out through the chimney.  A big difference to using heating hot water and fin-tube radiators.  But the same principle nonetheless.  These wood-burners heated the cold air and created a heating convection current.  Just like those fin-tube radiators.

During Thunderstorms Clouds act like Charging and Discharging Capacitors

In the summertime when a cold front runs into a warm front it often generates some big thunderstorms.  And some dangerous lightning.  Which has started many building fires throughout history.  Especially churches with tall spires.  Which seemed to be magnets for lightning.  Which they were.  In a way.  Because thunder storms are electrical storms.  Which is why we have lightning.  But first a little about electricity.

Electricity flows between a positive and a negative charge.  The greater the difference in charges the greater the flow of electricity.  A battery can store a charge.  A battery has both a positive (plus) and a negative (minus) terminal.  You charge a battery by applying a voltage across these terminals.  The higher the voltage and/or the longer the charge the more energy is stored in the battery.  When we connect a light to a battery it completes the circuit between the plus and minus terminals.  And electricity flows through the light and illuminates it.  The light will stay lit until the battery runs out of charge.  Or until we open the circuit.  Depending on the voltage or amount of stored charge you may see sparks at the point where the circuit opens or closes.  The charge being strong enough to jump a small air gap just before the circuit is closed.  Or just after it opens.

A capacitor can also hold a charge.  What we used to call a condenser.  Which is a couple of plates separated by an insulator.  When we apply a voltage across the plus and minus terminals the plates charge.  The insulator keeps them from discharging internally.  The bigger the capacitor (i.e., the bigger the surface area of the plates) the bigger the stored charge.  After you charge a capacitor it will hold that charge.  It will dissipate slowly over time.  Or quickly if you short out the plus and minus terminals.  And if you discharge a capacitor quickly you’re going to see some sparking.  As the charge jumps the air gap just before the circuit is closed.  The bigger the capacitor the bigger the sparking.  Funny story.  I saw a kid cutting out the capacitor from an old television set.  The kind your parents had.  With a big glass cathode ray picture tube that used high voltage to move a scanning electron beam to excite (i.e., make glow) the phosphorous coating on the inside of the picture tube.  High voltage and a capacitor mean only one thing.  A very BIG stored charge.  No one turned on that TV for a long time.  But that capacitor held its charge.  As this kid quickly learned.  The hard way.  As he cut the wire going to the plus terminal his un-insulated side cutters touched the metal of the TV chassis.  Which was, of course, grounded.  So you had the plus terminal of a highly charged capacitor coming into contact with the minus terminal of said capacitor (via the grounded TV chassis).  It was like the Fourth of July in the back of that TV.  Threw that poor kid back on his butt.  Funny.  We all had a good laugh.  He was no worse for wear.  Except, perhaps, needing a new pair of undershorts.

All right, back to those electrical storms.  And lightning.  In a nutshell, those ugly black storm clouds are like capacitors.  As the atmosphere churns up these warm and cold weather fronts as they collide something happens.  They charge.  Like a capacitor.  With one plate being on the top of the cloud.  And the other plate being on the bottom of the cloud.  As the charge grows on the bottom of the cloud it induces an opposite charge in the ground below.  The old ‘opposites attract’.  So if a larger and larger minus charge is building up in the bottom of the cloud it attracts (i.e., induces) a larger and larger plus charge on the surface of the earth beneath the cloud.  Until the charges grow so great that they jump the air gap.  But this is no capacitor discharging.  The amount of energy in a lightning strike is so great it can melt sand into glass.  And anything that can do that can play havoc with trees.  And tall buildings.  Igniting a lot of fires along the way.  And killing a lot of people.  Until, that is, we started using lightning rods on our buildings.  Sharp pointed pieces of metal above the highest surfaces of the building.  We attach these rods to conductors running down the sides of the building to ground rods driven below the surface of the earth.  Providing a ‘path of least resistance’ for that charge to discharge through while causing minimal damage to the building.

Ben Franklin gave us Weather Forecasting, Convection Heating and Lightning Rods as well as the United States

Fascinating information, yes?  What’s even more fascinating is that we can trace these developments back to one point in time.  More fascinating still, we can trace them back to one man.  A curious fellow.  With a fascination for scientific experimentation.  Who went by the name of Benjamin Franklin.  Who pioneered weather predicting when a swirling northeaster hit Philadelphia with winds blowing in from the northeast.  Curiously, though, this storm had not yet ravished Boston.  In direct line with those winds.  But the storm moved on to Boston AFTER Philadelphia.  It was Franklin who observed that the northeaster was a counterclockwise spinning storm that moved northeast.  The winds in Philadelphia and Boston were only the top part of that spinning storm.  And weather forecasting was born.

Convection heat goes back to the Philadelphia stove.  What we later called the Franklin stove.  Franklin didn’t discover convection currents.  Or the stove using convection currents.  But he used the available knowledge to make a practical heating stove.  It wasn’t perfect.  But subsequent improvements made it the standard for indoor heating for about a century or two.

Ben Franklin did not discover electricity.  But electricity fascinated him.  And he discovered that lightning was electricity (yes, he actually flew a kite in a storm).  His experimentation gave us the first battery.  The first capacitor.  The standard of using ‘plus’ and ‘minus’ for electrical charges.  The conservation of charge (you can’t create or destroy an electrical charge.  You can only move it around).  The battery.  The capacitor.  Insulators.  Conductors.  Grounding.  All of the fundamentals of electrical circuits we use to this day.  And let us not forget that one other thing.  The effect of points on electrical charges (pointy metallic things help charges jump air gaps).  Which, of course, led to the lightning rod.  This after he set up the U.S. postal service and printed his newspapers and Poor Richard’s Almanac.  But before his political and diplomatic service.  And role as a key Founding Father.  Being the only one to sign the Declaration of Independence, the Treaty of Paris and the U.S. Constitution.  The document that started the Revolutionary War.  The document that ended it.  And the document that created the United States of America.  A busy man that Franklin was.  And a great man.



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