Elasticity and energy conversion in fleas, catapults, and bows - Part 2

Top of Page Catapults and Elastic energy conversion in fleas and archery - from FT Exploring

			How fleas, catapults, and some other devices and animals, use energy storage mechanisms to improve performance.		A poorly thought out demo of this page's subject.

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The Flea, the Catapult, and the Bow - Part 2
Wherin we see that human inventions do oft seem to copy nature - sometimes

	Muscles are Slow, Elastic Springs are Fast

The Energy Comes from the Muscles
In Part 1 of "The Flea, the Catapult, and the Bow", we introduced the fascinating notion that fleas and humans use the same basic principles to hurl themselves (in the case of fleas) or objects (in the case of stones and arrows) through the air much higher (in the case of the fleas) or faster (in the case of the stones and arrows) than their own muscles could fling them.

In this section, we will explain in a little more detail how they do it. Remember that the whole point is to get going as fast as possible in a short distance. Muscles can't always go as fast as we would like them to, but they still have to provide the energy. The bow, the catapult, and the flea's resilin store that muscle energy then release it much faster than the muscles could.

The Mysterious Everything is Still Flowing
Remember that everything that happens in this world happens because there has been a change of energy from one form to another. Archery practice and flea jumps are just continuations of the energy flows described in the Life Flows and Sunshine to Sugar sections.

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	How a Bow Transforms Energy 1. Bow Drawn - Energy Stored Look at the drawing on the right. In position 1, the bow is drawn, just like in both drawings above. The person who drew the bow, used his or her muscles to bend the bow by pulling back on the arrow and the string. All of the energy that the person used to pull the string back is now stored in the elastic material of the bow. Energy stored like this is called potential energy. The bow is made of elastic "springy" material that is good at storing and releasing energy. 2. Arrow Released - Energy Transferred to Arrow In position 2, the archer has let go of the string. The bow, because it is made of elastic material, has "sprung" back to its original shape. When the bow springs back it straightens the string which pushes the arrow forward very fast. Almost all of the muscle energy that was stored in the bow is transferred (very quickly) to the arrow.

From a middle ages safety pamphlet on improper maintenance practices:


	The Science of Elastic Energy Storage


			"I shot an arrow into the air, It fell to earth I knew not where." Henry Wadsworth Longfellow, apparantly discussing the mysteries of ballistics and energy conversion.

Converting Muscle Power into a Speeding Arrow

	It's Got To Be Elastic Bows must be made of "elastic" material. Elastic materials are good at storing and releasing energy. Steel and rubber are both very elastic. Steel can be made into springs, and everyone knows what you can do with a rubber band. Some of the more elastic materials found in nature include tendon, horn, resilin, and many types of wood. The famous english longbows were usually made of wood from Spanish yew-trees. Bows around the Mediterranean were sometimes made of horn, wood, and tendon combined in layers. These composite bows had wood in the middle, tendon on the outside surface away from the archer, and horn on the inside surface facing the archer. Yew is better in cool wet climates (like England), and tendon and horn are better in warm dry climates. So it all worked out nicely.
	Important Safety Tip Quiz: Every archer knows you must never never pull back and release a bow without an arrow in it. This can damage the bow and possibly injure the archer. Why?

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	How a Flea Changes Muscle Energy into a High Speed Jump
	1. In the first drawing the flea's leg is "cocked". The flea uses his leg muscles to bend the femur up against the coxa. Inside the coxa is a pad of resilin. The elastic resilin stores the muscle energy just like the bow stores human muscle energy. A trigger device in the leg keeps the leg bent. Otherwise the flea would have to use its muscles to keep the leg bent.

	2. In the second drawing, the flea has released the trigger and the resilin pad, like a spring, has released its energy which pushes the leg open very fast. Resilin is very efficient. Almost all of the muscle energy that was stored is converted to jumping energy. Energy of motion or velocity is sometimes called kinetic energy.

	3. Lift Off! The resilin "spring" throws the flea into the air at a much higher speed than would be possible if the leg muscles were used for jumping. Potential energy has been turned into kinetic energy. Some fleas are able to jump over a hundred times their body length. This is not bad for such a small animal, but is really just a mediocre jump. It is in no way equivalent to a human jumping 100 times its body height. In fact we think horses are far better jumpers than fleas. Something we will explore in another section.

Converting Slow Muscle Energy to a High Speed Jump

1


	1. Legs Cocked - The flea stores muscle energy in a resilin pad inside the coxa (looks kind of like a thigh). Resilin is an elastic (or "springy") material. Resilin is one of the best materials known for storing and releasing energy efficiently.

2


	2. Pop Goes the Flea! The "springy" resilin pad releases the energy and opens the leg much faster than the muscles can. The legs push the flea away from the ground and the flea accelerates (speeds up) upward at a high speed.

3


	3. Lift off! The flea tumbles several inches into the air. The resilin has changed muscle work into kinetic energy (energy of motion).

The catapults shown below were used by the Greeks and Romans. They were complicated and required a lot of experimentation and skill to develop.

The type of catapults shown here were very efficient. Almost all of the energy put into the tendon springs was converted into the kinetic energy of the ball or spear. The catapults below are shooting stones.






	A fidgity flea "catapults" itself (literally) into the air without a catapult.
	Comments? Send me an e-mail.

Rubber is an elastic material

Warning: Do not try this at home.


	What It Means to be Elastic

	Stretch a rubber band. What does it do? Let go of the rubber band (carefully). What does it do? When you stretched it, it got longer and thinner. You changed it's shape, or deformed it, as an engineer might say. When you let it go, it returned to its original shape. We hope. A material that can return to its original shape after being bent or stretched or squashed is elastic. Bend a bow then let it go. It returns to its original shape and is none the worse for having been bent. Try to bend a glass rod. It will break pretty quickly. Glass is more brittle than it is elastic. Squash a rubber ball. It springs back to just like it was without damage (unless you squash it too much). Try to squash a stone. It doesn't want to squash, and if you push it hard enough, it will fracture and crumble. Stone is brittle with very little elasticity. Of coarse, even elastic materials have their limit. Bend a bow too far and it will break. Stretch a rubber band too far it will snap. Squash a rubber ball too hard and it will crumble. Engineers would say they have reached their "elastic" limit.

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	How a Catapult Really Looked

Sometimes they threw big spears, sometimes they threw stones.

	How a Catapult Changes Human Muscle Work into a Speeding Rock or Spear
	The catapult arms were stuck in an elastic material (usually the tendons of cows or horses, but sometimes human hair was used). The elastic tendons were stretched very tight. Two or more men had to work very hard to crank back the arms.


	1. In position 1 above, almost all of the hard work that the men had to do to pull back the arms is now stored as potential energy in the tendon springs. The arms are pulling very hard on the string which is stretched very tight. A locking mechanism holds the string in place, just like in the flea.


	2. In 2 above, the locking trigger has been released and the arms are being swung around by the unwinding tendon springs. As they move forward they pull on the string. The string pushes on the stone ball, accelerating it greatly.


	3. Now the string is straight, the arms have stopped moving, and all the energy that was stored in the tendon springs has been transferred into the projectile (big word for rock or bullet or arrow or whatever). The rock leaves the catapult at a very high velocity.


	Same Important Safety Tip: Releasing a catapult without a projectile in it was extremely dangerous. The catapult could fly apart, seriously injuring or even killing the operators. What's going on with that?


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	It's Not a Catapult!
	The machine below is often called a catapult, but is really more correctly called a trebuchet.

	The trebuchet stored muscle energy in a raised weight, rather than in an elastic material like tendon or resilin. When the weight falls, it raises the long arm and the large stone is flung out of the sling at a high speed.

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		Definitions
		Kinetic Energy - The energy of motion. All objects that are moving have kinetic energy. When a baseball is flying through the air, the energy that determined how fast it is going is kinetic energy. The faster the ball travels the more kinetic energy it has. As the ball moves through the air it is slowed down by air resistance. The ball has to push the air molecules out of the way. This air resistance slows the ball down as it travels. As it slows down its kinetic energy gets smaller also. Some of the ball's kinetic energy is being transferred to billions and billions of air molecules. When the ball hits the ground, much of the rest of the kinetic energy is transferred into the ground as heat. Some of the energy is used to move the dirt or grass out of the way. Some of the energy is used to smash the ball a little and the ground a little. The ball and the ground have a little elasticity so the ball might bounce a few times. When a ball bounces, the kinetic energy is stored for a moment in the squashed ball, then the ball springs back and the energy is turned back into kinetic energy. This can happen over and over, but eventually all of the kinetic energy is turned by friction into heat in the ground and the ball, until the ball finally stops. When the ball stops completely, that means all of the kinetic energy has been turned into heat. Really, all of the energy has been turned into heat. Though the change is too small to be measured, the air, the ball, and the ground, are actually a little warmer because all of the kinetic energy has heated them up. Kinetic Energy is just another one of the Mysterious Everything's personalities.

		Potential Energy - Potential Energy is kind of like energy that is ready or waiting or willing to happen. (I must now ask forgiveness from all the physics and mechanical engineering professors for proceeding without formulas or math). Examples are helpful when trying to avoid formulas and numbers, so here come some examples. When you stretch and hold a rubber band, the energy your muscles exerted to stretch it, is now being stored in the deformed rubber band (as long as you keep it stretched). The Potential Energy stored in the rubber band is exactly equal to the amount of energy used to stretch it. If you shoot the rubber band off your finger, making sure to aim away from people's eyes, almost all of the potential energy that was stored in the rubber band is turned into the kinetic energy (see above) of the rubber band flying through the air. Pick up a stone and lift it over your head (not a very big stone please). It takes energy to lift the stone. Your muscles have to push the stone up against the force of gravity. The force of gravity is trying to pull it back down to the ground. As long as you hold the stone over your head the stone is storing the energy you exerted to lift it, as gravitational potential energy. If you let it fall back to earth, the potential energy you put into the stone with your muscles will be converted into kinetic energy as it falls (except for a little bit of energy that is used to push air molecules out of the way). All of the kinetic energy, that was formerly potential energy, is turned into heat when the rock smacks into the ground. Really, it all turns into heat. The ground and the rock, and even the air a little bit, get a tiny bit warmer.

		Acceleration - This is a big word for speeding up or increasing speed. When you are in a car starting up from a stop light, with your gas pedal shoved down, your car is accelerating forward (unless you have a really wimpy engine - then it might be stalling). You feel yourself being pushed into the seat back. You look down at the speedometer and see that the needle is moving to higher and higher numbers. No it's not the twilight zone, it's just the ordinary mysterious world we live in. You probably don't think about it often (or ever) but when you press down on the gas pedal you are converting the chemical energy stored in the gasoline (energy which came from the sun originally and was put there by photosynthesis a long time ago) into power which is being used to push the car forward at a faster and faster speed. As long as the car keeps going faster and faster it is accelerating. When it reaches the speed you want to go, you ease up on the gas pedal and try to keep the car at a constant velocity (see the next definition down). When speed is constant or unchanging, there is no acceleration. Speed is constant and acceleration is zero. In order to accelerate an object, a force is required. Your body is accelerated by the pushing force of the car seat on your back. The car is pushed forward by the force of the tires on the road. The tires are turned by the turning force (torque) of the transmission through a bunch of gears onto the axle. The transmission is turned by the turning force of the crankshaft in the engine. The crankshaft is turned by the force of the connecting rods pushing down. The connecting rods are pushed down by the pistons. The pistons are pushed down by the force of the burning gasoline and air expanding in the cylinders. "Whole lot of pushing going on."

		Velocity - As most of us laypersons use it, this is another word for speed (vector stuff below). Speed is measured or described by how far an object travels in a certain amount of time. When a car is traveling 60 miles per hour that means that if the car keeps moving at that speed for one hour it will travel 60 miles. It also means that the car travels 88 feet every second or 88 feet per second or 88 feet/second. If the car is speeding up (going faster and faster) then it is accelerating. If the car is slowing down it is decelerating. If the velocity is constant than there is no acceleration. An engineer would say the acceleration is zero, because engineers always put numbers on things. One more thing about velocity (for the more advanced students): To be more correct, and to please the physicists in our "audience", I must add that velocity is more correctly defined as a vector quantity. That means that to completely and correctly describe velocity you have to define a direction for it as well as a speed. This is done mathmatically and graphically with a vector diagram. A line with an arrow at one end is how this is usually shown. The angle of the line compared to some reference line(s) gives the direction relative to other vectors. The length of the line is proportional to the speed in units like meters per second, or kilometers per hour. And then there are some fun vector math and vector calculus techniques to do the "figuring", but alas not covered here.

		Elastic - See Definition Above

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