Swinging In A Swing w/o Touching the Ground

But you are touching something: the swing. When you move your legs up, you're increasing your potential energy. By doing that at the proper place in the swing arc, it converts to kinetic energy.

Paul Cardinale

Parametric amplification. Raise the resonant frequency (kid shortens rope) at twice the systems frequency.

By conservation... The spinning skater raises frequency by pulling arms in.

Same principle in both.

Extra credit: Can the spinning skater increase momentum by flapping arms at 2f ?

Sue...

Dear Bret Cahill:

Can you do it without gravitation?

The two bodies are the swinger and the Earth.

David A. Smith

In the case of swinging without touching the ground...the energy comes from the food that was ingested, earlier, and is being used to contract muscle tissue and redistribute the mass of the swinging person in sync with the swing's pendulum period.

This pre Galileo nonsense has got to stop!

I'm looking for _equations_. I'm looking for _numbers_.

Here I'll try again:

When the swinger raises his legs and leans back at the end of the back "stroke" momentum is conserved but kinetic and/or potential energy is increased.

Total momentum and kinetic energy of two or more bodies at rest is zero. If one body shoves off another momentum is still zero in the two body system but the kinetic energy has increased.

Now how does this kinetic energy, generated at the extreme ends of the swing, feed the amplitude of the swing?

Bret Cahill

"Bret Cahill" wrote in news:1163901488.240238.67170 @m73g2000cwd.googlegroups.com:

Whoever mentioned non linearity is on the exactly right track.

The numbers and equations are reasonably straightforward, why would you learn more from me working them out, than you?

by moving your legs and body (using muscle energy) to add energy.

The law of conservation of energy applies here, just as does the law of conservation of momentum.

You have given no parameters, and by the law of conservation of engineering energy, your answer was in the parameters of your question .

It is more complicated than just energy -- but basically

1) At the point where the mass on the swing-mass system is just below its maximum potential energy (mgh), the attached mass rotates rapidly around a point below its own center of mass, turning chemical energy into rotational kinetic energy (1/2 I w^2). When the mass is at the point of maximum potential energy of the swing-mass system, the just-rotated mass stops rotating. Since the mass subsytem's rotation is below the center of mass, then when it stops rotating, the mass moves linearly in the plane of the swing arc. If properly timed, it moves the mass farther along the arc at the arc's end than would have happened by swinging alone. Since energy must be conserved, and since the mass is no longer rotating and does not re-absorb the energy, that 1/2 I w^2 becomes 1/2 m v^2, which is added to the swing-mass system potential energy mgh.

Or, to put it another way - when the swinger gets to the top of the arc, they jump up, thus lifting their body higher. The added height from the swinger jumping up adds potential energy to the swing-mass system.

Momentum also has to be conserved, but since you only wanted to know about the energy...

Let's just see if we can do small angle pendulum swings first.

The spring/mass and LRC oscillators are easy and I once figured it out qualitatively while swinging in a hammock.

Without the forcing function the tangential component of the force from the rope on the weight is mg sin theta.

The tangential force is zero at the bottom of the swing and at a maximum at the ends.

Rotating or moving a limb just before the end of each swing and then decellerating it at the extreme end increases the force in the rope and the tangential component.

So you _are_ pulling on something.

Bret Cahill

On 18 Nov 2006 17:58:08 -0800, "Bret Cahill" wrote: ///

A pendulum shuttles energy between two modes like most oscillators. A pendulum does the potential to kinetic thing. The swing pumping action can be described as an increase in potential energy delivered by raising the feet behind or forward and higher off the ground at the end of each swing. This converts to higher speed at mid swing.

Brian Whatcott Altus OK

Total energy of the system is the potential energy + the kinetic energy of the mass(es).

If there are 2 or more masses that can either stick together or exert forces and move relative to each other and increase _overall_ kinetic energy, then maximum potential energy and the overall energy of the system must increase as well.

Bret Cahill

"Bret Cahill" wrote in news:1164924787.640515.217720@

16g2000cwy.googlegroups.com:

Yes, swinging your legs requires energy.The KE of your legs is then used to increase the total energy of the system.

Now I can optimize:

For maximum effect, for maximum KE, accellerate the smallest mass possible to the fastest speed possible to receive all the momentum that was formerly associated with the entire system.

All that's left is optimization of the timing.

I'm sure this has been done many times before but sometimes you just feel like doing it yourself.

Bret Cahill

"Bret Cahill" wrote in news: snipped-for-privacy@73g2000cwn.googlegroups.com:

Hmmmmmmmm. Generally it is a good idea to accelerate the largest mass available to the slowest speed necessary. For instance, you probably put as much or more effort into throwing a cricketball or baseball as in swinging your legs/body, yet I strongly suspect that swinging your legs would have a bigger effect.

Oh yes, very much so.

I suspect that if you came up with an analytical description, rather than just doing a time based stepwise simulation, you'll have some very scary maths to do. Which is fun. You may find something of relevance in the dynamics of a compound pendulum.

Cheers

Greg Locock

That's what happens when you accelerate the smallest mass to the highest speed.

Try swinging in a conventional swing where you move the heaviest part of your body, your back, in the direction of the swing just before the end of the swing.

Then try a hammock using one leg raised straight up to get yourself swinging. You are lying at right angles to the direction of the swing so move your leg left - right just as you muve your back back-forth in a swing.

Notice how you get up to altitude a lot faster in the hammock? You can approach 90 degrees.

The hammock situation is clearly superior to the swing.

That's because your foot-lower leg is lighter than your back and it can be accelerated much faster which means more KE each stroke.

Nothing new except this:

Once you swing in a hammock, you'll never go back to a swing.

Bret Cahill

It's not because your foot/lower leg is lighter, it's because your leg muscles are far more powerful than your abs/back.

If you were capable of putting the same energy in to various parts of your body, it would be more efficient to move a large mass slowly than a small mass quickly. Our bodies aren't set up that way though, and we're far more capable of generating energy with our leg muscles than any other part of our body.

Tom.

If you are lying in the hammock normal to the swing direction, the leg muscle used to power the hammock is the abductor, a pussy muscle compared to the big one you use to bend your knees.

Or at least my abductors are pretty wimpy.

Try to remember swinging involves two masses.

You increase the momentum of a small mass _only_ by decreasing the momentum of the large mass by the same amount.

So you might just be looking at the large mass when I'm looking at the small mass (as well as the big mass).

The net effect is the _overall_ KE increases and it increases most when the smallest mass is increased to the highest speed.

Bret Cahill

That's probably because you'll be in hospital after falling out of the hammock!

Swinging is so second nature it was hard to determine what was actually happening from a dynamics POV. I needed to get _out_ of the swing.

I made a simple test rig that could be operated without any instinctive reactions on my part.

The easiest "swing" turns out to be a torsion spring oscillator, basically a foam plate with a few feet of 1/4" tubing coiled on the perimeter. One end goes to a barb elbow mounted in the center for balance then another short section goes up from the elbow to the edge of a desk or some other support. A syringe is stuffed into the top end of the vertical piece of tubing .

The vertical tubing acts as a torsion spring.

Fill the tube with water and then pump the water back amd forth until you get the timing and direction right for good swing action.

The best result was to pump of the water at maximum deflection, in the direction the plate was going to spin.

Then I immediately understood how swinging works.

In swinging you use the force or torque of the spring or swing at maximum deflection to accellerate part of the system.

Momentum is conserved so the spring and the rest of the mass is temporarily held back.

At the end of the accelleration or power stroke the entire mass then starts to move forward because the spring is no longer opposed by the reaction force.

The momentum of the accellerated mass is transferred to the entire system, increasing the KE of the entire system.

The increase in KE increases the amplitude which gives the swinger a larger force to "push" against next time.

Bret Cahill