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Riding the Wave

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Wed Apr 06, 2011 4:28 pm PostPost subject:
cloud camper
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Harvey wrote:

Now for a mind-blower - time = energy. The larger the diameter, the longer we are able to apply a small force to overcome the moment of inertia of the wheel. The MOI remains constant for all time frames. But the longer we apply a force, the better our chances of bringing a mass from zero velocity up to 9.8 m/s. We know that if we drop a weight that it will accelerate from zero to 9.8 meters per second the first second it is allowed to fall. But if you attach that same weight to the circumference of a big drum, it will not accelerate to 9.8 m/s because it is fighting the MOI of the drum. So there is a specific ratio between the time the force is applied, to the time that the desired velocity is reached. And that ratio is determined by the circumference of the arc the applied weight must travel. That's how you convert time into energy using gravity - by allowing the small force to be applied to the long lever for a longer period of time we can get a huge balanced mass to turn and store the energy in its angular momentum.
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I'm right on top of you Harv (hope you're cute!). I already know where you're going with this and am busy simming it! It gets rid of the rope and pulley system entirely, doesn't it? Can't wait to finish the sim!
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Thu Apr 07, 2011 9:03 pm PostPost subject:
Harvey
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LOL - I'm probably about as cute (and fat) as this Rabbit:
http://www.youtube.com/watch?v=XSGBVzeBUbk

But I get your point Wink

Looking forward to the sim.

I recall hearing that any two points cut through the Earth's crust in a straight line will take 42 minutes to traverse using gravity as the propulsion system regardless of the distance. Hmmm "we don't need no stinkin' straight line". Brachiostone anyone? Mr. Green http://www.google.com/search?q=Brachiostone&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a
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Fri Apr 08, 2011 5:03 am PostPost subject:
Frank
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Harvey wrote:
LOL - I'm probably about as cute (and fat) as this Rabbit:
http://www.youtube.com/watch?v=XSGBVzeBUbk

But I get your point Wink

Looking forward to the sim.

I recall hearing that any two points cut through the Earth's crust in a straight line will take 42 minutes to traverse using gravity as the propulsion system regardless of the distance. Hmmm "we don't need no stinkin' straight line". Brachiostone anyone? Mr. Green http://www.google.com/search?q=Brachiostone&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a

The cycloid applies to gravity acting vertically downwards throughout the curve. I doubt if it applies where the gravity vector is changing angle. For example, what about the case where the path goes through the centre of the earth?
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Fri Apr 08, 2011 11:14 pm PostPost subject:
Harvey
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Hi Frank,

Yes that is interesting to consider because it implies a geometric limit. For example, if we build a runway for landing space planes and it is say 10 km long and "Level" would it truly be 'flat' ? At what length do we lose our 'flatness' even though the old bubble or plumb bob is well aligned at each end?

However, with regards to the 42 minute constant, it holds regardless of the distance as long as the path is laser straight even through the center of the Earth.

My fantasy was if the path was a chord through the crust, then we could apply the Brachiostone path to reduce the time constant and it will work as long as the slopes are configured to maximize the acceleration at the outset. The time is reduced because the average velocity to distance ratio is higher for the Brachiostone than it is for the flat line. Is there a difference between the Brachiostone and the Brachistochrone? I'm not sure the Brachiostone even exists. Razz

Here is something to consider:
A zero resistance track is built around the planet with a consistent slope of 0.00000000789:1 so that on each full revolution it drops 1 foot toward the center of the Earth. The initial acceleration would be almost unreadable but constant. The track geometry maps out a spiral and if allowed to continue to the center of the Earth would represent an ever increasing velocity. Could escape velocity ever be reached with this arrangement?

Cool
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Mon Apr 11, 2011 8:43 am PostPost subject:
Frank
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I've discovered one can show mathematically that the Keenie wheel generates energy from the gravitational field.

Let the excursion time = t

The excursion time is the time interval between a weight leaving the outer High Inertia Wheel (HIW) for the inner Low Inertia Wheel (LIW) at 2 o'clock, say, and returning from the inner Low Inertia Wheel (LIW) to the outer High Inertia Wheel (HIW) at 4 o'clock.

This weight transfer causes LIW weight to accelerate clockwise at 28 ft/s, say, and the HIW weight to accelerate anticlockwise at 4 ft/second.

Therefore the LIW is subjected to a high CW Jerk Force. It speeds up.

and the HIW is subjected to a low CCW Jerk Force. It slows down.

so HIW Fj > LIW Fj

Now as show previously Jerk force x time = energy.

But the excursion time, t, is the same for both wheels.

Therefore,

Energy gained by LIW > Energy lost by HIW.

and there is a net CW energy gain.

Greendoor had the right idea in thinking force x time was important.

It is - but one has to use the correct order of force, i.e. one has to use Fj , not Fa .
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Mon Apr 11, 2011 9:22 pm PostPost subject:
Harvey
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Hi Frank,

If the moving mass is drawn by gravity to leave the outer wheel and join the inner wheel, then it must be shown mathematically that centrifugal force is properly nullified or exceeded to allow that transaction as gravity is being used to counteract that.

You State:
"Therefore the LIW is subjected to a high CW Jerk Force. It speeds up.

and the HIW is subjected to a low CCW Jerk Force. It slows down. "

But the equation " so HIW Fj > LIW Fj " states just the opposite ???

In order for a Jerk to occur, there must be an abrupt change in acceleration. There is no doubt that a mass moving CCW at some constant velocity is in a state of acceleration and by moving that mass to the inner wheel the mass itself will experience an abrupt change in acceleration, specifically a reversal. The momentum stored in the mass will be transferred to the inner LIW in the CCW direction, thus acting to slow that wheel or even stop it depending on the inertial differences. So there will be an initial Negative Jerk applied to the inner LIW acting against it. Once this energy exchange is effected, then gravity can act on the mass and subsequently accelerate the LIW as the mass moves from 2:00 to 4:00 (or more specifically 60 straddle the gravitational horizon) where it leaves the LIW and rejoins the HIW where again the mass momentum is applied as a counter productive Jerk force to the outer HIW after which gravity acts to slow the HIW as the mass moves from 4:00 back to 2:00.

So we now have 4 Jerk transactions: Exit HIW, Enter LIW, Exit LIW & Enter HIW.
We also have 4 paths: HIW ---> LIW, LIW ARC, LIW ---> HIW, HIW ARC.

The respective ARC's are dependent upon the lateral transition angle relative to the gravitational horizon. The path HIW ---> LIW must have a slope steep enough to overcome the centrifugal force of the mass moving at HIW angular velocity in its travel position. The path LIW ---> HIW needs a slope that allows the gravitational force to move the mass from LIW to HIW. The ARC lengths for LIW ARC and HIW ARC depend also on the length of the two lateral paths but in order for gravity to work on the lateral transitions the LIW ARC length must be less than the HIW ARC length.

We therefore have a velocity and time associated with each of the four paths, and a time associated with the four Jerk transactions. The time associated with each ARC length is dependent on the angular velocity of the respective wheels which could be selected to make the times equal. But since W = Fd, and in this case we are considering d to only be orthogonal to the gravitational horizon, we find that the energy added by the LIW is less than the energy subtracted by the HIW as the HIW lifts the mass against gravity for another go-round.

The path of the mass is a quasi-trapezoid with at least two arcs on the wheels, but we could employ the cycloid to the lateral paths to adjust the timing as required.

It should be noted also, that when centripetal force is dropped to zero, centrifugal force also drops to zero simultaneously so that at that instant the force on the mass becomes tangent to the circular path it inscribed when the centripetal force was active. IOW, if you swing a can on a string and cut the string the centrifugal force disappears and the momentum of the can carries it in a straight tangential path. This applies to the LIW ---> HIW path when the mass is released from the LIW, the force it produces will be tangent to the LIW ARC, not perpendicular to it. So if the mass is released at th 4:00 position, its momentum would carry it toward the 6:00 position with a slightly larger radius than the LIW. Some mechanical restraint or mechanism could be employed to carry that momentum out and back to the 4:00 position where it intersects the HIW ARC, and that mechanism would probably be some means to store the momentum of the mass as angular momentum and then release it to the HIW with inversion in a productive manner and similarly in the HIW ---> LIW path. A swing arm with a 180 travel and a diameter equal to the lateral path length would suffice.

Cool
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Tue Apr 12, 2011 5:43 am PostPost subject:
Frank
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"In order for a Jerk to occur, there must be an abrupt change in acceleration"

The change in acceleration (towards the centre) is continuous over the excursion time, t.

And I should ad that the weight remains effectively at the same radius. It does not move in towards the centre.
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Sun May 01, 2011 12:10 am PostPost subject:
Harvey
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I think that would be a change in velocity, right?

On a related note:
If you have 10 Newtons of horizontal force pushing a pendulum that has 60 Newtons of gravitational force pulling down on it - at what angle will the forces reach equilibrium?

After calculating the distance traveled in the X and Y directions and the energy involved, is there any gain? Does the pendulum store more energy than is provided by the X force alone?

Hmmm.
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Sun May 01, 2011 5:30 am PostPost subject:
Frank
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Harvey wrote:
I think that would be a change in velocity, right ...

Wrong.

The mass is moving along a curve, not a straight line.

If it were moving along a mathematically straight line it would be a change in velocity.

But it isn't.
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Mon May 02, 2011 9:15 am PostPost subject:
Harvey
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Velocity represents speed and direction. If either changes, then the velocity changes. Therefore, any change in direction represents a change in velocity which is known as acceleration.

A constant speed object traveling in a circle is in a state of constant acceleration.

Changing the speed of the object, or the direction of its travel does not necessarily mean there is a change in acceleration. Whacking a baseball with a pure horizontal force does not alter the gravitational (Y) acceleration - it remains constant even though the velocity path is changed.

In order for Jerk to occur, there must be a change in acceleration and this means a force must exist along the path of the acceleration that will cause it to be changed.

Speed: I'm moving 60 MPH
Velocity: I'm moving Eastbound @ 60 MPH
Acceleration: I'm in a curve transitioning from East bound to North bound at the constant speed of 60 MPH
Jerk: A vehicle moving 80 MPH hit me from behind in the curve and caused my vehicle to now be moving 70 MPH thus changing my acceleration value.
Jerk (alternate): A sudden malfunction has caused my vehicle to swerve into a tightening spiral where the acceleration continues to increase.

Cheers,

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Mon May 02, 2011 12:10 pm PostPost subject:
Frank
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I suppose I should have said that change of velocity in a straight line is a boundary case of acceleration where the radius of curvature is infinite - not of much interest in our case.

Increase of rpm, of jerk in other words, does involve a change of force - the increase in the force of whatever is holding the body in a circular path.

One must distinguish between the popular concept of jerk and the maths definition.
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Sat Feb 07, 2015 1:12 am PostPost subject:
Frank
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Hmm!

Long time ago since anyone posted anything on this Forum.

Is anyone still alive and monitoring it?

I know cloud camper is because he is still on Bessler?

Anyone else? Harvey? Al aka Tinsey? Laughing
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Sat Feb 14, 2015 5:42 am PostPost subject: Long Time
Harvey
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I still get e-mail notification when a new post is put up . . . now all I have to do is check my e-mail more often Wink

I've been out of touch with nearly everyone here - no ambition I suppose.

Good to here from you Frank.

Best Regards,

Harvey
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Sun Oct 25, 2015 5:04 am PostPost subject:
Angus
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I'm here, just because Trim pointed out it is still churning, so I came over from the 'trap. Haven't seen you there in ages, Frank.

Angus
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Sun Oct 25, 2015 5:05 am PostPost subject:
Angus
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I'm here, just because Trim pointed out it is still churning, so I came over from the 'trap. Haven't seen you there in ages, Frank.

Angus
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Wed Dec 02, 2015 8:49 pm PostPost subject:
WhiteLite
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My God, next year it will be 10 years since this whole thing started. Makes me feel old, lol Sad
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