Gravity assisted Normal Energy

[mickegg]

Hi Fletcher

The Rolamite Bearing looks useful and fairly easy to make.

I'm making a version the same as KAS's at the moment.If it works out ok I'll try to do a video.

Regards

Mick

[ME]

WM2d.... I wasn't yet searching for the physics, I was searching for the math of the motion (physics follows).
Can a circular motion on a ramp keep that motion purely horizontal? It can't.
Does it matter: I don't know.

just out of interest, could you obtain some Ke against GPe values with the ramp angles between 30 and 35deg. I know there would be loss of Gpe but I am not sure how the Ke responds to this.

I thought it wasn't supposed to loose GPE ??
Anyway, my WM model is only Similar and not Equal, so GPE/KE will not produce a good result: I screwed up the MoI of the arc by replacing it with a Center of Mass equivalent. When RKE is off then KE is off, and it's possible that has an effect on the minimum required mass of the arc.
If you ask me, I don't expect anything unusual, even when calculus is done by hand.

I am not sure what your sim depicts happens in reality.

I guess we first have to agree on the motion.

Interesting observation from the pictures, the Radius of Gyration (RoG) of the Main-weight coincides with the Radius of Gyration of the Center of Mass of the Arc.

[mickegg]

Hi Guys

I've put together a mechanism based on KAS's design using bits and pieces that came to hand.

This consists of:
the weight cut from an old steel bolt
arc section cut from a piece of underground waste pipe
plywood for the deck
some batten for the feet/ribbon clamps
cotton tape from my wife's sewing box.

My initial observations and thoughts:

Operation shows a difference from KAS's version which I attribute to the materials and
dimensions of my construction.

I measure the angle where overbalance occurs to be 38 to 40 degrees.

Viewed from the side, looking at the centre of the weight mass to the tangent point
where the tapes cross it can be seen that the deck must be raised to a point where the
two points converge before the action starts.

If a larger diameter weight had been used pushing the mass nearer to the arc centre
then I would expect the action to start at a lower angle.

The weight travels on a trochoidal path.

The weight of the arc material contributes to the balance and thus the tipping point.

May be possible to tune the design to use the best part of the trochoid curve to
obtain the minimum variation of height of the weight.

A short video placed on YouTube:

https://youtu.be/3xNup9C1zfw


I'm wondering if one used a special curve on the roller, designed for weight position and tipping angle,
if a true horizontal weight path could be obtained.

Any thoughts?

Regards

Mick
Edit
The steel bar is 19mm dia. and weighs 167 grammes
The arc is cut from 110mm dia. pipe of 3.3mm wall thickness and
weighs 62 grammes

[Fletcher]

Mighty effort (in quick time) mickegg. Much appreciated.

I will be interested in KAS's comments, comparing to his own observations of his devices.

The construction seems very similar.

[mickegg]

Double post cancelled

[ME]

The weight travels on a trochoidal path.
The weight of the arc material contributes to the balance and thus the tipping point.
I measure the angle where overbalance occurs to be 38 to 40 degrees.

Yes.
You are setting it manually beyond that potential hill: see attachment.
My guess: Either the arc needs to be heavier, or those jacob straps are to tight.

I'm wondering if one used a special curve on the roller, designed for weight position and tipping angle, if a true horizontal weight path could be obtained.

Yes one could. Design a cog or shaped gear, it could be the roller, the ramp itself, or both. But if it doesn't loose GPE, it will not move.

[KAS]

Nice Mick, you knocked that up pretty quickly.

Similar results to mine although the moment happens at a slightly different angle with my smaller radius arc. You can see from the video that the moment the Oob occurs between the Bob and the cross over straps, the acceleration or Oob chase starts. Although difficult to see with the naked eye, I would agree that the path does appear trochoidial when rolled on a flat surface.
I have found that the acceleration occurs earlier in the moment (and probably a slightly different path) if the ramp was removed and the arc is allowed to descend resting on the taught straps but I put this down to a little sag in the straps. The weight of your arc material is obviously contributing to the moment. We would probably get a better Idea of its influence if a lighter material was used but aye, its a good starting point. I am not a mathematician but as with my experiments, (some with lighter materials) it is my view that the acceleration (and therefor Ke produced) does appear in exess for relatively little loss of Weight height although I could be wrong.

I like your suggestion to utilise an arc profile that ties the weight path to a more linear moment.
I had the same thoughts a few years ago where I was beginning to think a Fibonacci curve may be the answer. Never took it any further though.
A Fibonacci curve is found everywhere in nature where gravity is concerned: the break of a wave, the water as it drains down the plug hole and even the rotation of the Galaxy. Maybe Gravity is trying to tell us something.

Thanks Mick. I am interested to know all your thoughts. Is it worth further investigation, or have hit a wall here?

[mickegg]

Hi KAS

Thinking more on this I too believe that a spiral arc will be the better option.

Thanks ME..yes you're correct that the motion is driven by the loss in height of the arc.
The higher angle also puts the weight mass into a downward path sooner which spoils the effect.

Calculating a spiral to keep the weight horizontal will put all of the driving
force onto the descending weight of the arc.

Thanks Fletcher...."The construction seems very similar."

...err....that was by design old chap <grin>

Regards

Mick

[ME]

Mick, your main-weight needs to be moved (about) half its radius towards the center to make it go at 30°.

[mickegg]

Hi ME

As the weight clamps the tapes in place it's a bit fiddly to change.

The operating angle was not that important to me only the motion and method of operation....I saw what I wanted to see.

I am now trying to calculate the spiral formula I need to keep the weight path on a horizontal track for any given operating angle, whether that might be 20,25,30 degrees etc.

Obviously each one would need a dedicated form.

Your maths skills would be appreciated...!!

At the moment I'm trying a scale drawing to determine the curve for a 20 degree ramp.

Regards

Mick

[ME]

* As the weight clamps the tapes in place it's a bit fiddly to change.

KAS uses screws (which might direct the Main-weight's CoM a little more to the center). You could try the same and stack another weight on top of the one present.

This distance from the center seems important when you want it to be able to start at 30°.
The animation uses a distance of 61% of the radius (at 100% the CoM would be on the Rim). When I changed that distance to 64% -to reflect KAS's mechanism- the needed weight for the arc needed to be doubled to make it able to go to the end. (I measured your radius at 80% ±1%)

This distance is also important because its changes the path of the main-weight being a cycloid at 100%, and a line at 0% - plus a skewing factor because of the slope.
And this path is important because even the (actually amazingly) small deviations in GPE, can make it work or not, and results in a variety of (KE+RKE)-values.
And the 30° (or so) angle is (probably) more important because it almost ensures the small loss in GPE.

It's possible the KAS-mechanism is as efficient as you can get: In terms of GPE vs (R)KE.

Before you calculate your spiral-path you first need to determine its required initial speed: because (as far as my simulation shows, which might be correct or not) the KAS-mechanism makes the Main weight dip first. And then determine the allowed loss in GPE of the arc and then assure all velocities of that system along that path to be positive. Meaning: the Main-weight could be made to go purely horizontal, but it requires the arc to make a dip in height and eventually climb a hill again, which could be too steep. All combine: not an easy task I think.

* Your maths skills would be appreciated...!!
Assuming I didn't make a mistake, this is the math:

For a slope (just for testing purposes), Direction =Right-top to Left-bottom
x = -r·&#946;·cos(&#945;)
y = -r·&#946;·sin(&#945;)

&#945; : slope angle (rad)
&#946; : rotation of the arc: 0..&#960;
r : arc radius
a rotation of 1·&#960; becomes a distance of r·&#960;

To make the Main-weight keep its vertical position, the slope path should be:

x= -r·&#946;·cos(&#945;)
y= N·r·(cos(&#946;)-1)

&#945; : slope angle (rad)
&#946; : rotation of the arc: 0..&#960;
r : arc radius
N : fraction of the arc-radius ( about 0.8 in your case)
x : the same as for the simple slope
y : Actually the motion of the Main-mass on a slope, but sign reversed to compensate.

- I didn't check if some other part of the arc collides with some other part of that path.

Add:
Just realised I just naively adjusted the height, while the path length should be Pi ... hmm

[mickegg]

Thanks ME

That'll take me a while to digest.

Regards

Mick

[ME]

I like your [Mickegg's] suggestion to utilise an arc profile that ties the weight path to a more linear moment.

Attached is a path-profile for a 30° ramp and the MainWeight CoM at 80% of the radius.
In Green a straight ramp profile,
In Blue the faulty one (that previous sin/cos stuff) where the profile length exceeds Pi (so don't use it)
In Red a numerically determined profile (I'm also not a mathematician: Thus no formula, but I could find one that's close)
The regression-line/formula gives a means to somewhat copy that curve, but it's a terrible estimation at both the start and the end.

The Green-profile stops at [-pi*cos(30), -pi*sin(30)]&#8776;[2.721 , -1.571]
The Red-profile stops at [-2.553 , -1.6]

[WaltzCee]

Thanks ME

That'll take me a while to digest.

Regards

Mick

I seriously doubt I'll live long enough to digest it. Just sayin'.

[KAS]

It's possible the KAS-mechanism is as efficient as you can get: In terms of GPE vs (R)KE.

Come on ME! Where's you sense of invitation? This is nowhere near as efficient as you can get.

The reason I think we have a head start with this concept compared to our other attempts is two fold;
(a). It is Pivotless. Nearly everything we've tried in the past involved movement of mass about a static point or pivot. Let's face it, it has to be connected to a secondary device in some way. This design has turned that on its head by ensuring that the contact anchor point is fluid and free to find its own position.
(B) secondly, it is vertually friction free. If we discount air resistance for a moment, I have never been able to reduce contact friction to this low level before which has to be encouraging.

This concept is only in its infancy and is ripe for development.

I don't have a drawing package on my iPad but I will sketch a drawing and post it later which should take this to the next stage which (if successful) may ruffle a few Newtonion establishments feathers along the way. This is because I may have discovered a way to raise (yes raise!) the weight to a higher level and only by utilising the Ke generated by the same weight. Blimey, this can send you nuts!