Maths Of Self-Propelling Spinning Radiating Helix Required

[common_sense_seeker]

Hi mathematicians,

I'm in need of some help in formalizing the dynamic model of a helix which radiates matter due to the centrifugal force of it's spin.

This simulation model from Wikipedia is a good starting point: Spinning Helix

Now imagine that particles are emitted radially from the edge of the helix loops. These particles will travel in a diagonal line due to the lateral motion of the hoops along the axis of spin in addition to the perpendicular lateral motion due to circular spin of the hoops. My hypothesis is that this dynamic model will induce a self-propelled helix which will move along the z-axis due to the reaction force of it's particle emission 'behind' it. For simplicity I wasn't intending to model the loss of 'mass' of the helix because it can be assumed that particles are absorbed back into the helix by an even distribution of incoming particles.

Does this make any sense to anyone?

 

[Uncle Pythagoras]

Neat! Is this for a liquid?, air? Quantum?

 

[origin]

Hi mathematicians,

I'm in need of some help in formalizing the dynamic model of a helix which radiates matter due to the centrifugal force of it's spin.

This simulation model from Wikipedia is a good starting point: Spinning Helix

Now imagine that particles are emitted radially from the edge of the helix loops. These particles will travel in a diagonal line due to the lateral motion of the hoops along the axis of spin in addition to the perpendicular lateral motion due to circular spin of the hoops. My hypothesis is that this dynamic model will induce a self-propelled helix which will move along the z-axis due to the reaction force of it's particle emission 'behind' it. For simplicity I wasn't intending to model the loss of 'mass' of the helix because it can be assumed that particles are absorbed back into the helix by an even distribution of incoming particles.

Does this make any sense to anyone?

Not really.

I think the diagram was trying to show simple hamonic motion.

I think any particles would be emitted perpendicular to the Z axis, so there would be no force in the Z direction.

Edit to add: In a viscous medium where only laminar flow can be developed a rotating helix would impart a force to the left due to shear. Actually a fish in a viscous medium where only laminar flow could be developed would not be able to propel itself through the medium. This is why sperm cells actually have a helical tail that rotates and not a tail that moves back and forth like a tadpole.

 

[Aqueous Id]

Does this make any sense to anyone?

There are two components for the motion of the ejected particle, radial and axial: v = (ωr)[sub]r[/sub] + v[sub]a[/sub], where ω is the angular velocity. You would have to provide more information as to the axial component.

 

[origin]

There are two components for the motion of the ejected particle, radial and axial: v = (ωr)[sub]r[/sub] + v[sub]a[/sub], where ω is the angular velocity. You would have to provide more information as to the axial component.

Why would there be an axial component? Wouldn't each individual atom in the helix be moving only in a ciruclar motion about the Z axis, assuming no preexisting axial movement of the helix?

 

[Aqueous Id]

Why would there be an axial component? Wouldn't each individual atom in the helix be moving only in a ciruclar motion about the Z axis, assuming no preexisting axial movement of the helix?

Hey Origin. Yes you're absolutely right. I had it in mind that this thing was screwing forward with some initial translation, but on second read I can see that there's no reason to assume so. Good catch! The naysayers should take note that Origin rules, while cranks just drool.

 

[Aqueous Id]

My hypothesis is that this dynamic model will induce a self-propelled helix which will move along the z-axis due to the reaction force of it's particle emission 'behind' it.

I think I see now what you mean by this, so the answer would have to be no. There can be no "behind" without an initial axial velocity and/or the presence of a fluid of some kind through which it can screw, for which case it needs a motor of some sort. Otherwise, as Origin noted, there is only a radial component. Assuming uniform loss of particles the net change in momentum, as far as axial propulsion is concerned, would be zero.

 

[common_sense_seeker]

Neat! Is this for a liquid?, air? Quantum?

Thanks for the vote of confidence. It's a conceptual model at the moment of the spinning radiating helix moving through empty space.

 

[common_sense_seeker]

There are two components for the motion of the ejected particle, radial and axial: v = (ωr)[sub]r[/sub] + v[sub]a[/sub], where ω is the angular velocity. You would have to provide more information as to the axial component.

There *is* an axial component. If it were just a circle which is spinning it would only radiate on the X-Y plane. Because the helix shape changes rotational momentum into lateral momentum, the same way an Archimedes screw lifts water, then the radiated particle also has this initial component in the X-Z plane. I imagine that the radiated particle would travel at 45 degrees if the two components are equal, which they appear to be. That's 45 degrees in the X-Y plane and 45 degrees in the X-Z plane.

 

[Ickyrus]

Sounds like he wants the math for a twin arm grass water sprinkler!

 

[origin]

There *is* an axial component. If it were just a circle which is spinning it would only radiate on the X-Y plane. Because the helix shape changes rotational momentum into lateral momentum, the same way an Archimedes screw lifts water, then the radiated particle also has this initial component in the X-Z plane. I imagine that the radiated particle would travel at 45 degrees if the two components are equal, which they appear to be. That's 45 degrees in the X-Y plane and 45 degrees in the X-Z plane.

Then you would not be talking about radiating you would be talking about displacement. Assume I had a 2 ft by 2 ft board with drops of water on it and the board was at a 45 degree angle to the Y axis and it was moving at V in the +Y direction. Now if that board were to be instantly stopped the water droplets would 'fly off' the board in the +Y direction only. This is akin to radiating.

If the same board with the same orientation was moving in the same directions and there were a bunch of ping-pong balls floating in it's path, the board would hit the balls and they would 'fly off' in the +Y directions and the X or Z direction (depending on the orientation) this is akin to displacement.

 

[origin]

Hey Origin. Yes you're absolutely right. I had it in mind that this thing was screwing forward with some initial translation, but on second read I can see that there's no reason to assume so. Good catch! The naysayers should take note that Origin rules, while cranks just drool.

Aww shucks, even a blind squirel...

 

[common_sense_seeker]

Aqueous, can you see the simplicity of what I'm proposing? Any point on the helix has a radial component of velocity as well as an axial component of velocity. If a particle departs from the surface of the point on the helix, then it will travel on the vector of these two components.

 

[common_sense_seeker]

Aqueous, can you see the simplicity of what I'm proposing? Any point on the helix has a radial component of velocity as well as an axial component of velocity. If a particle departs from the surface of the point on the helix, then it will travel on the vector of these two components.

The speed of rotation is greater than the speed of travel. Could the lateral speed be cosine 45 degrees, 0.707 times slower than the speed of rotation?

 

[Aqueous Id]

Aqueous, can you see the simplicity of what I'm proposing? Any point on the helix has a radial component of velocity as well as an axial component of velocity. If a particle departs from the surface of the point on the helix, then it will travel on the vector of these two components.

Whether or not it works as an Archimedes screw is up to you. For that you need Archimedes to turn the crank or an equivalent power source. And of course you need to immerse it in a fluid. If your screw is turning in a vacuum then it's not getting any traction if that's what you mean. For that case there is no axial velocity unless you launched it forward from another power source. I wasn't exactly sure what you were describing, so I left the axial velocity as something for you to specify.

As I understand now, this is an idealized object of some kind rotating on its axis in a vacuum and for some reason it's disintegrating. Unless you specify further then there is no other velocity component to consider. The thing just paints the cylinder of space around it with a helical ribbon of particles the same as it would if sitting still and emitting particles normal to the axis.

I guess since you were looking for the math which describes it, then I might need to clarify that rω is the magnitude of the velocity of each particle, but the velocity vector is r x ω, which is a vector cross product. Apply the right hand rule and you'll note that while particles paint space radially, each one is actually leaving at a tangent to the circular at the given point, but still normal to the axis. That is, there is no axial component to r x ω. Note you can reverse the sense of rotation and it merely throws the particles in the opposite direction. The net effect is the same then whether it's turning one way or the other or not at all (but still emitting).

The speed of rotation is greater than the speed of travel. Could the lateral speed be cosine 45 degrees, 0.707 times slower than the speed of rotation?

You can make it anything you want since it's yours. But first clarify whether it's immersed in a fluid. We can try to come up with an upper limit for a screw but the real deal will operate below the limit. I have a feeling that's not what you're after.

 

[common_sense_seeker]

Aqueous, see post #8.

(i) It's a conceptual model of a spinning helix in empty space.

(ii) It's analogous to an Archimedes screw but without the water.

(iii) The matter of a turning helix has two velocity components, one radially and one axially.

(iv) Get a bottle opener and see for yourself. Turn a corkscrew in your hand and FEEL the two components!

 

[Aqueous Id]

Aqueous, see post #8.

Ok but see post #7.

(i) It's a conceptual model of a spinning helix in empty space.

Ok so a vacuum. I'm on page with that now.

(ii) It's analogous to an Archimedes screw but without the water.

Then there is no analogy. It needs a fluid for that to apply.

(iii) The matter of a turning helix has two velocity components, one radially and one axially.

Only if it's screwing, which is impossible outside of a fluid.

(iv) Get a bottle opener and see for yourself. Turn a corkscrew in your hand and FEEL the two components!

Now take the corkscrew and turn it in the air and you feel nothing.

Now do this. Take a cylinder into orbit and set it into rotation (no translation) while it for some reason disintegrates. You'll get a uniform radial spread, but no axial component. Repeat the experiment, but this time mask off the entire cylinder with a sleeve. But give this sleeve a helical shaped window for particles to exit through. Same thing, right? They still leave radially with no axial component.

I'm saying radially when in fact each particle actually leaves tangentially in the direction of (r x ω). But the effect is the same insofar as sweeping the entire range from 0 to 2π.

 

[common_sense_seeker]

I give up on you. I've decided to email this author instead HOW DO PHOTONS TRAVEL?

Btw I think that a 45 degree angle might just mean 1/2 the force in the direction of travel. This would give the spin rate at twice the velocity.

 

[origin]

I give up on you. I've decided to email this author instead HOW DO PHOTONS TRAVEL?

This guy might actually agree with your premise, since he seems to just make all his stuff up there is no telling what he will accept.

 

[Uncle Pythagoras]

I give up on you. I've decided to email this author instead HOW DO PHOTONS TRAVEL?

Btw I think that a 45 degree angle might just mean 1/2 the force in the direction of travel. This would give the spin rate at twice the velocity.

You could have mentioned photons before. If you put photons in wormholes the energy is not escaping outwards it is trapped. In this scenario the photons act as clouds stretched out. But also at this scale you lose the smooth helix shape, and it becomes more angled to individual lines in linear directions. You sort of invert your image to threading of space with wormholes.