Does the space elevator concept violates laws of physics?

[vgorelik]

Conservation of angular momentum (L=I x W), I – moment of inertia and W is angular velocity.<br /><br />An object on the surface of rotating body (Earth) has angular momentum associated with the object’s mass and its distance from the axis of rotation. Space elevator requires that the object’s angular velocity around the Earth’s axes remains unchanged as it (object) is being hoisted to the geo-stationary orbit. To preserve the conservation of angular momentum, the payload of the elevator would have to accelerate it’s rotational motion around the cable from 0 rad/sec at the surface to a very high RPM tearing the payload apart.<br /><br />I wonder, how the space elevator proponents intend to address this issue? <br />

 

[vogon13]

The earth, tether, and the tether's anchor mass constitute a closed system. Angular momentum is conserved, but would be redistributed amongst the components. I anticipate deflection of the tether (this, I think, is the consequence of your point) will be monitored, if it becomes excessive, the lift/lower speed will need to be decreased.<br /><br /><br /><br /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[vgorelik]

The elevated/descending payload is loosely coupled to the system. It will behave similar to the water or air particles forming vortex when going down into the sink or raising up when hurricanes form.

 

[rocketman5000]

you are rotating about the wrong axis

 

[vogon13]

Keep in mind, the tether can deflect miles (at the midpoint) and the bending stresses on the material, since they are distributed over such vast distances, are negligible.<br /><br />Should the tether develop 'standing waves' (or a 2 dimensional analog) the motions can be damped out by varying the lift/lower rate.<br /><br /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[josh_simonson]

Each payload that the elevator lifts will get it's energy from the earth's rotation, and eventually the rotation of the earth would slow down to the point where the elevator would fall, but the amount of material to climb the elevator would be astronomical for this to happen. Material sent down the elevator would speed the earth's spin up (like a figure skater pulling their arms in during a spin), so as long as what goes up is equal to what goes down the elevator could be used indefinitely.

 

[vgorelik]

Both - the energy and the momentum of the closed mechanical system must be preserved.<br /><br />Yes, energy/momentum of the entire Earth/tether/payload/counterweight system remains unchanged as the payload goes up or down. The problem, however, is that the payload is loosely coupled to the system via flexible tether and, as it moves along it, it will tend to preserve its rotational momentum as it used to be on the surface.<br /><br />Momentum is a vector. While the energy is applied to increase the payload's distance from the center of Earth and its angular velocity around Earth is forced to remain constant (by definition of the Geo-stationary destination point and fixed anchor,) the payload will tend to accelerate its spin around the tether to keep its rotational momentum the same as it was on the surface. <br />

 

[vogon13]

I am having trouble understanding just what you think the tether malfunction will manifest as.<br /><br />Angular momentum is transferred to the rising payloads or subtended from the lowering payloads via a mostly linear deflection of the tether. This effect is well understood and can be controlled via observing the tether system and modifying the lift schedule and/or lifting and lowering rates.<br /><br />IIRC, Arthur Clarke was well aware of these constraints in his (somewhat less than 100% fictional) Fountains of Paradise. He even understood how a tether could be used at Mars, without moving Phobos!<br /><br /><br /><br /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[halman]

vgorelik,<br /><br />You keep saying that the payload 'will spin around the tether,' implying that the payload is attached to the tether by a loop going around it, and lifted by a second tether. This is not correct. The payload is lifted by motors in the carrier, which grip the tether. The tether will bend slightly, but not spin. Energy is imparted to the payload, by the carrier vehicle, as it climbs. Conversely, when a payload is coming down the tether, energy is absorbed by the carrier vehicle, and stored, or transmitted back into the electrical system of the elevator.<br /><br />There are descriptions of the space elevator concept available which range from simple, (Clarke's "Fountains Of Paradise,") to the most advanced mathematical papers. Look up the ones that you feel comfortable reading, and study the concept and how it works.<br /><br />By the way, welcome to Uplink, the SDC discussion boards! <div class="Discussion_UserSignature"> The secret to peace of mind is a short attention span. </div>

 

[alokmohan]

Is it not a lift actually?

 

[vgorelik]

OK, I guess I should be a little more explicit.<br /><br />It appears to me that the concept works under one condition – the entire system never leaves the Earth’s equatorial plane to make sure that the Coriolis forces applied to the payload are always zero. Unfortunately, in case of Earth/Moon/Sun/Counterweight system you will get precession that will deflect the counterweight from the Equatorial plane creating Coriolis force applied to the payload and forcing it to rotate around the tether. That was my concern.<br /><br />I apologize for not mentioning this in the original post <br />

 

[willpittenger]

That's why it's called an "elevator". <div class="Discussion_UserSignature"> <hr style="margin-top:0.5em;margin-bottom:0.5em" />Will Pittenger<hr style="margin-top:0.5em;margin-bottom:0.5em" />Add this user box to your Wikipedia User Page to show your support for the SDC forums: <div style="margin-left:1em">{{User:Will Pittenger/User Boxes/Space.com Account}}</div> </div>

 

[spacechump]

<i>Unfortunately, in case of Earth/Moon/Sun/Counterweight system you will get precession that will deflect the counterweight from the Equatorial plane creating Coriolis force applied to the payload and forcing it to rotate around the tether. That was my concern. </i><br /><br />Do you mean both payload and tether spin around the axis of the tether like a stretched string that is given a circular motion? You're always going to get a Coriolis force as the payload rises. But it's pulling it West, not in a circle.

 

[halman]

vgorelik,<br /><br />Not being a mathematician, I have not the qualifications to respond to your question. However, as I recall, location of the Earth terminus within 1 or 2 degrees of the Equator is essential, and there are some equatorial sites which are unsuitable due to variations locally in the Earth's gravity field.<br /><br />The counterweight is supposed to be able to keep adequate tension on the tether to prevent the orbital terminus from wandering out of the desired location, although I am not sure if some station keeping might be required.<br /><br />Until we can actually deploy a tether from the Clarke orbit to the Earth's surface, all discussion of the space elevator concept is going to be theoretical. Coming up with a material which will not separate under its own weight is the greatest challenge facing the construction of a space elevator, which is not likely to be overcome any time soon. The carbon nanotube has the most promise, but, so far, lengths of less than a centimeter are the maximum that has been achieved, so far as I know. Probably, fabricating the tether will have to be done in a microgravity environment, so we will have to wait until launch technology has advanced somewhat before we can make it obsolete.<br /><br />Also, a sufficient quantity of carbon will have to be found in space, and relocated to the fabrication facility, in all probability, as lifting the amount of carbon to the Clarke orbit will be prohibitively expensive. The exact amount escapes me right now, but I believe that it is several thousand tons.<br /><br />Construction of a space elevator is definitely going to have to wait until our abilities have improved considerably. <div class="Discussion_UserSignature"> The secret to peace of mind is a short attention span. </div>

 

[vgorelik]

spacechump, Halman:<br /><br />I see your points and agree with them.<br /><br />However, another problem still remains - it looks to me that to keep the counterweight in the equatorial plane, its orbit must be frequently compensated, because if not, it will swing ~+-15 degrees' from North to South during a twelve month cycle. The question remains - how much energy you would need to spend for such orbital adjustments considering the mass of the counterweight? Would it be the same or greater amount that is required to lift the payload with future launch systems?<br />