SPACE ELEVATOR DEPLOYMENT FROM GEO ORBIT
This is one of many schemes that have been put forth to accomplish deployment of the space elevator. It starts with a large satellite positioned at GEO. This GEO satellite is constructed from sub-components delivered to GEO via (more or less) conventional rocket launches, and contains:
a. The Ribbon.
b. The Lower satellite. An earth-seeking guidance and control module, that delivers the bottom end of the ribbon to its anchor point,
c. The Upper satellite. A ballast-seeking guidance and control module, destined to become the ballast mass for the space elevator, and that also manages ribbon deployment rate.
As the ribbon deploys downward from GEO, these opposite-end modules perform a delicate guidance and control dance, to wit:
- as the lower satellite progressively moves deeper into the Earth's gravity well of ever increasing magnitude (thus creating downward force on the system), - the upper satellite must then move to ever higher altitudes creating a correspondingly greater centrifugal force to counter the increasing gravity pull.
The Control Task
The control task of the "upper" and "lower" satellites consists of 2 activities:
a. Altitude control, which is a combination of both vertical thrust adjustments and precise control of the amount of ribbon being deployed; this performs the "vertical balancing act".
b. Tangential thrusting (ie. thrust normal to the radial) to provide "make-up" in tangential velocity to keep each satellite's tangential velocity consistent with its altitude.
The series of animations below depict the natural tendencies of this process, as well as portrays examples of control schemes that produce failure modes, and finally, depicts how the deployment would appear when successfully accomplished.
Note 1: In ALL animations the time frame is highly accelerated; at the bottom will be seen a digital time stamp in which the leading digits will represent (obviously) "days" or "seconds" into the deployment (a normal deployment via this scheme takes 15 days).
Note 2: In ALL animations the eye is fixed in a frame that is rotating with the earth, thus the earth appears stationary (non-rotating) in these animations.
Note 3: In ALL animations, the main window eye point is looking down on the south-pole, thus you see the Antarctica land mass (mid-Pacific ocean area is at the top of the globe).
Note 4: In 3-View animations, the Upper-RH window eye point is located on the equator, and looking down onto South America; The Lower-RH window eye point is located above, and somewhat south of the initial GEO satellite position (note: the equator is tiled at 45 deg to the window frame).
Note 5: The ribbon will exhibit various shades of red during deployment operations to depict tension along the ribbon.
- "High intensity red" color depicts greater (maximum) tension,
- "Shades of pink" would depict intermediate tensions, and,
- "Pure white" would depict no (or very low) tension
Note: the notably active pendulus motions at the beginning of some animations is indeed intended, since it is a low fuel mechanism to start initial deployment of such a system. The mechanism of tether dynamics ensures that these initial motions will soon subside to insignificant import (the so-called "skater's effect").
1. The animation below shows the natural dynamic tendencies that will prevail if one were to simply start dropping the ribbon directly down towards Earth from GEO, using no compensating control interventions by the satellites at either end of the ribbon. It is seen that the entire system will progress westward, eventually plunging to Earth.
No Tangential Control
2. The animation below shows what would happen, if no Tangential Thrusting control mode were present - but with the "vertical control mode" remaining active; this indicates the importance of maintaining the proper centrifugal equilibration of gravity.
Fly-Away Control Failure
3. The animation below shows what happens when the control algorithm fails to maintain the proper bite into the gravity well to equilibrate the fly-away tendency of centrifugal effects, eventuating in a fly-away failure of the entire system.
Earth-Crash Control Failure
4. The animation below shows what happens when the control algorithm deploys into the gravity well faster than the upper-end module can gain altitude to equilibrate the increasing gravity load, eventuating in a crash-to-Earth of the entire system.
Controller Goes Resonant with 1st String Mode
5. The animation below shows how a controller design can interact adversely with the 1st string mode of the ribbon. Of interest is the resonance that develops fairly abruptly between the controller and the ribbon dynamics as the ribbon length and tension combine to create a critical frequency coalescence.
Controller Interacts with Transverse-Modes
6. The animation below shows how a controller design can interact adversely with the transverse string modes of the ribbon. Here, trouble is evident from the outset (unlike the previous animation where a resonant coalescence of frequencies occurred fairly abruptly). The controller starts exciting higher-frequency string modes early in the deployment, and everything degenerates from there.
Control System Slug-Fest
7. The animation below shows the two deployment controller modes (gravity -vs- centrifugal effects) at war with one another.
Control Software Bug Exposed
8. The animation below shows how solution-animations are helpful in detecting software bugs (in this case, in the controller logic).
Successful Deploy to Earth
9. The animation below shows a successful deployment to Earth. In particular, note how much faster the ballast must gain altitude to continue equilibrating the lower end that is becoming deeply embedded in the gravity well'. Near the Earth, small changes in altitude result in geometrically increasing gravity levels, while the increases in centrifugal forces is merely linear with altitude at the ballast.