# Climber Dynamics

## Overview

This subject addresses a myriad of dynamics phenomena, including issues related to launching climbers, overall elevator response as climbers execute full-length excursions, stopping and starting climbers in transit, and finally response from emergency and malfunction conditions.

Of all the various subjects addressed in the related paper, only two animations are shown here since in general, these animations are not very entertaining to watch. However, the physical concepts relating to the dynamics of space elevator climber operations (portrayed by these animations) are so basic, yet counter-intuitive (and misunderstood), that much can be learned by studying these animations in conjunction with the explanations below.

Much more can be learned about these phenomena, including a detailed discussion of the mechanism by which a "climber actually climbs a ribbon", in the related paper (noted in the preceding web page).

## Commentary and Explanations

Most normal human experience related to "climbing ropes" is typified by just that, for instance, climbing a rope on a playground. In this case, the rope hanging above you has an extremely high spring rate (ie. it would take hundred's of pounds to stretch the rope even a fraction of a meter). Thus as you grasp the rope, and "pull down on it to pull yourself up", the rope stretch experienced by you is usually un-noticeable. Now, boldly extrapolating your rope climbing experience, suppose for example, that the rope were a thin rubber band, capable of supporting your entire weight, BUT, every bit as springy as a long rubber band. Then you would find that as you pull down on the rope to climb, little would happen UNTIL you had pulled down enough rubber band to create a net tension near your own weight. At this point you could very-slowly bounce up and down, and even start to ascend, BUT, you would have a large pile of slack rubber band at you feet!

This is similar to the situation that the space elevator experiences, in the sense that the spring rate of the ribbon (above the climber) is quite low (on the order of .04 N/m, or, 0.003 lb/ft ). This means that if an elevator ribbon were attached to the ground, you would have to pull down one-meter of ribbon in order to increase its net-tension by 0.04 N over what it was initially setting at (paraphrased, this means you would have to pull down over 300 ft of ribbon to increase its tension by 1 lb).

Climber Lift-Off & Arrest dynamics are dominated by this little recognized mechanism. Ultimately this phenomenon affects how fast a climber can be accelerated, as well as how much static tension must be in the ribbon; this speaks to the issue of an elevator's practical capacity. The term practical capacity addresses the issue of how much a "climber" can weigh and still be effectively launched from the elevator - or - phrased another way, what "percentage of the static elevator ribbon tension can a climber's weight be".

The degree to which the climber's weight is less than the static ribbon tension, is exactly the degree to which lift off acceleration can be immediately realized. When the climber's weight equals the static tension (ie. essentially, the "climber taking the place of the anchor"), then little immediate initial acceleration can be realized, and ensuing acceleration build-up will be very slow. In general, the ribbon tension "below the climber" at the launch-pad represents the upper limit of the amount of vertical force that can be quickly applied to a climber to accelerate it upward.

# The Animations

The location of the climber is noted as the juncture between two styles of ribbon-depiction).

The animations are shown in 2-D.

## Max Weight Climber Liftoff

In this animation, the climber's weight is essentially the same as the tension in the ribbon (just above the climber), thus the climber effectively functions as the anchor (ie. the ribbon between the climber and anchor has zero tension). This is not a configuration that would be considered as "operational", and is merely presented to illustrate a point. The animation time scale is sped up by a factor of 1000x.

- The animation starts with the climber stationary at the anchor position (on the green/black horizon), and starting to pull in ribbon from above at an ever increasing rate (ie. ramping-up the ribbon spooling rate).

- Early on, the climber experiences extremely low vertical acceleration. In this case of maximum liftoff weight, the climber is merely pulling in ribbon from above, and depositing it in a pile on the ground; this slack ribbon beneath the climber can be seen as the white ribbon-trace accumulating vertically under the climber (that has moved but imperceptibly vertically).

- This accumulation of slack ribbon continues until sufficient tension increase occurs in the upper ribbon to create noticeable acceleration (in the video); at this point the climber is seen to slowly start moving upward.

- Once the climber begins to move upward at a rate greater than the climber's ribbon spooling rate, then slack ribbon deposition ceases to grow; at that point in this animation (about an hour after launch has began), there has accumulated a total of over 40 km of slack ribbon beneath the climber! (you were warned this whole process is counter-intuitve, and beyond anything you can relate to your normal experience!). From that point on, slack ribbon starts to be picked up from below the climber.

- After some point in time, these extreme climbing transients stabilize and the ribbon goes taut beneath the climber.

- How this all can be avoided is explained and demonstrated in the related paper.

Viewed in 2-D Low Altitude

## Early Climber Arrest

In this animation, the climber has reached full transit speed of 200 km/hr, when, at 2 km altitude, ribbon spooling is instantly stopped (simulating, say, a climber mechanism malfunction). The animation time scale is sped up by about a factor of 10x.

- The climber will be seen to be decelerated to a stop within about 5 seconds of the spooling arrest; this high deceleration occurs because the high effective spring rate of the relatively short 2 km section of ribbon beneath the climber immediately responds to its material strain being rapidly increased corresponding to a stretch-rate on the order of 200 km/hr (55 m/sec), which of course is the climber's speed at this point.

- The climber is brought to a standstill within a few hundred meters. At this point, it has "dynamically over-shot" (corresponding to this being an impact load situation), thus it starts to accelerate back downward under the influence of both gravity and the (now) highly over-stressed lower section of ribbon beneath it.

- The lower ribbon almost immediately goes slack under the climber's abrupt acceleration back towards earth; this initiates a rebounding return back upward - except - this upward response is quite different than the initial downward response; this is because as soon as the lower ribbon has gone slack, it is only the upper ribbon (with its very low spring rate) that prompts the upward return, said return, then occurring at a significantly reduced rate, taking about a minute to complete (a full oscillation).

- Again, this animation illustrates the interlay of two vastly different ribbon spring-rates when the climber is undergoing near-ground operations.

Viewed in 2-D Low Altitude