# How strong does the Space Elevator tether need to be – Part 2

In my previous post, I referred to Spaceward CEO Ben Shelef’s document (The Space Elevator Feasibility Equation) as a basis for discussing how strong a Space Elevator tether really has to be and I wrote this; “The answer to this question relates to how strong the climber power system is.  The stronger the power system is, the weaker the tether can be (and vice-versa).”

Why is this so?  Well, let’s look at an example.

Say you have a tether which is rated at 30 tons.  What this means is that you can have up to 30 tons of Climber/Payload weight on the tether at any one time.  Does this mean that you can only have one 30-ton Climber (or three 10-ton Climbers or six 5-ton Climbers) on the tether at one time?

The answer is no – you can have more than 30 tons of mass on the Climber at one time and the reason for this is the Climber, as it ascends, weighs less and less (though its mass, of course, never changes).  This is due to the force of gravity weakening as you get farther and farther away from earth.  So, a Climber which weighs 30 tons at ground zero will only weigh only half as much (15 tons) when it gets to 2,624 kilometers in height (where the force of gravity is one-half that at ground level).  When the Climber ascends to 6,400 kilometers, the Climber will weigh only one quarter as much (7.5 tons) and so on.  So this means that when a 30 ton Climber ascends to 6,400 kilometers (and weighs only 7.5 tons), you can then launch another Climber weighing 22.5 tons.  When that Climber gets to 6,400 kilometers (and the first one launched is now at 12,800 kilometers), the total Climber weight on the tether is now 10.8 tons (1/4 of 30 tons plus 1/9 of 30 tons) which means you can launch another 19.2 ton Climber (note that the Climbers will weigh even less than I’ve indicated as they ascend due to centrifugal force, but that factor doesn’t become significant until you get close to GEO and so I’ve ignored it here).

As you can see, one can play with these numbers in several different ways to get different launch schedules, but the bottom line is this; you can launch any number of Climbers you want to on this 30-ton rated tether as long as the total weight of these Climbers (as opposed to the total mass of these Climbers) does not exceed 30 tons.

From this, it should be pretty clear that it is advantageous to have the Climbers ascend as rapidly as possible.  The higher they ascend and the quicker they do so, the sooner you can launch another significant Climber.  And this brings us back to the statement; “The stronger the power system is, the weaker the tether can be”.

The stronger your power system is (with all other things being equal), the faster your climbers can ascend (up to a limit, of course).  So, if your goal is to get 20 tons to GEO every day, you need, say, a 30 ton rated tether with a power system strong enough to propel a 20 ton Climber at least 2,624 kilometers per day, or, you can have, say, a 60 ton rated tether with a weaker power system just able to propel a 20 ton Climber at least 1,312 kilometers per day.  Both tethers will do the job, but it’s certainly going to be easier (and faster) to build a 30-ton rated tether than a 60-ton rated one.  And what if a 60-ton rated tether is just not possible?

The stronger the power system is, the weaker the tether can be”.

Not only would we LIKE to lift the maximum amount possible on any specific tether, it is also going to be NECESSARY to lift the maximum amount possible on any specific tether.  This is because there are ‘housekeeping chores’ which will consume a very significant fraction of a Space Elevator’s capabilities, housekeeping chores which, if not done, will mean a Space Elevator will simply not be viable.  I will talk about these housekeeping chores in my next post.

(Picture of Stone-Wales defect from here – click on it for a slightly larger version)

## 4 thoughts on “How strong does the Space Elevator tether need to be – Part 2”

1. Aaron

My worry would be a weak elevator that never becomes a strong one (for bureaucratic reasons). The Space Shuttle was supposed to lift cargo at \$400 a pound, and that just didn’t happen.

A 50 gp tether strength should probably be the minimum goal to help reduce costs.

Although I might be completely wrong, and CNT strength will only improve whether an elevator is built earlier rather than later… but I’d still hate for the thing to be put up and then have no cost benefits over rockets.

2. donald Longerbeam

When an elevator climbs up the cable, its apparent weight is more than what it weighs. Acceleration up the cable equals more weight on the cable. So if the “strength” of the energy/motor system allows the elevator to accelerate very quickly, then the cable must be stronger,not weaker. Assume that you have a cable that can just support a 30 ton climber. That climber cannot move up the cable because as soon as it begins to move, it “looks” like a 31 ton climber and the cable will break. So — the more powerful the beaming system/motor combination, the stronger the cable needs to be in order to sustain the climber as it ascends. And the faster it ascends, the stronger the cable needs to be.

3. Herby Sagues

@Donald:
No. You are talking about the climber’s acceleration, and given the speeds involved that’s not a problem. You could accelerate the climber initially through ground-based structures (e.g. a tower) so it reaches its intended speed and maintains it through the climb. In that case, the weight of the climber (plus some amount of air friction) is the only load to worry about. More powerful motors don’t negatively impact the load needed.
But my concern with all these calculations is that they assume that the elevator will be built from earth up, whereas the most likely implementation would be an elevator built from geostationary orbit down. Getting the necessary materials to geostationary orbit would be definitely expensive, but given the tether weight to load capacity ratios, it would pay for itself quickly, even if the materials were brought from earth (as opposed to being captured from a small comet remnant deviated to pass through earth’s atmosphere to slow down and put into geosynchronous orbit). Putting a carbon nanotube or graphene factory in space is likely much easier than building the tether in phases.
OTOH, building the tether in phases could allow for a large number of low-capacity tethers, which could give the system much more resilience, I don’t know if that’s the point being made.