"Rapid Transit" Space Elevator Still Looks More Like Fiction

I’ll begin with the design of a modest-sized unit that is about half the size of the often-recommended 20-ton elevator carriage, which is imagined to be able to carry a 17-ton payload up in only a week.  (Which I believe impossible)

First, in order to ascertain the starting speed to drive the elevator all the way up an accelerating path to the top while gravity effects diminish to zero, we need to accurately plot out this path of variable gravity.  So, I designed a computer program to trace the path 10 miles at a time, with a new calculation of gravity pull and resultant speed in each of 2,175 steps from ground to orbit.  A speed limit is provided, usually run at 130 MPH, since that has already been suggested and probably will be necessary to prevent traction and stability problems in the drive mechanism.  In order to approach the desired transit time of one week, I ran the simulator with a starting speed of 65 MPH, and it got to 130 MPH at an altitude of 1,630 miles and went the rest of the way at that speed for a 7.2 day trip.  This simulation only shows the ideal time with perfect power transmission and does not include any real-world interferences with power.  So, here are the steps in the design:

  1.  For a simple model, let’s start with 10 tons as a full-load limit and a speed of 65 MPH at ground level.  
  2.  That would take 3,467 HP to lift 20,000 lbs. straight up at 65 MPH from earth’s surface.  We have to allow for at least an estimated 25% inefficiencies in the rollers and drive train, which brings the motors up to 4,622 HP to do the job.  Allowing 15% inefficiency in the motors, it would take about 4 MW of electrical power out of the photovoltaic cells to drive them.  The completed system may need more than that to overcome all the actual inefficiencies, but this will do for the present analysis.
  3.  Now, with the total power known, the photovoltaic cell array can be developed from there, coordinating the voltage and current of the array with motor requirements.  For a rough guide, the best practical solar cells I’ve seen reports on have an efficiency of about 42%.  Here, I’m assuming laser energy to be equivalent to the sun on solar cells.  Any improvement of laser energy over solar energy would upgrade this estimate in favor of a smaller array, of course.

On this basis, I would estimate that the area of the photovoltaic cell array would have to be about 9,500 square meters to provide the 4 MW of electrical power.  That’s the area of a square that is 320 ft x 320 ft.   Then I looked up commercial solar panels to get an approximation of weight per square meter.  One typical panel was 1.64 meters by .992 meters that weighed 20 kg.  So, I applied the math:  (9,500 x 20 x 2.2) / (1.64 x .992) = 256,934 lbs.  That monstrous array would weigh over 128 tons!  WHOOPS–we lost control of the weight!

Not only are we more than twelve times overweight on the photovoltaic cell array alone, but that doesn’t even include the 320 ft x 320 ft framework that would hold all those panels together, nor the wiring to handle 4 MW, and we haven’t added that 4,622 HP worth of electric motors in yet.  This study shows that it is a physical impossibility to power a 10-ton space elevator with laser power into photovoltaic cells and make it move up the tether at 65 MPH from ground level.  It turns out that the two main power elements, the motors and the photovoltaic array, are also the predominant factors that control the weight of the elevator.  Therefore, the limits on this design will affect every design at any size level.

Bad news, but all is not totally lost.  We could just scale the whole project down to get the weight to come out at 10 tons.  However, to continue this example, we simply have to gear the drive system down for extra torque and a slower start.  Let’s also assume that diligent special design of the array and its support bracket constrain the weight and that the motors totaling 4,622 HP don’t add much more than 10 tons, for an estimated total weight with operator and supplies at 150 tons.

Now, we end up with an elevator that can start out at 10/150 x 65 MPH = 4.33 MPH.  A run through the simulator, starting at 4.33 MPH, ends up with a total transit time of 4.3 weeks [30.4 days].  It finally attained its maximum speed of 130 MPH at an altitude of 12,500 miles, after 27.5 days had gone by.  Then, it traveled for over 9,000 miles at that speed to reach orbit altitude.

Conclusion:  

  With current photovoltaic cells and electric motors, it is not feasible for an elevator driven by laser power to ascend all the way from earth to orbital altitude in as little as two weeks.  The weight-limited starting speed under 5 MPH is the major bottleneck, and it will substantially impact all designs.  This example shows a full month in transit, and little improvement can be made on this time with present-day materials.  It must be kept in mind that this example is an ideal case with the best possible time, and does not include any of the hazardous interruptions of power cited in my original article.  Obviously every one of those interferences would extend the transit time even further out.

— EngrGene