Code to model a simple BeanStalk

100 REM Material Strength Density
110 REM ======== ======== =======
120 REM Steel Wire 340-2100MPa 7.8
130 REM Carbon Fiber 3000MPa 2.0
140 REM
150 REM

160 DEFDBL A-Z : REM Define all variable as double precision.

170 REM Earth Gravity are sea level in Meters per second/per second.
180 Gravity = 9.8 : OldGravity = Gravity
190 REM Pi Circumference / Diameter of a Circle.
200 Pi = 3.1415926
210 REM Earth's Radius in meters.
220 EarthRadius = 6.4 * 10^6
230 REM BeanStalk point being calculated.
240 BeanStalk = EarthRadius
250 REM Length of step used to model BeanStalk in meters.
260 BeanStep = 10^3
270 REM Density of material BeanStalk is made of.
280 BeanDensity = 2.0
290 REM Strength of BeanStalk material in Pascals per square meter.
300 BeanStrength = 10*10^9
310 REM Strength per square centimeter.
320 BeanStrength = BeanStrength / 10000.0
330 REM Pretension on cable at bottom in Pascals.
340 BeanStalkTension = 1000 * Gravity
350 REM Total mass of BeanStalk in Kilograms.
360 BeanStalkMass = 0.0
370 print "Distance CrossArea TotalMass LocalG OrbitG"
380 REM Calculate the cross-section of the BeanStalk in square centimeters.
390 BeanStalkArea = BeanStalkTension / BeanStrength
400 REM Next segment up BeanStalk.
410 BeanStalk = BeanStalk + BeanStep
420 REM Mass of BeanStalk segment in kilograms.
430 SegmentMass = BeanStalkArea * BeanStep * BeanDensity / 10.0
440 REM Speed of top of segment in meters per second.
450 BeanStalkSpeed = 2.0 * Pi * BeanStalk / 86400.0
460 REM Earth's Gravity accellaration
470 LocalGravity = Gravity / ((BeanStalk / EarthRadius)^2)
480 REM Centripetal force outwards countering Earth's Gravity.
490 OrbitalAccell = BeanStalkSpeed * BeanStalkSpeed / BeanStalk
500 LocalGravity = LocalGravity - OrbitalAccell
510 REM Weight new segment given in Pascals(Tension on BeanStalk).
520 SegmentWeight = SegmentMass * (LocalGravity + OldGravity) / 2.0
530 OldGravity = LocalGravity
540 REM Sum up the total mass used.
550 BeanStalkMass = BeanStalkMass + SegmentMass
560 REM Add additional tension.
570 BeanStalkTension = BeanStalkTension + SegmentWeight
580 print (BeanStalk-EarthRadius)/1000; BeanStalkArea; BeanStalkMass;
LocalGravity; OrbitalAccell
590 if LocalGravity 0 then goto 380
600 print "Distance CrossArea TotalMass LocalG OrbitG"
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Earl Colby Pottinger wrote:
590 if LocalGravity 0 then goto 380

You don't terminate the beanstalk at this point.
You terminate it when the tension meets the pull of the counterweight
you plan to install, or for overall minimum mass simply keep doing the sums
out until the tension falls to a similar level to the initial preload on
the bottom, and there put a tiny counterweight.

--
http://inquisitor.i.am/ | | Ian Stirling.
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