Tensile Strength Tether

GRAV_STD = 9.80665; // m/s2
MUL_KILO = 1000.0;
MUL_MEGA = 1000.0*1000.0;
MUL_MILLI = 1.0/1000.0;
MILLIMETER_PER_METER = 1000.0;
MM2_PER_M2 = 1000.0 * 1000.0; // millimeter² per m²
M3_TO_CM3 = 1000000.0; // cubic meter to cubic centimeter: (100*100*100) = 1 million
SEC_PER_HOUR = 3600.0;
function KgToNewton (kg) { return kg*GRAV_STD; }
function CircleAreaFromRadius (r) { return Math.PI * r * r; }
function CircleAreaFromDiameter (d) { return CircleAreaFromRadius(d*0.5); }

EARTH_RADIUS_KM = 6371.0; // MEAN
EARTH_RADIUSEQ_KM = 6378.1; // Equatorial
EARTH_CIRCUMFERENCE_KM = 2.0 * Math.PI * EARTH_RADIUS_KM;
EARTH_SURFACE_SPEED_EQUATOR_KM_PER_SEC = EARTH_CIRCUMFERENCE_KM / (24.0 * SEC_PER_HOUR);

function f0 (f) { return Math.round(f); }
function f1 (f) { return Math.round(f*10.0)/10.0; }
function f2 (f) { return Math.round(f*100.0)/100.0; }
function f3 (f) { return Math.round(f*1000.0)/1000.0; }

// console.log("EARTH_SURFACE_SPEED_EQUATOR ="+EARTH_SURFACE_SPEED_EQUATOR_KM_PER_SEC+" km/s");
// console.log("ghoulspace N/kg="+KgToNewton(1)+" pi="+Math.PI);
// console.log("ghoulspace circle 1 meter = "+CircleAreaFromDiameter(1.0));
// console.log("");

// tenstr in MPa (megapascal, 1 Pa = 1 N / m²)
// density in g/cm³
function MatTestPayloadAlt (payload_kg,altitude_km,name,tenstr,density)
{
	var diam_mm = 0.5;
	var restlen_km = altitude_km;
	var weightsum_kg = payload_kg;
	var altsum_km = 0.0;
	var bFirstSec = true;
	while (true) {
		diam_mm = diam_mm * Math.sqrt(2.0);
		var dia_m = diam_mm * MUL_MILLI;
		var area_m2 = CircleAreaFromDiameter(dia_m);
		var tenstr_pa = tenstr * MUL_MEGA;
		var brforce_n = tenstr_pa * area_m2;
		var brweight_kg = brforce_n/GRAV_STD;
		var volume_per_meter_in_m3 = area_m2*1.0;
		var weight_per_meter_in_kg = density * (volume_per_meter_in_m3 * M3_TO_CM3) / MUL_KILO;
		var weight_per_km_in_kg = 1000.0*weight_per_meter_in_kg;
		var brlengthE_km = (brweight_kg) / weight_per_km_in_kg; // wiki number total
		var brlength_km = (brweight_kg - weightsum_kg) / weight_per_km_in_kg;

		if (brlength_km < 0.0 && bFirstSec) continue;
		if (brlength_km < 0.0) { console.log("MatTest "+name+" d="+diam_mm+"mm: fail brkg="+brweight_kg+" wsum="+weightsum_kg); break; }
		bFirstSec = false;
		var uselen_km = brlength_km;
		if (uselen_km > restlen_km) uselen_km = restlen_km;
		altsum_km += uselen_km;
		restlen_km -= uselen_km;

		var useweight_kg = uselen_km * weight_per_km_in_kg;
		weightsum_kg += useweight_kg;
		console.log(" section "+payload_kg+"kg "+altitude_km+"km "+name+" d="+f2(diam_mm)+"mm (br="+f0(brweight_kg)+"kg) x "+f0(uselen_km)+"km ("+f0(useweight_kg)+"kg) tether="+f0(weightsum_kg-payload_kg)+"kg");
		if (restlen_km <= 0.0) {
			console.log("MatTest "+payload_kg+"kg "+altitude_km+"km "+name+" ("+tenstr+"MPa "+density+"g/cm^3 bL="+f0(brlengthE_km)+"km) d="+f2(diam_mm)+"mm tether="+f0(weightsum_kg-payload_kg)+"kg");
			break;
		}
	}
	// console.log("");
}

function MatTest (name,tenstr,density)
{
	MatTestPayloadAlt(500.0,350,name,tenstr,density);
}

MatTest("Zylon",			5800.0,1.56);
// MatTest("Aramid(Yield)",	3620.0,1.44);
// MatTest("Dyneema",	3600.0,0.97);
// MatTest("Kevlar",	3620.0,1.44);
// MatTest("Vectran",	2900.0,1.40);