redbull stratos fall simulation

fall.js

// redbull stratos fall simulation 
// node fall.js > fall.json
//
// port to js from python by @pybonacci
// more info: http://pybonacci.wordpress.com/2012/10/15/el-salto-de-felix-baumgartner-en-python/ 
//

// >> [ std_atm.alt2density(h, alt_units='m', density_units='kg/m**3') for h in xrange(0, 43000, 1000)]
// air density each 1000 meters 
var AIR_DENSITY = [1.225, 1.1116425767380347, 1.0064902527218418, 0.9091220810460088, 0.8191294202172186, 0.7361158590983954, 0.6596971404886504, 0.5895010832794331, 0.5251675031230921, 0.4663481315454516, 0.41270653342889785, 0.3639180227868754, 0.3108281589022067, 0.2654832635841079, 0.22675346883692057, 0.19367373647373748, 0.16541981206327336, 0.14128768681425868, 0.1206760556449457, 0.10307133434187116, 0.08803486247736621, 0.07487366111494297, 0.06372734460638993, 0.05428027105802167, 0.046267360336640966, 0.039465817649795336, 0.03368824062938579, 0.02877687388504317, 0.024598816068418232, 0.021042018277291016, 0.018011940446444, 0.01542875529531276, 0.013225008308169557, 0.011261986276505282, 0.0096088887240681, 0.00821392101750628, 0.007034412466278842, 0.0060351284310494364, 0.005186909284991773, 0.004465570167211259, 0.0038510093666613036, 0.0033264840369233825, 0.0028780204548397533];

var ALTITUDE = 39000;
var h = ALTITUDE;
var time = 0;
var velocity = 0;
var g = 9.81;
var C_D = 0.4;
var A = 1.0;  // m^2
var m = 80 + 20;  // kg: body + backpack


// return air density for altitude
function rho(h) {
  var i0 = Math.floor(h/1000);
  var i1 = i0 + 1;
  var r0 = AIR_DENSITY[i0];
  var r1 = AIR_DENSITY[i1];
  var t = (h - i0*1000)/1000;
  var d = (1 -t)*r0 + t*r1;
  return d;
}

var data = [];

function step(dt) {
  velocity += dt*(-g + rho(h) * velocity * velocity * C_D * A / (2 * m));
  h += velocity*dt;
  data.push({
    altitude: h,
    velocity: velocity,
    time: time
  });
  time += dt;
}

while (h>0) {
  step(0.5);
}
console.log(JSON.stringify(data));

For example: "If calculations prove to be accurate, and Felix is successful in his attempts to control his position, he will accelerate from standstill to the speed of sound - that's 0 to approximately 690 miles per hour in 40 seconds or less."

Taken from http://www.redbullstratos.com/science/speed-of-sound/