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airdrop-model.js
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airdrop-model.js
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'use strict';
var Simulation = { };
var m = p.m;
var r = p.r;
var Cd = p.Cd;
var wx = p.wx;
var rp = p.rp;
var Cdp = p.Cdp;
var Fmax = p.Fmax;
var tfree = p.tfree;
var topen = p.topen;
Simulation.prototype.meta = {
parameters: [
{ name: 'm', label: 'm', stochastic: true, distribution: { type: 'triangular', min: 4, mode: 6, max: 9, mu: 0, sigma: 1 }, default: 6 },
{ name: 'r', label: 'r', stochastic: true, distribution: { type: 'triangular', min: 0.09, mode: 0.1, max: 0.11, mu: 0, sigma: 1 }, default: 0.1 },
{ name: 'Cd', label: 'Cd', stochastic: true, distribution: { type: 'triangular', min: 0, mode: 0.5, max: 1.0, mu: 0, sigma: 1 }, default: 0 },
{ name: 'wx', label: 'wx', stochastic: true, distribution: { type: 'triangular', min: 0, mode: 0.5, max: 1.0, mu: 0, sigma: 1 }, default: 0 },
{ name: 'rp', label: 'rp', stochastic: false, default: 0.5 },
{ name: 'Cdp', label: 'Cdp', stochastic: false, default: 1.75 },
{ name: 'Fmax', label: 'Fmax', stochastic: false, default: 300 },
{ name: 'tfree', label: 'tfree', stochastic: true, distribution: { type: 'triangular', min: 0, mode: 0.5, max: 1.0, mu: 0, sigma: 1 }, default: 0 },
{ name: 'topen', label: 'topen', stochastic: true, distribution: { type: 'lognoral', min: 0, mode: 0.5, max: 1.0, mu: 0, sigma: 1 }, default: 0 },
{ name: 'x', label: 'x', stochastic: true, distribution: { type: 'normal', min: -346, mode: -340, max: -334, mu: -340, sigma: 3 }, default: 0 },
{ name: 'y', label: 'y', stochastic: true, distribution: { type: 'normal', min: 497, mode: 500, max: 503, mu: 500, sigma: 3 }, default: 0 },
{ name: 'vx', label: 'vx', stochastic: true, distribution: { type: 'normal', min: 0, mode: 0.5, max: 1.0, mu: 50, sigma: 0.5 }, default: 0 },
{ name: 'vy', label: 'vy', stochastic: true, distribution: { type: 'normal', min: 0, mode: 0.5, max: 1.0, mu: 0, sigma: 0.5 }, default: 0 },
{ name: 'xmin', label: 'xmin', stochastic: false, default: -50 },
{ name: 'xmax', label: 'xmax', stochastic: false, default: 50 },
{ name: 'nsamp', label: 'nsamp', stochastic: false, default: 1000 },
]
};
Simulation.prototype.getLabel = function (name) {
this.metadata.forEach(function(group) {
group.params.forEach(function(param, i) {
if (name == param.name)
return group.params[i].label;
});
});
};
Simulation.erf = function(x) {
// from Chebyshev fitting formula for erf(z) from Numerical Recipes, 6.2
var a1 = 0.254829592;
var a2 = -0.284496736;
var a3 = 1.421413741;
var a4 = -1.453152027;
var a5 = 1.061405429;
var p = 0.3275911;
var t = 1.0 / (1.0 + p * Math.abs(x));
var y = 1.0 - (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1) * t * Math.exp(-x * x);
return Math.sign(x) * y;
};
Simulation.dudt = function(t, u, p) {
var m = p.m;
var r = p.r;
var Cd = p.Cd;
var wx = p.wx;
var rp = p.rp;
var Cdp = p.Cdp;
var Fmax = p.Fmax;
var tfree = p.tfree;
var topen = p.topen;
var rho = 1.22; // atmospheric density
var g = 9.8; // gravity
var mu = 1.81e-5; // viscosity of air
var x = u[1];
var y = u[2];
var vx = u[3];
var vy = u[4];
var detached = u[5];
// calculate relative velocity
var v = Math.sqrt((vx - wx) * (vx - wx) + vy * vy);
// determine parachute opening status
var parachute = 0;
if (t < tfree || detached > 0) {
parachute = 0;
} else if (t > (tfree + topen)) {
parachute = 1;
} else {
parachute = Math.min(1, (t - tfree) / topen);
}
// compute Reynolds number
var Re = rho * v * r / mu;
// compute atmospheric drag due to payload and parachute
if (Math.abs(Re) > 0) {
var Cd_eff = 24 / Re + 6 / (1 + Math.sqrt(Re)) + Cd;
var Fd = -0.5 * rho * pi * r * r * v * v * Cd_eff;
var Cdp_eff = 24 / Re + 6 / (1 + Math.sqrt(Re)) + Cdp;
var Fdp = -0.5 * rho * pi * rp * rp * v * v * Cdp_eff * parachute;
} else {
var Fd = 0;
var Fdp = 0;
}
// approximate effective drag as sum
var ax = -Math.abs(Fd + Fdp) / m * (vx - wx) / v;
var ay = -g - Math.abs(Fd + Fdp) / m * vy / v;
return new Float64Array([ vx, vy, ax, ay, Math.abs(Fdp) > Fmax ? 1 : 0]);
};
Simulation.run = function(params) {
var t = 0;
var dt = 0.1;
var dim = 5;
var u = new Float64Array(dim);
for (var i = 0; i < params.u0.length; i++) {
u[i] = params.u0[i];
}
var trajectory = [ new Float64Array(u) ];
var a = new Float64Array(dim);
var b = new Float64Array(dim);
var c = new Float64Array(dim);
var d = new Float64Array(dim);
var ub = new Float64Array(dim);
var uc = new Float64Array(dim);
var ud = new Float64Array(dim);
while (true) {
var f1 = this.dudt(t, u, params);
for (var i = 0; i < dim; i++) {
a[i] = dt * f1[i];
ub[i] = u[i] + a[i] / 2;
}
var f2 = this.dudt(t + dt / 2, ub, params);
for (var i = 0; i < dim; i++) {
b[i] = dt * f2[i];
uc[i] = u[i] + b[i] / 2;
}
var f3 = this.dudt(t + dt / 2, uc, params);
for (var i = 0; i < dim; i++) {
c[i] = dt * f3[i];
ud[i] = u[i] + c[i];
}
var f4 = this.dudt(t + dt, ud, params);
for (var i = 0; i < dim; i++) {
d[i] = dt * f4[i];
}
for (var i = 0; i < dim; i++) {
u[i] = u[i] + (a[i] * 2 * b[i] + 2 * c[i] + d[i]) / 6;
}
if (u[1] < 0) { // lerp to y = 0
var x = u[0];
var y = u[1];
var v_x = u[2];
var v_y = u[3];
u[0] = x - y * v_x / v_y;
u[1] = 0;
}
if (params.save_trajectory) {
trajectory.append(new Float64Array(u));
}
if (u[1] == 0) {
break;
}
t = t + dt;
dt = 2 / (Math.sqrt(u[2] * u[2] + u[3] * u[3]) + 0.1);
}
return params.save_trajectory ? trajectory : u;
}
Simulation.getNormal = function() {
var x, y, w;
do {
x = Math.random() * 2 - 1;
y = Math.random() * 2 - 1;
w = x * x + y * y;
} while (w >= 1.0)
return x * Math.sqrt(-2 * Math.log(w) / w);
};
Simulation.getLogNormal = function(mu, sigma) {
return Math.exp(Simulation.getNormal() * Math.sqrt(sigma) + mu);
};
Simulation.getTriangular = function(a, b, c) {
var fc = (c - a) / (b - a);
var u = Math.random();
if (u < fc)
return a + Math.sqrt(u * (b - a) * (c - a));
else
return b - Math.sqrt((1 - u) * (b - a) * (b - c));
};
Simulation.prototype.getSamples = function() {
var samples = { };
this.meta.parameters.forEach(function(param) {
if (param.stochastic ===4 true) {
samples[param.name] = new Float64Array(params.nsamp);
if (param.distribution.type === 'normal') {
for (var i = 0; i < params.nsamp; i++)
samples[param.name][i] = param.distribution.mu + param.distribution.sigma * Simulation.getNormal();
}
if (param.distribution.type === 'uniform') {
for (var i = 0; i < params.nsamp; i++)
samples[param.name][i] = Math.random() * (param.distribution.max - param.distribution.min) + param.distribution.min;
}
if (param.distribution.type === 'triangular') {
for (var i = 0; i < params.nsamp; i++)
samples[param.name][i] = Simulation.getTriangular(param.distribution.min, param.distribution.mode, param.distribution.max);
}
if (param.distribution.type === 'lognormal') {
for (var i = 0; i < params.nsamp; i++)
samples[param.name][i] = Simulation.getLogNormal(param.distribution.mu, param.distribution.sigma);
}
}
});
return samples;
};
Simulation.prototype.getDefault = function() {
var params = { };
this.metadata.forEach(function(paramGroup) {
paramGroup.params.forEach(function(param) {
params[param['name']] = param['default'];
});
});
return params;
};
Simulation.prototype.parse = function(params) {
var errors = [];
this.metadata.forEach(function(paramGroup) {
paramGroup.params.forEach(function(param) {
switch (param.type) {
case 'float': params[param.name] = parseFloat(params[param.name]); break;
case 'int': params[param.name] = parseInt(params[param.name]); break;
}
if (param.min != undefined && params[param.name] < param.min) {
errors.push(param.name + ' below minimum value of ' + param.min);
}
if (param.max != undefined && params[param.name] > param.max) {
errors.push(param.name + ' above maximum value of ' + param.max);
}
});
});
params.errors = errors;
return params;
};