This is the source code of the page Centrifugal and Gravitational Acceleration in an Aircraft and Zentrifugal- und Gravitationsbeschleunigung in einem Flugzeug. See the math of that page that describes all variables used in this code.

#INCLUDE ControlPanel.inc

<style>
#InputPanel-calLat, #InputPanel-calAlt, #OutputPanel-g0cal { background-color: #fed;  }
#OutputPanel-grel { background-color: #ddf;  }
#OutputPanel-w0, #OutputPanel-dw { background-color: #fed;  }
#OutputPanel-g0, #OutputPanel-gh, #OutputPanel-dg { background-color: #dfd; }
#InputPanel-wCal, #OutputPanel-wh { background-color: #ffd }
</style>


<jscript>

function CModel() {
  // input
  this.vGS = 308.64;  // m/s, magnitude of ground speed
  this.dir = 90;      // deg, aircraft heading wrt. north
  this.lat = -35;     // deg, aircraft latitude
  this.alt = 12496.8; // m, aircraft altitude
  this.calLat = -35;  // deg, weight calibration latitude
  this.calAlt = 50;   // m, weight calibration altitude
  this.wCal = 500;    // units, weight mass in any mass units
  this.Model = 0;     // 0 -> ellipsoid, 1 -> spehere

  this.alpha = 0;     // rad, aircraft heading wrt. rotating grat circle (->dir)
  this.phi = 0;       // rad, aircraft latitude (->lat)
  this.theta = 0;     // rad, heading wrt. non-rotating grat circle

  // output, all values in metric units
  this.grel = 0;      // gh / g0, relative effective acceleration
  this.g0 = 0;        // effective acceleration on ground
  this.g0G = 0;       // gravitational acceleration on ground
  this.g0Gx = 0;      // x component of g0G
  this.g0Gz = 0;      // z component of g0G
  this.a0Z = 0;       // centrifugal acceleration on ground
  this.a0Zx = 0;      // x component of a0Z
  this.a0Zz = 0;      // z component of a0Z
  this.g0cal = 0;     // effective acceleration on weight calibratin location

  this.w0 = 0;        // weight of mass at sea level
  this.wh = 0;        // weight of mass at aircraft altitude
  this.dw = 0;        // wh - wCal

  this.gh = 0;        // effective acceleration at ac altitude
  this.ghG = 0;       // gravitational acceleration at ac altitude
  this.ghGx = 0;      // x component of ghG
  this.ghGz = 0;      // z component of ghG
  this.ahZ = 0;       // centrifugal acceleration at ac alt
  this.ahZx = 0;      // x component of ahZ
  this.ahZz = 0;      // z component of ahZ
  this.dg = 0;        // gh - g0

  this.P0x = 0;       // x component of ac pos at sea level
  this.P0z = 0;       // z component of ac pos at sea level
  this.Phx = 0;       // x component of ac pos at alt
  this.Phz = 0;       // z component of ac pos at alt
  this.R = 0;         // dist of ac pos at sea level from earth center
  this.rho = 0;       // radius of ac great circle path on sea level
  this.rhoh = 0;      // radius of ac great circle path at alt
  this.rho1 = 0;      // radius of red ellipse at ac pos and alt
  this.rho2 = 0;      // radius of blue ellipse at ac pos and alt

  this.v = 0;         // ac speed wrt geocentric coord sys
  this.vx = 0;        // x component of v 
  this.vy = 0;        // y component of v
  this.vRot = 0;      // tangential earth rotation speed at ac pos and alt
  this.vRotx = 0;     // x component of vRot
  this.vRoty = 0;     // y component of vRot
  this.vRelx = 0;     // x component of ac speed wrt ground at alt
  this.vRely = 0;     // y component of ac speed wrt ground at alt
  this.vEq = 0;       // tangential speed of earth surface at equator
  this.omega = 0;     // = 2 * pi / T [rad/s], rotation speed of earth

  // contstants
  // GM = G * Mass of earth without mass of atmosphere:
  this.GM = 3.986004418e14; // m^3/s^2, http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf
  this.G = 6.67408e-11;
  this.M = this.GM / this.G;
  this.T = 86164.098903691; // s, https://en.wikipedia.org/wiki/Earth
  this.Ra = 6378137; // m, http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf
  this.Rb = 6356752.314245; // m, http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf
  this.RMean = 6371008.7714; // m, http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf
  this.ge = 9.7803253359; // m/s^2, http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf
  this.gp = 9.8321849378; // m/s^2, http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf

  // units
  this.SpeedUnits = [ 'm/s', 'km/h', 'kt', 'mph' ];
  this.SpeedMults = [ 1, 1/3.6, 0.5144, 0.44704 ];
  this.SpeedUnitIx = 2;
  this.SpeedUnit = 'kt';
  this.SpeedMult = 0.5144;

  this.AltUnits = [ 'm', 'ft', 'FL' ];
  this.AltMults = [ 1, 0.3048, 30.48 ];
  this.AltUnitIx = 1;
  this.AltUnit = 'ft';
  this.AltMult = 0.3048;
}

CModel.prototype.Clear = function() {
  this.vGS = 0; // m/s
  this.dir = 0; // deg
  this.lat = 0; // deg
  this.alt = 0; // m
  this.calLat = 0;
  this.calAlt = 0;
  this.wCal = 0; // kg
  this.Model = 0; // 0 -> ellipsoid, 1 -> spehere
}

CModel.prototype.Update = function() {
  // functions
  var sin = Math.sin;
  var cos = Math.cos;
  var sqrt = Math.sqrt;
  function sqr( x ) { return x * x; }
  function len( x, y ) { return sqrt( sqr(x) + sqr(y) ); }
  function rad( a ) { return a * Math.PI / 180; }
  function sp( x1, y1, x2, y2 ) { return x1 * x2 + y1 * y2; } // scalar product
  function isSameDir( x1, y1, x2, y2 ) { return sp(x1,y1,x2,y2) >= 0; }

  // setup units
  this.SpeedUnit = this.SpeedUnits[this.SpeedUnitIx];
  this.SpeedMult = this.SpeedMults[this.SpeedUnitIx]
  this.AltUnit = this.AltUnits[this.AltUnitIx];
  this.AltMult = this.AltMults[this.AltUnitIx];

  // limit inputs
  if (this.dir < -180) this.dir = -180;
  if (this.dir > 360) this.dir = 360;
  if (this.lat < -90) this.lat = -90;
  if (this.lat > 90) this.lat = 90;

  // angles in radian, omega, GM
  this.alpha = rad( this.dir );
  this.phi = rad( this.lat );
  if (this.T == 0) {
    this.omega = 0;
  } else {
    this.omega = 2 * Math.PI / this.T;
  }
  this.GM = this.G * this.M;

  var a = this.Ra;
  var b = this.Rb;
  if (this.Model == 1) {
    // globe model
    a = this.RMean;
    b = this.RMean;
  }
  var cosp = cos( this.phi );
  var sinp = sin( this.phi );
  var cosp2 = sqr( cosp );
  var sinp2 = sqr( sinp );
  var a2 = sqr( a );
  var b2 = sqr( b );

  // positions
  // if globe model then a = b = this.RMean -> eps = 0 and Nphi = this.RMean
  var eps = sqrt( a2 - b2 ) / a;
  var Nphi = a / sqrt(1 - sqr(eps * sinp));
  this.P0x = Nphi * cosp;
  this.P0z = Nphi * (1 - sqr(eps)) * sinp;
  this.Phx = (Nphi + this.alt) * cosp;
  this.Phz = (Nphi * (1 - sqr(eps)) + this.alt) * sinp;
  this.R = len( this.P0x, this.P0z );

  // earth accelerations
  this.a0Zx = sqr(this.omega) * this.P0x;
  this.a0Zz = 0;
  this.a0Z  = len( this.a0Zx, this.a0Zz );
  if (this.Model == 1) {
    // globe model
    this.g0G = this.GM / sqr(this.RMean);
    this.g0Gx = - this.g0G * cosp;
    this.g0Gz = - this.g0G * sinp;
    var gx = this.g0Gx + this.a0Zx;
    var gz = this.g0Gz + this.a0Zz;
    this.g0 = len( gx, gz );
  } else {
    // ellipsoid model
    this.g0 = ( a * this.ge * cosp2 + b * this.gp * sinp2 ) / sqrt( a2 * cosp2 + b2 * sinp2 );
    var gx = - this.g0 * cosp;
    var gz = - this.g0 * sinp;
    this.g0Gx = gx - this.a0Zx;
    this.g0Gz = gz - this.a0Zz;
    this.g0G = len( this.g0Gx, this.g0Gz );
  }

  // geodesic radii for alpha
  // red ellipse
  var sx = cosp;
  var sz = sinp;
  var A = ( sqr(sx) / a2 ) + ( sqr(sz) / b2 );
  var B = ( 2 * this.P0x * sx / a2 ) + ( 2 * this.P0z * sz / b2 );
  var lambda = - B / A;
  var Ox = this.P0x + 0.5 * lambda * sx;
  var Oz = this.P0z + 0.5 * lambda * sz;
  var Opx = Ox;
  var Opz = (a / b) * Oz;
  var m = len( Opx, Opz );
  var as = sqrt( a2 - sqr(m) );
  var bs = Math.abs( lambda ) / 2;
  this.rho1 = sqr(as) / bs;
  // blue ellipse
  var as = a;
  var bs = b;
  this.rho2 = sqrt(Math.pow(Math.pow(as,4) * sqr(this.P0z) + Math.pow(bs,4) * sqr(this.P0x), 3)) / (Math.pow(as,4) * Math.pow(bs,4));

  // use rho(alpha) for correction of ground speed vGS to vRel
  this.rho = (this.rho1 + this.rho2) / 2 - (this.rho1 - this.rho2) / 2 * cos(2 * this.alpha);
  this.rhoh = this.rho + this.alt;

  // plane speed
  this.vEq = this.omega * a;
  this.vRotx = this.omega * this.Phx;
  this.vRoty = 0;
  this.vRot = this.vRotx;
  var vrel = this.vGS * this.rhoh / this.rho;
  this.vRelx = vrel * sin( this.alpha );
  this.vRely = vrel * cos( this.alpha );
  this.vx = this.vRotx + this.vRelx;
  this.vy = this.vRoty + this.vRely;
  this.v = len( this.vx, this.vy );

  // use rho(theta(v)) for centrifugal acceleration in plane
  if (this.v == 0) {
    this.theta = 0;
  } else {
    this.theta = Math.acos( this.vy / this.v );
  }
  this.rho = (this.rho1 + this.rho2) / 2 - (this.rho1 - this.rho2) / 2 * cos(2 * this.theta);
  this.rhoh = this.rho + this.alt;

  // plane accelerations
  var ahRot = sqr(this.omega) * this.Phx; 
  if (this.vGS != 0) {
    // plane is moving independent of earth
    this.ahZ = sqr(this.v) / this.rhoh;
    this.ahZx = this.ahZ * cosp;
    this.ahZz = this.ahZ * sinp;
  } else {
    // plane is bound to the earth
    this.ahZ = ahRot;
    this.ahZx = this.ahZ;
    this.ahZz = 0;
  }
  if (this.Model == 1) {
    // globe model
    this.ghG = this.GM / sqr(this.RMean + this.alt);
    this.ghGx = - this.ghG * cosp;
    this.ghGz = - this.ghG * sinp;
    var gx = this.ghGx + this.ahZx;
    var gz = this.ghGz + this.ahZz;
    this.gh = len( gx, gz );
  } else {
    // ellipsoid model
    var f = (a - b) / a;
    var m = sqr(this.omega * a) * b / this.GM;
    var ghRot = this.g0 * ( 1 - (2 / a) * ( 1 + f + m - 2 * f * sinp2 ) * this.alt + (3 / a2) * sqr(this.alt) );
    var ghRotx = - ghRot * cosp;
    var ghRotz = - ghRot * sinp;
    this.ghGx = ghRotx - ahRot;
    this.ghGz = ghRotz;
    this.ghG  = len( this.ghGx, this.ghGz );
    var gx = this.ghGx + this.ahZx;
    var gz = this.ghGz + this.ahZz;
    this.gh = len( gx, gz );
    if (!isSameDir( this.ghGx, this.ghGz, gx, gz )) {
      // g points outward!
      this.gh *= -1;
    }
  }
  this.dg = this.gh - this.g0;

  // acceleration at calibration localtion
  var phiCal = rad( this.calLat );
  var cospCal = cos( phiCal );
  var sinpCal = sin( phiCal );
  var cosp2Cal = sqr( cospCal );
  var sinp2Cal = sqr( sinpCal );

  if (this.Model == 1) {
    // globe model
    var hcal = this.RMean + this.calAlt;
    var g0Gcal = this.GM / sqr(hcal);
    var g0Gcalx = - g0Gcal * cospCal;
    var g0Gcalz = - g0Gcal * sinpCal;
    var a0cal = sqr(this.omega) * hcal * cospCal; 
    this.g0cal = len( g0Gcalx + a0cal, g0Gcalz );
  } else {
    // ellipsoid model
    // requires f and m are computed above
    var gCal0 = ( a * this.ge * cosp2Cal + b * this.gp * sinp2Cal ) / sqrt( a2 * cosp2Cal + b2 * sinp2Cal );
    this.g0cal = gCal0 * ( 1 - (2 / a) * ( 1 + f + m - 2 * f * sinp2Cal ) * this.calAlt + (3 / a2) * sqr(this.calAlt) );
  }

  // relative acceleration
  this.grel = this.gh / this.g0;

  // weights 
  this.w0 = this.wCal * this.g0 / this.g0cal;
  this.wh = this.w0 * this.grel;
  this.dw = this.wh - this.wCal;

}

var Model = new CModel();

function UpdateAll() {
  Model.Update();
  ControlPanels.Update();
}

function Reset() {
  ControlPanels.Reset();
  UpdateAll();
}

function Clear() {
  Model.Clear();
  UpdateAll();
}

ControlPanels.NewPanel( {
    Name: 'InputPanel',
    ModelRef: 'Model',
    OnModelChange: UpdateAll,
    Format: 'std',
    Digits: 7,
    NCols: 2
  }

).AddHeader( {
    Text: 'Flight and Test Mass Data',
    ColSpan: 3
  }

).AddHeader( { 
    Text: ControlPanels.ResetButtonR() + ControlPanels.SmallButtonR('Clear','Clear()')
  }

).AddTextField( {
    Name: 'vGS',
    Label: 'GS',
    UnitsRef: 'SpeedUnit',
    MultRef: 'SpeedMult'
  }

).AddTextField( {
    Name: 'dir',
    Label: 'Course',
    Units: '&deg;N'
  }

).AddTextField( {
    Name: 'lat',
    Label: 'Lat',
    Units: '&deg',
    ConvToModelFunc: function(s) { return NumFormatter.DmsStrToNum( s ); },
  }

).AddTextField( {
    Name: 'alt',
    Label: 'Alt',
    UnitsRef: 'AltUnit',
    MultRef: 'AltMult'
  }

).AddTextField( {
    Name: 'calLat',
    Label: 'Lat<sub>cal</sub>',
    Units: '&deg',
    ConvToModelFunc: function(s) { return NumFormatter.DmsStrToNum( s ); },
  }

).AddTextField( {
    Name: 'calAlt',
    Label: 'Alt<sub>cal</sub>',
    UnitsRef: 'AltUnit',
    MultRef: 'AltMult'
  }

).AddTextField( {
    Name: 'wCal',
    Label: 'W<sub>cal</sub>',
    Units: 'units',
  }

).AddRadiobuttonField( {
    Name: 'Model',
    ValueType: 'int',
    Items: [
      {
        Name: 'Ellipsoid',
        Value: '0'
      }, {
        Name: 'Sphere',
        Value: '1'
      }
    ]
  }

).Render();


ControlPanels.NewPanel( {
    Name: 'OutputPanel',
    ModelRef: 'Model',
    NCols: 2,
    Format: 'std',
    Digits: 7,
    ReadOnly: true
  }

).AddHeader( {
    Text: 'Results',
    ColSpan: 4
  }

).AddTextField( {
    Name: 'grel',
    Label: 'g<sub>rel</sub>',
    Units: 'g<sub>o</sub>'
  }

).AddTextField( {
    Name: 'dw',
    Label: 'W<sub>h</sub>-W<sub>cal</sub>',
    Units: 'units'
  }

).AddTextField( {
    Name: 'w0',
    Label: 'W<sub>o</sub>',
    Units: 'units'
  }

).AddTextField( {
    Name: 'wh',
    Label: 'W<sub>h</sub>',
    Units: 'units'
  }

).AddTextField( {
    Name: 'g0cal',
    Label: 'g<sub>o,cal</sub>',
    Units: 'm/s<sup>2</sup>'
  }

).AddTextField( {
    Name: 'dg',
    Label: 'g<sub>h</sub>-g<sub>o</sub>',
    Units: 'm/s<sup>2</sup>'
  }

).AddTextField( {
    Name: 'g0',
    Label: 'g<sub>o</sub>',
    Units: 'm/s<sup>2</sup>'
  }

).AddTextField( {
    Name: 'gh',
    Label: 'g<sub>h</sub>',
    Units: 'm/s<sup>2</sup>'
  }

).AddTextField( {
    Name: 'g0G',
    Label: 'g<sub>oG</sub>',
    Units: 'm/s<sup>2</sup>'
  }

).AddTextField( {
    Name: 'ghG',
    Label: 'g<sub>hG</sub>',
    Units: 'm/s<sup>2</sup>'
  }

).AddTextField( {
    Name: 'a0Z',
    Label: 'a<sub>oZ</sub>',
    Units: 'm/s<sup>2</sup>'
  }

).AddTextField( {
    Name: 'ahZ',
    Label: 'a<sub>hZ</sub>',
    Units: 'm/s<sup>2</sup>'
  }

).AddTextField( {
    Name: 'R',
    Label: 'R',
    Units: 'km',
    Mult: 1000
  }

).AddTextField( {
    Name: 'rhoh',
    Label: '&rho;<sub>h</sub>',
    Units: 'km',
    Mult: 1000
  }

).AddTextField( {
    Name: 'rho1',
    Label: '&rho;<sub>1</sub>',
    Units: 'km',
    Mult: 1000
  }

).AddTextField( {
    Name: 'rho2',
    Label: '&rho;<sub>2</sub>',
    Units: 'km',
    Mult: 1000
  }

).AddTextField( {
    Name: 'vEq',
    Label: 'v<sub>eq</sub>',
    UnitsRef: 'SpeedUnit',
    MultRef: 'SpeedMult'
  }

).AddTextField( {
    Name: 'v',
    Label: 'v',
    UnitsRef: 'SpeedUnit',
    MultRef: 'SpeedMult'
  }

).AddTextField( {
    Name: 'vRot',
    Label: 'v<sub>rot</sub>',
    UnitsRef: 'SpeedUnit',
    MultRef: 'SpeedMult'
  }

).Render();

ControlPanels.NewPanel( {
    Name: 'UnitsPanel',
    ModelRef: 'Model',
    OnModelChange: UpdateAll,
    NCols: 2
  }

).AddHeader( {
    Text: 'Units',
    ColSpan: 4
  }

).AddRadiobuttonField( { 
    Name: 'SpeedUnitIx', 
    ValueType: 'int', 
    Label: 'Speed', 
    NCols: 4, 
    Items: [
      { Name: 'm/s', Value: '0' },
      { Name: 'km/h', Value: '1' },
      { Name: 'kt', Value: '2' },
      { Name: 'mph', Value: '3' }
    ]
  } 

).AddRadiobuttonField( { 
    Name: 'AltUnitIx', 
    ValueType: 'int', 
    Label: 'Alt', 
    NCols: 3, 
    Items: [
      { Name: 'm', Value: '0' },
      { Name: 'ft', Value: '1' },
      { Name: 'FL', Value: '2' }
    ]
  } 

).Render();


xOnLoad( UpdateAll );