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getset.go
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getset.go
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package motion
import "math"
func (c *BikeCalc) SetBracket(x float64) {
if x < minBracketLen {
x = minBracketLen
}
c.bracketLen = x
if c.solverFunc != newtonRaphson {
c.tolVel = c.bracketLen
}
}
// SetTolNR sets iteration stop tolerance for Newton-Raphson method.
func (c *BikeCalc) SetTolNR(x float64) {
if x < minTolNR {
x = minTolNR
}
c.tolNR = x
if c.solverFunc == newtonRaphson {
c.tolVel = c.tolNR
}
}
func (c *BikeCalc) SetBaseElevation(m float64) { c.baseElevation = m }
func (c *BikeCalc) SetTemperature(t float64) { c.temperature = t }
func (c *BikeCalc) SetAirPressure(hPa float64) {
c.airPressure = hPa * 100 // hPa to Pascal
}
func (c *BikeCalc) SetCdA(x float64) {
if x > 0 {
c.cdA = x
}
if c.rho > 0 && c.cdA > 0 {
c.cDrag = 0.5 * c.cdA * c.rho
}
}
func (c *BikeCalc) SetCd(x float64) {
if x > 0 {
c.cd = x
}
if c.frontalArea > 0 && c.cd > 0 {
c.SetCdA(c.frontalArea * c.cd)
}
}
func (c *BikeCalc) SetFrontalArea(x float64) {
if x > 0 {
c.frontalArea = x
}
if c.cd > 0 && c.frontalArea > 0 {
c.SetCdA(c.frontalArea * c.cd)
}
}
// SetRho sets air density and updates the compound air drag coefficient cDrag.
func (c *BikeCalc) SetRho(x float64) {
if x > 0 {
c.rho = x
}
if c.cdA > 0 && c.rho > 0 {
c.cDrag = 0.5 * c.cdA * c.rho
}
}
// SetCbf sets the braking friction coefficient.
func (c *BikeCalc) SetCbf(x float64) {
if x > 0 {
c.cbf = x
}
c.mgCbf = c.mg * c.cbf
c.fBrake = c.cos * c.mgCbf
}
// SetCrr sets the rolling resistance coefficient and dependant forces fRoll and fGR.
func (c *BikeCalc) SetCrr(x float64) {
if x > 0 {
c.crr = x
}
c.mgCrr = c.mg * c.crr
c.fRoll = c.cos * c.mgCrr
c.fGR = c.fGrav + c.fRoll
}
func (c *BikeCalc) SetCcf(x float64) { c.ccf = x }
/*
Calculate cos and sin as function of tan
////////////////////////////////////////
tan = grade% / 100
Trigonometry: sin = sin(arctan(tan))
cos = cos(arctan(tan))
Pythagoras: cos = 1/sqrt(1 + tan^2).
sin = tan * cos
Taylor serie:
1/sqrt(1+s) = 1 - 1/2*s + 3/8*s^2 - 5/16*s^3 + O(s^4) =>
cos = 1 - 1/2*tan^2 + 3/8*tan^4 - 5/16*tan^6 + O(tan^8)
Below is rational polynomial approximation func cosFromTanP2 for
abs(tan) < 0.3 by R minimaxApprox package. Polynomial approximation is
efficient for 1/sqrt(1+x) and especially when x = tan * tan and tan's
in this application are small. Ratio of two polynomials seems more
efficient than a single polynomial with same number of terms.
R: r$> f <- function(x) 1/sqrt(1+x)
r$> minimaxApprox(f, 0, 0.09, degree=c(2,2))
*/
// SetGrade calculates sin and cos and dependant forces from tan = grade% /100.
func (c *BikeCalc) SetGrade(tan float64) {
if useSystemSqrt {
c.cos = cosFromTanSqrt(tan)
} else {
c.cos = cosFromTanP22(tan)
}
c.tan = tan
c.sin = tan * c.cos
c.setForces()
}
// SetGradeP2 calculates sin and cos and dependant forces from tan = grade% /100.
func (c *BikeCalc) SetGradeP2(tan float64) {
c.cos = cosFromTanP22(tan)
if false {
c.cos = cosFromTanP2NR(tan)
}
c.tan = tan
c.sin = tan * c.cos
c.setForces()
}
func cosFromTanSqrt(tan float64) (cos float64) {
cos = 1 / math.Sqrt(1+tan*tan)
return
}
// cosFromTanP22 returns 1/math.Sqrt(1+tan*tan) by a ratio of two 2. degree
// polynomials. Max error < 6.5e-10 for abs(tan) < 0.3. In benchmark loop
// hardware 1/math.Sqrt(1+tan*tan) is ~75% slower than cosFromTanP22.
// 3 ns vs. 1.7 ns. In cpu profiling the difference is not so clear.
func cosFromTanP22(tan float64) (cos float64) {
const (
a1 = 0.73656502
a2 = 0.05920391
b1 = 1.2365650
b2 = 0.3024874
)
tan *= tan
cos = (1 + tan*(a1+tan*a2)) / (1 + tan*(b1+tan*b2))
return
}
// Max error < 2.4e-10 for abs(tan) < 0.3
func cosFromTanP2NR(tan float64) (cos float64) {
const (
a1 = -0.4987452
a2 = 0.3364923
)
tan *= tan
z := 1 + tan*(a1+tan*a2)
x := 0.5 * (1 + tan)
cos = z * (1.5 - x*z*z) // Newton-Raphson iteration
return
}
// setForces updates all road slope (and mass) dependant forces.
func (c *BikeCalc) setForces() {
c.fBrake = c.cos * c.mgCbf
c.fRoll = c.cos * c.mgCrr
c.fGrav = c.sin * c.mg
c.fGR = c.fGrav + c.fRoll
}
// SetGravity sets gravity and calculates all weight dependant forces and intermediates.
func (c *BikeCalc) SetGravity(g float64) {
if g > 0 {
c.gravity = g
}
c.SetWeight(0)
}
func (c *BikeCalc) SetMinPower(w float64) {
if w < 0 {
w = 0
}
c.minPower = w
}
// func (c *BikeCalc) SetPower(x float64) { c.power = x }
func (c *BikeCalc) SetVelErrors(b bool) { c.calcVelErrors = b }
func (c *BikeCalc) SetVelSolver(i int) {
c.solverFunc = i
switch i {
case newtonRaphson:
velFromPower = (*BikeCalc).NewtonRaphson
case newtonHalley:
velFromPower = (*BikeCalc).NewtonHalley
case singleQuadratic:
velFromPower = (*BikeCalc).Quadratic
case doubleQuadratic:
velFromPower = (*BikeCalc).DoubleQuadratic
case doubleLinear:
velFromPower = (*BikeCalc).DoubleLinear
default:
velFromPower = (*BikeCalc).NewtonRaphson
c.solverFunc = newtonRaphson
}
c.tolVel = c.tolNR
if c.solverFunc != newtonRaphson && c.solverFunc != newtonHalley {
c.tolVel = c.bracketLen
}
}
// SetWeight sets total weight and updates all dependant forces
// and intermediates.
func (c *BikeCalc) SetWeight(kg float64) {
if kg > 0 {
c.mass = kg
}
c.mg = c.mass * c.gravity
c.mgCrr = c.mg * c.crr
c.mgCbf = c.mg * c.cbf
c.setForces()
c.SetWeightRotating(0)
}
// SetWeightRotating sets rotating mass.
// rotatingMass = weight of tyre + tube + rim.
func (c *BikeCalc) SetWeightRotating(kg float64) {
const rotatingMassReducingFactor = 0.9
// aproximating 0.9 reduction of the wheel radius, because
// the mass is not rotating at the outer edge of the wheel.
if kg > 0 {
c.massRotating = kg
}
c.massKin = c.mass + c.massRotating*rotatingMassReducingFactor
c.oMassKin = 1 / c.massKin
}
// SetWind sets +head/-tail wind speed in m/s.
func (c *BikeCalc) SetWind(ms float64) { c.wind = ms }
func (c *BikeCalc) AirPressure() float64 { return c.airPressure / 100 }
func (c *BikeCalc) BaseElevation() float64 { return c.baseElevation }
func (c *BikeCalc) Cbf() float64 { return c.cbf }
func (c *BikeCalc) Crr() float64 { return c.crr }
func (c *BikeCalc) CdA() float64 { return c.cdA }
func (c *BikeCalc) Cdrag() float64 { return c.cDrag }
func (c *BikeCalc) MassKin() float64 { return c.massKin }
func (c *BikeCalc) Fbrake() float64 { return c.fBrake }
func (c *BikeCalc) Fdrag(v float64) float64 { return c.cDrag * c.signSq(v) }
func (c *BikeCalc) Fgrav() float64 { return c.fGrav }
func (c *BikeCalc) Froll() float64 { return c.fRoll }
func (c *BikeCalc) Fgr() float64 { return c.fGR }
func (c *BikeCalc) Gravity() float64 { return c.gravity }
func (c *BikeCalc) Grade() float64 { return c.tan }
func (c *BikeCalc) Sin() float64 { return c.sin }
func (c *BikeCalc) Cos() float64 { return c.cos }
func (c *BikeCalc) Rho() float64 { return c.rho }
func (c *BikeCalc) SolverCalls() int { return c.callsSolver }
func (c *BikeCalc) MaxIter() int { return c.maxIter }
func (c *BikeCalc) SolverRounds() int {
if c.solverFunc == newtonRaphson || c.solverFunc == newtonHalley {
return c.iterNR
}
return c.callsf
}
func (c *BikeCalc) SolverFunc() int { return c.solverFunc }
func (c *BikeCalc) VelErrorMax() float64 { return c.velErrMax }
func (c *BikeCalc) VelErrorMean() float64 {
if c.callsErr == 0 {
return 0
}
return c.velErr / float64(c.callsErr)
}
func (c *BikeCalc) VelErrorAbsMean() float64 {
if c.callsErr == 0 {
return 0
}
return c.velErrAbs / float64(c.callsErr)
}
func (c *BikeCalc) VelErrorPos() float64 {
if c.callsErr == 0 {
return 0
}
return float64(c.velErrPos) / float64(c.callsErr)
}