def _getCPXPos(self, Mach):
'''
Finds the chordwise position of the center of pressure, relative to the tip of the root chord (self.position)
Methods from Tactical missile design by Fleeman through Niskanen
'''
if Mach < 0.5:
XF = self.XMACLeadingEdge + 0.25 * self.MACLength #As per open rocket documentation
elif Mach >= 2.0:
beta = AeroParameters.getBeta(Mach)
CPCalc = lambda AR, B: (AR * B - 0.67) / (
2 * AR * B - 1
) #Eq 3.35 of open rocket documentation (greater than M = 2)
XF = self.MACLength * CPCalc(
self.aspectRatio,
beta) + self.XMACLeadingEdge #As per open rocket documentation
else:
#Between the two extremes is a polynomial curve fit
#Fifth order polynomial fit as per Niskanen Eqn 3.36 (Originally from Fleeman)
# Old code: XF = np.polyval(self.x, Mach)*self.MACLength + self.XMACLeadingEdge
# Evaluate polynomial manually for maximum speed (8.5x improvement for 6 coeffs)
# Speed test in test/speedTests/PolyvalSpeed.py
polyval = 0
nTerms = len(self.x)
for i in range(nTerms):
polyval += self.x[i] * Mach**(nTerms - 1 - i)
XF = polyval * self.MACLength + self.XMACLeadingEdge # Polyval defines the fraction of the MAC that the Cp is behind the leading edge
return XF
def subsonicNormalForce(Mach): # Subsonic linear method
tempBeta = AeroParameters.getBeta(Mach)
CnAlpha = getFinCnAlpha_Subsonic_Barrowman(self.span,
self.planformArea,
tempBeta,
self.midChordSweep)
return getSubsonicFinNormalForce(airVelRelativeToFin,
unitSpanTangentialAirVelocity,
finNormal, self.spanwiseDirection,
self.CPSpanWisePosition.length(),
CnAlpha, self)
def supersonicNormalForce(Mach): # Supersonic Busemann method
gamma = AeroFunctions.getGamma()
tempBeta = AeroParameters.getBeta(Mach)
K1, K2, K3, Kstar = getBusemannCoefficients(Mach, tempBeta, gamma)
# Mach Cone coords
machAngle = asin(1 / Mach)
machCone_negZPerRadius = 1 / tan(machAngle)
machConeEdgeZPos = []
outerRadius = self.spanSliceRadii[-1]
for i in range(len(self.spanSliceRadii)):
machConeAtCurrentRadius = (
outerRadius - self.spanSliceRadii[i]
) * machCone_negZPerRadius + self.tipPosition
machConeEdgeZPos.append(machConeAtCurrentRadius)
return getSupersonicFinNormalForce(
airVelRelativeToFin, unitSpanTangentialAirVelocity, finNormal,
machConeEdgeZPos, self.spanwiseDirection,
self.CPSpanWisePosition.length(), K1, K2, K3, Kstar, self)
def test_getBeta(self):
self.assertAlmostEqual(AeroParameters.getBeta(0.5), 0.86602540)
self.assertAlmostEqual(AeroParameters.getBeta(1.5), 1.118033989)
