def forceFromCoefficients(rocketState, environment, Cd, Cl, CMx, CMy, CMz,
CPLocation, refArea, refLength):
''' Initialize ForceMomentSystem from all aerodynamic coefficients '''
q = AeroParameters.getDynamicPressure(rocketState, environment)
if q == 0.0:
# No force without dynamic pressure
return ForceMomentSystem(Vector(0, 0, 0))
nonDimConstant = q * refArea
#### Drag ####
localFrameAirVel = AeroParameters.getLocalFrameAirVel(
rocketState, environment)
dragDirection = localFrameAirVel.normalize()
dragForce = dragDirection * Cd
#### Lift ####
# Find the lift force direction
# Lift force will be in the same plane as the normalForceDirection & rocketFrameAirVel vectors
# But, the lift force will be perpendicular to rocketFraeAirVel, whereas the normalForceDirection might form an acute angle with it
# Rotate the normal force direction vector until it's perpendicular with rocketFrameAirVel
normalForceDir = AeroParameters.getNormalAeroForceDirection(
rocketState, environment)
rotAxis = localFrameAirVel.crossProduct(normalForceDir)
angle = math.pi / 2 - localFrameAirVel.angle(normalForceDir)
rotatorQuat = Quaternion(rotAxis, angle)
liftDirection = rotatorQuat.rotate(normalForceDir)
liftForce = liftDirection * Cl
# Combine and redimensionalize
totalForce = (dragForce + liftForce) * nonDimConstant
#### Moments ####
moments = Vector(CMx, CMy, CMz) * nonDimConstant * refLength
return ForceMomentSystem(totalForce, CPLocation, moments)
def forceFromCdCN(rocketState,
environment,
Cd,
CN,
CPLocation,
refArea,
moment=None):
'''
Convenience function for Barrowman Aero methods
Initialize ForceMomentSystem from aerodynamic coefficients Cd and CN
Cd should NOT already be adjusted for angle of attack
Moment should be a dimensional moment vector
'''
angleOfAttack = AeroParameters.getTotalAOA(rocketState, environment)
q = AeroParameters.getDynamicPressure(rocketState, environment)
#### Axial Force ####
CA = getDragToAxialForceFactor(angleOfAttack) * Cd
axialForce = Vector(0, 0, -CA) #Axial force is in the negative Z-direction
#### Normal Force ####
normalForce = AeroParameters.getNormalAeroForceDirection(
rocketState, environment) * CN
totalForce = (axialForce + normalForce) * refArea * q
return ForceMomentSystem(totalForce, CPLocation, moment)
def getAppliedForce(self, rocketState, time, environment, CG):
'''
Calculates force/moment applied by the recovery system using a simple drag coefficient + area model
'''
#### Calculate Aero Force ####
if self.currentStage == 0:
# No recovery system deployed yet
return ForceMomentSystem(Vector(0,0,0))
else:
# 3DoF force-only aero
airVel = AeroParameters.getAirVelRelativeToVehicle(rocketState, environment)
dragForceMagnitude = self.chuteCds[self.currentStage] * self.chuteAreas[self.currentStage] * AeroParameters.getDynamicPressure(rocketState, environment)
totalForce = airVel.normalize() * dragForceMagnitude
return ForceMomentSystem(totalForce)
def test_dynamicPressure(self):
self.assertAlmostEqual(AeroParameters.getDynamicPressure(self.rocketState1,self.currentConditions), self.correctDynamicPressure1)
self.assertAlmostEqual(AeroParameters.getDynamicPressure(self.rocketState3,self.currentConditions), self.correctDynamicPressure2)
def _barrowmanAeroFunc(self,
rocketState,
time,
environment,
precomputedData,
CG=Vector(0, 0, 0),
finDeflectionAngle=None):
'''
Precomputed Data is a named tuple (PreComputedFinAeroData) which contains data/results from the parts of the fin aerodynamics calculation
that are common to all fins in a FinSet (drag calculations mostly). These calculations are performed at the FinSet level.
Only the parts of the Fin Aero Computation that change from fin to fin (normal force mostly, since different fins can have different angles of attack) are computed here
'''
Mach = AeroParameters.getMachNumber(rocketState, environment)
dynamicPressure = AeroParameters.getDynamicPressure(
rocketState, environment)
if finDeflectionAngle == None:
finDeflectionAngle = self.finAngle # Adjusted by parent finset during each timestep, when the FinSet is controlled
# Unpack precomputedData
airVelRelativeToFin, CPXPos, totalDragCoefficient = precomputedData
#### Compute normal force-----------------------------------------------------------------------------------------------------------------
# Find fin normal vector after fin deflection
finDeflectionRotation = Quaternion(
axisOfRotation=self.spanwiseDirection,
angle=radians(finDeflectionAngle))
finNormal = finDeflectionRotation.rotate(self.undeflectedFinNormal)
# Get the tangential velocity component vector, per unit radial distance from the rocket centerline
rollAngVel = AngularVelocity(0, 0, rocketState.angularVelocity.Z)
unitSpanTangentialAirVelocity = rollAngVel.crossProduct(
self.spanwiseDirection) * (-1)
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)
if Mach <= 0.8:
normalForceMagnitude, finMoment = subsonicNormalForce(Mach)
elif Mach < 1.4:
# Interpolate in transonic region
# TODO: Do this with less function evaluations? Perhaps precompute AOA and Mach combinations and simply interpolate? Lazy precompute? Cython?
x1, x2 = 0.8, 1.4 # Start, end pts of interpolated region
dx = 0.001
# Find normal force and derivative at start of interpolation interval
f_x1, m_x1 = subsonicNormalForce(x1)
f_x12, m_x12 = subsonicNormalForce(x1 + dx)
# Find normal force and derivative at end of interpolation interval
f_x2, m_x2 = supersonicNormalForce(x2)
f_x22, m_x22 = supersonicNormalForce(x2 + dx)
normalForceMagnitude = Interpolation.cubicInterp(
Mach, x1, x2, f_x1, f_x2, f_x12, f_x22, dx)
finMoment = Interpolation.cubicInterp(Mach, x1, x2, m_x1, m_x2,
m_x12, m_x22, dx)
else:
normalForceMagnitude, finMoment = supersonicNormalForce(Mach)
# Complete redimensionalization of normal force coefficients by multiplying by dynamic pressure
# Direct the normal force along the fin's normal direction
normalForce = normalForceMagnitude * dynamicPressure * finNormal
finMoment *= dynamicPressure
#### Get axial force-----------------------------------------------------------------------------------------------------------------------
avgAOA = getFinSliceAngleOfAttack(
self.spanSliceRadii[round(len(self.spanSliceAreas) / 2)],
airVelRelativeToFin, unitSpanTangentialAirVelocity, finNormal,
self.spanwiseDirection,
self.stallAngle) # Approximate average fin AOA
totalAxialForceCoefficient = AeroFunctions.getDragToAxialForceFactor(
avgAOA) * totalDragCoefficient
axialForceMagnitude = totalAxialForceCoefficient * self.rocket.Aref * dynamicPressure
axialForceDirection = self.spanwiseDirection.crossProduct(finNormal)
axialForce = axialForceDirection * axialForceMagnitude
#### Get CP Location ----------------------------------------------------------------------------------------------------------------------
CPChordWisePosition = self.position - Vector(
0, 0, CPXPos
) # Ignoring the change in CP position due to fin deflection for now
globalCP = self.CPSpanWisePosition + CPChordWisePosition
#### Assemble total force moment system objects--------------------------------------------------------------------------------------------
totalForce = normalForce + axialForce
return ForceMomentSystem(totalForce,
globalCP,
moment=Vector(0, 0, finMoment)), globalCP
def _getPreComputedFinAeroData(self, rocketState, environment, CG):
#General Info ---------------------------------------------------------------------------------------------------------------------
Aref = self.rocket.Aref
Mach = AeroParameters.getMachNumber(rocketState, environment)
dynamicPressure = AeroParameters.getDynamicPressure(
rocketState, environment)
# Skin Friction Drag -------------------------------------------------------------------------------------------------------------
skinFrictionCoefficient = AeroFunctions.getSkinFrictionCoefficient(
rocketState, environment, self.MACLength, Mach,
self.surfaceRoughness, self.rocket.fullyTurbulentBL)
# Adjust to the rocket reference area (skinFrictionCoefficient is based on wetted area)
skinFrictionDragCoefficient = skinFrictionCoefficient * (
self.wettedArea / Aref)
# Correct for additional surface area due to fin thickness - Niskanen Eqn 3.85
skinFrictionDragCoefficient *= (1 +
2 * self.thickness / self.MACLength)
# Pressure Drag ------------------------------------------------------------------------------------------------------------------
# Leading edge drag coefficient
if self.leadingEdgeShape == "Round":
leadingEdgeCd = AeroFunctions.getCylinderCrossFlowCd_ZeroBaseDrag(
Mach)
LEthickness = self.leadingEdgeRadius * 2
elif self.leadingEdgeShape == "Blunt":
leadingEdgeCd = AeroFunctions.getBluntBodyCd_ZeroBaseDrag(Mach)
LEthickness = self.leadingEdgeThickness
# Adjust for leading edge angle and convert reference area to rocket reference area - Barrowman Eqn 4-22
leadingEdgeCdAdjustmentFactor = LEthickness * self.span * cos(
self.sweepAngle)**2 / Aref
leadingEdgeCd *= leadingEdgeCdAdjustmentFactor
# Trailing edge drag coefficient - simpler method from Niskanen section 3.4.4. Corrected to use only the trailing edge area, not the full fin frontal area
# more intricate method available in Barrowman
baseDragCd = AeroFunctions.getBaseDragCoefficient(Mach)
if self.trailingEdgeShape == "Tapered":
TEthickness = 0 # Zero base drag
elif self.trailingEdgeShape == "Round":
TEthickness = self.trailingEdgeRadius # 0.5 base drag
elif self.trailingEdgeShape == "Blunt":
TEthickness = self.trailingEdgeThickness # Full base drag
# Convert to standard rocket reference Area
trailingEdgeCd = baseDragCd * self.span * TEthickness / Aref
# Thickness / Wave Drag
#TODO: This section doesn't seem to be working quite right
if Mach <= 1:
# Thickness drag, subsonic
thicknessDrag = 4*skinFrictionCoefficient*((self.thickness/self.rootChord)*cos(self.midChordSweep) + \
(30 * (self.thickness/self.rootChord)**4 * cos(self.midChordSweep)**2) / \
(self.subsonicFinThicknessK - Mach**2 * cos(self.midChordSweep)**2)**(3/2))
else:
# Supersonic wave drag
# Using simplistic method from Hoerner - assumes diamond profile (pg 17-12, Eqn 29)
# TODO: Implement method from Barrowman's FIN program
thicknessDrag = 2.3 * self.aspectRatio * (self.thickness /
self.MACLength)**2
thicknessDrag *= self.planformArea / Aref
pressureDragCoefficient = leadingEdgeCd + trailingEdgeCd + thicknessDrag
# Total Drag --------------------------------------------------------------------------------------------------------------------
totalDragCoefficient = pressureDragCoefficient + skinFrictionDragCoefficient
localFrameRocketVelocity = AeroParameters.getLocalFrameAirVel(
rocketState, environment)
axialPositionRelCG = self.position - CG
finVelocityDueToRocketPitchYaw = rocketState.angularVelocity.crossProduct(
axialPositionRelCG)
airVelRelativeToFin = localFrameRocketVelocity - finVelocityDueToRocketPitchYaw # The negative puts it in the wind frame
CPXPos = self._getCPXPos(Mach)
#### Transfer info to fins ####
return PreComputedFinAeroData(airVelRelativeToFin, CPXPos,
totalDragCoefficient)
