def execute(self):
"""applying lifting line theory"""
AR = self.AR
N = self.N
a0 = 2*pi # Sectional lift curve slope
theta = numpy.linspace(pi/2, pi-pi/2/N, N) # locations of collocation points
a_inf , a_zeroLift = convert_units(self.a_inf, 'deg', 'rad') , convert_units(self.a_zeroLift, 'deg', 'rad')
M = numpy.zeros([N,N]) # coefficient matrix
F = numpy.zeros([N,1]) # right hand side array
for ii in range(N): # loop over span-wise location
for jj in range(N): # loop over A_n unknowns
M[ii,jj] = 4*AR/a0*sin((2*jj+1)*theta[ii]) + (2*jj+1)*sin((2*jj+1)*theta[ii])/sin(theta[ii]); # filling the coefficient matrix
####rectangular wing only#### otherwise AR = b**2/S = b/c
F[:] = (a_inf - a_zeroLift) # assuming no twist
A = numpy.linalg.solve(M,F) # solving the sys
self.A = A
## OUTPUT
#CL
self.CL = pi*self.AR*A[0][0]
#CDi & K
sum = 0;
for i in range(N):
sum = sum + (2*i+1)*A[i][0]**2;
Del = sum/A[0][0]**2 - 1
e = 1/(1+Del)
self.K = 1/(pi*AR*e)
self.CDi = pi*self.AR*sum;
print'CL', self.CL
print'CDi', self.CDi
def execute(self):
""" Simulate the vehicle model at full throttle."""
# Set initial throttle, gear, and velocity
time = 0.0
velocity = 0.0
throttle = 1.0
gear = 1
while velocity < self.end_speed:
self._velocity_str_expr.set(velocity)
self._throttle_str_expr.set(throttle)
self._gear_str_expr.set(gear)
self.run_iteration()
acceleration = self._acceleration_str_expr.evaluate(self.parent)
overspeed = self._overspeed_str_expr.evaluate(self.parent)
# If the next gear can produce more torque, let's shift.
if gear < 5:
self._gear_str_expr.set(gear + 1)
self.run_iteration()
acceleration2 = self._acceleration_str_expr.evaluate(
self.parent)
if acceleration2 > acceleration:
gear += 1
acceleration = acceleration2
overspeed = self._overspeed_str_expr.evaluate(self.parent)
# If RPM goes over MAX RPM, shift gears
# (i.e.: shift at redline)
if overspeed:
gear += 1
self._gear_str_expr.set(gear)
self.run_iteration()
acceleration = self._acceleration_str_expr.evaluate(
self.parent)
overspeed = self._overspeed_str_expr.evaluate(self.parent)
if overspeed:
self.raise_exception("Gearing problem in Accel test.",
RuntimeError)
acceleration = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
if acceleration <= 0.0:
self.raise_exception("Vehicle could not reach maximum speed "+\
"in Acceleration test.", RuntimeError)
velocity += (acceleration * self.timestep)
time += self.timestep
self.accel_time = time
def execute(self):
""" Simulate the vehicle model at full throttle."""
# Set initial throttle, gear, and velocity
time = 0.0
velocity = 0.0
throttle = 1.0
gear = 1
while velocity < self.end_speed:
self.set_parameter_by_name('velocity', velocity)
self.set_parameter_by_name('throttle', throttle)
self.set_parameter_by_name('gear', gear)
self.run_iteration()
objectives = self.get_objectives()
acceleration = objectives['acceleration'].evaluate(self.parent)
overspeed = objectives['overspeed'].evaluate(self.parent)
# If the next gear can produce more torque, let's shift.
if gear < 5:
self.set_parameter_by_name('gear', gear+1)
self.run_iteration()
acceleration2 = objectives['acceleration'].evaluate(self.parent)
if acceleration2 > acceleration:
gear += 1
acceleration = acceleration2
overspeed = objectives['overspeed'].evaluate(self.parent)
# If RPM goes over MAX RPM, shift gears
# (i.e.: shift at redline)
if overspeed:
gear += 1
self.set_parameter_by_name('gear', gear)
self.run_iteration()
acceleration = objectives['acceleration'].evaluate(self.parent)
overspeed = objectives['overspeed'].evaluate(self.parent)
if overspeed:
self.raise_exception("Gearing problem in Accel test.",
RuntimeError)
acceleration = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
if acceleration <= 0.0:
self.raise_exception("Vehicle could not reach maximum speed "+\
"in Acceleration test.", RuntimeError)
velocity += (acceleration*self.timestep)
time += self.timestep
self.accel_time = time
def execute(self):
Velocity = 35.0 #assume 35ft/s
Len_fuse = self.Len_fuse
Wid_fuse = self.Wid_fuse
Hgt_fuse = self.Hgt_fuse
S_ref = self.S_wing # reference area = wing area for small twist & dihedral
c_wr = self.c_wr
c_ht = self.c_ht
c_vt = self.c_vt
Airfoil_t_over_c_wing = self.Airfoil_t_over_c_wing
Airfoil_t_over_c_tail = self.Airfoil_t_over_c_tail
# Wetted surfaces
Swet_wing = self.S_wing*2.0*(1+0.2*Airfoil_t_over_c_wing) # wetted area for wing
Swet_ht = self.S_ht*2.0*(1+0.2*Airfoil_t_over_c_tail)
Swet_vt = self.S_vt*2.0*(1+0.2*Airfoil_t_over_c_tail)
Swet_fuse = Len_fuse * (Wid_fuse + Hgt_fuse)*2 # in**3
Swet_fuse = convert_units(Swet_fuse, 'inch**3', 'ft**3')
# form factors
k_wing = 1 + 2*1.1*(Airfoil_t_over_c_wing) + 1.1**2*(Airfoil_t_over_c_wing)**2*(1+5)/2
k_tail = 1 + 2*1.1*(Airfoil_t_over_c_tail) + 1.1**2*(Airfoil_t_over_c_tail)**2*(1+5)/2
d = (Wid_fuse**2+Hgt_fuse**2)**0.5/Len_fuse
D = (1-d**2)**0.5
a = 2*d**2/(D**3*(math.atanh(D)-D))
k_fuse = (1 + 2.3*(a/(2-a)))**2
# skin friction coefficient
cf_fuse = 1.328/((Len_fuse/12)*Velocity/(1.58*10**-4))**.5
cf_w = 1.328/((c_wr/12)*Velocity/(1.58*10**-4))**.5
cf_ht = 1.328/((c_ht/12)*Velocity/(1.58*10**-4))**.5
cf_vt = 1.328/((c_vt/12)*Velocity/(1.58*10**-4))**.5
self.Cd_p = (k_wing*cf_w*Swet_wing+k_fuse*cf_fuse*Swet_fuse+k_tail*cf_ht*Swet_ht+k_tail*cf_vt*Swet_vt)/S_ref
print 'cdp', self.Cd_p
def set(self, obj, name, value):
""" Set all target values. """
for wref, attr, indices in self._targets:
if indices:
obj = getattr(wref(), attr)
for index in indices[:-1]:
obj = object[index]
if isinstance(value, AttrWrapper):
src_units = value.metadata['units']
dst_units = obj.trait(name).units
if dst_units and src_units and src_units != dst_units:
obj[indices[-1]] = \
convert_units(value.value, src_units, dst_units)
else:
obj[indices[-1]] = value.value
else:
obj[indices[-1]] = value
else:
setattr(wref(), attr, value)
def set(self, obj, name, value):
""" Set all target values. """
for wref, attr, indices in self._targets:
if indices:
obj = getattr(wref(), attr)
for index in indices[:-1]:
obj = object[index]
if isinstance(value, AttrWrapper):
src_units = value.metadata['units']
dst_units = obj.trait(name).units
if dst_units and src_units and src_units != dst_units:
obj[indices[-1]] = \
convert_units(value.value, src_units, dst_units)
else:
obj[indices[-1]] = value.value
else:
obj[indices[-1]] = value
else:
setattr(wref(), attr, value)
def execute(self):
""" The 5-speed manual transmission is simulated by determining the
torque output and engine RPM via the gear ratios.
"""
ratios = [0.0, self.ratio1, self.ratio2, self.ratio3, self.ratio4,
self.ratio5]
gear = self.current_gear
differential = self.final_drive_ratio
tire_circ = self.tire_circ
velocity = convert_units(self.velocity, 'mi/h', 'inch/min')
self.RPM = (ratios[gear]*differential \
*velocity)/(tire_circ)
self.torque_ratio = ratios[gear]*differential
# At low speeds, hold engine speed at 1000 RPM and
# partially engage clutch
if self.RPM < 1000.0 and self.current_gear == 1 :
self.RPM = 1000.0
def execute(self):
""" Simulate the vehicle over a velocity profile."""
# Set initial throttle, gear, and velocity
throttle = 1.0
gear = 1
time1 = 0.0
velocity1 = 0.0
profile_stream = resource_stream('openmdao.examples.enginedesign',
self.profilename)
profile_reader = reader(profile_stream, delimiter=',')
distance = 0.0
fuelburn = 0.0
self._gear_str_expr.set(gear)
for row in profile_reader:
time2 = float(row[0])
velocity2 = float(row[1])
converged = 0
command_accel = (velocity2-velocity1)/(time2-time1)
#------------------------------------------------------------
# Choose the correct Gear
#------------------------------------------------------------
# First, if speed is less than 10 mph, put it in first gear.
# Note: some funky gear ratios might not like this.
# So, it's a hack for now.
if velocity1 < self.shiftpoint1:
gear = 1
self._gear_str_expr.set(gear)
# Find out min and max accel in current gear.
throttle = self.throttle_min
self._velocity_str_expr.set(velocity1)
self._throttle_str_expr.set(throttle)
gear = self._findgear(velocity1, throttle, gear)
acceleration = self._acceleration_str_expr.evaluate(self.parent)
accel_min = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
# Upshift if commanded accel is less than closed-throttle accel
# The net effect of this will often be a shift to a higher gear
# when the vehicle stops accelerating, which is reasonable.
# Note, this isn't a While loop, because we don't want to shift
# to 5th every time we slow down.
if command_accel < accel_min and gear < 5 and \
velocity1 > self.shiftpoint1:
gear += 1
self._gear_str_expr.set(gear)
gear = self._findgear(velocity1, throttle, gear)
acceleration = self._acceleration_str_expr.evaluate(self.parent)
accel_min = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
throttle = self.throttle_max
self._throttle_str_expr.set(throttle)
self.run_iteration()
acceleration = self._acceleration_str_expr.evaluate(self.parent)
accel_max = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
# Downshift if commanded accel > wide-open-throttle accel
while command_accel > accel_max and gear > 1:
gear -= 1
self._gear_str_expr.set(gear)
gear = self._findgear(velocity1, throttle, gear)
acceleration = self._acceleration_str_expr.evaluate(self.parent)
accel_max = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
# If engine cannot accelerate quickly enough to match profile,
# then raise exception
if command_accel > accel_max:
self.raise_exception("Vehicle is unable to achieve " \
"acceleration required to match EPA driving profile.",
RuntimeError)
#------------------------------------------------------------
# Bisection solution to find correct Throttle position
#------------------------------------------------------------
# Deceleration at closed throttle
throttle = self.throttle_min
self._throttle_str_expr.set(throttle)
self.run_iteration()
acceleration = self._acceleration_str_expr.evaluate(self.parent)
if command_accel >= accel_min:
min_acc = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
max_acc = accel_max
min_throttle = self.throttle_min
max_throttle = self.throttle_max
new_throttle = .5*(min_throttle + max_throttle)
# Numerical solution to find throttle that matches accel
while not converged:
throttle = new_throttle
self._throttle_str_expr.set(throttle)
self.run_iteration()
acceleration = self._acceleration_str_expr.evaluate(self.parent)
new_acc = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
if abs(command_accel-new_acc) < self.tolerance:
converged = 1
else:
if new_acc < command_accel:
min_throttle = new_throttle
min_acc = new_acc
step = (command_accel-min_acc)/(max_acc-new_acc)
new_throttle = min_throttle + \
step*(max_throttle-min_throttle)
else:
max_throttle = new_throttle
step = (command_accel-min_acc)/(new_acc-min_acc)
new_throttle = min_throttle + \
step*(max_throttle-min_throttle)
max_acc = new_acc
distance += .5*(velocity2+velocity1)*(time2-time1)
burn_rate = self._fuel_burn_str_expr.evaluate(self.parent)
fuelburn += burn_rate*(time2-time1)
velocity1 = velocity2
time1 = time2
#print "T = %f, V = %f, Acc = %f" % (time1, velocity1,
#command_accel)
#print gear, accel_min, accel_max
# Convert liter to gallon and sec/hr to hr/hr
distance = convert_units(distance, 'mi*s/h', 'mi')
fuelburn = convert_units(fuelburn, 'L', 'galUS')
self.fuel_economy = distance/fuelburn
def example_218WD_3MW():
example = optimizationSpar()
tt = time.time()
example.spar.number_of_sections = 4
example.spar.outer_diameter = [5., 6., 6., 9.]
example.spar.length = [6., 12., 15., 47.]
example.spar.end_elevation = [7., -5., -20., -67.]
example.spar.start_elevation = [13., 7., -5., -20.]
example.spar.bulk_head = ['N', 'T', 'N', 'B']
example.spar.water_depth = 218.
example.spar.load_condition = 'N'
example.spar.significant_wave_height = 10.820
example.spar.significant_wave_period = 9.800
example.spar.wind_reference_speed = 11.
example.spar.wind_reference_height = 75.
example.spar.alpha = 0.110
example.spar.RNA_keel_to_CG = 142.
example.spar.RNA_mass = 125000.
example.spar.tower_mass = 127877.
example.spar.tower_center_of_gravity = 23.948
example.spar.tower_wind_force = 19950.529
example.spar.RNA_wind_force = 391966.178
example.spar.RNA_center_of_gravity_x = 4.1
example.spar.mooring_total_cost = 810424.053596
example.spar.mooring_keel_to_CG = 54.000
example.spar.mooring_vertical_load = 1182948.791
example.spar.mooring_horizontal_stiffness = 3145.200
example.spar.mooring_vertical_stiffness =7111.072
example.spar.sum_forces_x = [7886.848,437.844,253.782,174.651,124.198,85.424,50.689,17.999,-13.222,-43.894,-74.245,-105.117,-136.959,-170.729,-207.969,-251.793,-307.638,-386.514,-518.734,-859.583,-11091.252]
example.spar.offset_x = [-40.362,-35.033,-29.703,-24.373,-19.044,-13.714,-8.385,-3.055,2.274,7.604,12.933,18.263,23.593,28.922,34.252,39.581,44.911,50.240,55.570,60.900,66.229]
example.spar.damaged_mooring = [-40.079,65.824]
example.spar.intact_mooring = [-39.782,65.399]
example.spar.run()
example.run()
yna = convert_units(example.spar.neutral_axis ,'m','inch')
fullStiffeners = full_stiffeners_table()
for i in range (0,len(fullStiffeners)-1):
stiffener_bef = fullStiffeners[i]
stiffener_aft = fullStiffeners[i+1]
if yna > stiffener_bef[6] and yna<stiffener_aft[6]:
opt_index = i+1
second_fit = Spar()
second_fit.wall_thickness = example.spar.wall_thickness
second_fit.number_of_rings = example.spar.number_of_rings
second_fit.stiffener_curve_fit = False
second_fit.stiffener_index = opt_index
second_fit.number_of_sections = example.spar.number_of_sections
second_fit.outer_diameter = example.spar.outer_diameter
second_fit.length = example.spar.length
second_fit.end_elevation = example.spar.end_elevation
second_fit.start_elevation = example.spar.start_elevation
second_fit.bulk_head = example.spar.bulk_head
second_fit.water_depth = example.spar.water_depth
second_fit.load_condition = example.spar.load_condition
second_fit.significant_wave_height = example.spar.significant_wave_height
second_fit.significant_wave_period = example.spar.significant_wave_period
second_fit.wind_reference_speed = example.spar.wind_reference_speed
second_fit.wind_reference_height = example.spar.wind_reference_height
second_fit.alpha = example.spar.alpha
second_fit.RNA_keel_to_CG = example.spar.RNA_keel_to_CG
second_fit.RNA_mass = example.spar.RNA_mass
second_fit.tower_mass = example.spar.tower_mass
second_fit.tower_center_of_gravity = example.spar.tower_center_of_gravity
second_fit.tower_wind_force = example.spar.tower_wind_force
second_fit.RNA_wind_force = example.spar.RNA_wind_force
second_fit.RNA_center_of_gravity_x = example.spar.RNA_center_of_gravity_x
second_fit.mooring_total_cost = example.spar.mooring_total_cost
second_fit.mooring_keel_to_CG = example.spar.mooring_keel_to_CG
second_fit.mooring_vertical_load = example.spar.mooring_vertical_load
second_fit.mooring_horizontal_stiffness = example.spar.mooring_horizontal_stiffness
second_fit.mooring_vertical_stiffness = example.spar.mooring_vertical_stiffness
second_fit.sum_forces_x = example.spar.sum_forces_x
second_fit.offset_x = example.spar.offset_x
second_fit.damaged_mooring = example.spar.damaged_mooring
second_fit.intact_mooring = example.spar.intact_mooring
second_fit.run()
cost = second_fit.total_cost
index = opt_index
best_index = opt_index
unity = max(second_fit.web_compactness,second_fit.flange_compactness,max(second_fit.VAL),max(second_fit.VAG),max(second_fit.VEL),max(second_fit.VEG))
for i in range(opt_index,326):
index += 1
second_fit.stiffener_index = index
second_fit.run()
unity = max(second_fit.web_compactness,second_fit.flange_compactness,max(second_fit.VAL),max(second_fit.VAG),max(second_fit.VEL),max(second_fit.VEG))
if unity < 1.0:
if second_fit.total_cost < cost :
cost=second_fit.total_cost
best_index = i
second_fit.stiffener_index = best_index
second_fit.run()
print '--------------example_218WD_3MW------------------'
print "Elapsed time: ", time.time()-tt, " seconds"
sys_print(second_fit)
def execute(self):
""" Simulate the vehicle over a velocity profile."""
# Set initial throttle, gear, and velocity
throttle = 1.0
gear = 1
time1 = 0.0
velocity1 = 0.0
profile_stream = resource_stream('openmdao.examples.enginedesign',
self.profilename)
profile_reader = reader(profile_stream, delimiter=',')
distance = 0.0
fuelburn = 0.0
self._gear_str_expr.set(gear)
for row in profile_reader:
time2 = float(row[0])
velocity2 = float(row[1])
converged = 0
command_accel = (velocity2 - velocity1) / (time2 - time1)
#------------------------------------------------------------
# Choose the correct Gear
#------------------------------------------------------------
# First, if speed is less than 10 mph, put it in first gear.
# Note: some funky gear ratios might not like this.
# So, it's a hack for now.
if velocity1 < self.shiftpoint1:
gear = 1
self._gear_str_expr.set(gear)
# Find out min and max accel in current gear.
throttle = self.throttle_min
self._velocity_str_expr.set(velocity1)
self._throttle_str_expr.set(throttle)
gear = self._findgear(velocity1, throttle, gear)
acceleration = self._acceleration_str_expr.evaluate(self.parent)
accel_min = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
# Upshift if commanded accel is less than closed-throttle accel
# The net effect of this will often be a shift to a higher gear
# when the vehicle stops accelerating, which is reasonable.
# Note, this isn't a While loop, because we don't want to shift
# to 5th every time we slow down.
if command_accel < accel_min and gear < 5 and \
velocity1 > self.shiftpoint1:
gear += 1
self._gear_str_expr.set(gear)
gear = self._findgear(velocity1, throttle, gear)
acceleration = self._acceleration_str_expr.evaluate(
self.parent)
accel_min = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
throttle = self.throttle_max
self._throttle_str_expr.set(throttle)
self.run_iteration()
acceleration = self._acceleration_str_expr.evaluate(self.parent)
accel_max = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
# Downshift if commanded accel > wide-open-throttle accel
while command_accel > accel_max and gear > 1:
gear -= 1
self._gear_str_expr.set(gear)
gear = self._findgear(velocity1, throttle, gear)
acceleration = self._acceleration_str_expr.evaluate(
self.parent)
accel_max = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
# If engine cannot accelerate quickly enough to match profile,
# then raise exception
if command_accel > accel_max:
self.raise_exception("Vehicle is unable to achieve " \
"acceleration required to match EPA driving profile.",
RuntimeError)
#------------------------------------------------------------
# Bisection solution to find correct Throttle position
#------------------------------------------------------------
# Deceleration at closed throttle
throttle = self.throttle_min
self._throttle_str_expr.set(throttle)
self.run_iteration()
acceleration = self._acceleration_str_expr.evaluate(self.parent)
if command_accel >= accel_min:
min_acc = convert_units(acceleration, 'm/(s*s)', 'mi/(h*s)')
max_acc = accel_max
min_throttle = self.throttle_min
max_throttle = self.throttle_max
new_throttle = .5 * (min_throttle + max_throttle)
# Numerical solution to find throttle that matches accel
while not converged:
throttle = new_throttle
self._throttle_str_expr.set(throttle)
self.run_iteration()
acceleration = self._acceleration_str_expr.evaluate(
self.parent)
new_acc = convert_units(acceleration, 'm/(s*s)',
'mi/(h*s)')
if abs(command_accel - new_acc) < self.tolerance:
converged = 1
else:
if new_acc < command_accel:
min_throttle = new_throttle
min_acc = new_acc
step = (command_accel - min_acc) / (max_acc -
new_acc)
new_throttle = min_throttle + \
step*(max_throttle-min_throttle)
else:
max_throttle = new_throttle
step = (command_accel - min_acc) / (new_acc -
min_acc)
new_throttle = min_throttle + \
step*(max_throttle-min_throttle)
max_acc = new_acc
distance += .5 * (velocity2 + velocity1) * (time2 - time1)
burn_rate = self._fuel_burn_str_expr.evaluate(self.parent)
fuelburn += burn_rate * (time2 - time1)
velocity1 = velocity2
time1 = time2
#print "T = %f, V = %f, Acc = %f" % (time1, velocity1,
#command_accel)
#print gear, accel_min, accel_max
# Convert liter to gallon and sec/hr to hr/hr
distance = convert_units(distance, 'mi*s/h', 'mi')
fuelburn = convert_units(fuelburn, 'L', 'galUS')
self.fuel_economy = distance / fuelburn
#Radiative area = surface area
self.radArea = self.convArea
check('radArea',self.radArea,3374876.115)
#P/A = SB*emmisitivity*(T^4 - To^4)
self.qRad = self.SBconst*self.tubeEmissivity*((self.tubeWallTemp**4) - (self.ambientTemp**4))
check('qRad',self.qRad,59.7)
#P = A * (P/A)
self.qRadTot = self.radArea * self.qRad
check('qRadTot',self.qRadTot,201533208)
#------------
#Sum Up
self.Qout = self.qRadTot + self.naturalConvectionTot
self.Qin = self.solarHeatTotal + self.podQTot
check('Qout',self.Qout,394673364.)
#run stand-alone component
if __name__ == "__main__":
from openmdao.main.api import set_as_top
test = tubeModel()
set_as_top(test)
print ""
test.run()
print "-----Completed Tube Heat Flux Model Calculations---"
print ""
print "Equilibrium Wall Temperature: {} K or {} F".format(test.tubeWallTemp, convert_units(test.tubeWallTemp,'degK','degF'))
print "Ambient Temperature: {} K or {} F".format(test.ambientTemp, convert_units(test.ambientTemp,'degK','degF'))
print "Q Out = {} W ==> Q In = {} W ==> Error: {}%".format(test.Qout,test.Qin,((test.Qout-test.Qin)/test.Qout)*100)
def execute(self):
Len_fuse = convert_units(self.Len_fuse,'inch','ft')
Wid_fuse = convert_units(self.Wid_fuse,'inch','ft')
Hgt_fuse = convert_units(self.Hgt_fuse,'inch','ft')
c_w = self.c_w
c_ht = self.c_ht
c_vt = self.c_vt
x_wLE = self.x_wLE
x_tLE = self.x_tLE
x_cg = self.x_cg
b_w = self.b_w
b_ht = self.b_ht
b_vt = self.b_vt
#itername = self.itername
count = self.exec_count
fig1 = plt.figure(1)
fig2 = plt.figure(2)
ax1 = fig1.add_subplot(111,projection='3d')
ax2 = fig2.add_subplot(111)
ax1.cla()
ax2.cla()
# Fuselage
x = [0.0 , 0.0 , 0.0 , 0.0 , 0.0 , Len_fuse , Len_fuse , Len_fuse , Len_fuse , Len_fuse]
y = [-Wid_fuse/2 , -Wid_fuse/2 , Wid_fuse/2 , Wid_fuse/2 , -Wid_fuse/2 , -Wid_fuse/2 , -Wid_fuse/2 , Wid_fuse/2 , Wid_fuse/2 , -Wid_fuse/2]
z = [-Hgt_fuse/2 , Hgt_fuse/2 , Hgt_fuse/2 , -Hgt_fuse/2 , -Hgt_fuse/2 , -Hgt_fuse/2 , Hgt_fuse/2 , Hgt_fuse/2 , -Hgt_fuse/2 , -Hgt_fuse/2]
ax1.plot(x, y, z, 'k-')
ax2.plot(x, y, 'k-')
x = [0.0 , Len_fuse]
y = [-Wid_fuse/2 , -Wid_fuse/2]
z = [Hgt_fuse/2 , Hgt_fuse/2]
ax1.plot(x, y, z, 'k-')
ax2.plot(x, y, 'k-')
x = [0.0 , Len_fuse]
y = [Wid_fuse/2 , Wid_fuse/2]
z = [-Hgt_fuse/2 , -Hgt_fuse/2]
ax1.plot(x, y, z, 'k-')
ax2.plot(x, y, 'k-')
x = [0.0 , Len_fuse]
y = [Wid_fuse/2 , Wid_fuse/2]
z = [Hgt_fuse/2 , Hgt_fuse/2]
ax1.plot(x, y, z, 'k-')
ax2.plot(x, y, 'k-')
# Wing
x = [x_wLE , x_wLE , x_wLE+c_w , x_wLE+c_w]
y = [Wid_fuse/2, b_w/2 , b_w/2 , Wid_fuse/2]
z = [0.0 , 0.0 , 0.0 , 0.0]
ax1.plot(x, y, z, 'b-')
ax2.plot(x, y, 'b-')
x = [x_wLE , x_wLE , x_wLE+c_w , x_wLE+c_w]
y = [-Wid_fuse/2, -b_w/2 , -b_w/2 , -Wid_fuse/2]
ax1.plot(x, y, z, 'b-')
ax2.plot(x, y, 'b-')
# Tailboom
x = [x_wLE+c_w*0.25 , x_tLE]
y = [0.0 , 0.0]
z = [0.0 , 0.0]
ax1.plot(x, y, z, 'r-')
ax2.plot(x, y, 'r-')
# HT
x = [x_tLE , x_tLE , x_tLE+c_ht , x_tLE+c_ht , x_tLE]
y = [b_ht/2 , -b_ht/2 , -b_ht/2 , b_ht/2 , b_ht/2]
z = [0.0 , 0.0 , 0.0 , 0.0 , 0.0]
ax1.plot(x, y, z, 'g-')
ax2.plot(x, y, 'g-')
# VT
x = [x_tLE , x_tLE , x_tLE+c_vt , x_tLE+c_vt , x_tLE]
y = [0.0 , 0.0 , 0.0 , 0.0 , 0.0]
z = [0.0 , b_vt , b_vt , 0.0 , 0.0]
ax1.plot(x, y, z, 'g-')
ax2.plot(x, y, 'g-')
# c.g.
x = x_cg
y = 0.0
ax2.plot(x,y,'kx')
# Wing ac location
x = x_wLE+0.25*c_w
y = 0.0
ax2.plot(x,y,'b+')
# H-tail ac location
x = x_tLE+0.25*c_ht
y = 0.0
ax2.plot(x,y,'g+')
#plt.xlim([-10,10])
#plt.ylim([-10,10])
ax1.auto_scale_xyz([-5,9],[-7,7],[-7,7])
ax2.axis([-5,9,-7,7])
ax1.view_init(35.27,225)
ax1.set_xlabel('x')
ax1.set_ylabel('y')
ax1.set_zlabel('z')
ax2.set_xlabel('x')
ax2.set_ylabel('y')
#fname1 = 'movie/3D/%10s_image3D.png' %itername
#fname2 = 'movie/2D/%10s_image2D.png' %itername
fname1 = 'movie/3D/%03d_image3D.png' %count
fname2 = 'movie/2D/%03d_image2D.png' %count
p = 'Payload: %.2f lbs' %self.W_payload
ax1.text(2, -2, -7, p, color='red')
#fig1.savefig('movie/image1.png')
#fig2.savefig('movie/image2.png')
fig1.savefig(fname1)
fig2.savefig(fname2)
def execute(self):
'''
'''
# assign all varibles
gravity = self.gravity
air_density = self.air_density
water_density = self.water_density
water_depth = self.water_depth
load_condition = self.load_condition
significant_wave_height = self.significant_wave_height
significant_wave_period = self.significant_wave_period
if significant_wave_height != 0:
significant_wave_height = 1.86 * significant_wave_height
significant_wave_period = 0.71 * significant_wave_period
WAVEL = gravity * significant_wave_period**2 / (2 * pi)
WAVEN = 2 * pi / WAVEL
wind_reference_speed = self.wind_reference_speed
wind_reference_height = self.wind_reference_height
alpha = self.alpha
material_density = self.material_density
E = self.E
nu = self.nu
yield_stress = self.yield_stress
permanent_ballast_height = self.permanent_ballast_height
permanent_ballast_density = self.permanent_ballast_density
fixed_ballast_height = self.fixed_ballast_height
fixed_ballast_density = self.fixed_ballast_density
RNA_mass = self.RNA_mass
RNA_kell_to_CG = self.RNA_keel_to_CG
tower_mass = self.tower_mass
tower_center_of_gravity = self.tower_center_of_gravity
tower_wind_force = self.tower_wind_force
RNA_wind_force = self.RNA_wind_force
RNA_center_of_gravity_x = self.RNA_center_of_gravity_x
mooring_vertical_load = self.mooring_vertical_load
mooring_horizontal_stiffness = self.mooring_horizontal_stiffness
mooring_vertical_stiffness = self.mooring_vertical_stiffness
mooring_keel_to_CG = self.mooring_keel_to_CG
outer_diameter_array = array(self.outer_diameter)
base_outer_diameters = outer_diameter_array[-1] # base outer diameter
wall_thickness_array = array(self.wall_thickness)
end_elevation = array(self.elevations[1:]) # end elevation
ELS = array(self.elevations[0:-1]) # start elevation
NSEC = self.number_of_sections
for i in range(0, NSEC + 1):
if self.elevations[i] > 0:
ODTW = outer_diameter_array[i + 1]
LB = ELS - end_elevation # lengths of each section
DRAFT = abs(min(end_elevation))
FB = ELS[0] # freeboard
BH = self.bulk_head
N = array(self.number_of_rings)
if self.stiffener_curve_fit: # curve fits
YNA = self.neutral_axis
D = 0.0029 + 1.3345977 * YNA
IR = 0.051 * YNA**3.7452
TW = exp(0.88132868 + 1.0261134 * log(IR) - 3.117086 * log(YNA))
AR = exp(4.6980391 + 0.36049717 * YNA**0.5 - 2.2503113 / (TW**0.5))
TFM = 1.2122528 * YNA**0.13430232 * YNA**1.069737
BF = (0.96105249 * TW**-0.59795001 * AR**0.73163096)
IR = 0.47602202 * TW**0.99500847 * YNA**2.9938134
else: # discrete, actual stiffener
allStiffeners = full_stiffeners_table()
stiffener = allStiffeners[self.stiffener_index]
stiffenerName = stiffener[0]
AR = convert_units(stiffener[1], 'inch**2', 'm**2')
D = convert_units(stiffener[2], 'inch', 'm')
TW = convert_units(stiffener[3], 'inch', 'm')
BF = convert_units(stiffener[4], 'inch', 'm')
TFM = convert_units(stiffener[5], 'inch', 'm')
YNA = convert_units(stiffener[6], 'inch', 'm')
self.neutral_axis = YNA
IR = convert_units(stiffener[7], 'inch**4', 'm**4')
HW = D - TFM # web height
SHM, RGM, BHM, SHB, SWF, SWM, SCF, SCM, KCG, KCB = calculateWindCurrentForces(
0., 0., N, AR, BH, outer_diameter_array, NSEC,
wall_thickness_array, LB, material_density, DRAFT, end_elevation,
ELS, water_density, air_density, gravity, significant_wave_height,
significant_wave_period, water_depth, wind_reference_speed,
wind_reference_height, alpha)
SHBUOY = sum(SHB) # shell buoyancy
SHMASS = sum(SHM) * self.shell_mass_factor # shell mass - VALUE
BHMASS = sum(BHM) * self.bulkhead_mass_factor # bulkhead mass - VALUE
RGMASS = sum(RGM) * self.ring_mass_factor # ring mass - VALUE
SHRMASS = SHMASS + BHMASS + RGMASS # shell and bulkhead and ring mass - VALUE
SHRM = array(SHM) + array(BHM) + array(
RGM) # # shell and bulkhead and ring mass - ARRAY
percent_shell_mass = RGMASS / SHMASS * 100.
outfitting_mass = SHRMASS * self.outfitting_factor
SMASS = SHRMASS * self.spar_mass_factor + outfitting_mass
KCG = dot(SHRM, array(KCG)) / SHRMASS # keel to center of gravity
KB = dot(array(SHB), array(KCB)) / SHBUOY # keel to center of buoyancy
BM = ((pi / 64) * ODTW**4) / (SHBUOY / water_density)
SWFORCE = sum(SWF) # shell wind force
SCFORCE = sum(
SCF
) # shell current force - NOTE: inaccurate; setting an initial value and reruns later
BVL = pi / 4. * (base_outer_diameters - 2 * wall_thickness_array[-1]
)**2. # ballast volume per length
KGPB = (permanent_ballast_height / 2.) + wall_thickness_array[-1]
PBM = BVL * permanent_ballast_height * permanent_ballast_density # permanent ballast mass
KGFB = (fixed_ballast_height /
2.) + permanent_ballast_height + wall_thickness_array[-1]
FBM = BVL * fixed_ballast_height * fixed_ballast_density # fixed ballast mass
WPA = pi / 4 * (ODTW)**2
KGT = tower_center_of_gravity + FB + DRAFT # keel to center of gravity of tower
WBM = SHBUOY - SMASS - RNA_mass - tower_mass - mooring_vertical_load / gravity - FBM - PBM # water ballast mass
WBH = WBM / (water_density * BVL) # water ballast height
KGWB = WBH / 2. + permanent_ballast_height + fixed_ballast_height + wall_thickness_array[
-1]
KGB = (SMASS * KCG + WBM * KGWB + FBM * KGFB + PBM * KGPB +
tower_mass * KGT + RNA_mass * RNA_kell_to_CG) / (
SMASS + WBM + FBM + PBM + tower_mass + RNA_mass)
KG = (SMASS * KCG + WBM * KGWB + FBM * KGFB + PBM * KGPB +
tower_mass * KGT + RNA_mass * RNA_kell_to_CG +
mooring_vertical_load / gravity * mooring_keel_to_CG) / SHBUOY
GM = KB + BM - KG
self.platform_stability_check = KG / KB
total_mass = SMASS + RNA_mass + tower_mass + WBM + FBM + PBM
VD = (RNA_wind_force + tower_wind_force + SWFORCE +
SCFORCE) / (SMASS + RNA_mass + tower_mass + FBM + PBM + WBM)
SHM, RGM, BHM, SHB, SWF, SWM, SCF, SCM, KCG, KCB = calculateWindCurrentForces(
KG, VD, N, AR, BH, outer_diameter_array, NSEC,
wall_thickness_array, LB, material_density, DRAFT, end_elevation,
ELS, water_density, air_density, gravity, significant_wave_height,
significant_wave_period, water_depth, wind_reference_speed,
wind_reference_height, alpha)
SCFORCE = sum(SCF)
# calculate moments
RWM = RNA_wind_force * (RNA_kell_to_CG - KG)
TWM = tower_wind_force * (KGT - KG)
# costs
columns_mass = sum(SHM[1::2]) + sum(RGM[1::2]) + sum(BHM[1::2])
tapered_mass = sum(SHM[0::2]) + sum(RGM[0::2]) + sum(BHM[0::2])
COSTCOL = self.straight_col_cost
COSTTAP = self.tapered_col_cost
COSTOUT = self.outfitting_cost
COSTBAL = self.ballast_cost
self.spar_cost = COSTCOL * columns_mass / 1000. + COSTTAP * tapered_mass / 1000.
self.outfit_cost = COSTOUT * outfitting_mass / 1000.
self.ballasts_cost = COSTBAL * (FBM + PBM) / 1000.
self.total_cost = self.spar_cost + self.outfit_cost + self.ballasts_cost + self.mooring_total_cost
##### SIZING TAB #####
# [TOP MASS(RNA+TOWER)]
top_mass = RNA_mass + tower_mass
KG_top = (RNA_mass * RNA_kell_to_CG + tower_mass * KGT)
# [INERTIA PROPERTIES - LOCAL]
I_top_loc = (1. / 12.) * top_mass * KG_top**2
I_hull_loc = (1. / 12.) * SMASS * (DRAFT + FB)**2
I_WB_loc = (1. / 12.) * WBM * WBH**2
I_FB_loc = (1. / 12.) * FBM * fixed_ballast_height**2
I_PB_loc = (1. / 12.) * PBM * permanent_ballast_height**2
# [INERTIA PROPERTIES - SYSTEM]
I_top_sys = I_top_loc + top_mass * (KG_top - KG)**2
I_hull_sys = I_hull_loc + SMASS * (KCG - KG)**2
I_WB_sys = I_WB_loc + WBM * (KGWB - KGB)**2
I_FB_sys = I_FB_loc + FBM * (KGFB - KGB)**2
I_PB_sys = I_PB_loc + PBM * (KGPB - KGB)**2
I_total = I_top_sys + I_hull_sys + I_WB_sys + I_FB_sys + I_PB_sys
I_yaw = total_mass * (base_outer_diameters / 2.)**2
# [ADDED MASS]
surge = (pi / 4.) * base_outer_diameters**2 * DRAFT * water_density
heave = (1 / 6.) * water_density * base_outer_diameters**3
pitch = (surge * ((KG - DRAFT) -
(KB - DRAFT))**2 + surge * DRAFT**2 / 12.) * I_total
# [OTHER SYSTEM PROPERTIES]
r_gyration = (I_total / total_mass)**0.5
CM = (SMASS * KCG + WBM * KGWB + FBM * KGFB +
PBM * KGPB) / (SMASS + WBM + FBM + PBM)
surge_period = 2 * pi * (
(total_mass + surge) / mooring_horizontal_stiffness)**0.5
# [PLATFORM STIFFNESS]
K33 = water_density * gravity * (
pi / 4.)**ODTW**2 + mooring_vertical_stiffness #heave
K44 = abs(water_density * gravity *
((pi / 4.) * (ODTW / 2.)**4 -
(KB - KG) * SHBUOY / water_density)) #roll
K55 = abs(water_density * gravity *
((pi / 4.) * (ODTW / 2.)**4 -
(KB - KG) * SHBUOY / water_density)) #pitch
# [PERIOD]
T_surge = 2 * pi * (
(total_mass + surge) / mooring_horizontal_stiffness)**0.5
T_heave = 2 * pi * ((total_mass + heave) / K33)**0.5
K_pitch = GM * SHBUOY * gravity
T_pitch = 2 * pi * (pitch / K_pitch)**0.5
F_total = RNA_wind_force + tower_wind_force + sum(SWF) + sum(SCF)
sum_FX = self.sum_forces_x
X_Offset = self.offset_x
if np.isnan(sum_FX).any() or sum_FX[-1] > (-F_total / 1000.):
self.max_offset_unity = 10.
self.min_offset_unity = 10.
else:
for j in range(1, len(sum_FX)):
if sum_FX[j] < (-F_total / 1000.):
X2 = sum_FX[j]
X1 = sum_FX[j - 1]
Y2 = X_Offset[j]
Y1 = X_Offset[j - 1]
max_offset = (Y1 + (-F_total / 1000. - X1) * (Y2 - Y1) /
(X2 - X1)) * self.offset_amplification_factor
i = 0
while sum_FX[i] > (F_total / 1000.):
i += 1
min_offset = (
X_Offset[i - 1] + (F_total / 1000. - sum_FX[i - 1]) *
(X_Offset[i] - X_Offset[i - 1]) /
(sum_FX[i] - sum_FX[i - 1])) * self.offset_amplification_factor
# unity checks!
if self.load_condition == 'E':
self.max_offset_unity = max_offset / self.damaged_mooring[1]
self.min_offset_unity = min_offset / self.damaged_mooring[0]
elif self.load_condition == 'N':
self.max_offset_unity = max_offset / self.intact_mooring[1]
self.min_offset_unity = min_offset / self.intact_mooring[0]
M_total = RWM + TWM + sum(SWM) + sum(SCM) + (
-F_total * (mooring_keel_to_CG - KG)) + (RNA_mass * gravity *
-RNA_center_of_gravity_x)
self.heel_angle = (M_total / K_pitch) * 180. / pi
##### API BULLETIN #####
# shell data
RO = outer_diameter_array / 2. # outer radius
R = RO - wall_thickness_array / 2. # radius to centerline of wall/mid fiber radius
# ring data
LR = LB / (N + 1.) # number of ring spacing
#shell and ring data
RF = RO - HW # radius to flange
MX = LR / (R * wall_thickness_array)**0.5 # geometry parameter
# effective width of shell plate in longitudinal direction
LE = np.array([0.] * NSEC)
for i in range(0, NSEC):
if MX[i] <= 1.56:
LE[i] = LR[i]
else:
LE = 1.1 * (2 * R * wall_thickness_array)**0.5 + TW
# ring properties with effective shell plate
AER = AR + LE * wall_thickness_array # cross sectional area with effective shell
YENA = (LE * wall_thickness_array * wall_thickness_array / 2 +
HW * TW * (HW / 2 + wall_thickness_array) + TFM * BF *
(TFM / 2 + HW + wall_thickness_array)) / AER
IER = IR + AR * (
YNA + wall_thickness_array / 2.
)**2 * LE * wall_thickness_array / AER + LE * wall_thickness_array**3 / 12. # moment of inertia
RC = RO - YENA - wall_thickness_array / 2. # radius to centroid of ring stiffener
# set loads (0 mass loads for external pressure)
MBALLAST = PBM + FBM + WBM # sum of all ballast masses
W = (RNA_mass + tower_mass + MBALLAST + SMASS) * gravity
P = water_density * gravity * abs(
end_elevation) # hydrostatic pressure at depth of section bottom
if significant_wave_height != 0: # dynamic head
DH = significant_wave_height / 2 * (
np.cosh(WAVEN * (water_depth - abs(end_elevation))) /
np.cosh(WAVEN * water_depth))
else:
DH = 0
P = P + water_density * gravity * DH # hydrostatic pressure + dynamic head
GF = self.gust_factor
#-----RING SECTION COMPACTNESS (SECTION 7)-----#
self.flange_compactness = (0.5 * BF / TFM) / (0.375 *
(E / yield_stress)**0.5)
self.web_compactness = (HW / TW) / ((E / yield_stress)**0.5)
#-----PLATE AND RING STRESS (SECTION 11)-----#
# shell hoop stress at ring midway
Dc = E * wall_thickness_array**3 / (12 * (1 - nu**2)) # parameter D
BETAc = (E * wall_thickness_array /
(4 * RO**2 * Dc))**0.25 # parameter beta
TWS = AR / HW
dum1 = BETAc * LR
KT = 8 * BETAc**3 * Dc * (np.cosh(dum1) - np.cos(dum1)) / (
np.sinh(dum1) + np.sin(dum1))
KD = E * TWS * (RO**2 - RF**2) / (RO * ((1 + nu) * RO**2 +
(1 - nu) * RF**2))
dum = dum1 / 2.
PSIK = 2 * (np.sin(dum) * np.cosh(dum) + np.cos(dum) *
np.sinh(dum)) / (np.sinh(dum1) + np.sin(dum1))
PSIK = PSIK.clip(
min=0) # psik >= 0; set all negative values of psik to zero
SIGMAXA = -W / (2 * pi * R * wall_thickness_array)
PSIGMA = P + (nu * SIGMAXA * wall_thickness_array) / RO
PSIGMA = np.minimum(PSIGMA, P) # PSIGMA has to be <= P
dum = KD / (KD + KT)
KTHETAL = 1 - PSIK * PSIGMA / P * dum
FTHETAS = KTHETAL * P * RO / wall_thickness_array
# shell hoop stress at ring
KTHETAG = 1 - (PSIGMA / P * dum)
FTHETAR = KTHETAG * P * RO / wall_thickness_array
#-----LOCAL BUCKLING (SECTION 4)-----#
# axial compression and bending
ALPHAXL = 9 / (300 + (2 * R) / wall_thickness_array)**0.4
CXL = (1 + (150 / ((2 * R) / wall_thickness_array)) * (ALPHAXL**2) *
(MX**4))**0.5
FXEL = CXL * (pi**2 * E / (12 * (1 - nu**2))) * (wall_thickness_array /
LR)**2 # elastic
FXCL = np.array(NSEC * [0.])
for i in range(0, len(FXEL)):
FXCL[i] = plasticityRF(FXEL[i], yield_stress) # inelastic
# external pressure
BETA = np.array([0.] * NSEC)
ALPHATHETAL = np.array([0.] * NSEC)
global ZM
ZM = 12 * (MX**2 * (1 - nu**2)**.5)**2 / pi**4
for i in range(0, NSEC):
f = lambda x: x**2 * (1 + x**2)**4 / (2 + 3 * x**2) - ZM[i]
ans = roots(f, 0., 15.)
ans_array = np.asarray(ans)
is_scalar = False if ans_array.ndim > 0 else True
if is_scalar:
BETA[i] = ans
else:
BETA[i] = float(min(ans_array))
if MX[i] < 5:
ALPHATHETAL[i] = 1
elif MX[i] >= 5:
ALPHATHETAL[i] = 0.8
n = np.round(BETA * pi * R / LR) # solve for smallest whole number n
BETA = LR / (pi * R / n)
left = (1 + BETA**2)**2 / (0.5 + BETA**2)
right = 0.112 * MX**4 / ((1 + BETA**2)**2 * (0.5 + BETA**2))
CTHETAL = (left + right) * ALPHATHETAL
FREL = CTHETAL * pi**2 * E * (wall_thickness_array / LR)**2 / (
12 * (1 - nu**2)) # elastic
FRCL = np.array(NSEC * [0.])
for i in range(0, len(FREL)):
FRCL[i] = plasticityRF(FREL[i], yield_stress) # inelastic
#-----GENERAL INSTABILITY (SECTION 4)-----#
# axial compression and bending
AC = AR / (LR * wall_thickness_array) # Ar bar
ALPHAX = 0.85 / (1 + 0.0025 *
(outer_diameter_array / wall_thickness_array))
ALPHAXG = np.array([0.] * NSEC)
for i in range(0, NSEC):
if AC[i] >= 0.2:
ALPHAXG[i] = 0.72
elif AC[i] > 0.06 and AC[i] < 0.2:
ALPHAXG[i] = (3.6 - 0.5 * ALPHAX[i]) * AC[i] + ALPHAX[i]
else:
ALPHAXG[i] = ALPHAX[i]
FXEG = ALPHAXG * 0.605 * E * wall_thickness_array / R * (
1 + AC)**0.5 # elastic
FXCG = np.array(NSEC * [0.])
for i in range(0, len(FXEG)):
FXCG[i] = plasticityRF(FXEG[i], yield_stress) # inelastic
# external pressure
ALPHATHETAG = 0.8
LAMBDAG = pi * R / LB
k = 0.5
PEG = np.array([0.] * NSEC)
for i in range(0, NSEC):
t = wall_thickness_array[i]
r = R[i]
lambdag = LAMBDAG[i]
ier = IER[i]
rc = RC[i]
ro = RO[i]
lr = LR[i]
def f(x, E, t, r, lambdag, k, ier, rc, ro, lr):
return E * (t / r) * lambdag**4 / (
(x**2 + k * lambdag**2 - 1) *
(x**2 + lambdag**2)**2) + E * ier * (x**2 -
1) / (lr * rc**2 * ro)
x0 = [2]
m = float(
fmin(f,
x0,
xtol=1e-3,
args=(E, t, r, lambdag, k, ier, rc, ro,
lr))) # solve for n that gives minimum P_eG
PEG[i] = f(m, E, t, r, lambdag, k, ier, rc, ro, lr)
ALPHATHETAG = 0.8 #adequate for ring stiffeners
FREG = ALPHATHETAG * PEG * RO * KTHETAG / wall_thickness_array # elastic
FRCG = np.array(NSEC * [0.])
for i in range(0, len(FREG)):
FRCG[i] = plasticityRF(FREG[i], yield_stress) # inelastic
# General Load Case
NPHI = W / (2 * pi * R)
NTHETA = P * RO
K = NPHI / NTHETA
#-----Local Buckling (SECTION 6) - Axial Compression and bending-----#
C = (FXCL + FRCL) / yield_stress - 1
KPHIL = 1
CST = K * KPHIL / KTHETAL
FTHETACL = np.array([0.] * NSEC)
bnds = (0, None)
for i in range(0, NSEC):
cst = CST[i]
fxcl = FXCL[i]
frcl = FRCL[i]
c = C[i]
x = Symbol('x')
ans = solve((cst * x / fxcl)**2 - c * (cst * x / fxcl) *
(x / frcl) + (x / frcl)**2 - 1, x)
FTHETACL[i] = float(min([a for a in ans if a > 0]))
FPHICL = CST * FTHETACL
#-----General Instability (SECTION 6) - Axial Compression and bending-----#
C = (FXCG + FRCG) / yield_stress - 1
KPHIG = 1
CST = K * KPHIG / KTHETAG
FTHETACG = np.array([0.] * NSEC)
for i in range(0, NSEC):
cst = CST[i]
fxcg = FXCG[i]
frcg = FRCG[i]
c = C[i]
x = Symbol('x', real=True)
ans = solve((cst * x / fxcg)**2 - c * (cst * x / fxcg) *
(x / frcg) + (x / frcg)**2 - 1, x)
FTHETACG[i] = float(min([a for a in ans if a > 0]))
FPHICG = CST * FTHETACG
#-----Allowable Stresses-----#
# factor of safety
FOS = 1.25
if load_condition == 'N' or load_condition == 'n':
FOS = 1.65
FAL = np.array([0.] * NSEC)
F*G = np.array([0.] * NSEC)
FEL = np.array([0.] * NSEC)
FEG = np.array([0.] * NSEC)
for i in range(0, NSEC):
# axial load
FAL[i] = FPHICL[i] / (FOS * calcPsi(FPHICL[i], yield_stress))
F*G[i] = FPHICG[i] / (FOS * calcPsi(FPHICG[i], yield_stress))
# external pressure
FEL[i] = FTHETACL[i] / (FOS * calcPsi(FTHETACL[i], yield_stress))
FEG[i] = FTHETACG[i] / (FOS * calcPsi(FTHETACG[i], yield_stress))
# unity check
self.VAL = abs(SIGMAXA / FAL)
self.VAG = abs(SIGMAXA / F*G)
self.VEL = abs(FTHETAS / FEL)
self.VEG = abs(FTHETAS / FEG)
self.water_ballast_height = WBH
print 'surge period: ', T_surge
print 'heave period: ', T_heave
print 'pitch stiffness: ', K_pitch
print 'pitch period: ', T_pitch
print 'YNA: ', YNA
print 'number of stiffeners: ', self.number_of_rings
print 'wall thickness: ', self.wall_thickness
print 'VAL: ', self.VAL
print 'VAG: ', self.VAG
print 'VEL: ', self.VEL
print 'VEG: ', self.VEG
print 'web compactness: ', self.web_compactness
print 'flange compactness: ', self.flange_compactness
print 'heel angle: ', self.heel_angle
print 'outer diameters: ', self.outer_diameter
self.spar_mass = SHRMASS
self.ballast_mass = PBM + FBM + WBM
self.system_total_mass = SHRMASS + PBM + FBM + WBM + self.mooring_mass
self.shell_mass = SHMASS
self.bulkhead_mass = BHMASS
self.stiffener_mass = RGMASS
print 'spar mass: ', self.spar_mass
print 'shell mass: ', self.shell_mass
print 'bulkhead mass: ', self.bulkhead_mass
print 'stiffener mass: ', self.stiffener_mass
#-----------------------------------------------------------------
def execute(self):
'''
'''
def plasticityRF(F):
dum = FY/F
if F > FY/2:
return F*dum*(1+3.75*dum**2)**(-0.25)
else:
return F*1
def frustrumVol(D1,D2,H): # array inputs
l = len(D1)
fV = np.array([0.]*l)
r1 = D1/2.
r2 = D2/2.
fV = pi * (H / 3) * (r1**2 + r1*r2 + r2**2)
return fV
def frustrumCG(D1,D2,H): # array inputs
# frustrum vertical CG
l = len(D1)
fCG = np.array([0.]*l)
r1 = D1/2.
r2 = D2/2.
dum1 = r1**2 + 2.*r1*r2 + 3.*r2**2
dum2 = r1**2 + r1 * r2 + r2**2
fCG = H / 4. * (dum1/dum2)
return fCG
def ID(D,WALL): # array inputs
D = np.asarray(D)
is_scalar = False if D.ndim>0 else True
D.shape = (1,)*(1-D.ndim) + D.shape
l = len(D)
ID = np.array([0.]*l)
ID = D - 2.*WALL
return ID if not is_scalar else (ID)
def waveHeight(Hs):
return 1.1*Hs
def wavePeriod(H):
return 11.1*(H/G)**0.5
def waveNumber(T,D):
k0 = 2 * pi / ( T * (G * D) **0.5)
ktol =1
while ktol > 0.001:
k = ( 2* pi/T) **2 / (G * np.tanh(k0*D))
ktol = abs(k-k0)
k0 = k
return k
def waveU(H,T,k,z,D,theta):
return (pi*H/T)*(np.cosh(k*(z+D))/np.sinh(k*D))*np.cos(theta)
def waveUdot(H,T,k,z,D,theta):
return (2*pi**2*H/T**2)* (np.cosh(k*(z+D))/np.sinh(k*D))*np.sin(theta)
def CD(U,D,DEN):
RE = np.log10(abs(U) * D / DEN)
if RE <= 5.:
return 1.2
elif RE < 5.301:
return 1.1
elif RE < 5.477:
return 0.5
elif RE < 6.:
return 0.2
elif RE < 6.301:
return 0.4
elif RE < 6.477:
return 0.45
elif RE < 6.699:
return 0.5
elif RE < 7.:
return 0.6
else:
return 0.8
def inertialForce(D,CA,L,A,VDOT,DEN):
IF = 0.25 * pi * DEN * D** 2 * L * (A + CA * (A - VDOT))
if A < 0:
IF = -IF
return IF
def windPowerLaw(uref,href,alpha,H) :
return uref*(H/href)**alpha
def pipeBuoyancy(D):
return pi/4 * D**2 *WDEN
def dragForce(D,CD,L,V,DEN):
DF = 0.5 * DEN * CD * D * L * V**2
if V < 0 :
DF = -DF
return DF
def calcPsi(F):
dum = FY/2
if F <= dum:
return 1.2
elif F > dum and F < FY:
return 1.4 - 0.4*F/FY
else: return 1
def currentSpeed(XNEW):
CDEPTH = [0.000, 61.000, 91.000, 130.000]
CSPEED = [0.570, 0.570, 0.100, 0.100]
return np.interp(abs(XNEW),CDEPTH,CSPEED)
def curWaveDrag(Hs,Tp,WD,ODT,ODB,ELS,SL,CG,VDOT):
if Hs != 0:
H = waveHeight(Hs)
k = waveNumber(Tp,WD)
# calculate current and wave drag
DL = SL /10. # step sizes
dtheta = pi/30.
S = (ODB - ODT)/SL
b = ODT
L = 0
m = 0
for i in range(1,11):
L2 = L + DL/2
D2 = ELS -L2
D = S * L2 +b
fmax = 0.
if (JMAX[i-1] == 0.):
JS = 1
JE = 31
else:
JS = JMAX[i-1]
JE = JMAX[i-1]
for j in range(JS,JE+1):
V = currentSpeed(L2)
A = 0.
if Hs != 0:
V = V + waveU(H,Tp,k,D2,WD,dtheta*(j-1))
A = waveUdot(H,Tp,k,D2,WD,dtheta*(j-1))
if V != 0:
CDT = CD(V,D,WDEN)
f = dragForce(D,CDT,DL,V,WDEN)
else:
f = 0
if Hs != 0:
f = f + inertialForce(D,1,DL,A,VDOT,WDEN)
if f > fmax :
fmax = f
JMAX[i-1] =j
m = m + fmax*L2
L = DL*i
return m/(SL-CG)
def calculateWindCurrentForces (flag):
if flag == 1:
VD = self.system_acceleration
else:
VD = 0
ODT = OD # outer diameter - top
ODB = np.append(OD[1:NSEC],OD[-1]) # outer diameter - bottom
WOD = (ODT+ODB)/2 # average outer diameter
COD = WOD # center outer diameter
IDT = ID(ODT,T)
IDB = ID(ODB,T)
OV = frustrumVol(ODT,ODB,LB)
IV = frustrumVol(IDT,IDB,LB)
MV = OV - IV # shell volume
SHM = MV * MDEN # shell mass
SCG = frustrumCG(ODB,ODT,LB) # shell center of gravity
KCG = DRAFT + ELE + SCG # keel to shell center of gravity
KCB = DRAFT + ELE + SCG
SHB = OV*WDEN # outer volume --> displaced water mass
coneH = np.array([0.]*NSEC)
for i in range(0,len(LB)):
if ODB[i]==ODT[i]:
coneH[i]=LB[i]
else:
coneH[i] = -LB[i] * (ODB[i]/ODT[i]) / (1 - ODB[i]/ODT[i]) # cone height
# initialize arrays
SCF = np.array([0.]*NSEC)
KCS = np.array([0.]*NSEC)
SCM = np.array([0.]*NSEC)
SWF = np.array([0.]*NSEC)
KWS = np.array([0.]*NSEC)
SWM = np.array([0.]*NSEC)
BHM = np.array([0.]*NSEC)
RGM = np.array([0.]*NSEC)
for i in range (0,NSEC):
#for i in range(0,NSEC) : # iterate through the sections
if i <(NSEC-1) : # everything but the last section
if ELE[i] <0 : # if bottom end underwater
HWL = abs(ELE[i])
if HWL >= LB[i]: # COMPLETELY UNDERWATER
SCF[i] = curWaveDrag(Hs,Tp,WD,OD[i],OD[i+1],ELS[i],LB[i],SCG[i],VD)
KCS[i] = KCB[i]
if SCF[i] == 0:
KCS[i] = 0.
SCM[i] = SCF[i] * (KCS[i]-KCGO)
SWF[i] = 0.
KWS[i] = 0.
SWM[i] = 0.
else: # PARTIALLY UNDER WATER
if ODT[i] == ODB[i]: # cylinder
SHB[i] = pipeBuoyancy(ODT[i])*HWL # redefine
SCG[i] = HWL/2 # redefine
KCB[i] = DRAFT + ELE[i] + SCG[i] # redefine
ODW = ODT[i] # assign single variable
else: # frustrum
ODW = ODB[i]*(coneH[i]-HWL)/coneH[i] # assign single variable
WOD[i] = (ODT[i]+ODW[i])/2 # redefine
COD[i] = (ODW[i]+ODB[i])/2 # redefine
SHB[i] = frustrumVol(ODW[i],ODB[i],HWL) # redefine
SCG[i] = frustrumCG(ODW,ODB[i],HWL) # redefine
KCB[i] = DRAFT + ELE[i] + SCG[i] # redefine
SCF[i] = curWaveDrag(Hs,Tp,WD,ODW,ODB[i],0.,HWL,SCG[i],VD)
KCS[i] = KCB[i]
if SCF[i] == 0 :
KCS[i] = 0.
SCM[i] = SCF[i]*(KCS[i]-KCGO)
if WREFS != 0: # if there is wind
WSPEED = windPowerLaw(WREFS,WREFH,ALPHA,(LB[i]-HWL)/2) # assign single variable
CDW = CD(WSPEED,WOD[i],ADEN) # assign single variable
SWF[i] = dragForce(WOD[i],CDW,LB[i]-HWL,WSPEED,ADEN)
KWS[i]= KCG[i]
SWM[i] = SWF[i]*(KWS[i]-KCGO)
else: # no wind
SWF[i] = 0.
KWS[i] = 0.
SWM[i] = 0.
else: # FULLY ABOVE WATER
SHB[i] = 0. # redefines
KCB[i] = 0.
SCF[i] = 0.
KCS[i] = 0.
SCM[i] = 0.
if WREFS != 0: # if there is wind
WSPEED = windPowerLaw(WREFS,WREFH,ALPHA,ELE[i]+LB[i]/2) # assign single variable
CDW = CD(WSPEED,WOD[i],ADEN) # assign single variable
SWF[i] = dragForce(WOD[i],CDW,LB[i],WSPEED,ADEN)
KWS[i]= KCG[i]
SWM[i] = SWF[i]*(KWS[i]-KCGO)
else: # no wind
SWF[i] = 0.
KWS[i] = 0.
SWM[i] = 0.
RGM[i] = N[i]*(pi*ID(WOD[i],T[i])*AR)*MDEN # ring mass
else: # last section
# SHM unchanged
KCG[i] = DRAFT + ELE[i] + LB[i]/2 #redefine
# SHB already calculated
# KCB already calculated
SCF[i] = curWaveDrag(Hs,Tp,WD,OD[i],OD[i],ELS[i],LB[i],KCG[i],VD)
KCS[i] = KCG [i] # redefines
if SCF[i] ==0:
KCS[i] = 0.
SCM[i] = SCF[i]*(KCS[i]-KCGO)
SWF[i] = 0.
KWS[i] = 0.
SWM[i] = 0.
RGM[i] = N[i]*(pi*ID(OD[i],T[i])*AR)*MDEN # ring mass
if BH[i] == 'T':
BHM[i] = pi / 4 * IDT[i]**2 * T[i] * MDEN
KCG[i] = (KCG[i] * SHM[i] + (DRAFT + ELS[i] - 0.5 * T[i]) * BHM[i]) / (SHM[i] + BHM[i])
elif BH[i] == 'B' :
BHM[i] = pi / 4 * IDB[i]**2 * T[i] * MDEN
KCG[i] = (KCG[i] * SHM[i] + (DRAFT + ELE[i] + 0.5 * T[i]) * BHM[i]) / (SHM[i] + BHM[i])
else:
KCG[i] = KCG[i]
return sum(SHM)+sum(RGM)+sum(BHM)
def rootsearch(f,a,b,dx):
x1 = a; f1 = f(a)
x2 = a + dx; f2 = f(x2)
while f1*f2 > 0.0:
if x1 >= b:
return None,None
x1 = x2; f1 = f2
x2 = x1 + dx; f2 = f(x2)
return x1,x2
def bisect(f,x1,x2,switch=0,epsilon=1.0e-9):
f1 = f(x1)
if f1 == 0.0:
return x1
f2 = f(x2)
if f2 == 0.0:
return x2
if f1*f2 > 0.0:
print('Root is not bracketed')
return None
n = int(math.ceil(math.log(abs(x2 - x1)/epsilon)/math.log(2.0)))
for i in range(n):
x3 = 0.5*(x1 + x2); f3 = f(x3)
if (switch == 1) and (abs(f3) >abs(f1)) and (abs(f3) > abs(f2)):
return None
if f3 == 0.0:
return x3
if f2*f3 < 0.0:
x1 = x3
f1 = f3
else:
x2 =x3
f2 = f3
return (x1 + x2)/2.0
def roots(f, a, b, eps=1e-3):
#print ('The roots on the interval [%f, %f] are:' % (a,b))
while 1:
x1,x2 = rootsearch(f,a,b,eps)
if x1 != None:
a = x2
root = bisect(f,x1,x2,1)
if root != None:
pass
#print (round(root,-int(math.log(eps, 10))))
return root
else:
#print ('\nDone')
break
# assign all varibles so its easier to read later
G = self.gravity
ADEN = self.air_density
WDEN = self.water_density
WD = self.water_depth
LOADC = self.load_condition
Hs = self.significant_wave_height
Tp = self.significant_wave_period
if Hs!= 0:
WAVEH = 1.86*Hs
WAVEP = 0.71*Tp
WAVEL = G*WAVEP**2/(2*pi)
WAVEN = 2*pi/WAVEL
KCG = self.keel_cg_mooring
KCGO = self.keel_cg_operating_system
WREFS = self.reference_wind_speed
WREFH = self.reference_height
ALPHA = self.alpha
MDEN = self.material_density
E = self.E
PR = self.nu
FY = self.yield_stress
RMASS = self.rotor_mass
TMASS = self.tower_mass
FB = self.free_board
DRAFT = self.draft
FBM = self.fixed_ballast_mass
PBM = self.permanent_ballast_mass
OD = np.array(self.outer_diameter)
T = np.array(self.wall_thickness)
LB = np.array(self.length)
ELE = np.array(self.end_elevation)
ELS = np.array(self.start_elevation)
BH = self.bulk_head
N = np.array(self.number_of_rings)
NSEC = self.number_of_sections
if self.initial_pass: # curve fits
YNA=self.neutral_axis
D = 0.0029+1.3345977*YNA
IR =0.051*YNA**3.7452
TW =np.exp(0.88132868+1.0261134*np.log(IR)-3.117086*np.log(YNA))
AR =np.exp(4.6980391+0.36049717*YNA**0.5-2.2503113/(TW**0.5))
TFM =1.2122528*YNA**0.13430232*YNA**1.069737
BF = (0.96105249*TW**-0.59795001*AR**0.73163096)
IR = 0.47602202*TW**0.99500847*YNA**2.9938134
SMASS = self.hull_mass
else: # discrete, actual stiffener
SMASS = 1.11*self.shell_ring_bulkhead_mass
allStiffeners = filtered_stiffeners_table()
stiffener = allStiffeners[self.stiffener_index]
stiffenerName = stiffener[0]
AR = convert_units( stiffener[1],'inch**2','m**2')
D = convert_units(stiffener[2],'inch','m')
TW = convert_units(stiffener[3],'inch','m')
BF= convert_units(stiffener[4],'inch','m')
TFM = convert_units(stiffener[5],'inch','m')
YNA = convert_units(stiffener[6],'inch','m')
IR = convert_units(stiffener[7],'inch**4','m**4')
HW = D - TFM
WBM = self.variable_ballast_mass
# shell data
RO = OD/2. # outer radius
R = RO-T/2. # radius to centerline of wall/mid fiber radius
# ring data
LR = LB/(N+1.) # number of ring spacing
#shell and ring data
RF = RO - HW # radius to flange
MX = LR/(R*T)**0.5 # geometry parameter
# effective width of shell plate in longitudinal direction
LE=np.array([0.]*NSEC)
for i in range(0,NSEC):
if MX[i] <= 1.56:
LE[i]=LR[i]
else:
LE = 1.1*(2*R*T)**0.5+TW
# ring properties with effective shell plate
AER = AR+LE*T # cross sectional area with effective shell
YENA = (LE*T*T/2 + HW*TW*(HW/2+T) + TFM*BF*(TFM/2+HW+T))/AER
IER = IR+AR*(YNA+T/2.)**2*LE*T/AER+LE*T**3/12. # moment of inertia
RC = RO-YENA-T/2. # radius to centroid of ring stiffener
# set loads (0 mass loads for external pressure)
MTURBINE = RMASS
MTOWER = TMASS
MBALLAST = PBM + FBM + WBM # sum of all ballast masses
MHULL = SMASS
W = (MTURBINE + MTOWER + MBALLAST + MHULL) * G
P = WDEN * G* abs(ELE) # hydrostatic pressure at depth of section bottom
if Hs != 0: # dynamic head
DH = WAVEH/2*(np.cosh(WAVEN*(WD-abs(ELE)))/np.cosh(WAVEN*WD))
else:
DH = 0
P = P + WDEN*G*DH # hydrostatic pressure + dynamic head
#-----RING SECTION COMPACTNESS (SECTION 7)-----#
self.flange_compactness = (0.5*BF/TFM)/(0.375*(E/FY)**0.5)
self.web_compactness = (HW/TW)/((E/FY)**0.5)
#-----PLATE AND RING STRESS (SECTION 11)-----#
# shell hoop stress at ring midway
Dc = E*T**3/(12*(1-PR**2)) # parameter D
BETAc = (E*T/(4*RO**2*Dc))**0.25 # parameter beta
TWS = AR/HW
dum1 = BETAc*LR
KT = 8*BETAc**3 * Dc * (np.cosh(dum1) - np.cos(dum1))/ (np.sinh(dum1) + np.sin(dum1))
KD = E * TWS * (RO**2 - RF**2)/(RO * ((1+PR) * RO**2 + (1-PR) * RF**2))
dum = dum1/2.
PSIK = 2*(np.sin(dum) * np.cosh(dum) + np.cos(dum) * np.sinh(dum)) / (np.sinh(dum1) + np.sin(dum1))
PSIK = PSIK.clip(min=0) # psik >= 0; set all negative values of psik to zero
SIGMAXA = -W/(2*pi*R*T)
PSIGMA = P + (PR*SIGMAXA*T)/RO
PSIGMA = np.minimum(PSIGMA,P) # PSIGMA has to be <= P
dum = KD/(KD+KT)
KTHETAL = 1 - PSIK*PSIGMA/P*dum
FTHETAS = KTHETAL*P*RO/T
# shell hoop stress at ring
KTHETAG = 1 - (PSIGMA/P*dum)
FTHETAR = KTHETAG*P*RO/T
#-----LOCAL BUCKLING (SECTION 4)-----#
# axial compression and bending
ALPHAXL = 9/(300+(2*R)/T)**0.4
CXL = (1+(150/((2*R)/T))*(ALPHAXL**2)*(MX**4))**0.5
FXEL = CXL * (pi**2 * E / (12 * (1 - PR**2))) * (T/LR)**2 # elastic
FXCL=np.array(NSEC*[0.])
for i in range(0,len(FXEL)):
FXCL[i] = plasticityRF(FXEL[i]) # inelastic
# external pressure
BETA = np.array([0.]*NSEC)
ALPHATHETAL = np.array([0.]*NSEC)
global ZM
ZM = 12*(MX**2 * (1-PR**2)**.5)**2/pi**4
for i in range(0,NSEC):
f=lambda x:x**2*(1+x**2)**4/(2+3*x**2)-ZM[i]
ans = roots(f, 0.,15.)
ans_array = np.asarray(ans)
is_scalar = False if ans_array.ndim>0 else True
if is_scalar:
BETA[i] = ans
else:
BETA[i] = float(min(ans_array))
if MX[i] < 5:
ALPHATHETAL[i] = 1
elif MX[i] >= 5:
ALPHATHETAL[i] = 0.8
n = np.round(BETA*pi*R/LR) # solve for smallest whole number n
BETA = LR/(pi*R/n)
left = (1+BETA**2)**2/(0.5+BETA**2)
right = 0.112*MX**4 / ((1+BETA**2)**2*(0.5+BETA**2))
CTHETAL = (left + right)*ALPHATHETAL
FREL = CTHETAL * pi**2 * E * (T/LR)**2 / (12*(1-PR**2)) # elastic
FRCL=np.array(NSEC*[0.])
for i in range(0,len(FREL)):
FRCL[i] = plasticityRF(FREL[i]) # inelastic
#-----GENERAL INSTABILITY (SECTION 4)-----#
# axial compression and bending
AC = AR/(LR*T) # Ar bar
ALPHAX = 0.85/(1+0.0025*(OD/T))
ALPHAXG = np.array([0.]*NSEC)
for i in range(0,NSEC):
if AC[i] >= 0.2 :
ALPHAXG[i] = 0.72
elif AC[i] > 0.06 and AC[i] <0.2:
ALPHAXG[i] = (3.6-0.5*ALPHAX[i])*AC[i]+ALPHAX[i]
else:
ALPHAXG[i] = ALPHAX[i]
FXEG = ALPHAXG * 0.605 * E * T / R * (1 + AC)**0.5 # elastic
FXCG = np.array(NSEC*[0.])
for i in range(0,len(FXEG)):
FXCG[i] = plasticityRF(FXEG[i]) # inelastic
# external pressure
ALPHATHETAG = 0.8
LAMBDAG = pi * R / LB
k = 0.5
PEG = np.array([0.]*NSEC)
for i in range(0,NSEC):
t = T[i]
r = R[i]
lambdag = LAMBDAG[i]
ier = IER[i]
rc = RC[i]
ro = RO[i]
lr = LR[i]
def f(x,E,t,r,lambdag,k,ier,rc,ro,lr):
return E*(t/r)*lambdag**4/((x**2+k*lambdag**2-1)*(x**2+lambdag**2)**2) + E*ier*(x**2-1)/(lr*rc**2*ro)
x0 = [2]
m = float(fmin(f, x0, xtol=1e-3, args=(E,t,r,lambdag,k,ier,rc,ro,lr))) # solve for n that gives minimum P_eG
PEG[i] = f(m,E,t,r,lambdag,k,ier,rc,ro,lr)
ALPHATHETAG = 0.8 #adequate for ring stiffeners
FREG = ALPHATHETAG*PEG*RO*KTHETAG/T # elastic
FRCG = np.array(NSEC*[0.])
for i in range(0,len(FREG)):
FRCG[i] = plasticityRF(FREG[i]) # inelastic
# General Load Case
NPHI = W/(2*pi*R)
NTHETA = P * RO
K = NPHI/NTHETA
#-----Local Buckling (SECTION 6) - Axial Compression and bending-----#
C = (FXCL + FRCL)/FY -1
KPHIL = 1
CST = K * KPHIL /KTHETAL
FTHETACL = np.array([0.]*NSEC)
bnds = (0,None)
#print FRCL
for i in range(0,NSEC):
cst = CST[i]
fxcl = FXCL[i]
frcl = FRCL[i]
c = C[i]
x = Symbol('x')
ans = solve((cst*x/fxcl)**2 - c*(cst*x/fxcl)*(x/frcl) + (x/frcl)**2 - 1, x)
FTHETACL[i] = float(min([a for a in ans if a>0]))
FPHICL = CST*FTHETACL
#-----General Instability (SECTION 6) - Axial Compression and bending-----#
C = (FXCG + FRCG)/FY -1
KPHIG = 1
CST = K * KPHIG /KTHETAG
FTHETACG = np.array([0.]*NSEC)
for i in range(0,NSEC):
cst = CST[i]
fxcg = FXCG[i]
frcg = FRCG[i]
c = C[i]
x = Symbol('x',real=True)
ans = solve((cst*x/fxcg)**2 - c*(cst*x/fxcg)*(x/frcg) + (x/frcg)**2 - 1, x)
FTHETACG[i] = float(min([a for a in ans if a>0]))
FPHICG = CST*FTHETACG
#-----Allowable Stresses-----#
# factor of safety
FOS = 1.25
if LOADC == 'N' or LOADC == 'n':
FOS = 1.65
FAL = np.array([0.]*NSEC)
F*G = np.array([0.]*NSEC)
FEL = np.array([0.]*NSEC)
FEG = np.array([0.]*NSEC)
for i in range(0,NSEC):
# axial load
FAL[i] = FPHICL[i]/(FOS*calcPsi(FPHICL[i]))
F*G[i] = FPHICG[i]/(FOS*calcPsi(FPHICG[i]))
# external pressure
FEL[i] = FTHETACL[i]/(FOS*calcPsi(FTHETACL[i]))
FEG[i] = FTHETACG[i]/(FOS*calcPsi(FTHETACG[i]))
# unity check
self.VAL = abs(SIGMAXA / FAL)
self.VAG = abs(SIGMAXA / F*G)
self.VEL = abs(FTHETAS / FEL)
self.VEG = abs(FTHETAS / FEG)
global JMAX
JMAX = np.array([0]*10)
self.shell_ring_bulkhead_mass=calculateWindCurrentForces(0)
self.shell_ring_bulkhead_mass=calculateWindCurrentForces(1)
def example_218WD_10MW():
example = optimizationSpar()
tt = time.time()
example.water_depth = 218.
example.load_condition = 'N'
example.significant_wave_height = 10.820
example.significant_wave_period = 9.800
example.keel_cg_mooring = 45.
example.keel_cg_operating_system = 30.730
example.reference_wind_speed = 11.
example.reference_height = 119.
example.alpha = 0.110
example.material_density = 7850.
example.E = 200.e9
example.nu = 0.3
example.yield_stress = 345000000.
example.rotor_mass = 677000.000
example.tower_mass = 698235.000
example.free_board = 13.
example.draft = 92.
example.fixed_ballast_mass = 6276669.794
example.hull_mass = 2816863.293
example.permanent_ballast_mass = 3133090.391
example.variable_ballast_mass = 1420179.260
example.number_of_sections = 4
example.outer_diameter = [8.,9.,9.,15.]
example.length = [6., 12., 15., 72.]
example.end_elevation = [7., -5., -20., -92.]
example.start_elevation = [13., 7., -5., -20.]
example.bulk_head = ['N', 'T', 'N', 'B']
#example.system_acceleration = 0.856545480516845
example.gust_factor = 1.0
example.tower_base_OD = 7.720
example.tower_top_OD = 4.050
example.tower_length = 102.63
example.cut_out_speed = 25.
example.turbine_size = '10MW'
example.rotor_diameter = 194.0
example.run()
yna = convert_units(example.spar.neutral_axis ,'m','inch')
filteredStiffeners = filtered_stiffeners_table()
for i in range (0,len(filteredStiffeners)-1):
stiffener_bef = filteredStiffeners[i]
stiffener_aft = filteredStiffeners[i+1]
if yna > stiffener_bef[6] and yna<stiffener_aft[6]:
opt_index = i+1
second_fit = Spar()
second_fit.wall_thickness = example.spar.wall_thickness
second_fit.number_of_rings = example.spar.number_of_rings
second_fit.stiffener_index = opt_index
second_fit.initial_pass = False
second_fit.water_depth = example.water_depth
second_fit.load_condition = example.load_condition
second_fit.significant_wave_height = example.significant_wave_height
second_fit.significant_wave_period = example.significant_wave_period
second_fit.keel_cg_mooring = example.keel_cg_mooring
second_fit.keel_cg_operating_system = example.keel_cg_operating_system
second_fit.reference_wind_speed = example.reference_wind_speed
second_fit.reference_height = example.reference_height
second_fit.alpha = example.alpha
second_fit.material_density = example.material_density
second_fit.E = example.E
second_fit.nu =example.nu
second_fit.yield_stress = example.yield_stress
second_fit.rotor_mass = example.rotor_mass
second_fit.tower_mass = example.tower_mass
second_fit.free_board = example.free_board
second_fit.draft = example.draft
second_fit.fixed_ballast_mass = example.fixed_ballast_mass
second_fit.hull_mass = example.hull_mass
second_fit.permanent_ballast_mass = example.permanent_ballast_mass
second_fit.variable_ballast_mass = example.variable_ballast_mass
second_fit.number_of_sections = example.number_of_sections
second_fit.outer_diameter = example.outer_diameter
second_fit.length = example.length
second_fit.end_elevation = example.end_elevation
second_fit.start_elevation = example.start_elevation
second_fit.bulk_head = example.bulk_head
#second_fit.system_acceleration=example.system_acceleration
second_fit.gust_factor = example.gust_factor
second_fit.tower_base_OD = example.tower_base_OD
second_fit.tower_top_OD = example.tower_top_OD
second_fit.tower_length = example.tower_length
second_fit.cut_out_speed = example.cut_out_speed
second_fit.turbine_size = example.turbine_size
second_fit.rotor_diameter = example.rotor_diameter
second_fit.run()
index = opt_index
unity = max(max(second_fit.VAL),max(second_fit.VAG),max(second_fit.VEL),max(second_fit.VEG))
while ((unity-1.0) > 1e-7):
if index <124:
index += 1
second_fit.stiffener_index = index
second_fit.run()
unity = max(max(second_fit.VAL),max(second_fit.VAG),max(second_fit.VEL),max(second_fit.VEG))
#print unity-1.0
else:
second_fit.stiffener_index = opt_index
for i in range(0,second_fit.number_of_sections):
if second_fit.VAL[i] >1. or second_fit.VAG[i]>1. or second_fit.VEL[i]>1. or second_fit.VEG[i]>1.:
second_fit.number_of_rings[i] += 1
second_fit.run()
unity = max(max(second_fit.VAL),max(second_fit.VAG),max(second_fit.VEL),max(second_fit.VEG))
#print second_fit.number_of_rings
print '--------------example_218WD_10MW------------------'
print "Elapsed time: ", time.time()-tt, " seconds"
sys_print(second_fit)
def example_218WD_6MW():
example = optimizationSpar()
tt = time.time()
example.water_depth = 218.
example.load_condition = 'N'
example.significant_wave_height = 10.820
example.significant_wave_period = 9.800
example.keel_cg_mooring = 37.177
example.keel_cg_operating_system = 24.059
example.reference_wind_speed = 11.
example.reference_height = 97.
example.alpha = 0.110
example.material_density = 7850.
example.E = 200.e9
example.nu = 0.3
example.yield_stress = 345000000.
example.rotor_mass = 365500.000
example.tower_mass = 366952.000
example.free_board = 13.
example.draft = 72.
example.fixed_ballast_mass = 3659547.034
example.hull_mass = 1593822.041
example.permanent_ballast_mass = 1761475.914
example.variable_ballast_mass = 820790.246
example.number_of_sections = 4
example.outer_diameter = [7., 8., 8., 13.]
example.length = [6., 12., 15., 52.]
example.end_elevation = [7., -5., -20., -72.]
example.start_elevation = [13., 7., -5., -20.]
example.bulk_head = ['N', 'T', 'N', 'B']
#example.system_acceleration = 1.12124749328663
example.gust_factor = 1.0
example.tower_base_OD = 6.0
example.tower_top_OD = 3.51
example.tower_length = 80.5
example.cut_out_speed = 25.
example.turbine_size = '6MW'
example.rotor_diameter = 154.0
example.run()
yna = convert_units(example.spar.neutral_axis ,'m','inch')
filteredStiffeners = filtered_stiffeners_table()
for i in range (0,len(filteredStiffeners)-1):
stiffener_bef = filteredStiffeners[i]
stiffener_aft = filteredStiffeners[i+1]
if yna > stiffener_bef[6] and yna<stiffener_aft[6]:
opt_index = i+1
second_fit = Spar()
second_fit.wall_thickness = example.spar.wall_thickness
second_fit.number_of_rings = example.spar.number_of_rings
second_fit.stiffener_index = opt_index
second_fit.initial_pass = False
second_fit.water_depth = example.water_depth
second_fit.load_condition = example.load_condition
second_fit.significant_wave_height = example.significant_wave_height
second_fit.significant_wave_period = example.significant_wave_period
second_fit.keel_cg_mooring = example.keel_cg_mooring
second_fit.keel_cg_operating_system = example.keel_cg_operating_system
second_fit.reference_wind_speed = example.reference_wind_speed
second_fit.reference_height = example.reference_height
second_fit.alpha = example.alpha
second_fit.material_density = example.material_density
second_fit.E = example.E
second_fit.nu =example.nu
second_fit.yield_stress = example.yield_stress
second_fit.rotor_mass = example.rotor_mass
second_fit.tower_mass = example.tower_mass
second_fit.free_board = example.free_board
second_fit.draft = example.draft
second_fit.fixed_ballast_mass = example.fixed_ballast_mass
second_fit.hull_mass = example.hull_mass
second_fit.permanent_ballast_mass = example.permanent_ballast_mass
second_fit.variable_ballast_mass = example.variable_ballast_mass
second_fit.number_of_sections = example.number_of_sections
second_fit.outer_diameter = example.outer_diameter
second_fit.length = example.length
second_fit.end_elevation = example.end_elevation
second_fit.start_elevation = example.start_elevation
second_fit.bulk_head = example.bulk_head
second_fit.gust_factor = example.gust_factor
second_fit.tower_base_OD = example.tower_base_OD
second_fit.tower_top_OD = example.tower_top_OD
second_fit.tower_length = example.tower_length
second_fit.cut_out_speed = example.cut_out_speed
second_fit.turbine_size = example.turbine_size
second_fit.rotor_diameter = example.rotor_diameter
#second_fit.system_acceleration=example.system_acceleration
second_fit.run()
index = opt_index
unity = max(max(second_fit.VAL),max(second_fit.VAG),max(second_fit.VEL),max(second_fit.VEG))
while ((unity-1.0) > 1e-7):
if index <124:
index += 1
second_fit.stiffener_index = index
second_fit.run()
unity = max(max(second_fit.VAL),max(second_fit.VAG),max(second_fit.VEL),max(second_fit.VEG))
else:
second_fit.stiffener_index = opt_index
for i in range(0,second_fit.number_of_sections):
if second_fit.VAL[i] >1. or second_fit.VAG[i]>1. or second_fit.VEL[i]>1. or second_fit.VEG[i]>1.:
second_fit.number_of_rings[i] += 1
second_fit.run()
unity = max(max(second_fit.VAL),max(second_fit.VAG),max(second_fit.VEL),max(second_fit.VEG))
print '--------------example_218WD_6MW------------------'
print "Elapsed time: ", time.time()-tt, " seconds"
sys_print(second_fit)
def example_130WD_3MW():
example = optimizationSpar()
example.water_depth = 130.
example.load_condition = 'N'
example.significant_wave_height = 10.660
example.significant_wave_period = 13.210
example.keel_cg_mooring = 51.
example.keel_cg_operating_system = 20.312
example.reference_wind_speed = 11.
example.reference_height = 75.
example.alpha = 0.110
example.material_density = 7850.
example.E = 200.e9
example.nu = 0.3
example.yield_stress = 345000000.
example.rotor_mass = 125000.
example.tower_mass = 83705.
example.free_board = 13.
example.draft = 64.
example.fixed_ballast_mass = 1244227.77
example.hull_mass = 890985.086
example.permanent_ballast_mass = 838450.256
example.variable_ballast_mass = 418535.462
example.number_of_sections = 4
example.outer_diameter = [5., 6., 6., 9.]
example.length = [6., 12., 15., 44.]
example.end_elevation = [7., -5., -20., -64.]
example.start_elevation = [13., 7., -5., -20.]
example.bulk_head = ['N', 'T', 'N', 'B']
#example.system_acceleration=1.2931
example.run()
yna = convert_units(example.spar.neutral_axis ,'m','inch')
filteredStiffeners = filtered_stiffeners_table()
for i in range (0,len(filteredStiffeners)-1):
stiffener_bef = filteredStiffeners[i]
stiffener_aft = filteredStiffeners[i+1]
if yna > stiffener_bef[6] and yna<stiffener_aft[6]:
opt_index = i+1
second_fit = Spar()
second_fit.wall_thickness = example.spar.wall_thickness
second_fit.number_of_rings = example.spar.number_of_rings
second_fit.stiffener_index = opt_index
second_fit.initial_pass = False
second_fit.water_depth = example.water_depth
second_fit.load_condition = example.load_condition
second_fit.significant_wave_height = example.significant_wave_height
second_fit.significant_wave_period = example.significant_wave_period
second_fit.keel_cg_mooring = example.keel_cg_mooring
second_fit.keel_cg_operating_system = example.keel_cg_operating_system
second_fit.reference_wind_speed = example.reference_wind_speed
second_fit.reference_height = example.reference_height
second_fit.alpha = example.alpha
second_fit.material_density = example.material_density
second_fit.E = example.E
second_fit.nu =example.nu
second_fit.yield_stress = example.yield_stress
second_fit.rotor_mass = example.rotor_mass
second_fit.tower_mass = example.tower_mass
second_fit.free_board = example.free_board
second_fit.draft = example.draft
second_fit.fixed_ballast_mass = example.fixed_ballast_mass
second_fit.hull_mass = example.hull_mass
second_fit.permanent_ballast_mass = example.permanent_ballast_mass
second_fit.variable_ballast_mass = example.variable_ballast_mass
second_fit.number_of_sections = example.number_of_sections
second_fit.outer_diameter = example.outer_diameter
second_fit.length = example.length
second_fit.end_elevation = example.end_elevation
second_fit.start_elevation = example.start_elevation
second_fit.bulk_head = example.bulk_head
second_fit.system_acceleration=example.system_acceleration
second_fit.run()
index = opt_index
unity = max(max(second_fit.VAL),max(second_fit.VAG),max(second_fit.VEL),max(second_fit.VEG))
while ((unity-1.0) > 1e-7):
if index <124:
index += 1
second_fit.stiffener_index = index
second_fit.run()
unity = max(max(second_fit.VAL),max(second_fit.VAG),max(second_fit.VEL),max(second_fit.VEG))
else:
second_fit.stiffener_index = opt_index
for i in range(0,second_fit.number_of_sections):
if second_fit.VAL[i] >1. or second_fit.VAG[i]>1. or second_fit.VEL[i]>1. or second_fit.VEG[i]>1.:
second_fit.number_of_rings[i] += 1
second_fit.run()
unity = max(max(second_fit.VAL),max(second_fit.VAG),max(second_fit.VEL),max(second_fit.VEG))
print '--------------example_130WD_3MW------------------'
print "Elapsed time: ", time.time()-tt, " seconds"
sys_print(second_fit)
def execute(self):
'''
'''
# assign all varibles
G = self.gravity
ADEN = self.air_density
WDEN = self.water_density
WD = self.water_depth
LOADC = self.load_condition
Hs = self.significant_wave_height
Ts = self.significant_wave_period
if Hs!= 0:
WAVEH = 1.86*Hs
WAVEP = 0.71*Ts
WAVEL = G*WAVEP**2/(2*pi)
WAVEN = 2*pi/WAVEL
WREFS = self.wind_reference_speed
WREFH = self.wind_reference_height
ALPHA = self.alpha
MDEN = self.material_density
E = self.E
PR = self.nu
FY = self.yield_stress
PBH = self.permanent_ballast_height
PBDEN = self.permanent_ballast_density
FBH = self.fixed_ballast_height
FBDEN = self.fixed_ballast_density
RMASS = self.RNA_mass
KGR = self.RNA_keel_to_CG
TMASS = self.tower_mass
TCG = self.tower_center_of_gravity
TWF = self.tower_wind_force
RWF = self.RNA_wind_force
RCGX = self.RNA_center_of_gravity_x
VTOP = self.mooring_vertical_load
MHK = self.mooring_horizontal_stiffness
MVK = self.mooring_vertical_stiffness
KGM = self.mooring_keel_to_CG
OD = np.array(self.outer_diameter)
ODB = OD[-1] # base outer diameter
T = np.array(self.wall_thickness)
ELE = np.array(self.elevations[1:]) # end elevation
ELS = np.array(self.elevations[0:-1]) # start elevation
NSEC = self.number_of_sections
for i in range(0,NSEC+1):
if self.elevations[i] >0:
ODTW = OD[i+1]
print ODTW
LB = ELS-ELE # lengths of each section
DRAFT = abs(min(ELE))
FB = ELS [0] # freeboard
BH = self.bulk_head
N = np.array(self.number_of_rings)
if self.stiffener_curve_fit: # curve fits
YNA=self.neutral_axis
D = 0.0029+1.3345977*YNA
IR =0.051*YNA**3.7452
TW =np.exp(0.88132868+1.0261134*np.log(IR)-3.117086*np.log(YNA))
AR =np.exp(4.6980391+0.36049717*YNA**0.5-2.2503113/(TW**0.5))
TFM =1.2122528*YNA**0.13430232*YNA**1.069737
BF = (0.96105249*TW**-0.59795001*AR**0.73163096)
IR = 0.47602202*TW**0.99500847*YNA**2.9938134
else: # discrete, actual stiffener
allStiffeners = full_stiffeners_table()
stiffener = allStiffeners[self.stiffener_index]
stiffenerName = stiffener[0]
AR = convert_units( stiffener[1],'inch**2','m**2')
D = convert_units(stiffener[2],'inch','m')
TW = convert_units(stiffener[3],'inch','m')
BF= convert_units(stiffener[4],'inch','m')
TFM = convert_units(stiffener[5],'inch','m')
YNA = convert_units(stiffener[6],'inch','m')
self.neutral_axis=YNA
IR = convert_units(stiffener[7],'inch**4','m**4')
HW = D - TFM # web height
SHM,RGM,BHM,SHB,SWF,SWM,SCF,SCM,KCG,KCB=calculateWindCurrentForces(0.,0.,N,AR,BH,OD,NSEC,T,LB,MDEN,DRAFT,ELE,ELS,WDEN,ADEN,G,Hs,Ts,WD,WREFS,WREFH,ALPHA)
SHBUOY = sum(SHB) # shell buoyancy
SHMASS = sum(SHM)*self.shell_mass_factor # shell mass - VALUE
BHMASS = sum(BHM)*self.bulkhead_mass_factor # bulkhead mass - VALUE
RGMASS = sum(RGM)*self.ring_mass_factor # ring mass - VALUE
SHRMASS = SHMASS + BHMASS + RGMASS # shell and bulkhead and ring mass - VALUE
SHRM = np.array(SHM)+np.array(BHM)+np.array(RGM) # # shell and bulkhead and ring mass - ARRAY
percent_shell_mass = RGMASS/SHMASS *100.
outfitting_mass = SHRMASS*self.outfitting_factor
SMASS = SHRMASS*self.spar_mass_factor + outfitting_mass
KCG = np.dot(SHRM,np.array(KCG))/SHRMASS # keel to center of gravity
KB = np.dot(np.array(SHB),np.array(KCB))/SHBUOY # keel to center of buoyancy
BM = ((np.pi/64)*ODTW**4)/(SHBUOY/WDEN)
SWFORCE = sum(SWF) # shell wind force
SCFORCE = sum(SCF) # shell current force - NOTE: inaccurate; setting an initial value and reruns later
BVL = np.pi/4.*(ODB-2*T[-1])**2. # ballast volume per length
KGPB = (PBH/2.)+T[-1]
PBM = BVL*PBH*PBDEN # permanent ballast mass
KGFB = (FBH/2.)+PBH+T[-1]
FBM = BVL*FBH*FBDEN # fixed ballast mass
WPA = np.pi/4*(ODTW)**2
KGT = TCG+FB+DRAFT # keel to center of gravity of tower
WBM = SHBUOY-SMASS-RMASS-TMASS-VTOP/G-FBM-PBM # water ballast mass
WBH = WBM/(WDEN*BVL) # water ballast height
KGWB = WBH/2.+PBH+FBH+T[-1]
KGB = (SMASS*KCG+WBM*KGWB+FBM*KGFB+PBM*KGPB+TMASS*KGT+RMASS*KGR)/(SMASS+WBM+FBM+PBM+TMASS+RMASS)
KG = (SMASS*KCG+WBM*KGWB+FBM*KGFB+PBM*KGPB+TMASS*KGT+RMASS*KGR+VTOP/G*KGM)/SHBUOY
GM = KB+BM-KG
self.platform_stability_check = KG/KB
total_mass = SMASS+RMASS+TMASS+WBM+FBM+PBM
VD = (RWF+TWF+SWFORCE+SCFORCE)/(SMASS+RMASS+TMASS+FBM+PBM+WBM)
SHM,RGM,BHM,SHB,SWF,SWM,SCF,SCM,KCG,KCB=calculateWindCurrentForces(KG,VD,N,AR,BH,OD,NSEC,T,LB,MDEN,DRAFT,ELE,ELS,WDEN,ADEN,G,Hs,Ts,WD,WREFS,WREFH,ALPHA)
SCFORCE = sum(SCF)
# calculate moments
RWM = RWF*(KGR-KG)
TWM = TWF*(KGT-KG)
# costs
columns_mass = sum(SHM[1::2])+sum(RGM[1::2])+sum(BHM[1::2])
tapered_mass = sum(SHM[0::2])+sum(RGM[0::2])+sum(BHM[0::2])
COSTCOL = self.straight_col_cost
COSTTAP = self.tapered_col_cost
COSTOUT = self.outfitting_cost
COSTBAL = self.ballast_cost
self.spar_cost = COSTCOL*columns_mass/1000. + COSTTAP*tapered_mass/1000.
self.outfit_cost = COSTOUT*outfitting_mass/1000.
self.ballasts_cost = COSTBAL*(FBM+PBM)/1000.
self.total_cost =self.spar_cost+self.outfit_cost+self.ballasts_cost+self.mooring_total_cost
##### SIZING TAB #####
# [TOP MASS(RNA+TOWER)]
top_mass = RMASS+TMASS
KG_top = (RMASS*KGR+TMASS*KGT)
# [INERTIA PROPERTIES - LOCAL]
I_top_loc = (1./12.)*top_mass*KG_top**2
I_hull_loc = (1./12.)*SMASS*(DRAFT+FB)**2
I_WB_loc = (1./12.)*WBM*WBH**2
I_FB_loc = (1./12.)*FBM*FBH**2
I_PB_loc = (1./12.)*PBM*PBH**2
# [INERTIA PROPERTIES - SYSTEM]
I_top_sys = I_top_loc + top_mass*(KG_top-KG)**2
I_hull_sys = I_hull_loc + SMASS*(KCG-KG)**2
I_WB_sys = I_WB_loc + WBM*(KGWB-KGB)**2
I_FB_sys = I_FB_loc + FBM*(KGFB-KGB)**2
I_PB_sys = I_PB_loc + PBM*(KGPB-KGB)**2
I_total = I_top_sys + I_hull_sys + I_WB_sys + I_FB_sys + I_PB_sys
I_yaw = total_mass*(ODB/2.)**2
# [ADDED MASS]
surge = (pi/4.)*ODB**2*DRAFT*WDEN
heave = (1/6.)*WDEN*ODB**3
pitch = (surge*((KG-DRAFT)-(KB-DRAFT))**2+surge*DRAFT**2/12.)*I_total
# [OTHER SYSTEM PROPERTIES]
r_gyration = (I_total/total_mass)**0.5
CM = (SMASS*KCG+WBM*KGWB+FBM*KGFB+PBM*KGPB)/(SMASS+WBM+FBM+PBM)
surge_period = 2*pi*((total_mass+surge)/MHK)**0.5
# [PLATFORM STIFFNESS]
K33 = WDEN*G*(pi/4.)**ODTW**2+MVK #heave
K44 = abs(WDEN*G*((pi/4.)*(ODTW/2.)**4-(KB-KG)*SHBUOY/WDEN)) #roll
K55 = abs(WDEN*G*((pi/4.)*(ODTW/2.)**4-(KB-KG)*SHBUOY/WDEN)) #pitch
# [PERIOD]
T_surge = 2*pi*((total_mass+surge)/MHK)**0.5
T_heave = 2*pi*((total_mass+heave)/K33)**0.5
K_pitch = GM*SHBUOY*G
T_pitch = 2*pi*(pitch/K_pitch)**0.5
F_total = RWF+TWF+sum(SWF)+sum(SCF)
sum_FX = self.sum_forces_x
X_Offset = self.offset_x
if np.isnan(sum_FX).any() or sum_FX[-1] > (-F_total/1000.):
self.max_offset_unity = 10.
self.min_offset_unity = 10.
else:
for j in range(1,len(sum_FX)):
if sum_FX[j]< (-F_total/1000.):
X2 = sum_FX[j]
X1 = sum_FX[j-1]
Y2 = X_Offset[j]
Y1 = X_Offset[j-1]
max_offset = (Y1+(-F_total/1000.-X1)*(Y2-Y1)/(X2-X1))*self.offset_amplification_factor
i=0
while sum_FX[i]> (F_total/1000.):
i+=1
min_offset = (X_Offset[i-1]+(F_total/1000.-sum_FX[i-1])*(X_Offset[i]-X_Offset[i-1])/(sum_FX[i]-sum_FX[i-1]))*self.offset_amplification_factor
# unity checks!
if self.load_condition == 'E':
self.max_offset_unity = max_offset/self.damaged_mooring[1]
self.min_offset_unity = min_offset/self.damaged_mooring[0]
elif self.load_condition == 'N':
self.max_offset_unity = max_offset/self.intact_mooring[1]
self.min_offset_unity = min_offset/self.intact_mooring[0]
M_total = RWM+TWM+sum(SWM)+sum(SCM)+(-F_total*(KGM-KG))+(RMASS*G*-RCGX)
self.heel_angle = (M_total/K_pitch)*180./pi
##### API BULLETIN #####
# shell data
RO = OD/2. # outer radius
R = RO-T/2. # radius to centerline of wall/mid fiber radius
# ring data
LR = LB/(N+1.) # number of ring spacing
#shell and ring data
RF = RO - HW # radius to flange
MX = LR/(R*T)**0.5 # geometry parameter
# effective width of shell plate in longitudinal direction
LE=np.array([0.]*NSEC)
for i in range(0,NSEC):
if MX[i] <= 1.56:
LE[i]=LR[i]
else:
LE = 1.1*(2*R*T)**0.5+TW
# ring properties with effective shell plate
AER = AR+LE*T # cross sectional area with effective shell
YENA = (LE*T*T/2 + HW*TW*(HW/2+T) + TFM*BF*(TFM/2+HW+T))/AER
IER = IR+AR*(YNA+T/2.)**2*LE*T/AER+LE*T**3/12. # moment of inertia
RC = RO-YENA-T/2. # radius to centroid of ring stiffener
# set loads (0 mass loads for external pressure)
MBALLAST = PBM + FBM + WBM # sum of all ballast masses
W = (RMASS + TMASS + MBALLAST + SMASS) * G
P = WDEN * G* abs(ELE) # hydrostatic pressure at depth of section bottom
if Hs != 0: # dynamic head
DH = WAVEH/2*(np.cosh(WAVEN*(WD-abs(ELE)))/np.cosh(WAVEN*WD))
else:
DH = 0
P = P + WDEN*G*DH # hydrostatic pressure + dynamic head
GF = self.gust_factor
#-----RING SECTION COMPACTNESS (SECTION 7)-----#
self.flange_compactness = (0.5*BF/TFM)/(0.375*(E/FY)**0.5)
self.web_compactness = (HW/TW)/((E/FY)**0.5)
#-----PLATE AND RING STRESS (SECTION 11)-----#
# shell hoop stress at ring midway
Dc = E*T**3/(12*(1-PR**2)) # parameter D
BETAc = (E*T/(4*RO**2*Dc))**0.25 # parameter beta
TWS = AR/HW
dum1 = BETAc*LR
KT = 8*BETAc**3 * Dc * (np.cosh(dum1) - np.cos(dum1))/ (np.sinh(dum1) + np.sin(dum1))
KD = E * TWS * (RO**2 - RF**2)/(RO * ((1+PR) * RO**2 + (1-PR) * RF**2))
dum = dum1/2.
PSIK = 2*(np.sin(dum) * np.cosh(dum) + np.cos(dum) * np.sinh(dum)) / (np.sinh(dum1) + np.sin(dum1))
PSIK = PSIK.clip(min=0) # psik >= 0; set all negative values of psik to zero
SIGMAXA = -W/(2*pi*R*T)
PSIGMA = P + (PR*SIGMAXA*T)/RO
PSIGMA = np.minimum(PSIGMA,P) # PSIGMA has to be <= P
dum = KD/(KD+KT)
KTHETAL = 1 - PSIK*PSIGMA/P*dum
FTHETAS = KTHETAL*P*RO/T
# shell hoop stress at ring
KTHETAG = 1 - (PSIGMA/P*dum)
FTHETAR = KTHETAG*P*RO/T
#-----LOCAL BUCKLING (SECTION 4)-----#
# axial compression and bending
ALPHAXL = 9/(300+(2*R)/T)**0.4
CXL = (1+(150/((2*R)/T))*(ALPHAXL**2)*(MX**4))**0.5
FXEL = CXL * (pi**2 * E / (12 * (1 - PR**2))) * (T/LR)**2 # elastic
FXCL=np.array(NSEC*[0.])
for i in range(0,len(FXEL)):
FXCL[i] = plasticityRF(FXEL[i],FY) # inelastic
# external pressure
BETA = np.array([0.]*NSEC)
ALPHATHETAL = np.array([0.]*NSEC)
global ZM
ZM = 12*(MX**2 * (1-PR**2)**.5)**2/pi**4
for i in range(0,NSEC):
f=lambda x:x**2*(1+x**2)**4/(2+3*x**2)-ZM[i]
ans = roots(f, 0.,15.)
ans_array = np.asarray(ans)
is_scalar = False if ans_array.ndim>0 else True
if is_scalar:
BETA[i] = ans
else:
BETA[i] = float(min(ans_array))
if MX[i] < 5:
ALPHATHETAL[i] = 1
elif MX[i] >= 5:
ALPHATHETAL[i] = 0.8
n = np.round(BETA*pi*R/LR) # solve for smallest whole number n
BETA = LR/(pi*R/n)
left = (1+BETA**2)**2/(0.5+BETA**2)
right = 0.112*MX**4 / ((1+BETA**2)**2*(0.5+BETA**2))
CTHETAL = (left + right)*ALPHATHETAL
FREL = CTHETAL * pi**2 * E * (T/LR)**2 / (12*(1-PR**2)) # elastic
FRCL=np.array(NSEC*[0.])
for i in range(0,len(FREL)):
FRCL[i] = plasticityRF(FREL[i],FY) # inelastic
#-----GENERAL INSTABILITY (SECTION 4)-----#
# axial compression and bending
AC = AR/(LR*T) # Ar bar
ALPHAX = 0.85/(1+0.0025*(OD/T))
ALPHAXG = np.array([0.]*NSEC)
for i in range(0,NSEC):
if AC[i] >= 0.2 :
ALPHAXG[i] = 0.72
elif AC[i] > 0.06 and AC[i] <0.2:
ALPHAXG[i] = (3.6-0.5*ALPHAX[i])*AC[i]+ALPHAX[i]
else:
ALPHAXG[i] = ALPHAX[i]
FXEG = ALPHAXG * 0.605 * E * T / R * (1 + AC)**0.5 # elastic
FXCG = np.array(NSEC*[0.])
for i in range(0,len(FXEG)):
FXCG[i] = plasticityRF(FXEG[i],FY) # inelastic
# external pressure
ALPHATHETAG = 0.8
LAMBDAG = pi * R / LB
k = 0.5
PEG = np.array([0.]*NSEC)
for i in range(0,NSEC):
t = T[i]
r = R[i]
lambdag = LAMBDAG[i]
ier = IER[i]
rc = RC[i]
ro = RO[i]
lr = LR[i]
def f(x,E,t,r,lambdag,k,ier,rc,ro,lr):
return E*(t/r)*lambdag**4/((x**2+k*lambdag**2-1)*(x**2+lambdag**2)**2) + E*ier*(x**2-1)/(lr*rc**2*ro)
x0 = [2]
m = float(fmin(f, x0, xtol=1e-3, args=(E,t,r,lambdag,k,ier,rc,ro,lr))) # solve for n that gives minimum P_eG
PEG[i] = f(m,E,t,r,lambdag,k,ier,rc,ro,lr)
ALPHATHETAG = 0.8 #adequate for ring stiffeners
FREG = ALPHATHETAG*PEG*RO*KTHETAG/T # elastic
FRCG = np.array(NSEC*[0.])
for i in range(0,len(FREG)):
FRCG[i] = plasticityRF(FREG[i],FY) # inelastic
# General Load Case
NPHI = W/(2*pi*R)
NTHETA = P * RO
K = NPHI/NTHETA
#-----Local Buckling (SECTION 6) - Axial Compression and bending-----#
C = (FXCL + FRCL)/FY -1
KPHIL = 1
CST = K * KPHIL /KTHETAL
FTHETACL = np.array([0.]*NSEC)
bnds = (0,None)
for i in range(0,NSEC):
cst = CST[i]
fxcl = FXCL[i]
frcl = FRCL[i]
c = C[i]
x = Symbol('x')
ans = solve((cst*x/fxcl)**2 - c*(cst*x/fxcl)*(x/frcl) + (x/frcl)**2 - 1, x)
FTHETACL[i] = float(min([a for a in ans if a>0]))
FPHICL = CST*FTHETACL
#-----General Instability (SECTION 6) - Axial Compression and bending-----#
C = (FXCG + FRCG)/FY -1
KPHIG = 1
CST = K * KPHIG /KTHETAG
FTHETACG = np.array([0.]*NSEC)
for i in range(0,NSEC):
cst = CST[i]
fxcg = FXCG[i]
frcg = FRCG[i]
c = C[i]
x = Symbol('x',real=True)
ans = solve((cst*x/fxcg)**2 - c*(cst*x/fxcg)*(x/frcg) + (x/frcg)**2 - 1, x)
FTHETACG[i] = float(min([a for a in ans if a>0]))
FPHICG = CST*FTHETACG
#-----Allowable Stresses-----#
# factor of safety
FOS = 1.25
if LOADC == 'N' or LOADC == 'n':
FOS = 1.65
FAL = np.array([0.]*NSEC)
F*G = np.array([0.]*NSEC)
FEL = np.array([0.]*NSEC)
FEG = np.array([0.]*NSEC)
for i in range(0,NSEC):
# axial load
FAL[i] = FPHICL[i]/(FOS*calcPsi(FPHICL[i],FY))
F*G[i] = FPHICG[i]/(FOS*calcPsi(FPHICG[i],FY))
# external pressure
FEL[i] = FTHETACL[i]/(FOS*calcPsi(FTHETACL[i],FY))
FEG[i] = FTHETACG[i]/(FOS*calcPsi(FTHETACG[i],FY))
# unity check
self.VAL = abs(SIGMAXA / FAL)
self.VAG = abs(SIGMAXA / F*G)
self.VEL = abs(FTHETAS / FEL)
self.VEG = abs(FTHETAS / FEG)
self.water_ballast_height = WBH
print 'YNA: ', YNA
print 'number of stiffeners: ',self.number_of_rings
print 'wall thickness: ',self.wall_thickness
print 'VAL: ',self.VAL
print 'VAG: ',self.VAG
print 'VEL: ',self.VEL
print 'VEG: ',self.VEG
print 'web compactness: ',self.web_compactness
print 'flange compactness: ',self.flange_compactness
print 'heel angle: ', self.heel_angle
print 'outer diameters: ', self.outer_diameter
self.spar_mass = SHRMASS
self.ballast_mass = PBM + FBM + WBM
self.system_total_mass = SHRMASS + PBM + FBM + WBM + self.mooring_mass
self.shell_mass = SHMASS
self.bulkhead_mass = BHMASS
self.stiffener_mass = RGMASS
print 'spar mass: ', self.spar_mass
print 'shell mass: ', self.shell_mass
print 'bulkhead mass: ', self.bulkhead_mass
print 'stiffener mass: ', self.stiffener_mass
#-----------------------------------------------------------------
def example_218WD_3MW():
example = optimizationSpar()
tt = time.time()
example.spar.number_of_sections = 4
example.spar.outer_diameter = [5., 6., 6., 9.]
example.spar.length = [6., 12., 15., 47.]
example.spar.end_elevation = [7., -5., -20., -67.]
example.spar.start_elevation = [13., 7., -5., -20.]
example.spar.bulk_head = ['N', 'T', 'N', 'B']
example.spar.water_depth = 218.
example.spar.load_condition = 'N'
example.spar.significant_wave_height = 10.820
example.spar.significant_wave_period = 9.800
example.spar.wind_reference_speed = 11.
example.spar.wind_reference_height = 75.
example.spar.alpha = 0.110
example.spar.RNA_keel_to_CG = 142.
example.spar.RNA_mass = 125000.
example.spar.tower_mass = 127877.
example.spar.tower_center_of_gravity = 23.948
example.spar.tower_wind_force = 19950.529
example.spar.RNA_wind_force = 391966.178
example.spar.RNA_center_of_gravity_x = 4.1
example.spar.mooring_total_cost = 810424.053596
example.spar.mooring_keel_to_CG = 54.000
example.spar.mooring_vertical_load = 1182948.791
example.spar.mooring_horizontal_stiffness = 3145.200
example.spar.mooring_vertical_stiffness = 7111.072
example.spar.sum_forces_x = [
7886.848, 437.844, 253.782, 174.651, 124.198, 85.424, 50.689, 17.999,
-13.222, -43.894, -74.245, -105.117, -136.959, -170.729, -207.969,
-251.793, -307.638, -386.514, -518.734, -859.583, -11091.252
]
example.spar.offset_x = [
-40.362, -35.033, -29.703, -24.373, -19.044, -13.714, -8.385, -3.055,
2.274, 7.604, 12.933, 18.263, 23.593, 28.922, 34.252, 39.581, 44.911,
50.240, 55.570, 60.900, 66.229
]
example.spar.damaged_mooring = [-40.079, 65.824]
example.spar.intact_mooring = [-39.782, 65.399]
example.spar.run()
example.run()
yna = convert_units(example.spar.neutral_axis, 'm', 'inch')
fullStiffeners = full_stiffeners_table()
for i in range(0, len(fullStiffeners) - 1):
stiffener_bef = fullStiffeners[i]
stiffener_aft = fullStiffeners[i + 1]
if yna > stiffener_bef[6] and yna < stiffener_aft[6]:
opt_index = i + 1
second_fit = Spar()
second_fit.wall_thickness = example.spar.wall_thickness
second_fit.number_of_rings = example.spar.number_of_rings
second_fit.stiffener_curve_fit = False
second_fit.stiffener_index = opt_index
second_fit.number_of_sections = example.spar.number_of_sections
second_fit.outer_diameter = example.spar.outer_diameter
second_fit.length = example.spar.length
second_fit.end_elevation = example.spar.end_elevation
second_fit.start_elevation = example.spar.start_elevation
second_fit.bulk_head = example.spar.bulk_head
second_fit.water_depth = example.spar.water_depth
second_fit.load_condition = example.spar.load_condition
second_fit.significant_wave_height = example.spar.significant_wave_height
second_fit.significant_wave_period = example.spar.significant_wave_period
second_fit.wind_reference_speed = example.spar.wind_reference_speed
second_fit.wind_reference_height = example.spar.wind_reference_height
second_fit.alpha = example.spar.alpha
second_fit.RNA_keel_to_CG = example.spar.RNA_keel_to_CG
second_fit.RNA_mass = example.spar.RNA_mass
second_fit.tower_mass = example.spar.tower_mass
second_fit.tower_center_of_gravity = example.spar.tower_center_of_gravity
second_fit.tower_wind_force = example.spar.tower_wind_force
second_fit.RNA_wind_force = example.spar.RNA_wind_force
second_fit.RNA_center_of_gravity_x = example.spar.RNA_center_of_gravity_x
second_fit.mooring_total_cost = example.spar.mooring_total_cost
second_fit.mooring_keel_to_CG = example.spar.mooring_keel_to_CG
second_fit.mooring_vertical_load = example.spar.mooring_vertical_load
second_fit.mooring_horizontal_stiffness = example.spar.mooring_horizontal_stiffness
second_fit.mooring_vertical_stiffness = example.spar.mooring_vertical_stiffness
second_fit.sum_forces_x = example.spar.sum_forces_x
second_fit.offset_x = example.spar.offset_x
second_fit.damaged_mooring = example.spar.damaged_mooring
second_fit.intact_mooring = example.spar.intact_mooring
second_fit.run()
cost = second_fit.total_cost
index = opt_index
best_index = opt_index
unity = max(second_fit.web_compactness, second_fit.flange_compactness,
max(second_fit.VAL), max(second_fit.VAG), max(second_fit.VEL),
max(second_fit.VEG))
for i in range(opt_index, 326):
index += 1
second_fit.stiffener_index = index
second_fit.run()
unity = max(second_fit.web_compactness, second_fit.flange_compactness,
max(second_fit.VAL), max(second_fit.VAG),
max(second_fit.VEL), max(second_fit.VEG))
if unity < 1.0:
if second_fit.total_cost < cost:
cost = second_fit.total_cost
best_index = i
second_fit.stiffener_index = best_index
second_fit.run()
print '--------------example_218WD_3MW------------------'
print "Elapsed time: ", time.time() - tt, " seconds"
sys_print(second_fit)
def execute(self): NumRibs = 26/8.9375* self.b_w/12 Airfoil_t_over_c_wing = self.Airfoil_t_over_c_wing Airfoil_t_over_c_tail = self.Airfoil_t_over_c_tail BalsaDens = self.BalsaDens SpruceDens = self.SpruceDens BassDens = self.BassDens Len_fuse = self.Len_fuse Wid_fuse = self.Wid_fuse Hgt_fuse = self.Hgt_fuse EngWeight = self.EngWeight ESCWeight = self.ESCWeight BatteryWeight = self.BatteryWeight Alum2024Dens = self.Alum2024Dens W_payload = self.W_payload x_cg_payload = self.x_cg_payload x_wLE = self.x_wLE c_w = self.c_w c_ht = self.c_ht c_vt = self.c_vt b_vt = self.b_vt RibArea = Airfoil_t_over_c_wing*(self.c_w)**2 #inch**2 RibWeight = BalsaDens*RibArea*.125 #lb FrontWeight = EngWeight + BatteryWeight + ESCWeight FrontCG = float(3) #FuseVolume = Len_fuse*Wid_fuse*Hgt_fuse #inch**3 #FuseWeight = (FuseVolume*BassDens) #lb FuseWeight = 1.7 FuseCG = Len_fuse / 2 #inch TailBoomLen = self.x_tLE - (self.x_wLE+self.c_w*0.25) #inch TailBoomVol = TailBoomLen*(pi*(3.0/4.0)**2/4) #in**3 SparLen = self.b_w * 0.25 SparVol = SparLen*(pi*(7.0/8.0)**2/4 + pi*(3.0/8.0)**2/4) TailBoomSparAssemWeight = (TailBoomVol + SparVol ) * Alum2024Dens #lb TailBoomSparAssemCG = ((TailBoomLen/2+(self.x_wLE+self.c_w*0.25))*TailBoomVol + (self.x_wLE+self.c_w*0.25)*SparLen*(pi*(7.0/8.0)**2/4) + (self.x_wLE+self.c_w*0.66)* SparLen*(pi*(3.0/8.0)**2/4))/(TailBoomVol + SparVol) W_wing = (NumRibs*RibWeight+2*self.b_w*SpruceDens*.5*.25*2+self.b_w*BalsaDens*Airfoil_t_over_c_wing*(self.c_w)*.125)+.1080851064*self.S_wing W_ht = self.S_ht*0.245614035 W_vt = self.S_vt*0.245614035 x_cg_w = self.x_wLE + 0.35*self.c_w #inch x_cg_ht = self.x_tLE + (0.35*self.c_ht) x_cg_vt = self.x_tLE + (0.35*self.c_vt) x_cg_t = self.x_tLE + (0.35*self.c_ht*W_ht+0.35*self.c_vt*W_vt)/(W_ht+W_vt) #inch x_cg_payload = self.x_cg_payload #inch self.W_empty = W_wing + W_ht + W_vt + FrontWeight + FuseWeight + TailBoomSparAssemWeight self.x_cg_empty = (FrontWeight*FrontCG + W_wing*x_cg_w + (W_ht+W_vt)*x_cg_t + FuseWeight*FuseCG + TailBoomSparAssemWeight*TailBoomSparAssemCG)/self.W_empty self.W_0 = self.W_empty + self.W_payload self.x_cg = x_cg = (self.W_empty*self.x_cg_empty + self.W_payload*x_cg_payload)/self.W_0 print 'W_wing', W_wing print 'W_ht', W_ht print 'W_vt', W_vt print 'TailBoomLen', TailBoomLen print 'TailBoomSparAssemWeight', TailBoomSparAssemWeight print 'TailBoomSparAssemCG', TailBoomSparAssemCG print 'FuseCG', FuseCG print 'Len_fuse', Len_fuse print 'Wid_fuse', Wid_fuse print 'Hgt_fuse', Hgt_fuse print 'W_empty', self.W_empty print 'W_payload', self.W_payload print 'W_0', self.W_0 print 'x_cg_w', x_cg_w print 'x_cg_t', x_cg_t print 'x_cg_payload', self.x_cg_payload print 'x_cg', self.x_cg # I_y calculation FrontCG = convert_units(FrontCG, 'inch','ft') FuseCG = convert_units(FuseCG,'inch','ft') x_cg_w = convert_units(x_cg_w,'inch','ft') x_cg_ht = convert_units(x_cg_ht,'inch','ft') x_cg_vt = convert_units(x_cg_vt,'inch','ft') TailBoomLen = convert_units(TailBoomLen,'inch','ft') x_cg_payload = convert_units(x_cg_payload,'inch','ft') x_cg = convert_units(x_cg,'inch','ft') c_w = convert_units(c_w,'inch','ft') c_ht = convert_units(c_ht,'inch','ft') c_vt = convert_units(c_vt,'inch','ft') b_vt = convert_units(b_vt,'inch','ft') # I_y_front I_y_front = (FrontWeight/32.1740)*(FrontCG - x_cg)**2 # I_y_fuse I_y_fuse = (1.0/12.0)*(FuseWeight/32.1740)*(Len_fuse**2+Hgt_fuse**2)+(FuseWeight/32.1740)*(FuseCG - x_cg)**2 #I_y_wing I_y_wing = (1.0/12.0)*(W_wing/32.1740)*(c_w**2+(Airfoil_t_over_c_wing*c_w*0.5)**2)+(W_wing/32.1740)*(x_cg_w - x_cg)**2 #I_y_spar I_y_spar = 0.5*(SparLen*(pi*(7.0/8.0)**2/4)*Alum2024Dens)/32.1740*((7.0/8.0)/12/2)**2 + (SparLen*(pi*(7.0/8.0)**2/4)*Alum2024Dens)/32.1740*((x_wLE+c_w*0.25) - x_cg)**2 + 0.5*(SparLen*(pi*(3.0/8.0)**2/4)*Alum2024Dens)/32.1740*((3.0/8.0)/12/2)**2 + (SparLen*(pi*(3.0/8.0)**2/4)*Alum2024Dens)/32.1740*((x_wLE+c_w*0.66) - x_cg)**2 #I_y_tail I_y_tail = (1.0/12.0)*(W_ht/32.1740)*(c_ht**2+(Airfoil_t_over_c_tail*c_ht*0.5)**2)+(W_ht/32.1740)*(x_cg_ht - x_cg)**2 + (1.0/12.0)*(W_vt/32.1740)*(c_vt**2+b_vt**2)+(W_vt/32.1740)*((x_cg_vt - x_cg)**2+(b_vt/2)**2) #I_y_tailboom I_y_tailboom = (1.0/12.0)*(TailBoomVol*Alum2024Dens)/32.1740*(TailBoomLen)**2 + (TailBoomVol*Alum2024Dens)/32.1740*((TailBoomLen/2+(x_wLE+c_w*0.25)) - x_cg)**2 self.I_y = I_y = I_y_front + I_y_fuse + I_y_wing + I_y_spar + I_y_tail + I_y_tailboom #self.I_y = I_y = W_payload/32.1740*(x_cg_payload - x_cg)**2 + FrontWeight/32.1740*(FrontCG - x_cg)**2 + W_wing/32.1740*(x_cg_w - x_cg)*2 + (W_ht+W_vt)/32.1740*(x_cg_t - x_cg)**2 + FuseWeight/32.1740*(FuseCG - x_cg)**2 + TailBoomSparAssemWeight/32.1740*(TailBoomSparAssemCG - x_cg)**2 print 'I_y', I_y