def setup(self, Nclimb1, Nclimb2, Ncruise, substitutions = None, **kwargs):
eng = 0
# vectorize
with Vectorize(Nclimb1 +Nclimb2 + Ncruise):
enginestate = FlightState()
#build the submodel
ac = Aircraft(Nclimb1 + Nclimb2, Ncruise, enginestate, eng)
#Vectorize
with Vectorize(Nclimb1):
climb1 = ClimbSegment(ac)
#Vectorize
with Vectorize(Nclimb2):
climb2 = ClimbSegment(ac)
with Vectorize(Ncruise):
cruise = CruiseClimbSegment(ac)
statelinking = StateLinking(climb1.state, climb2.state, cruise.state, enginestate, Nclimb1, Nclimb2, Ncruise)
#declare new variables
W_ftotal = Variable('W_{f_{total}}', 'N', 'Total Fuel Weight')
W_fclimb1 = Variable('W_{f_{climb1}}', 'N', 'Fuel Weight Burned in Climb 1')
W_fclimb2 = Variable('W_{f_{climb2}}', 'N', 'Fuel Weight Burned in Climb 2')
W_fcruise = Variable('W_{f_{cruise}}', 'N', 'Fuel Weight Burned in Cruise')
W_total = Variable('W_{total}', 'N', 'Total Aircraft Weight')
CruiseAlt = Variable('CruiseAlt', 'ft', 'Cruise Altitude [feet]')
ReqRng = Variable('ReqRng', 'nautical_miles', 'Required Cruise Range')
W_dry = Variable('W_{dry}', 'N', 'Aircraft Dry Weight')
RCmin = Variable('RC_{min}', 'ft/min', 'Minimum allowed climb rate')
dhftholdcl1 = Variable('dhftholdcl1', 'ft', 'Climb 1 Hold Variable')
dhftholdcl2 = Variable('dhftholdcl2', 'ft', 'Climb 2 Hold Variable')
dhftholdcr = Variable('dhftholdcr', 'ft', 'Cruise Hold Variable')
h1 = climb1['h']
hftClimb1 = climb1['hft']
dhftcl1 = climb1['dhft']
h2 = climb2['h']
hftClimb2 = climb2['hft']
dhftcl2 = climb2['dhft']
dhftcr = cruise['dhft']
hftCruise = cruise['hft']
#make overall constraints
constraints = []
with SignomialsEnabled():
constraints.extend([
#weight constraints
TCS([ac['W_{e}'] + ac['W_{payload}'] + ac['numeng'] * ac['W_{engine}'] + ac['W_{wing}'] <= W_dry]),
TCS([W_dry + W_ftotal <= W_total]),
climb1['W_{start}'][0] == W_total,
climb1['W_{end}'][-1] == climb2['W_{start}'][0],
climb2['W_{end}'][-1] == cruise['W_{start}'][0],
TCS([climb1['W_{start}'] >= climb1['W_{end}'] + climb1['W_{burn}']]),
TCS([climb2['W_{start}'] >= climb2['W_{end}'] + climb2['W_{burn}']]),
TCS([cruise['W_{start}'] >= cruise['W_{end}'] + cruise['W_{burn}']]),
climb1['W_{start}'][1:] == climb1['W_{end}'][:-1],
climb2['W_{start}'][1:] == climb2['W_{end}'][:-1],
cruise['W_{start}'][1:] == cruise['W_{end}'][:-1],
TCS([W_dry <= cruise['W_{end}'][-1]]),
TCS([W_ftotal >= W_fclimb1 + W_fclimb2 + W_fcruise]),
TCS([W_fclimb1 >= sum(climb1['W_{burn}'])]),
TCS([W_fclimb2 >= sum(climb2['W_{burn}'])]),
TCS([W_fcruise >= sum(cruise['W_{burn}'])]),
#altitude constraints
hftCruise[0] == CruiseAlt,
## TCS([hftCruise[1:Ncruise] >= hftCruise[:Ncruise-1] + dhftcr]),
SignomialEquality(hftCruise[1:Ncruise], hftCruise[:Ncruise-1] + dhftholdcr),
TCS([hftClimb2[1:Nclimb2] <= hftClimb2[:Nclimb2-1] + dhftholdcl2]),
TCS([hftClimb2[0] <= dhftholdcl2 + 10000*units('ft')]),
hftClimb2[-1] == hftCruise,
TCS([hftClimb1[1:Nclimb1] >= hftClimb1[:Nclimb1-1] + dhftholdcl1]),
TCS([hftClimb1[0] == dhftcl1[0]]),
hftClimb1[-1] == 10000*units('ft'),
#compute the dh2
dhftholdcl2 >= (hftCruise-10000*units('ft'))/Nclimb2,
## SignomialEquality(dhftholdcl2, (hftCruise-10000*units('ft'))/Nclimb2,),
dhftholdcl2 == dhftcl2,
#compute the dh1
dhftholdcl1 == 10000*units('ft')/Nclimb1,
dhftholdcl1 == dhftcl1,
dhftcr == dhftholdcr,
sum(cruise['RngCruise']) + sum(climb2['RngClimb']) + sum(climb1['RngClimb']) >= ReqRng,
#compute fuel burn from TSFC
cruise['W_{burn}'] == ac['numeng']*ac.engine['TSFC'][Nclimb1 + Nclimb2:] * cruise['thr'] * ac.engine['F'][Nclimb1 + Nclimb2:],
climb1['W_{burn}'] == ac['numeng']*ac.engine['TSFC'][:Nclimb1] * climb1['thr'] * ac.engine['F'][:Nclimb1],
climb2['W_{burn}'] == ac['numeng']*ac.engine['TSFC'][Nclimb1:Nclimb1 + Nclimb2] * climb2['thr'] * ac.engine['F'][Nclimb1:Nclimb1 + Nclimb2],
#min climb rate constraint
## climb1['RC'][0] >= RCmin,
climb1['V'] <= 250*units('knots'),
])
M2 = .8
M25 = .6
M4a = .1025
Mexit = 1
M0 = .8
engineclimb1 = [
ac.engine.engineP['M_2'][:Nclimb1] == climb1['M'],
ac.engine.engineP['M_{2.5}'] == M25,
ac.engine.engineP['hold_{2}'] == 1+.5*(1.398-1)*M2**2,
ac.engine.engineP['hold_{2.5}'] == 1+.5*(1.354-1)*M25**2,
ac.engine.engineP['c1'] == 1+.5*(.401)*M0**2,
#constraint on drag and thrust
ac['numeng']*ac.engine['F_{spec}'][:Nclimb1] >= climb1['D'] + climb1['W_{avg}'] * climb1['\\theta'],
#climb rate constraints
TCS([climb1['excessP'] + climb1.state['V'] * climb1['D'] <= climb1.state['V'] * ac['numeng'] * ac.engine['F_{spec}'][:Nclimb1]]),
]
M2 = .8
M25 = .6
M4a = .1025
Mexit = 1
M0 = .8
engineclimb2 = [
ac.engine.engineP['M_2'][Nclimb1:Nclimb1 + Nclimb2] == climb2['M'],
#constraint on drag and thrust
ac['numeng']*ac.engine['F_{spec}'][Nclimb1:Nclimb1 + Nclimb2] >= climb2['D'] + climb2['W_{avg}'] * climb2['\\theta'],
#climb rate constraints
TCS([climb2['excessP'] + climb2.state['V'] * climb2['D'] <= climb2.state['V'] * ac['numeng'] * ac.engine['F_{spec}'][Nclimb1:Nclimb1 + Nclimb2]]),
]
M2 = .8
M25 = .6
M4a = .1025
Mexit = 1
M0 = .8
enginecruise = [
ac.engine.engineP['M_2'][Nclimb1 + Nclimb2:] == cruise['M'],
## cruise['M'] >= .7,
#constraint on drag and thrust
ac['numeng'] * ac.engine['F_{spec}'][Nclimb1 + Nclimb2:] >= cruise['D'] + cruise['W_{avg}'] * cruise['\\theta'],
#climb rate constraints
TCS([cruise['excessP'] + cruise.state['V'] * cruise['D'] <= cruise.state['V'] * ac['numeng'] * ac.engine['F_{spec}'][Nclimb1 + Nclimb2:]]),
]
return constraints + ac + climb1 + climb2 + cruise + enginecruise + engineclimb1 + engineclimb2 + enginestate + statelinking
def setup(self, Nclimb, Ncruise, Nfleet, substitutions=None, **kwargs):
eng = 0
#two level vectorization to make a fleet
with Vectorize(Nfleet):
# vectorize
with Vectorize(Nclimb + Ncruise):
enginestate = FlightState()
ac = Aircraft(Nclimb, Ncruise, enginestate, eng, Nfleet)
#two level vectorization to make a fleet
with Vectorize(Nfleet):
#Vectorize
with Vectorize(Nclimb):
climb = ClimbSegment(ac)
with Vectorize(Ncruise):
cruise = CruiseSegment(ac)
statelinking = StateLinking(climb.state, cruise.state, enginestate,
Nclimb, Ncruise)
with Vectorize(Nfleet):
#declare new variables
W_ftotal = Variable('W_{f_{total}}', 'N', 'Total Fuel Weight')
W_fclimb = Variable('W_{f_{climb}}', 'N',
'Fuel Weight Burned in Climb')
W_fcruise = Variable('W_{f_{cruise}}', 'N',
'Fuel Weight Burned in Cruise')
W_total = Variable('W_{total}', 'N', 'Total Aircraft Weight')
CruiseAlt = Variable('CruiseAlt', 'ft', 'Cruise Altitude [feet]')
ReqRng = Variable('ReqRng', 'nautical_miles',
'Required Cruise Range')
W_dry = Variable('W_{dry}', 'N', 'Aircraft Dry Weight')
dhfthold = Variable('dhfthold', 'ft', 'Hold Variable')
W_ffleet = Variable('W_{f_{fleet}}', 'N', 'Total Fleet Fuel Burn')
h = climb['h']
hftClimb = climb['hft']
dhft = climb['dhft']
hftCruise = cruise['hft']
#make overall constraints
constraints = []
constraints.extend([
#weight constraints
TCS([
ac['W_{e}'] + ac['W_{payload}'] +
ac['numeng'] * ac['W_{engine}'] + ac['W_{wing}'] <= W_dry
]),
TCS([W_dry + W_ftotal <= W_total]),
climb['W_{start}'][0] == W_total,
climb['W_{end}'][-1] == cruise['W_{start}'][0],
# similar constraint 1
TCS([climb['W_{start}'] >= climb['W_{end}'] + climb['W_{burn}']]),
# similar constraint 2
TCS([
cruise['W_{start}'] >= cruise['W_{end}'] + cruise['W_{burn}']
]),
climb['W_{start}'][1:] == climb['W_{end}'][:-1],
cruise['W_{start}'][1:] == cruise['W_{end}'][:-1],
TCS([W_dry <= cruise['W_{end}'][-1]]),
TCS([W_ftotal >= W_fclimb + W_fcruise]),
TCS([W_fclimb >= sum(climb['W_{burn}'])]),
TCS([W_fcruise >= sum(cruise['W_{burn}'])]),
#altitude constraints
hftCruise == CruiseAlt,
TCS([
hftClimb[1:Nclimb] >= hftClimb[:Nclimb - 1] + dhft[:Nclimb - 1]
]),
TCS([hftClimb[0] >= dhft[0]]),
hftClimb[-1] <= hftCruise,
#compute the dh
dhfthold == hftCruise[0] / Nclimb,
dhft == dhfthold,
#set the range for each cruise segment, doesn't take credit for climb
#down range disatnce covered
cruise.cruiseP['Rng'] == ReqRng / (Ncruise),
#compute fuel burn from TSFC
cruise['W_{burn}'] == ac['numeng'] * ac.engine['TSFC'][Nclimb:] *
cruise['thr'] * ac.engine['F'][Nclimb:],
climb['W_{burn}'] == ac['numeng'] * ac.engine['TSFC'][:Nclimb] *
climb['thr'] * ac.engine['F'][:Nclimb],
CruiseAlt >= 30000 * units('ft'),
#min climb rate constraint
climb['RC'] >= 500 * units('ft/min'),
])
fleetfuel = [
#compute the fleet fuel burn
W_ffleet >= .375 * W_ftotal[0] + .375 * W_ftotal[1] +
.125 * W_ftotal[2] + .125 * W_ftotal[3],
]
M2 = .8
M25 = .6
M4a = .1025
M0 = .8
engineclimb = [
ac.engine.engineP['M_2'][:Nclimb] == climb['M'],
ac.engine.engineP['M_{2.5}'][:Nclimb] == M25,
ac.engine.engineP['hold_{2}'] == 1 + .5 * (1.398 - 1) * M2**2,
ac.engine.engineP['hold_{2.5}'] == 1 + .5 * (1.354 - 1) * M25**2,
ac.engine.engineP['c1'] == 1 + .5 * (.401) * M0**2,
#constraint on drag and thrust
ac['numeng'] * ac.engine['F_{spec}'][:Nclimb] >=
climb['D'] + climb['W_{avg}'] * climb['\\theta'],
#climb rate constraints
TCS([
climb['excessP'] + climb.state['V'] * climb['D'] <=
climb.state['V'] * ac['numeng'] *
ac.engine['F_{spec}'][:Nclimb]
]),
]
M25 = .6
enginecruise = [
ac.engine.engineP['M_2'][Nclimb:] == cruise['M'],
ac.engine.engineP['M_{2.5}'][Nclimb:] == M25,
#steady level flight constraint on D
cruise['D'] == ac['numeng'] * ac.engine['F_{spec}'][Nclimb:],
#breguet range eqn
TCS([
cruise['z_{bre}'] >=
(ac.engine['TSFC'][Nclimb:] * cruise['thr'] * cruise['D']) /
cruise['W_{avg}']
]),
]
ranges = [
ReqRng[0] == 500 * units('nautical_miles'),
ReqRng[1] == 1000 * units('nautical_miles'),
ReqRng[2] == 1500 * units('nautical_miles'),
ReqRng[3] == 2000 * units('nautical_miles'),
]
return constraints + ac + climb + cruise + enginecruise + engineclimb + enginestate + statelinking + ranges + fleetfuel
def setup(self, Nclimb, Ncruise, substitutions=None, **kwargs):
eng = 0
# vectorize
with Vectorize(Nclimb + Ncruise):
enginestate = FlightState()
#build the submodel
ac = Aircraft(Nclimb, Ncruise, enginestate, eng)
#Vectorize
with Vectorize(Nclimb):
climb = ClimbSegment(ac)
with Vectorize(Ncruise):
cruise = CruiseClimbSegment(ac)
statelinking = StateLinking(climb.state, cruise.state, enginestate,
Nclimb, Ncruise)
#declare new variables
W_ftotal = Variable('W_{f_{total}}', 'N', 'Total Fuel Weight')
W_fclimb = Variable('W_{f_{climb}}', 'N',
'Fuel Weight Burned in Climb')
W_fcruise = Variable('W_{f_{cruise}}', 'N',
'Fuel Weight Burned in Cruise')
W_total = Variable('W_{total}', 'N', 'Total Aircraft Weight')
CruiseAlt = Variable('CruiseAlt', 'ft', 'Cruise Altitude [feet]')
ReqRng = Variable('ReqRng', 'nautical_miles', 'Required Cruise Range')
W_dry = Variable('W_{dry}', 'N', 'Aircraft Dry Weight')
dhftholdcl = Variable('dhftholdcl', 'ft', 'Climb Hold Variable')
dhftholdcr = Variable('dhftholdcr', 'ft', 'Cruise Hold Variable')
RCmin = Variable('RC_{min}', 'ft/min', 'Minimum allowed climb rate')
h = climb['h']
hftClimb = climb['hft']
dhftcl = climb['dhft']
dhftcr = cruise['dhft']
hftCruise = cruise['hft']
#make overall constraints
constraints = []
with SignomialsEnabled():
constraints.extend([
#weight constraints
TCS([
ac['W_{e}'] + ac['W_{payload}'] +
ac['numeng'] * ac['W_{engine}'] + ac['W_{wing}'] <= W_dry
]),
TCS([W_dry + W_ftotal <= W_total]),
climb['W_{start}'][0] == W_total,
climb['W_{end}'][-1] == cruise['W_{start}'][0],
# similar constraint 1
TCS([
climb['W_{start}'] >= climb['W_{end}'] + climb['W_{burn}']
]),
# similar constraint 2
TCS([
cruise['W_{start}'] >=
cruise['W_{end}'] + cruise['W_{burn}']
]),
climb['W_{start}'][1:] == climb['W_{end}'][:-1],
cruise['W_{start}'][1:] == cruise['W_{end}'][:-1],
TCS([W_dry <= cruise['W_{end}'][-1]]),
TCS([W_ftotal >= W_fclimb + W_fcruise]),
TCS([W_fclimb >= sum(climb['W_{burn}'])]),
TCS([W_fcruise >= sum(cruise['W_{burn}'])]),
#altitude constraints
hftCruise[0] == CruiseAlt,
## TCS([hftCruise[1:Ncruise] >= hftCruise[:Ncruise-1] + dhftcr]),
SignomialEquality(hftCruise[1:Ncruise],
hftCruise[:Ncruise - 1] + dhftholdcr),
TCS([hftClimb[1:Nclimb] >= hftClimb[:Nclimb - 1] + dhftholdcl
]),
TCS([hftClimb[0] >= dhftcl[0]]),
hftClimb[-1] <= hftCruise,
#compute the dh
dhftholdcl == hftCruise[0] / Nclimb,
dhftcl == dhftholdcl,
dhftcr == dhftholdcr,
sum(cruise['RngCruise']) + sum(climb['RngClimb']) >= ReqRng,
#compute fuel burn from TSFC
cruise['W_{burn}'] == ac['numeng'] *
ac.engine['TSFC'][Nclimb:] * cruise['thr'] *
ac.engine['F'][Nclimb:],
climb['W_{burn}'] == ac['numeng'] *
ac.engine['TSFC'][:Nclimb] * climb['thr'] *
ac.engine['F'][:Nclimb],
#min climb rate constraint
## climb['RC'][0] >= RCmin,
])
M2 = .8
M25 = .6
M4a = .1025
Mexit = 1
M0 = .8
engineclimb = [
ac.engine.engineP['M_2'][:Nclimb] == climb['M'],
ac.engine.engineP['M_{2.5}'] == M25,
ac.engine.engineP['hold_{2}'] == 1 + .5 * (1.398 - 1) * M2**2,
ac.engine.engineP['hold_{2.5}'] == 1 + .5 * (1.354 - 1) * M25**2,
ac.engine.engineP['c1'] == 1 + .5 * (.401) * M0**2,
#constraint on drag and thrust
ac['numeng'] * ac.engine['F'][:Nclimb] >=
climb['D'] + climb['W_{avg}'] * climb['\\theta'],
#climb rate constraints
TCS([
climb['excessP'] + climb.state['V'] * climb['D'] <=
climb.state['V'] * ac['numeng'] * ac.engine['F'][:Nclimb]
]),
]
M2 = .8
M25 = .6
M4a = .1025
Mexit = 1
M0 = .8
enginecruise = [
ac.engine.engineP['M_2'][Nclimb:] == cruise['M'],
## cruise['M'] == .8,
cruise['M'] >= .76,
ac.engine.engineP['M_{2.5}'][2] == M25,
ac.engine.engineP['M_{2.5}'][3] == M25,
#constraint on drag and thrust
ac['numeng'] * ac.engine['F'][Nclimb:] >=
cruise['D'] + cruise['W_{avg}'] * cruise['\\theta'],
#climb rate constraints
TCS([
cruise['excessP'] + cruise.state['V'] * cruise['D'] <=
cruise.state['V'] * ac['numeng'] * ac.engine['F'][Nclimb:]
]),
]
return constraints + ac + climb + cruise + enginecruise + engineclimb + enginestate + statelinking