# Commercial Aircraft Range Maximization by Differential Inclusion#

In this example we seek to maximize the range of a commercial aircraft flying at a constant Mach number with a fixed initial fuel load. The initial and final altitudes are constrained to 10000 ft (that is, in this simplified example we’re ignoring the aircraft behavior near the ground).

This example is simplified in several ways. The Mach number is fixed at 0.8. When only considering fuel burn, the aircraft will tend to fly slower to conserve fuel, ignoring the running costs of being airborne.

For a more detailed optimization of commercial aircraft performance, see Betts [CBC95].

## Differential Inclusion#

In this case we also use the steady flight assumption to allow the problem to be parameterized with a different control set. Rather than providing throttle/thrust and angle of attack as control variables, we use a differential inclusion approach. Whereas altitude and velocity are often treated as state variables to be integrated, here we take a slightly different approach.

Rather than using the differential equations to compute rates for the flight path angle and true airspeed, we use a nonlinear solver to determine the alpha and thrust time-history which is needed to make the given altitude and airspeed time-history possible. This technique is known as differential inclusion. It was demonstrated by Seywald [CSey94]. Since the collocation techniques in Dymos are based on polynomial approximations, rates of the control variables can be easily calculated, which can then be applied to the reordered dynamics equations to solve for angle of attack and thrust.

The use of collocation/psuedospectral techniques in solving problems via differential inclusion has been examined by Fahroo and Ross [CFR01] and Kumar and Seywald [CKS96]. Since the differential inclusion approach demonstrated here relies on nonlinear solvers running within the ODE model, obtaining accurate derivatives is paramount. Computing derivatives with finite differences in the presence of nonlinear solvers can lead to inaccurate derivatives based on the properties of the solver. With OpenMDAO’s unified derivatives framework, the sensitivity to solver tolerances is greatly reduced.

### Pitfalls of Differential Inclusion#

Differential inclusion works well in this case but it is highly dependent on the parameterization of the problem. For instance, it is possible for the optimizer to suggest a flight profile that requires thrust well beyond the capabilities of the vehicle. In our case, the throttle parameter $$\tau$$ is path constrained within the optimizer, so that the optimizer can make the solution physically attainable by our model.

We have two options for how to tackle this problem. We could specify altitude as a control variable, and use it’s approximate derivative ($$alt\_rate$$) to provide the altitude rate for the flight equilibrium conditions. In practice, however, this noisy derivative of altitude can cause numerical difficulties. Other times, the optimizer will shape the control to satisfy our equilibrium conditions at the collocation nodes but be wildly wrong in between these nodes. One simple way to get around this is to still integrate altitude, but to provide $$climb\_rate$$ as the control variable. This makes it easy to constraint $$climb\_rate$$ with bounds constraints, and the time-history of altitude will be smoother since it is the time integral of the rate of climb.

#### Solver Options#

In general, openmdao.api.AnalysisError should be raised when the design variables provided by the optimizer result in nonconvergence of the solvers. This informs pyoptsparse to backtrack along its line search for a solution. This error can be raised by the compute method of a component. The nonlinear solver can also raise this error if it fails to converge by setting the following options:

self.nonlinear_solver.options['maxiter'] = 150
self.nonlinear_solver.options['err_on_maxiter'] = True


In the course of solving, an outer NewtonSolver won’t necessarily force subsystems to be solved, instead relying on the derivative at the at the previous solution. In the context of OpenMDAO, even explicit components constitute subsystems. This can lead to poorly converged solutions.

Setting the solve_subsystems option to True will force subsystems to be updated, making sure that all derivative information is up-to-date.

self.nonlinear_solver.options['solve_subsystems'] = True
self.nonlinear_solver.options['max_sub_solves'] = 10


#### The Impact of Choice of Transcription#

The high-order Gauss-Lobatto method used by Dymos evaluates the ordinary differential equations in a two-step process. First, the ODEs are evaluated at the state discretization nodes. Using the state values and derivatives, values and rates at the collocation nodes are then interpolated. If a large rate is found at one of the state discretization nodes, the interpolation at the collocation node can be outside of the expected range, leading to nonconvergence of solvers within the ODEs.

There is also an overhead cost to invoking solvers. While differential inclusion reduces the number of design variables for the optimizer, it also slows down each evaluation of the ODE somewhat. Since evaluating the collocation constraints in the Gauss-Lobatto method requires two evaluations of the ODE, it typically suffers greater slowdown that the Radau Pseudospectral method, which evaluates the defects of the ODE with a single evaluation that encompasses all the nodes.

For these reasons the Radau Pseudospectral transcription is typically preferable when using a differential inclusion approach to problems.

## Problem Formulation#

### State Variables#

Name

Description

Fixed Initial Value

Fixed Final Value

range

distance flown along ground

True (0 NM)

False

mass_fuel

mass of fuel aboard aircraft

True (30000 lbm)

True (0 lbm)

alt

aircraft altitude

True (10000 ft)

True (10000 ft)

### Dynamic Controls#

Name

Description

Optimized

Fixed Initial Value

Fixed Final Value

climb_rate

aircraft rate of climb

True

False

False

### Parameters#

Name

Description

Optimized

mach

mach number

False (0.8)

S

aerodynamic reference area

False (427.8 m**2)

mass_empty

aircraft empty mass

False (330693.393 lbm)

False (74100 lbm)

### Objective#

Name

Description

Location

Minimized or Maximized

r

range

final

Maximized

### Nonlinear Path Constraints#

Name

Description

Lower

Upper

tau

engine throttle parameter

0.01

1.0

None

## Models#

### Atmosphere#

This problem uses an analytic fit to the 1976 standard atmosphere.

Name

Description

Input or Output

alt

altitude (m)

input

pres

static pressure (Pa)

output

temp

temperature (K)

output

sos

speed of sound (m/s)

output

rho

density (kg/m**3)

output

### True Airspeed#

TrueAirspeedComp uses the Mach number, provided as a control, and the speed of sound from the atmosphere model to compute the true airspeed of the aircraft.

(33)#\begin{align} TAS &= mach \cdot sos \end{align}

Name

Description

Input or Output

mach

Mach number

input

sos

speed of sound (m/s)

input

TAS

true airspeed (m/s)

output

### Flight Path Angle#

SteadyFlightPathAngleComp uses the true airspeed and the climb rate, obtained by differentiating the altitude time history at the nodes, to compute the flight path angle.

(34)#\begin{align} \gamma &= \arcsin \frac{\dot h}{TAS} \end{align}

Name

Description

Input or Output

TAS

true airspeed (m/s)

input

alt_rate

climb rate (m/s)

input

gamma

output

### Range Rate#

RangeRateComp uses the true airspeed and the flight path angle to determine the velocity projected along the ground. This is the derivative of the state variable range.

(35)#\begin{align} \dot{range} &= TAS \cos \gamma \end{align}

Name

Description

Input or Output

TAS

true airspeed (m/s)

input

gamma

input

dXdt:range

range rate (m/s)

output

### Mass#

The component MassComp defined in mass_comp.py computes the aircraft total mass based on its empty mass, payload mass, and current fuel mass. It also computes total weight which simplifies some equations later on.

(36)#\begin{align} mass_{total} &= mass_{empty} + mass_{payload} + mass_{fuel} \\ W_{total} &= 9.80665 \, mass_{total} \end{align}

Name

Description

Input or Output

mass_empty

aircraft empty mass (kg)

input

input

mass_fuel

fuel mass (kg)

input

mass_total

total aircraft mass (kg)

output

W_total

total aircraft weight (N)

output

### Dynamic Pressure#

The DynamicPressureComp computes the dynamic pressure from true airspeed and atmospheric density.

(37)#\begin{align} q &= \frac{1}{2} \rho TAS^2 \end{align}

Name

Description

Input or Output

TAS

true airspeed (m/s)

input

rho

atmospheric density (kg/m**3)

input

q

dynamic pressure (Pa)

output

### Aerodynamics#

The aerodynamics group computes the aerodynamic coefficients and forces on the vehicle. It consists of an interpolation component which outputs lift, drag, and moment coefficients as a function of Mach number, angle of attack, altitude, and tail rotation angle. A second component then uses these coefficients, along with dynamic pressure and aerodynamic reference area, to compute the lift and drag forces on the vehicle.

The aerodynamics group resides within the flight equilibrium group. As that group iterates to find the combination of thrust coefficient, angle of attack, and tail rotation angle, aerodynamics needs to update the values of the interpolated coefficients and resulting forces.

Organizationally speaking, we logically could have put the dynamic pressure component within the aerodynamics group. However, since that group doesn’t need to be updated with changes in alpha and tail angle, it’s more efficient to leave it outside of flight equilibrium group.

Name

Description

Input or Output

mach

mach number

input

alt

altitude (m)

input

alpha

angle of attack (deg)

input

eta

tail rotation angle (deg)

input

CL

lift coefficient

output

CD

drag coefficient

output

CM

moment coefficient

output

L

lift force (N)

output

D

drag force (N)

output

Note

This example uses openmdao.api.MetaModelStructuredComp to interpolate aerodynamic properties of the vehicle. This component is somewhat easier to use since it is distributed as part of OpenMDAO, but it can be significantly slower than alternatives such as SMT.

### Flight Equilibrium#

The steady flight equilibrium group uses balances to solve for the angle of attack and tail plane rotation angle such that the aircraft is in steady flight (the rates of change in flight path angle and true airspeed are zero) and the aerodynamic moment in the pitch axis is zero.

Of course, in reality the vehicle will accelerate, but the flight profile being modeled is so benign that assuming steady flight at discrete points (nodes) in the trajectory is not terribly inaccurate.

The thrust necessary for steady flight is computed by balancing the drag equation

(38)#\begin{align} C_T &= W_{total} \frac{sin \gamma}{q \cdot S \cdot \cos \alpha} + \frac{C_D}{\cos \alpha} \end{align}

The lift coefficient required for steady flight is found by balancing lift and weight:

(39)#\begin{align} \tilde{C_L} &= W_{total} \frac{cos \gamma}{q \cdot S} - C_T \sin \alpha \end{align}

Using coefficients in the balance equations is better scaled from a numerical standpoint.

### Propulsion#

Having determined the thrust, the propulsion group then computes the rate of fuel burn. In addition, by normalizing thrust at any point by the maximum possible thrust, we obtain the throttle parameter $$\tau$$. The propulsion group uses a number of components to perform these calculations.

(40)#\begin{align} T &= C_T \cdot q \cdot S \end{align}

Maximum thrust is computed by multiplying sea-level thrust by the ratio of pressure to sea-level atmospheric pressure.

(41)#\begin{align} T_{max} &= T_{max,sl} \frac{P}{P_{sl}} \end{align}

The throttle parameter is then the ratio current thrust to maximum possible thrust.

(42)#\begin{align} \tau &= \frac{T}{T_{max}} \end{align}

The thrust specific fuel consumption is computed as follows:

(43)#\begin{align} TSFC &= TSFC_{sl} - 1.5 E - 10 \cdot 9.80665 \cdot alt \end{align}

Finally, fuel burn rate is:

(44)#\begin{align} \dot{mass_{fuel}} &= -TSFC \frac{T}{9.80665} \end{align}

## The ODE System: aircraft_ode.py#

class AircraftODE(om.Group):

def initialize(self):
self.options.declare('num_nodes', types=int,
desc='Number of nodes to be evaluated in the RHS')

def setup(self):
nn = self.options['num_nodes']

subsys=MassComp(num_nodes=nn),
promotes_inputs=['mass_fuel'])

self.connect('mass_comp.W_total', 'flight_equilibrium.W_total')

subsys=USatm1976Comp(num_nodes=nn),
promotes_inputs=[('h', 'alt')])

self.connect('atmos.pres', 'propulsion.pres')
self.connect('atmos.sos', 'tas_comp.sos')
self.connect('atmos.rho', 'q_comp.rho')

subsys=TrueAirspeedComp(num_nodes=nn))

self.connect('tas_comp.TAS',
('gam_comp.TAS', 'q_comp.TAS', 'range_rate_comp.TAS'))

self.connect('gam_comp.gam', ('flight_equilibrium.gam', 'range_rate_comp.gam'))

subsys=DynamicPressureComp(num_nodes=nn))

self.connect('q_comp.q', ('aero.q', 'flight_equilibrium.q', 'propulsion.q'))

promotes_inputs=['aero.*', 'alt'],
promotes_outputs=['aero.*'])

self.connect('flight_equilibrium.CT', 'propulsion.CT')

promotes_inputs=['alt'])

# We promoted multiple inputs to the group named 'alt'.
# In order to automatically create a source variable for 'alt', we must specify their units
# since they have different units in different components.
self.set_input_defaults('alt', val=np.ones(nn,), units='m')


In this case the system has only two integrated states: range and mass_fuel. There are six parameters. Two of them (alt and climb_rate) will be varied dynamically in the phase The other four (mach, S, mass_empty, and mass_payload), will be set to fixed values as non-optimized parameters. More details on the various models involved can be found in the examples code.

## Building the problem#

In the following code we define and solve the optimal control problem. Note that we demonstrate the use of externally-connected design parameters in this case. The four parameters are connected to a source provided by the assumptions IndepVarComp.

Hide code cell outputs
import numpy as np
import openmdao.api as om
from dymos.models.atmosphere import USatm1976Comp

from .dynamic_pressure_comp import DynamicPressureComp
from .propulsion.propulsion_group import PropulsionGroup
from .range_rate_comp import RangeRateComp
from .true_airspeed_comp import TrueAirspeedComp
from .mass_comp import MassComp

class AircraftODE(om.Group):

def initialize(self):
self.options.declare('num_nodes', types=int,
desc='Number of nodes to be evaluated in the RHS')

def setup(self):
nn = self.options['num_nodes']

subsys=MassComp(num_nodes=nn),
promotes_inputs=['mass_fuel'])

self.connect('mass_comp.W_total', 'flight_equilibrium.W_total')

subsys=USatm1976Comp(num_nodes=nn),
promotes_inputs=[('h', 'alt')])

self.connect('atmos.pres', 'propulsion.pres')
self.connect('atmos.sos', 'tas_comp.sos')
self.connect('atmos.rho', 'q_comp.rho')

subsys=TrueAirspeedComp(num_nodes=nn))

self.connect('tas_comp.TAS',
('gam_comp.TAS', 'q_comp.TAS', 'range_rate_comp.TAS'))

self.connect('gam_comp.gam', ('flight_equilibrium.gam', 'range_rate_comp.gam'))

subsys=DynamicPressureComp(num_nodes=nn))

self.connect('q_comp.q', ('aero.q', 'flight_equilibrium.q', 'propulsion.q'))

promotes_inputs=['aero.*', 'alt'],
promotes_outputs=['aero.*'])

self.connect('flight_equilibrium.CT', 'propulsion.CT')

promotes_inputs=['alt'])

# We promoted multiple inputs to the group named 'alt'.
# In order to automatically create a source variable for 'alt', we must specify their units
# since they have different units in different components.
self.set_input_defaults('alt', val=np.ones(nn,), units='m')

import openmdao.api as om
import dymos as dm

from dymos.utils.lgl import lgl

p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'IPOPT'
p.driver.opt_settings['print_level'] = 0
p.driver.declare_coloring()

num_seg = 15
seg_ends, _ = lgl(num_seg + 1)

dm.Phase(ode_class=AircraftODE,
segment_ends=seg_ends,
order=3, compressed=False)))

# Pass Reference Area from an external source

phase.set_time_options(fix_initial=True,
duration_bounds=(300, 10000),
duration_ref=1000)

rate_source='range_rate_comp.dXdt:range',
fix_initial=True, fix_final=False, ref=1e-3,
defect_ref=1e-3, lower=0, upper=2000)

rate_source='propulsion.dXdt:mass_fuel',
fix_initial=True, fix_final=True,
upper=1.5E5, lower=0.0, ref=1e2, defect_ref=1e2)

rate_source='climb_rate',
fix_initial=True, fix_final=True,
lower=0.0, upper=60, ref=1e-3, defect_ref=1e-3)

targets=['gam_comp.climb_rate'],
rate_continuity=True, rate2_continuity=False)

targets=['aero.S', 'flight_equilibrium.S', 'propulsion.S'],
units='m**2')

p.model.connect('assumptions.S', 'traj.phase0.parameters:S')
p.model.connect('assumptions.mass_empty', 'traj.phase0.parameters:mass_empty')

p.setup()

--- Constraint Report [traj] ---
--- phase0 ---
[path]    1.0000e-02 <= propulsion.tau <= 2.0000e+00  [None]

<openmdao.core.problem.Problem at 0x7f2212863cd0>


## Set the initial guesses and assumptions#

phase.set_time_val(initial=0.0, duration=3600)
phase.set_state_val('range', (0, 724.0))
phase.set_state_val('mass_fuel', (30000, 1e-3))
phase.set_state_val('alt', 10.0)
phase.set_control_val('mach', 0.8)

p['assumptions.S'] = 427.8
p['assumptions.mass_empty'] = 0.15E6


## Run the problem#

The dymos run_problem method is used to automatically run the driver and follow the driver execution with a simulation run to help verify the results. Plots of the resulting solution and simulation will be generated.

dm.run_problem(p, simulate=True, make_plots=True)

Model viewer data has already been recorded for Driver.

Full total jacobian for problem 'problem' was computed 3 times, taking 0.6714747909999232 seconds.
Total jacobian shape: (224, 221)

Jacobian shape: (224, 221)  (2.51% nonzero)
FWD solves: 11   REV solves: 0
Total colors vs. total size: 11 vs 221  (95.02% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity:   0.6715 sec
Time to compute coloring:   0.1106 sec
Memory to compute coloring:   0.1250 MB
Coloring created on: 2024-08-29 21:47:07

Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc

Solution:
--------------------------------------------------------------------------------
Total Time:                   19.3589
User Objective Time :      17.0626
User Sensitivity Time :     1.9749
Interface Time :            0.1370
Opt Solver Time:            0.1844
Calls to Objective Function :      34
Calls to Sens Function :           32

Objectives
Index  Name                                Value
0  traj.phase0.states:range    -7.260052E+02

Variables (c - continuous, i - integer, d - discrete)
Index  Name                                 Type      Lower Bound            Value      Upper Bound     Status
0  traj.phase0.t_duration_0                c     3.000000E-01     5.637564E+00     1.000000E+01
1  traj.phase0.states:range_0              c     0.000000E+00     4.300778E+03     2.000000E+06
2  traj.phase0.states:range_1              c     0.000000E+00     1.019478E+04     2.000000E+06
3  traj.phase0.states:range_2              c     0.000000E+00     1.205044E+04     2.000000E+06
4  traj.phase0.states:range_3              c     0.000000E+00     1.205044E+04     2.000000E+06
5  traj.phase0.states:range_4              c     0.000000E+00     2.179716E+04     2.000000E+06
6  traj.phase0.states:range_5              c     0.000000E+00     3.502521E+04     2.000000E+06
7  traj.phase0.states:range_6              c     0.000000E+00     3.915789E+04     2.000000E+06
8  traj.phase0.states:range_7              c     0.000000E+00     3.915789E+04     2.000000E+06
9  traj.phase0.states:range_8              c     0.000000E+00     5.336791E+04     2.000000E+06
10  traj.phase0.states:range_9              c     0.000000E+00     7.250027E+04     2.000000E+06
11  traj.phase0.states:range_10             c     0.000000E+00     7.845561E+04     2.000000E+06
12  traj.phase0.states:range_11             c     0.000000E+00     7.845561E+04     2.000000E+06
13  traj.phase0.states:range_12             c     0.000000E+00     9.625935E+04     2.000000E+06
14  traj.phase0.states:range_13             c     0.000000E+00     1.208337E+05     2.000000E+06
15  traj.phase0.states:range_14             c     0.000000E+00     1.286109E+05     2.000000E+06
16  traj.phase0.states:range_15             c     0.000000E+00     1.286109E+05     2.000000E+06
17  traj.phase0.states:range_16             c     0.000000E+00     1.498279E+05     2.000000E+06
18  traj.phase0.states:range_17             c     0.000000E+00     1.791031E+05     2.000000E+06
19  traj.phase0.states:range_18             c     0.000000E+00     1.883686E+05     2.000000E+06
20  traj.phase0.states:range_19             c     0.000000E+00     1.883686E+05     2.000000E+06
21  traj.phase0.states:range_20             c     0.000000E+00     2.121241E+05     2.000000E+06
22  traj.phase0.states:range_21             c     0.000000E+00     2.449018E+05     2.000000E+06
23  traj.phase0.states:range_22             c     0.000000E+00     2.552758E+05     2.000000E+06
24  traj.phase0.states:range_23             c     0.000000E+00     2.552758E+05     2.000000E+06
25  traj.phase0.states:range_24             c     0.000000E+00     2.805971E+05     2.000000E+06
26  traj.phase0.states:range_25             c     0.000000E+00     3.155354E+05     2.000000E+06
27  traj.phase0.states:range_26             c     0.000000E+00     3.265932E+05     2.000000E+06
28  traj.phase0.states:range_27             c     0.000000E+00     3.265932E+05     2.000000E+06
29  traj.phase0.states:range_28             c     0.000000E+00     3.524437E+05     2.000000E+06
30  traj.phase0.states:range_29             c     0.000000E+00     3.881121E+05     2.000000E+06
31  traj.phase0.states:range_30             c     0.000000E+00     3.994010E+05     2.000000E+06
32  traj.phase0.states:range_31             c     0.000000E+00     3.994010E+05     2.000000E+06
33  traj.phase0.states:range_32             c     0.000000E+00     4.247223E+05     2.000000E+06
34  traj.phase0.states:range_33             c     0.000000E+00     4.596605E+05     2.000000E+06
35  traj.phase0.states:range_34             c     0.000000E+00     4.707183E+05     2.000000E+06
36  traj.phase0.states:range_35             c     0.000000E+00     4.707183E+05     2.000000E+06
37  traj.phase0.states:range_36             c     0.000000E+00     4.944738E+05     2.000000E+06
38  traj.phase0.states:range_37             c     0.000000E+00     5.272515E+05     2.000000E+06
39  traj.phase0.states:range_38             c     0.000000E+00     5.376255E+05     2.000000E+06
40  traj.phase0.states:range_39             c     0.000000E+00     5.376255E+05     2.000000E+06
41  traj.phase0.states:range_40             c     0.000000E+00     5.588425E+05     2.000000E+06
42  traj.phase0.states:range_41             c     0.000000E+00     5.881176E+05     2.000000E+06
43  traj.phase0.states:range_42             c     0.000000E+00     5.973831E+05     2.000000E+06
44  traj.phase0.states:range_43             c     0.000000E+00     5.973831E+05     2.000000E+06
45  traj.phase0.states:range_44             c     0.000000E+00     6.151931E+05     2.000000E+06
46  traj.phase0.states:range_45             c     0.000000E+00     6.397625E+05     2.000000E+06
47  traj.phase0.states:range_46             c     0.000000E+00     6.475361E+05     2.000000E+06
48  traj.phase0.states:range_47             c     0.000000E+00     6.475361E+05     2.000000E+06
49  traj.phase0.states:range_48             c     0.000000E+00     6.612680E+05     2.000000E+06
50  traj.phase0.states:range_49             c     0.000000E+00     6.805947E+05     2.000000E+06
51  traj.phase0.states:range_50             c     0.000000E+00     6.868473E+05     2.000000E+06
52  traj.phase0.states:range_51             c     0.000000E+00     6.868473E+05     2.000000E+06
53  traj.phase0.states:range_52             c     0.000000E+00     6.963491E+05     2.000000E+06
54  traj.phase0.states:range_53             c     0.000000E+00     7.096820E+05     2.000000E+06
55  traj.phase0.states:range_54             c     0.000000E+00     7.139547E+05     2.000000E+06
56  traj.phase0.states:range_55             c     0.000000E+00     7.139547E+05     2.000000E+06
57  traj.phase0.states:range_56             c     0.000000E+00     7.182109E+05     2.000000E+06
58  traj.phase0.states:range_57             c     0.000000E+00     7.241240E+05     2.000000E+06
59  traj.phase0.states:range_58             c     0.000000E+00     7.260052E+05     2.000000E+06
60  traj.phase0.states:mass_fuel_0          c     0.000000E+00     2.957208E+02     1.500000E+03
61  traj.phase0.states:mass_fuel_1          c     0.000000E+00     2.900371E+02     1.500000E+03
62  traj.phase0.states:mass_fuel_2          c     0.000000E+00     2.882890E+02     1.500000E+03
63  traj.phase0.states:mass_fuel_3          c     0.000000E+00     2.882890E+02     1.500000E+03
64  traj.phase0.states:mass_fuel_4          c     0.000000E+00     2.794117E+02     1.500000E+03
65  traj.phase0.states:mass_fuel_5          c     0.000000E+00     2.680940E+02     1.500000E+03
66  traj.phase0.states:mass_fuel_6          c     0.000000E+00     2.647067E+02     1.500000E+03
67  traj.phase0.states:mass_fuel_7          c     0.000000E+00     2.647067E+02     1.500000E+03
68  traj.phase0.states:mass_fuel_8          c     0.000000E+00     2.535688E+02     1.500000E+03
69  traj.phase0.states:mass_fuel_9          c     0.000000E+00     2.401846E+02     1.500000E+03
70  traj.phase0.states:mass_fuel_10         c     0.000000E+00     2.364961E+02     1.500000E+03
71  traj.phase0.states:mass_fuel_11         c     0.000000E+00     2.364961E+02     1.500000E+03
72  traj.phase0.states:mass_fuel_12         c     0.000000E+00     2.271299E+02     1.500000E+03
73  traj.phase0.states:mass_fuel_13         c     0.000000E+00     2.167574E+02     1.500000E+03
74  traj.phase0.states:mass_fuel_14         c     0.000000E+00     2.137292E+02     1.500000E+03
75  traj.phase0.states:mass_fuel_15         c     0.000000E+00     2.137292E+02     1.500000E+03
76  traj.phase0.states:mass_fuel_16         c     0.000000E+00     2.055422E+02     1.500000E+03
77  traj.phase0.states:mass_fuel_17         c     0.000000E+00     1.942336E+02     1.500000E+03
78  traj.phase0.states:mass_fuel_18         c     0.000000E+00     1.906363E+02     1.500000E+03
79  traj.phase0.states:mass_fuel_19         c     0.000000E+00     1.906363E+02     1.500000E+03
80  traj.phase0.states:mass_fuel_20         c     0.000000E+00     1.813581E+02     1.500000E+03
81  traj.phase0.states:mass_fuel_21         c     0.000000E+00     1.684993E+02     1.500000E+03
82  traj.phase0.states:mass_fuel_22         c     0.000000E+00     1.644355E+02     1.500000E+03
83  traj.phase0.states:mass_fuel_23         c     0.000000E+00     1.644355E+02     1.500000E+03
84  traj.phase0.states:mass_fuel_24         c     0.000000E+00     1.545567E+02     1.500000E+03
85  traj.phase0.states:mass_fuel_25         c     0.000000E+00     1.410094E+02     1.500000E+03
86  traj.phase0.states:mass_fuel_26         c     0.000000E+00     1.367383E+02     1.500000E+03
87  traj.phase0.states:mass_fuel_27         c     0.000000E+00     1.367383E+02     1.500000E+03
88  traj.phase0.states:mass_fuel_28         c     0.000000E+00     1.267738E+02     1.500000E+03
89  traj.phase0.states:mass_fuel_29         c     0.000000E+00     1.130185E+02     1.500000E+03
90  traj.phase0.states:mass_fuel_30         c     0.000000E+00     1.086503E+02     1.500000E+03
91  traj.phase0.states:mass_fuel_31         c     0.000000E+00     1.086503E+02     1.500000E+03
92  traj.phase0.states:mass_fuel_32         c     0.000000E+00     9.882577E+01     1.500000E+03
93  traj.phase0.states:mass_fuel_33         c     0.000000E+00     8.534598E+01     1.500000E+03
94  traj.phase0.states:mass_fuel_34         c     0.000000E+00     8.113325E+01     1.500000E+03
95  traj.phase0.states:mass_fuel_35         c     0.000000E+00     8.113325E+01     1.500000E+03
96  traj.phase0.states:mass_fuel_36         c     0.000000E+00     7.218113E+01     1.500000E+03
97  traj.phase0.states:mass_fuel_37         c     0.000000E+00     5.977770E+01     1.500000E+03
98  traj.phase0.states:mass_fuel_38         c     0.000000E+00     5.576974E+01     1.500000E+03
99  traj.phase0.states:mass_fuel_39         c     0.000000E+00     5.576974E+01     1.500000E+03
100  traj.phase0.states:mass_fuel_40         c     0.000000E+00     4.741800E+01     1.500000E+03
101  traj.phase0.states:mass_fuel_41         c     0.000000E+00     3.592791E+01     1.500000E+03
102  traj.phase0.states:mass_fuel_42         c     0.000000E+00     3.239650E+01     1.500000E+03
103  traj.phase0.states:mass_fuel_43         c     0.000000E+00     3.239650E+01     1.500000E+03
104  traj.phase0.states:mass_fuel_44         c     0.000000E+00     2.595940E+01     1.500000E+03
105  traj.phase0.states:mass_fuel_45         c     0.000000E+00     1.877799E+01     1.500000E+03
106  traj.phase0.states:mass_fuel_46         c     0.000000E+00     1.714587E+01     1.500000E+03
107  traj.phase0.states:mass_fuel_47         c     0.000000E+00     1.714587E+01     1.500000E+03
108  traj.phase0.states:mass_fuel_48         c     0.000000E+00     1.500522E+01     1.500000E+03
109  traj.phase0.states:mass_fuel_49         c     0.000000E+00     1.243555E+01     1.500000E+03
110  traj.phase0.states:mass_fuel_50         c     0.000000E+00     1.141787E+01     1.500000E+03
111  traj.phase0.states:mass_fuel_51         c     0.000000E+00     1.141787E+01     1.500000E+03
112  traj.phase0.states:mass_fuel_52         c     0.000000E+00     9.500576E+00     1.500000E+03
113  traj.phase0.states:mass_fuel_53         c     0.000000E+00     5.938689E+00     1.500000E+03
114  traj.phase0.states:mass_fuel_54         c     0.000000E+00     4.560755E+00     1.500000E+03
115  traj.phase0.states:mass_fuel_55         c     0.000000E+00     4.560755E+00     1.500000E+03
116  traj.phase0.states:mass_fuel_56         c     0.000000E+00     3.066294E+00     1.500000E+03
117  traj.phase0.states:mass_fuel_57         c     0.000000E+00     7.801232E-01     1.500000E+03
118  traj.phase0.states:alt_0                c     0.000000E+00     1.152283E+04     6.000000E+04
119  traj.phase0.states:alt_1                c     0.000000E+00     1.362403E+04     6.000000E+04
120  traj.phase0.states:alt_2                c     0.000000E+00     1.428905E+04     6.000000E+04
121  traj.phase0.states:alt_3                c     0.000000E+00     1.428905E+04     6.000000E+04
122  traj.phase0.states:alt_4                c     0.000000E+00     1.781028E+04     6.000000E+04
123  traj.phase0.states:alt_5                c     0.000000E+00     2.266886E+04     6.000000E+04
124  traj.phase0.states:alt_6                c     0.000000E+00     2.420659E+04     6.000000E+04
125  traj.phase0.states:alt_7                c     0.000000E+00     2.420659E+04     6.000000E+04
126  traj.phase0.states:alt_8                c     0.000000E+00     2.947162E+04     6.000000E+04
127  traj.phase0.states:alt_9                c     0.000000E+00     3.563844E+04     6.000000E+04
128  traj.phase0.states:alt_10               c     0.000000E+00     3.710397E+04     6.000000E+04
129  traj.phase0.states:alt_11               c     0.000000E+00     3.710397E+04     6.000000E+04
130  traj.phase0.states:alt_12               c     0.000000E+00     3.977280E+04     6.000000E+04
131  traj.phase0.states:alt_13               c     0.000000E+00     4.064814E+04     6.000000E+04
132  traj.phase0.states:alt_14               c     0.000000E+00     4.061934E+04     6.000000E+04
133  traj.phase0.states:alt_15               c     0.000000E+00     4.061934E+04     6.000000E+04
134  traj.phase0.states:alt_16               c     0.000000E+00     4.049112E+04     6.000000E+04
135  traj.phase0.states:alt_17               c     0.000000E+00     4.035333E+04     6.000000E+04
136  traj.phase0.states:alt_18               c     0.000000E+00     4.033651E+04     6.000000E+04
137  traj.phase0.states:alt_19               c     0.000000E+00     4.033651E+04     6.000000E+04
138  traj.phase0.states:alt_20               c     0.000000E+00     4.037081E+04     6.000000E+04
139  traj.phase0.states:alt_21               c     0.000000E+00     4.051553E+04     6.000000E+04
140  traj.phase0.states:alt_22               c     0.000000E+00     4.056200E+04     6.000000E+04
141  traj.phase0.states:alt_23               c     0.000000E+00     4.056200E+04     6.000000E+04
142  traj.phase0.states:alt_24               c     0.000000E+00     4.064375E+04     6.000000E+04
143  traj.phase0.states:alt_25               c     0.000000E+00     4.069402E+04     6.000000E+04
144  traj.phase0.states:alt_26               c     0.000000E+00     4.069892E+04     6.000000E+04
145  traj.phase0.states:alt_27               c     0.000000E+00     4.069892E+04     6.000000E+04
146  traj.phase0.states:alt_28               c     0.000000E+00     4.070254E+04     6.000000E+04
147  traj.phase0.states:alt_29               c     0.000000E+00     4.075181E+04     6.000000E+04
148  traj.phase0.states:alt_30               c     0.000000E+00     4.079372E+04     6.000000E+04
149  traj.phase0.states:alt_31               c     0.000000E+00     4.079372E+04     6.000000E+04
150  traj.phase0.states:alt_32               c     0.000000E+00     4.093548E+04     6.000000E+04
151  traj.phase0.states:alt_33               c     0.000000E+00     4.107640E+04     6.000000E+04
152  traj.phase0.states:alt_34               c     0.000000E+00     4.106576E+04     6.000000E+04
153  traj.phase0.states:alt_35               c     0.000000E+00     4.106576E+04     6.000000E+04
154  traj.phase0.states:alt_36               c     0.000000E+00     4.093921E+04     6.000000E+04
155  traj.phase0.states:alt_37               c     0.000000E+00     4.085653E+04     6.000000E+04
156  traj.phase0.states:alt_38               c     0.000000E+00     4.093627E+04     6.000000E+04
157  traj.phase0.states:alt_39               c     0.000000E+00     4.093627E+04     6.000000E+04
158  traj.phase0.states:alt_40               c     0.000000E+00     4.129897E+04     6.000000E+04
159  traj.phase0.states:alt_41               c     0.000000E+00     4.178379E+04     6.000000E+04
160  traj.phase0.states:alt_42               c     0.000000E+00     4.181541E+04     6.000000E+04
161  traj.phase0.states:alt_43               c     0.000000E+00     4.181541E+04     6.000000E+04
162  traj.phase0.states:alt_44               c     0.000000E+00     4.146282E+04     6.000000E+04
163  traj.phase0.states:alt_45               c     0.000000E+00     3.890556E+04     6.000000E+04
164  traj.phase0.states:alt_46               c     0.000000E+00     3.730605E+04     6.000000E+04
165  traj.phase0.states:alt_47               c     0.000000E+00     3.730605E+04     6.000000E+04
166  traj.phase0.states:alt_48               c     0.000000E+00     3.341148E+04     6.000000E+04
167  traj.phase0.states:alt_49               c     0.000000E+00     2.654155E+04     6.000000E+04
168  traj.phase0.states:alt_50               c     0.000000E+00     2.420659E+04     6.000000E+04
169  traj.phase0.states:alt_51               c     0.000000E+00     2.420659E+04     6.000000E+04
170  traj.phase0.states:alt_52               c     0.000000E+00     2.068536E+04     6.000000E+04
171  traj.phase0.states:alt_53               c     0.000000E+00     1.582678E+04     6.000000E+04
172  traj.phase0.states:alt_54               c     0.000000E+00     1.428905E+04     6.000000E+04
173  traj.phase0.states:alt_55               c     0.000000E+00     1.428905E+04     6.000000E+04
174  traj.phase0.states:alt_56               c     0.000000E+00     1.276622E+04     6.000000E+04
175  traj.phase0.states:alt_57               c     0.000000E+00     1.066502E+04     6.000000E+04
176  traj.phase0.controls:climb_rate_0       c    -3.000000E+03     3.000000E+03     3.000000E+03          U
177  traj.phase0.controls:climb_rate_1       c    -3.000000E+03     3.000000E+03     3.000000E+03          U
178  traj.phase0.controls:climb_rate_2       c    -3.000000E+03     3.000000E+03     3.000000E+03          U
179  traj.phase0.controls:climb_rate_3       c    -3.000000E+03     3.000000E+03     3.000000E+03          U
180  traj.phase0.controls:climb_rate_4       c    -3.000000E+03     3.000000E+03     3.000000E+03          U
181  traj.phase0.controls:climb_rate_5       c    -3.000000E+03     3.000000E+03     3.000000E+03          U
182  traj.phase0.controls:climb_rate_6       c    -3.000000E+03     3.000000E+03     3.000000E+03          U
183  traj.phase0.controls:climb_rate_7       c    -3.000000E+03     2.834019E+03     3.000000E+03
184  traj.phase0.controls:climb_rate_8       c    -3.000000E+03     2.059977E+03     3.000000E+03
185  traj.phase0.controls:climb_rate_9       c    -3.000000E+03     1.683328E+03     3.000000E+03
186  traj.phase0.controls:climb_rate_10      c    -3.000000E+03     6.801683E+02     3.000000E+03
187  traj.phase0.controls:climb_rate_11      c    -3.000000E+03     8.640705E-01     3.000000E+03
188  traj.phase0.controls:climb_rate_12      c    -3.000000E+03    -4.385431E+01     3.000000E+03
189  traj.phase0.controls:climb_rate_13      c    -3.000000E+03    -4.578020E+01     3.000000E+03
190  traj.phase0.controls:climb_rate_14      c    -3.000000E+03    -2.088465E+01     3.000000E+03
191  traj.phase0.controls:climb_rate_15      c    -3.000000E+03    -6.349033E+00     3.000000E+03
192  traj.phase0.controls:climb_rate_16      c    -3.000000E+03     2.513665E+01     3.000000E+03
193  traj.phase0.controls:climb_rate_17      c    -3.000000E+03     3.612377E+01     3.000000E+03
194  traj.phase0.controls:climb_rate_18      c    -3.000000E+03     3.176021E+01     3.000000E+03
195  traj.phase0.controls:climb_rate_19      c    -3.000000E+03     1.817241E+01     3.000000E+03
196  traj.phase0.controls:climb_rate_20      c    -3.000000E+03     4.887917E+00     3.000000E+03
197  traj.phase0.controls:climb_rate_21      c    -3.000000E+03     2.003396E+00     3.000000E+03
198  traj.phase0.controls:climb_rate_22      c    -3.000000E+03     2.206328E+00     3.000000E+03
199  traj.phase0.controls:climb_rate_23      c    -3.000000E+03     2.285925E+01     3.000000E+03
200  traj.phase0.controls:climb_rate_24      c    -3.000000E+03     3.431755E+01     3.000000E+03
201  traj.phase0.controls:climb_rate_25      c    -3.000000E+03     4.562492E+01     3.000000E+03
202  traj.phase0.controls:climb_rate_26      c    -3.000000E+03     5.247888E+00     3.000000E+03
203  traj.phase0.controls:climb_rate_27      c    -3.000000E+03    -2.105477E+01     3.000000E+03
204  traj.phase0.controls:climb_rate_28      c    -3.000000E+03    -4.836622E+01     3.000000E+03
205  traj.phase0.controls:climb_rate_29      c    -3.000000E+03     3.274753E+01     3.000000E+03
206  traj.phase0.controls:climb_rate_30      c    -3.000000E+03     8.711916E+01     3.000000E+03
207  traj.phase0.controls:climb_rate_31      c    -3.000000E+03     1.552940E+02     3.000000E+03
208  traj.phase0.controls:climb_rate_32      c    -3.000000E+03     6.174254E+01     3.000000E+03
209  traj.phase0.controls:climb_rate_33      c    -3.000000E+03    -1.319143E+01     3.000000E+03
210  traj.phase0.controls:climb_rate_34      c    -3.000000E+03    -3.453113E+02     3.000000E+03
211  traj.phase0.controls:climb_rate_35      c    -3.000000E+03    -1.352390E+03     3.000000E+03
212  traj.phase0.controls:climb_rate_36      c    -3.000000E+03    -1.803711E+03     3.000000E+03
213  traj.phase0.controls:climb_rate_37      c    -3.000000E+03    -2.502393E+03     3.000000E+03
214  traj.phase0.controls:climb_rate_38      c    -3.000000E+03    -2.971240E+03     3.000000E+03
215  traj.phase0.controls:climb_rate_39      c    -3.000000E+03    -3.000000E+03     3.000000E+03          L
216  traj.phase0.controls:climb_rate_40      c    -3.000000E+03    -3.000000E+03     3.000000E+03          L
217  traj.phase0.controls:climb_rate_41      c    -3.000000E+03    -3.000000E+03     3.000000E+03          L
218  traj.phase0.controls:climb_rate_42      c    -3.000000E+03    -3.000000E+03     3.000000E+03          L
219  traj.phase0.controls:climb_rate_43      c    -3.000000E+03    -3.000000E+03     3.000000E+03          L
220  traj.phase0.controls:climb_rate_44      c    -3.000000E+03    -3.000000E+03     3.000000E+03          L

Constraints (i - inequality, e - equality)
Index  Name                                                             Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
0  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -2.380902E-12    0.000000E+00              9.00000E+100
1  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.380902E-12    0.000000E+00              9.00000E+100
2  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
3  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -2.477402E-11    0.000000E+00              9.00000E+100
4  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.752669E-12    0.000000E+00              9.00000E+100
5  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -1.101067E-11    0.000000E+00              9.00000E+100
6  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -2.096598E-11    0.000000E+00              9.00000E+100
7  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -2.515917E-11    0.000000E+00              9.00000E+100
8  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    5.031834E-11    0.000000E+00              9.00000E+100
9  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    9.831065E-11    0.000000E+00              9.00000E+100
10  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.785469E-10    0.000000E+00              9.00000E+100
11  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    6.007873E-10    0.000000E+00              9.00000E+100
12  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    9.694752E-10    0.000000E+00              9.00000E+100
13  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    8.328378E-10    0.000000E+00              9.00000E+100
14  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.212225E-10    0.000000E+00              9.00000E+100
15  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -1.675548E-10    0.000000E+00              9.00000E+100
16  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    3.788195E-10    0.000000E+00              9.00000E+100
17  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.047082E-09    0.000000E+00              9.00000E+100
18  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.694517E-09    0.000000E+00              9.00000E+100
19  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    3.005124E-09    0.000000E+00              9.00000E+100
20  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    1.553036E-11    0.000000E+00              9.00000E+100
21  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    3.012433E-10    0.000000E+00              9.00000E+100
22  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.687407E-09    0.000000E+00              9.00000E+100
23  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -7.927455E-12    0.000000E+00              9.00000E+100
24  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    6.988660E-10    0.000000E+00              9.00000E+100
25  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    6.336385E-09    0.000000E+00              9.00000E+100
26  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    1.118186E-09    0.000000E+00              9.00000E+100
27  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.112647E-10    0.000000E+00              9.00000E+100
28  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    7.357839E-09    0.000000E+00              9.00000E+100
29  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.593456E-09    0.000000E+00              9.00000E+100
30  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -9.759817E-11    0.000000E+00              9.00000E+100
31  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    3.988512E-09    0.000000E+00              9.00000E+100
32  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.771788E-09    0.000000E+00              9.00000E+100
33  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    3.823192E-11    0.000000E+00              9.00000E+100
34  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    1.054109E-09    0.000000E+00              9.00000E+100
35  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    1.392734E-09    0.000000E+00              9.00000E+100
36  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    4.947970E-10    0.000000E+00              9.00000E+100
37  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    3.690012E-10    0.000000E+00              9.00000E+100
38  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.096598E-11    0.000000E+00              9.00000E+100
39  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    3.550943E-10    0.000000E+00              9.00000E+100
40  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.477402E-11    0.000000E+00              9.00000E+100
41  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    6.331138E-11    0.000000E+00              9.00000E+100
42  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -9.642654E-11    0.000000E+00              9.00000E+100
43  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -3.809444E-11    0.000000E+00              9.00000E+100
44  traj.phase0.collocation_constraint.defects:range                    e   0.000000E+00    4.880850E-10    0.000000E+00              9.00000E+100
45  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -3.580877E-14    0.000000E+00              9.00000E+100
46  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -5.028465E-14    0.000000E+00              9.00000E+100
47  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    2.742799E-14    0.000000E+00              9.00000E+100
48  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.092259E-13    0.000000E+00              9.00000E+100
49  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    4.228099E-14    0.000000E+00              9.00000E+100
50  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -9.337052E-14    0.000000E+00              9.00000E+100
51  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -1.341822E-13    0.000000E+00              9.00000E+100
52  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    5.367290E-14    0.000000E+00              9.00000E+100
53  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -1.422332E-13    0.000000E+00              9.00000E+100
54  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    5.418009E-14    0.000000E+00              9.00000E+100
55  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    3.498985E-12    0.000000E+00              9.00000E+100
56  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    2.528812E-11    0.000000E+00              9.00000E+100
57  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    4.683880E-11    0.000000E+00              9.00000E+100
58  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.182963E-10    0.000000E+00              9.00000E+100
59  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    2.394159E-10    0.000000E+00              9.00000E+100
60  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    2.949267E-10    0.000000E+00              9.00000E+100
61  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    2.794825E-10    0.000000E+00              9.00000E+100
62  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.156064E-10    0.000000E+00              9.00000E+100
63  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    6.406458E-11    0.000000E+00              9.00000E+100
64  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -1.272247E-12    0.000000E+00              9.00000E+100
65  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    9.078425E-11    0.000000E+00              9.00000E+100
66  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    9.939634E-11    0.000000E+00              9.00000E+100
67  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.909185E-11    0.000000E+00              9.00000E+100
68  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    2.451296E-11    0.000000E+00              9.00000E+100
69  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    2.464978E-11    0.000000E+00              9.00000E+100
70  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    7.183721E-12    0.000000E+00              9.00000E+100
71  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    3.319048E-10    0.000000E+00              9.00000E+100
72  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    3.576312E-10    0.000000E+00              9.00000E+100
73  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.379859E-10    0.000000E+00              9.00000E+100
74  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    2.099942E-11    0.000000E+00              9.00000E+100
75  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    4.602470E-11    0.000000E+00              9.00000E+100
76  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    7.607973E-12    0.000000E+00              9.00000E+100
77  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    8.527842E-11    0.000000E+00              9.00000E+100
78  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.190756E-10    0.000000E+00              9.00000E+100
79  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.151746E-10    0.000000E+00              9.00000E+100
80  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    2.173233E-11    0.000000E+00              9.00000E+100
81  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    4.863436E-12    0.000000E+00              9.00000E+100
82  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.294859E-13    0.000000E+00              9.00000E+100
83  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -5.367290E-15    0.000000E+00              9.00000E+100
84  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -3.523416E-15    0.000000E+00              9.00000E+100
85  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    6.606405E-15    0.000000E+00              9.00000E+100
86  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -5.285124E-15    0.000000E+00              9.00000E+100
87  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -1.523777E-15    0.000000E+00              9.00000E+100
88  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.904722E-15    0.000000E+00              9.00000E+100
89  traj.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -1.142833E-15    0.000000E+00              9.00000E+100
90  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    4.166579E-12    0.000000E+00              9.00000E+100
91  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.785677E-12    0.000000E+00              9.00000E+100
92  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -3.273741E-12    0.000000E+00              9.00000E+100
93  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
94  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    2.064501E-12    0.000000E+00              9.00000E+100
95  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -6.881672E-13    0.000000E+00              9.00000E+100
96  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    7.338092E-12    0.000000E+00              9.00000E+100
97  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -2.096598E-12    0.000000E+00              9.00000E+100
98  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -4.193195E-12    0.000000E+00              9.00000E+100
99  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.024069E-11    0.000000E+00              9.00000E+100
100  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.365426E-12    0.000000E+00              9.00000E+100
101  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.896062E-11    0.000000E+00              9.00000E+100
102  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    5.744059E-12    0.000000E+00              9.00000E+100
103  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    4.109798E-11    0.000000E+00              9.00000E+100
104  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.254289E-11    0.000000E+00              9.00000E+100
105  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -6.733635E-12    0.000000E+00              9.00000E+100
106  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -8.138699E-12    0.000000E+00              9.00000E+100
107  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -4.817768E-11    0.000000E+00              9.00000E+100
108  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -4.813804E-11    0.000000E+00              9.00000E+100
109  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -3.947804E-11    0.000000E+00              9.00000E+100
110  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -2.441784E-11    0.000000E+00              9.00000E+100
111  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    6.967490E-12    0.000000E+00              9.00000E+100
112  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    3.679609E-11    0.000000E+00              9.00000E+100
113  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.518913E-11    0.000000E+00              9.00000E+100
114  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -4.904802E-11    0.000000E+00              9.00000E+100
115  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -5.578188E-11    0.000000E+00              9.00000E+100
116  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -4.888119E-11    0.000000E+00              9.00000E+100
117  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    4.859031E-11    0.000000E+00              9.00000E+100
118  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    7.327675E-11    0.000000E+00              9.00000E+100
119  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    6.402823E-11    0.000000E+00              9.00000E+100
120  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    2.709366E-11    0.000000E+00              9.00000E+100
121  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -5.317067E-11    0.000000E+00              9.00000E+100
122  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -3.293938E-11    0.000000E+00              9.00000E+100
123  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -3.719718E-11    0.000000E+00              9.00000E+100
124  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    3.294090E-11    0.000000E+00              9.00000E+100
125  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    3.550107E-11    0.000000E+00              9.00000E+100
126  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.415203E-11    0.000000E+00              9.00000E+100
127  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    3.144896E-12    0.000000E+00              9.00000E+100
128  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -2.096598E-12    0.000000E+00              9.00000E+100
129  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    8.946173E-12    0.000000E+00              9.00000E+100
130  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
131  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -2.752669E-12    0.000000E+00              9.00000E+100
132  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    6.845094E-12    0.000000E+00              9.00000E+100
133  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -2.976128E-13    0.000000E+00              9.00000E+100
134  traj.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -2.976128E-13    0.000000E+00              9.00000E+100
135  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
136  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
137  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
138  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
139  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
140  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
141  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
142  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
143  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
144  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
145  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
146  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
147  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
148  traj.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
149  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
150  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
151  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
152  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
153  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
154  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
155  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
156  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
157  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
158  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
159  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
160  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
161  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
162  traj.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
163  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
164  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
165  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
166  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
167  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
168  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
169  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
170  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
171  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
172  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
173  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
174  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
175  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
176  traj.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
177  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    1.265232E-11    0.000000E+00              9.00000E+100
178  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00   -1.735434E-12    0.000000E+00              9.00000E+100
179  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    1.502149E-11    0.000000E+00              9.00000E+100
180  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    2.425344E-12    0.000000E+00              9.00000E+100
181  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00   -2.347107E-13    0.000000E+00              9.00000E+100
182  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    7.823692E-14    0.000000E+00              9.00000E+100
183  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00   -9.779614E-15    0.000000E+00              9.00000E+100
184  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    7.823692E-14    0.000000E+00              9.00000E+100
185  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
186  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    6.258953E-13    0.000000E+00              9.00000E+100
187  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
188  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00   -1.752507E-11    0.000000E+00              9.00000E+100
189  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    1.463052E-11    0.000000E+00              9.00000E+100
190  traj.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    5.563294E-11    0.000000E+00              9.00000E+100
191  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    4.547474E-13    0.000000E+00              9.00000E+100
192  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    4.547474E-13    0.000000E+00              9.00000E+100
193  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    4.547474E-13    0.000000E+00              9.00000E+100
194  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00   -4.263256E-14    0.000000E+00              9.00000E+100
195  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    3.552714E-15    0.000000E+00              9.00000E+100
196  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    7.105427E-15    0.000000E+00              9.00000E+100
197  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00   -3.108624E-15    0.000000E+00              9.00000E+100
198  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
199  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
200  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
201  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00   -1.776357E-14    0.000000E+00              9.00000E+100
202  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
203  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00   -4.547474E-13    0.000000E+00              9.00000E+100
204  traj.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00   -4.547474E-13    0.000000E+00              9.00000E+100
205  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    5.293064E-01    2.000000E+00              9.00000E+100
206  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    5.459977E-01    2.000000E+00              9.00000E+100
207  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    5.710745E-01    2.000000E+00              9.00000E+100
208  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    5.795573E-01    2.000000E+00              9.00000E+100
209  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    5.795573E-01    2.000000E+00              9.00000E+100
210  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    6.296025E-01    2.000000E+00              9.00000E+100
211  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.166094E-01    2.000000E+00              9.00000E+100
212  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.497818E-01    2.000000E+00              9.00000E+100
213  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.497818E-01    2.000000E+00              9.00000E+100
214  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    8.706197E-01    2.000000E+00              9.00000E+100
215  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    9.783658E-01    2.000000E+00              9.00000E+100
216  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    9.719171E-01    2.000000E+00              9.00000E+100
217  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    9.719171E-01    2.000000E+00              9.00000E+100
218  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    8.846859E-01    2.000000E+00              9.00000E+100
219  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.714090E-01    2.000000E+00              9.00000E+100
220  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.598725E-01    2.000000E+00              9.00000E+100
221  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.598725E-01    2.000000E+00              9.00000E+100
222  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.532663E-01    2.000000E+00              9.00000E+100
223  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.518356E-01    2.000000E+00              9.00000E+100
224  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.538601E-01    2.000000E+00              9.00000E+100
225  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.538601E-01    2.000000E+00              9.00000E+100
226  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.607271E-01    2.000000E+00              9.00000E+100
227  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.668866E-01    2.000000E+00              9.00000E+100
228  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.671541E-01    2.000000E+00              9.00000E+100
229  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.671541E-01    2.000000E+00              9.00000E+100
230  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.659290E-01    2.000000E+00              9.00000E+100
231  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.630016E-01    2.000000E+00              9.00000E+100
232  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.619396E-01    2.000000E+00              9.00000E+100
233  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.619396E-01    2.000000E+00              9.00000E+100
234  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.606801E-01    2.000000E+00              9.00000E+100
235  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.651005E-01    2.000000E+00              9.00000E+100
236  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.685938E-01    2.000000E+00              9.00000E+100
237  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.685938E-01    2.000000E+00              9.00000E+100
238  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.751747E-01    2.000000E+00              9.00000E+100
239  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.698311E-01    2.000000E+00              9.00000E+100
240  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.629953E-01    2.000000E+00              9.00000E+100
241  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.629953E-01    2.000000E+00              9.00000E+100
242  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.508314E-01    2.000000E+00              9.00000E+100
243  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.635175E-01    2.000000E+00              9.00000E+100
244  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.778124E-01    2.000000E+00              9.00000E+100
245  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.778124E-01    2.000000E+00              9.00000E+100
246  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    8.060098E-01    2.000000E+00              9.00000E+100
247  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    8.034674E-01    2.000000E+00              9.00000E+100
248  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.873297E-01    2.000000E+00              9.00000E+100
249  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    7.873297E-01    2.000000E+00              9.00000E+100
250  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    6.985483E-01    2.000000E+00              9.00000E+100
251  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    4.201176E-01    2.000000E+00              9.00000E+100
252  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    3.127165E-01    2.000000E+00              9.00000E+100
253  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    3.127165E-01    2.000000E+00              9.00000E+100
254  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    1.836616E-01    2.000000E+00              9.00000E+100
255  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    1.531111E-01    2.000000E+00              9.00000E+100
256  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    1.633905E-01    2.000000E+00              9.00000E+100
257  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    1.633905E-01    2.000000E+00              9.00000E+100
258  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    1.816829E-01    2.000000E+00              9.00000E+100
259  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    2.026853E-01    2.000000E+00              9.00000E+100
260  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    2.082759E-01    2.000000E+00              9.00000E+100
261  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    2.082759E-01    2.000000E+00              9.00000E+100
262  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    2.133263E-01    2.000000E+00              9.00000E+100
263  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    2.195263E-01    2.000000E+00              9.00000E+100
264  traj.phases.phase0->path_constraint->tau                            i   1.000000E-02    2.213099E-01    2.000000E+00              9.00000E+100

Exit Status
Inform  Description
0  Solve Succeeded
--------------------------------------------------------------------------------

/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/visualization/opt_report/opt_report.py:625: UserWarning: Attempting to set identical low and high ylims makes transformation singular; automatically expanding.
ax.set_ylim([ymin_plot, ymax_plot])

/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/group.py:1104: DerivativesWarning:Constraints or objectives [ode_eval.control_interp.control_rates:climb_rate_rate2, ode_eval.control_interp.control_rates:mach_rate2] cannot be impacted by the design variables of the problem because no partials were defined for them in their parent component(s).

Simulating trajectory traj
Model viewer data has already been recorded for Driver.

Done simulating trajectory traj

Problem: problem
Driver:  pyOptSparseDriver
success     : True
iterations  : 36
runtime     : 2.0909E+01 s
model_evals : 36
model_time  : 1.7749E+01 s
deriv_evals : 33
deriv_time  : 1.4336E+00 s
exit_status : SUCCESS

from IPython.display import HTML
# Define the path to the HTML file
html_file_path = p.get_reports_dir() / 'traj_results_report.html'