Added a balanced field length example

[robfalck]

Summary

Added a balanced field length example consisting of five phases. This example uses notional Boeing 737 data from publicly available sources to model a low-fidelity propagation of the aircraft down the runway and into the initial climb.

The example propagates down the runway until some airspeed 'V1' which is the latest point at which a successful rejected takeoff can be performed in case of a single engine outage.

• Beyond V1, the aircraft must continue takeoff with a single engine.
• Before V1, the aircraft can reject the takeoff and come to a stop before the end of the runway.
• At V1, both options must be available.

The objective of this problem is to find the minimum length runway such that:

• The takeoff-branch of the trajectory reaches the end of the runway with an altitude of 35ft and an airspeed that is 1.2 times the stall speed.
• The rejected takeoff branch of the trajectory reaches the end of the runway with zero speed.
• The range traveled at the end of the climb phase (when above the end of the runway) and the range traveled by the end of the rejected takeoff phase (stopped at the end of the runway), must be the same.
• The minimum runway length that accommodates both the takeoff and abort scenarios is called the balanced field length.

This pull request is in process - documentation is pending but the PR is started to get some initial feedback on the implementation.

Related Issues

• Resolves Add example of a balanced field length calculation (FAA FAR25) #425
• Resolves Default values for states, polynomial controls, and time are not sticking #531

When developing this example we found that some default values for states, and time were not taking effect. This has been fixed.

• Resolves Trajectory parameters are not being loaded from restart files. #532

We also found that trajectory parameters were not being saved in the simulation database recording. This has been fixed.

Status

• Ready for merge

Backwards incompatibilities

None

New Dependencies

None

[robfalck]

These restart cases test that all of the appropriate data is stored in the databases. Trajectory parameters were previously not being saved before this PR.

[robfalck]

The "default values" case is an experiment to play with setting all values via the add_state, add_control, set_time_options, etc methods. When playing around with adding and removing phases, having the phase definition and the values setting in two parts of the file is a bit annoying. The downside of this method is that the values have to be set with their problem units, unlike using the set_val method.

[Kenneth-T-Moore]

This makes those methods more consistent with all the other openmdao methods too.

[coveralls]

Coverage increased (+0.09%) to 96.578% when pulling 7263cb8 on robfalck:balanced_field2 into d455456 on OpenMDAO:master.