Add example of a balanced field length calculation (FAA FAR25)

[robfalck]

Summary of Issue

The question of how to use dymos to calculate the balanced field length (From FAA FAR25) has come up several times. We should have an example that does this in the documentation.

Issue Type

• Bug
• Enhancement

Description

For a multi-engine aircraft, during its takeoff roll it encountered a speed (v_1) during its takeoff roll. At v_1, if an engine fails, the aircraft may still take off and achieve a successful takeoff (v_2 at 35 ft altitude), and it may still decelerate to a stop on the runway. The minimum runway length that accommodates the deceleration is the balanced field length.

This is a branching trajectory behavior. Both the takeoff and deceleration branches branch from a common takeoff roll phase.

The optimization problem is to minimize the runway length (range at the end of the deceleration branch) such that the takeoff branch achieves v_2 with an altitude of at least 35 ft by the time it reaches the end of the runway.

https://www.faa.gov/other_visit/aviation_industry/airline_operators/training/media/takeoff_safety.pdf

Environment

N/A