This is an example of an emergency landing of a two stage space transport vehicle. After the
separation of the first stage the engine of the upper stage cannot be re-ignited. Due to this
propulsion system damage the upper stage cannot reach a safe orbit.

The optimal control problem is fully discretized using Euler's method and implemented in AMPL;
this leads to a sparse large-scale nonlinear optimisation problem. The problem dimensions are
determined by the number of points n used for the discretization, specifically it has
N = 8n+1 optimisation variables subject to M = 6(n-1)+4n+7 constraints.

The picture on the right shows an example of an emergency trajectory. The reentry point is
situated over the city of Bremen, Germany and the objective function is to maximize the flight
distance without propulsion from this reentry point.

The following table summarizes the results for different number of discrete points. The tests
were run on an Intel Core2 Quad CPU Q6600 @ 2.40GHz with tolerances for constraint violations of
10^{-6} and for KKT conditions of 10^{-5}.

n

N

M

Time

201

1609

2011

4.88s

2001

16009

20011

45.47s

5001

40009

50011

281.30s

10001

80009

100011

424.25s

20001

160009

200011

2261.35s

40001

320009

400011

4898.53s

Ascent trajectories

WORHP was succesfully integrated within the
ESA project "eNLP" in the
Astos software. Within the software it is
possible to describe ascent optimal control problems for rockets, e.g. Ariane V.

Ascent trajectory for an Ariane V from Kourou within Astos 6.1