DSOPT 
Dynamic Soaring simulation and optimization program  

Summary Description
-------------------

DSOPT uses the "Inverse Dynamics" approach to simulating
a Dynamic Soaring orbit.  The code is two nested loops,
with an inverse-dynamics integrator on the inside, 
as summarized below.


INPUT
   set all fixed parameters
   initialize parameters to be optimized as chosen by user
END INPUT

OPTIMIZER loop
   set orbit path in xyz space
   set shear wind field in xyz space

   ORBIT loop
      sets initial velocity Vi

      ORBIT1
        integrates inverse equations of motion for specified path
        final velocity Vf is an output
      END ORBIT1

      if (Vf=Vi) then
       exit to OPTIMIZER
      else
       adjust Vi to make Vf -> Vi next time, and call ORBIT1 again
      endif
   END ORBIT

   if (Vmeasured is maximum) then
    exit to OUTPUT
   else
    adjust optimizable parameters to increase Vmeasured
    repeat OPTIMIZER loop
   endif

END OPTIMIZER

OUTPUT
STOP



The bulk of the calculations are performed in SUBROUTINE ORBIT1, 
which assumes that the path shape in xyz space is assumed known, 
and is prescribed to be an ellipse of specified size, oriented 
at some tip and lean angles within the atmospheric 
wind shear layer.  SUBROUTINE ORBIT1 is also provided 
with an initial velocity Vi at the first point in the orbit,
and then integrates the equations of motion along the 
known trajectory, using simple representations of the 
airplane's CL and CD.  One output is the final velocity Vf
at the last point in the orbit (which is at the same 
spatial location as the first point).  In general Vi and Vf
will not match, in which case Vi is modified and the orbit 
is recalculated again.  When Vf matches Vi to within some
small tolerance the orbit is "converged".  This means that 
it is periodic, and hence represents sustained DS.

The outputs are the following quantities along the converged orbit:

 t     time
 xyz   position
 V     ground speed
 Vair  air speed
 CL    lift coefficient

and a number of others.

The code is heavily commented, and it's fairly easy to locate
the formulas used for the various models for CL, CDi, CDp, CDw,
wind shear field, etc.  The dynamic equations which are integrated 
are simply F=ma, with three separate components in the xyz directions.

The outermost OPTIMIZER loop is optional.  This adjusts the selected
parameters of the formulation via gradient-descent steps, so as to 
maximize the speed Vmeasured at a chosen point in the DS orbit.