public HohmannXfer(OrbitData fromOrbit, OrbitData toOrbit, bool rendezvous) : base(fromOrbit, toOrbit)
{
name = "Hohmann";
if (rendezvous)
{
name += " Rendezvous";
}
else
{
name += " Transfer";
}
// Check both objects are orbiting in the same direction
if (Vector3d.Dot(fromOrbit.GetAxis(), toOrbit.GetAxis()) < 0)
{
Debug.LogWarning("Objects orbiting in different directions. Will not proceed.");
return;
}
// Hohmann xfer is via an ellipse from one circle to another. The ellipse is uniquely
// defined by the radius of from and to.
// Equations from Chobotov Ch 5.4
float r_inner = 0f;
float r_outer = 0f;
// From orbit result is in physics quantities
if (fromOrbit.a < toOrbit.a)
{
r_inner = fromOrbit.a;
r_outer = toOrbit.a;
}
else
{
r_inner = toOrbit.a;
r_outer = fromOrbit.a;
}
// (mass scale was applied in Orbit data)
float v_inner = Mathf.Sqrt(fromOrbit.mu / r_inner);
float rf_ri = r_outer / r_inner;
float dV_inner = v_inner * (Mathf.Sqrt(2f * rf_ri / (1f + rf_ri)) - 1f);
// Debug.LogFormat("dv_iner={0} v_inner={1} r_i={2} r_o={3}", dV_inner, v_inner, r_inner, r_outer);
float v_outer = Mathf.Sqrt(fromOrbit.mu / r_outer);
//simplify per Roy (12.22)
float dV_outer = v_outer * (1f - Mathf.Sqrt(2 / (1 + rf_ri)));
// Debug.LogFormat("r_in={0} r_out={1} v_inner={2} v_outer={3}", r_inner, r_outer, v_inner, v_outer);
// transfer time
// Need to flip rf_ri for inner orbits to get the correct transfer_time
// (should re-derive for this case sometime to see why)
transfer_time = 0f;
// time to wait for first maneuver (rendezvous case)
float tWait = 0f;
// Build the manuevers required
deltaV = 0f;
float worldTime = GravityEngine.Instance().GetPhysicalTime();
Maneuver m1;
m1 = new Maneuver();
m1.nbody = fromOrbit.nbody;
m1.mtype = Maneuver.Mtype.scalar;
m1.worldTime = worldTime;
Maneuver m2;
m2 = new Maneuver();
m2.nbody = fromOrbit.nbody;
m2.mtype = Maneuver.Mtype.scalar;
// If the orbit is almost circular, then can be some omega which will impact rendezvous phasing
float fromPhase = fromOrbit.phase + fromOrbit.omega_lc;
float toPhase = toOrbit.phase + toOrbit.omega_lc;
if (fromOrbit.a < toOrbit.a)
{
// inner to outer
float subexpr = 1f + rf_ri;
transfer_time = fromOrbit.period / Mathf.Sqrt(32) * Mathf.Sqrt(subexpr * subexpr * subexpr);
if (rendezvous)
{
// need to determine wait time for first maneuver to phase the arrival
// find angle by which outer body must lead (radians)
// Chobotov 7.3
float subexpr2 = 0.5f * (1f + r_inner / r_outer);
float theta_h = Mathf.PI * (1f - Mathf.Sqrt(subexpr2 * subexpr2 * subexpr2));
// find current angular seperation
float phase_gap = toPhase - fromPhase;
if (phase_gap < 0)
{
phase_gap += 360f;
}
// need seperation to be theta_h
float dTheta = Mathf.Deg2Rad * phase_gap - theta_h;
if (dTheta < 0)
{
dTheta += TWO_PI;
}
// need to wait for phase_gap to reduce to this value. It reduces at a speed based on the difference
// in the angular velocities.
float dOmega = TWO_PI / fromOrbit.period - TWO_PI / toOrbit.period;
tWait = dTheta / dOmega;
//Debug.LogFormat("inner_phase= {0} out_phase={1} phase_gap(deg)={2} thetaH={3} dTheta(rad)={4} dOmega={5} tWait={6}",
// fromOrbit.phase, toOrbit.phase, phase_gap, theta_h, dTheta, dOmega, tWait);
}
// from inner to outer
// first maneuver is to a higher orbit
m1.dV = dV_inner;
deltaV += dV_inner;
maneuvers.Add(m1);
// second manuever is opposite to velocity
m2.dV = dV_outer;
deltaV += dV_outer;
maneuvers.Add(m2);
}
else
{
// outer to inner
float subexpr_in = 1f + r_inner / r_outer;
transfer_time = fromOrbit.period / Mathf.Sqrt(32) * Mathf.Sqrt(subexpr_in * subexpr_in * subexpr_in);
if (rendezvous)
{
// Chobotov 7.2/7.3 (modified for outer to inner, use (Pi+Theta) and Pf not Pi
float subexpr2 = 0.5f * (1f + r_outer / r_inner);
float theta_h = Mathf.PI * (1f + Mathf.Sqrt(subexpr2 * subexpr2 * subexpr2));
// find current angular seperation
float phase_gap = fromPhase - toPhase;
if (phase_gap < 0)
{
phase_gap += 360f;
}
// need seperation to be -theta_h
float dTheta = Mathf.Deg2Rad * phase_gap - theta_h;
// Can need inner body to go around more than once...
while (dTheta < 0)
{
dTheta += TWO_PI;
}
// larger (inner) omega first
float dOmega = TWO_PI / toOrbit.period - TWO_PI / fromOrbit.period;
tWait = dTheta / dOmega;
//Debug.LogFormat("inner_phase= {0} out_phase={1} phase_gap(deg)={2} thetaH(deg)={3} dTheta(rad)={4} dOmega={5} tWait={6}",
// toOrbit.phase, fromOrbit.phase, phase_gap, Mathf.Rad2Deg*theta_h, dTheta, dOmega, tWait);
}
// from outer to inner
// first maneuver is to a lower orbit
m1.dV = -dV_outer;
deltaV += dV_outer;
maneuvers.Add(m1);
// second manuever is opposite to velocity
m2.dV = -dV_inner;
deltaV += dV_outer;
maneuvers.Add(m2);
}
m1.worldTime = worldTime + tWait;
m2.worldTime = worldTime + tWait + transfer_time;
deltaT = tWait + transfer_time;
// maneuver positions and info for KeplerSeq conversion and velocity directions
Vector3d h_unit = fromOrbit.GetAxis();
float phaseAtXfer = fromOrbit.phase + (TWO_PI / fromOrbit.period) * tWait * Mathf.Rad2Deg;
m1.physPosition = new Vector3d(fromOrbit.GetPhysicsPositionforEllipse(phaseAtXfer));
m1.relativePos = new Vector3d(fromOrbit.GetPhysicsPositionforEllipseRelative(phaseAtXfer));
m1.relativeVel = Vector3d.Cross(h_unit, m1.relativePos).normalized;
m1.relativeTo = fromOrbit.centralMass;
m2.physPosition = new Vector3d(toOrbit.GetPhysicsPositionforEllipse(phaseAtXfer + 180f));
m2.relativePos = new Vector3d(toOrbit.GetPhysicsPositionforEllipseRelative(phaseAtXfer + 180f));
m2.relativeVel = Vector3d.Cross(h_unit, m2.relativePos).normalized;
m2.relativeTo = fromOrbit.centralMass;
// Determine the relative velocities
if (fromOrbit.a < toOrbit.a)
{
// inner to outer
m1.relativeVel *= v_inner + m1.dV;
m2.relativeVel *= v_outer;
}
else
{
// outer to inner
m1.relativeVel *= v_outer + m1.dV;
m2.relativeVel *= v_inner;
}
}