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Optimum bi-impulsive non coplanar elliptic Hohmann type transfer

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2010

Vol. 14, nr 1

81-104

We optimize the Hohmann type bi-impulsive transfer between inclined elliptic orbits having a common center of attraction, for the four feasible configurations. Our criterion for optimization is the characteristic velocity ΔvT = Δv1 + Δv2 which is a measure of fuel consumption. We assigned the optimum value of our variable x (ratio between velocity after initial impulse and velocity before initial impulse) by a numerical solution of an algebraic eight degree equation. We have a single plane change angle α. We present terse new formulae constituting a new alternative approach for tackling the problem. The derivations of formulae of our treatment are simple, straightforward and exceptionally clear. This is advantageous. By this semi-analytic analysis we avoid many complexities and ambiguity that appear in previous work.

Velocity Correction in Generalized Hohmann and Bi-elliptic Impulsive Orbital Maneuvers Using Energy Concepts

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2008

Vol. 12, nr 1

31-49

We applied small tangential impulses due to motor thrusts at peri-apse and apo-apse perpendicular to major axis of the elliptic orbits. Our aim is to obtain a precise final orbit stemming from an initial orbit. We executed these tangential correctional velocities to all the four feasible configurations. The correctional increments of velocities ΔvA & ΔvB at the points A, B for the Hohmann transfer and at the points A, B, C for the Bi-Elliptic transfer induce the precise final orbit. Throughout the treatment we encounter relationships for both cases of transfer that describe the alteration in major axes and eccentricities due to these motor thrusts supplied by a rocket. The whole theory is a correctional improvement process.