What is the merit of the Hohmann Transfer?

[T.C.]

I've been reading about the Hohmann transfer. Nothing I've read claims that the maneuver achieves the lowest Delta V for any given orbital transfer.

1. Is this an omission? Is the Hohmann transfer optimal for at least some orbital transfers?

2. If the Hohmann Transfer is never optimal, then what is its appeal? Its conceptual and/or computational simplicity? Its ease of execution? Its speed?

3. If it is never optimal, then does anyone have a sense of how much Delta V is lost in a Hohmann Transfer relative to the optimal?

For the record, I'm aware that the Bi-elliptic transfer is known to be more efficient for some orbital transfers.

-TC

Edited May 30, 2014 by T.C.

[Kasuha]

In absence of other bodies (i.e. without possibility to use gravity slingshot) and assuming circular initial and ending orbits, Hohmann transfer is optimal up to their diameter ratio of 1:12 (or 12:1) For greater ratio bi-elliptic transfer is better but usually not by a big margin and takes a lot more time.

[Mr Shifty]

Hohmann transfers are the most efficient, delta-V-wise, except for the few cases where a bi-elliptic is more efficient. (Ratio of the semi-major axes has to be greater than 12. For instance, a transfer from Earth to Uranus or beyond would be more efficient with a bi-elliptic transfer.) The problem with bi-elliptic is that it can be much much much slower than a Hohmann transfer (sometimes by several orders of magnitude.)

Hohmann generally uses the least delta-V, but there are constant thrust transfers that can use less propellant, simply because low-thrust engines are more efficient. In KSP, constant-thrust interplanetary transfers are impractical because you can only do 4x physics warp during them.

There are problems with Hohmann transfers that might make you decide to use other trajectories:

- Hohmann only applies to circular orbits in the same plane. It's relatively easy to adjust for small eccentricities or inclination differences, but big differences will require different calculations.

- Hohmann transfers can only be accomplished at a particular time in the resonant period of the two bodies, thus the concept of launch windows, which might only arise every couple years (e.g. 26 months for Earth-to-Mars) If you want to launch earlier, it might make sense to use a less efficient trajectory.

- Hohmann transfers cannot provide a free return path to the source planet. Something like the Aldrin cycler might be appropriate if you want the spacecraft to cycle back and forth without energy input.

- Hohmann transfers make use of the gravity of the source and destination planets only. Many of NASA's interplanetary missions make use of trajectories that utilize one or more extra gravity assists. (Example: last October's flyby of the Earth by Juno on its way to Jupiter.)

- Hohmann transfers do not account for the gravitational influence of distant bodies during transfer. These influences will distort the trajectory and/or lend themselves to more efficient paths, e.g. the Interplanetary Transportation Network.

[T.C.]

Thank you for the excellent answers. It is much clearer now.

-TC