Talk:Bi-elliptic transfer

Incorrect numbers?
The introduction to the article contains the following quote: "the bi-elliptic transfer may require a lower amount of total delta-v than a Hohmann transfer in situations where the ratio of final to the initial semi-major axis is greater than 15.58." This implies that the Hohmann transfer requires a lower delta-v than the bi-elliptic transfer at a final to initial semi-major axis ratio of lower than 15.58. This is shown to be incorrect later in the article. The example given at the end uses a ratio of 14:1 (93800:6700) and shows that the bi-elliptic transfer requires a lower delta-v. Either the 15.58 is wrong (or misleading) or the example is wrong, and I don't know which. Also worth noting, the Hohmann transfer article indicates that the bi-elliptic transfer may require less delta-v for ratios exceeding 12. One of the two articles, or both, probably need to be edited to correct this error/discrepancy. 137.240.136.81 22:04, 11 September 2007 (UTC)


 * There was a discussion in the forum for a flight simulator called Orbiter on the subject of bi-elliptic transfers. I tried searching today but there is an error at the moment so I can't post the specific thread but here is the forum where it resides .  During the discussion someone mentioned this discrepancy in the article here.  They attributed the difference to stemming from different ways of computing it, or a difference in assumptions, or something of that nature.  So both numbers are "correct" in some sense they are just the results based on different methods.  I am not sure what the methods, etc were so I cannot contribute that but I thought I would throw my 2 cents in none the less. -AndrewBuck 01:20, 22 September 2007 (UTC)


 * It's not a matter of different methods; you're forgetting that there's an extra degree of freedom in the bi-elliptic transfer: you can arbitrarily choose an apoapsis radius for the intermediate transfer. If you look in the cited reference 1 (Vallado), page 318 (you can get a free preview at books.google.com), he gives a chart of the delta V required vs. the semi-major axis ratio, which shows the Hohmann transfer as a single, knee-shaped curve (rises to a maximum at around 15.58, then tails off). The bi-elliptic transfers are a family of plots which show an inverse relationship, and cross under the Hohmann line in a cluster ranging from 11.94 to 15.58. After they intersect the Hohmann line again on the high side, they then rise discontinuously (and curiously switch to concave downward instead of concave upward.)


 * Based on this, I don't think it makes sense to give a single precise number; both articles should consistently say the crossover point is either the above range, or "around" the average, depending on the specific orbit ratio. JustinTime55 (talk) 18:41, 6 December 2011 (UTC)


 * Actually, I take part of that back; the advantage stays for a wide range of high ratios until it crosses the Hohmann line again; the 15.58 number represents the only point the bi-elliptic curve touches the Hohmann curve at minimum intermediate radius. You have to see the curve to understand this completely. JustinTime55 (talk) 18:53, 6 December 2011 (UTC)

Time has passed, and the article in its current form is now correct, but after reading this discussion I wanted to clarify the confusion. The graph from Vallado page 318 is misleading, but it shows that when the ratio R is greater than 11.94, a bi-elliptic transfer with sufficient R* is always theoretically cheaper than a Hohmann transfer. The R*=infinity line on the graph is always below the Hohmann line for R > 11.94 - they converge as R tends toward infinity, but never cross again. For practical reasons, though, it's important to consider finite values for R*, and several are also drawn on the graph. It shows that R* must be at least 15.58, and for any chosen R* value greater than 15.58, the bi-elliptic transfer will be more efficient so long as R* > R > X(R*), for some X in the range (11.94, 15.58) whose value depends on R*. If R* < R then it's not a true bi-elliptic transfer, because the intermediate radius was lower than the target radius. If R < X(R*) but still R > 11.94, then your R* is not high enough to be more efficient than Hohmann.

However, the graph is misleading because in practice you would not choose R* first - you would almost always already know R. In that case, inverting the inequality, bi-elliptic transfer is more efficient so long as R > 11.94, provided you choose a high enough R* (so that X(R*) < R). For R = 15.58, any R* > R is more efficient than a Hohmann transfer, but larger R* is always even more efficient. For 11.94 < R < 15.58, R* needs to be bigger before you break even with Hohmann - much more so at the lower end of the range, as Xinv(R) tends to infinity as R approaches 11.94. The graph of Xinv(R) is more relevant than the graph in Vallado. 217.154.84.20 (talk) 14:09, 2 January 2013 (UTC)

Initial diagram counter-intuitive?
The intial diagram doesn't seem to make much intuitive sense. It actually looks as though more delta v would be needed to make such a small change to a circular orbit using the bi-elliptic transfer illustrated, compared to the Hohmann transfer. Sketching out the later example to scale looks much more sensible, (if perhaps a little unwieldy). Nonetheless, would it be worth making the diagram match the later example's figures? —Preceding unsigned comment added by 84.69.96.243 (talk) 01:42, 23 February 2008 (UTC)

Reference needed
I removed a "reference needed" tag since the results can be easily obtained by simple algebraic manipulation of the vis viva equation included in the article. Dauto (talk) 16:34, 9 January 2013 (UTC)

Third delta-v negative
The delta-v expression for the third impulse, as it is right now, produces a negative value. While this may be correct in the sense that the third burn is a reduction in speed (accomplished with a retrograde burn), it might be misleading if one wants to compute the total delta-v expended during the transfer, for in that case one must remember the switch the sign of the third delta-v before adding it to the first two. Do you think it would be clearer if we give the *positive* value of the expression instead, and specify explicitly that the burn is to be done retrograde? Meithan (talk) 17:49, 20 August 2013 (UTC)

Eliminate negative Δv's in the example?
I think listing negative Δv's in the table of the example may be confusing, as a reader might think that the negative values are to be subtracted from the others in order to obtain the total. I would suggest listing all values as positive, and letting the color alone indicate the direction of the burns (i.e. whether prograde or retrograde). –Meithan (talk) 05:37, 13 February 2018 (UTC)

I've removed the negative signs for all delta-v's, as the recent edit by makes it clear when they're applied prograde/retrograde. I liked his/her solution! –Meithan (talk) 00:38, 16 February 2018 (UTC)

11.94 and 15.58
I would like to see a derivation of those numbers in the article, and what the exact (in terms of radicals / exponents / fundamental constants etc) values are. Grassynoel (talk) 12:16, 3 May 2019 (UTC)