Yes, I see the usefulness in that diagram! It shows how the horizontal offset and subsequent turn radii affect the offset circles. I still think my particular case in the lufbery fights was both of us both pulling tighter and tighter circles into the offset position. However, I do see where it can happen in initial merges as well.
In fact, in thinking about that illustration more, I see where this applies to many 1v1s I have had or seen in films, particularly at and after the second merge. Assuming both planes do a smooth Immelmann, going for the high ground at the first merge, and neither gains a significant advantage, resulting in a second co-E merge: the diagram shows what can happen after this second merge. If there is not enough E to do a true second Immelmann, instead both do an oblique climbing turn (chandelle) back into each other (just as you said). And then we have essentially what is shown in the diagram, two offset circles (albeit climbing spirals). The important point being, if I understand all this correctly, this is now a two circle fight -- so turn rate (v.s radius) is key!
This is what I usually see in this situation. By doing a smooth climbing turn, you let the con feel as though he is gaining position so he will turn tighter. He is now turning for radius, while I am maintaining rate. So, I should win the energy fight, provided I can stall him out before he has an effective shot. I usually do this by pointing my left wingtip at or just behind him (assuming left turns as illustrated) flying lag pursuit. Often they can only get their nose around to about the 9 o'clock position, but don't have the E to either pull lead or keep the nose up for a shot. At this third merge they usually fire just behind and/or below me and either stall or have lost in the vertical, so it just a matter of rolling in behind their 3/9 line.
That's just one application I see of that diagram. Cool stuff when you see the illustrations and theory applied and know that it really works!
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