Perhaps only the higher speeds provided by the transwarp engines allowed warp scientists to fully understand the sawtooth power curve that Sternbach and Okuda postulate for warp drive?

That is, the curve has nine "teeth" for optimal power use - the nine integral warp factors. But at low warp factors, the first of those might appear to fit a certain formula (warp factor cubed times lightspeed), and all the rattling and whining at higher factors in primitive TOS engines hides the fact that this formula does

*not* explain the higher "teeth". With better engines, one realizes that the previously assumed warp factors 7 and 8 were not matching the optimal speeds very well, and that factors like 12 or 14 were completely fictional and did not match optima at all.

So, new engines reveal the new formula, and ships from then on sail at the

*real* nine integer warp factors. Until even better engines come along, and new optimal teeth to the curve are discovered between the former warp 9 and warp 10... As seen in "All Good Things...". And perhaps given a few decades, a further set of optima is found. And yet further.

Timo Saloniemi