One of the things I hope to do with Aero Evo is to give some insights into how biomechanists like myself manage to make estimates of performance for fossil animals. In particular, of course, I will focus on how we know things about extinct flying animals.
Three of the parameters of typical interest are the speed at which a flying animal flew, the rate at which it flapped its wings, and how much room it needed to flap them: velocity, flapping frequency, and flapping amplitude, respectively.
These three factors are all correlated, and can be summarized by the Strouhal Number. The Strouhal Number is equal to fA/U, where f is frequency, A is amplitude, and U is velocity. As it turns out, the range of strouhal numbers at which a flapping wing or undulating fin can operate efficiently is pretty darn narrow. For creatures as seemingly different as dolphins, birds, fish, and dragonflies, Str in cruising locomotion only varies from about 0.2-0.4. This pattern occurs because of the narrow range of motion in which vortex shedding is efficient.
The classic paper on the topic is by Taylor et al., and can be found here. That link will take you to the abstract; those on campuses should be able to get the full paper, though it is behind a paywall. Fortunately, Nudds, Taylor, and Thomas wrote a followup paper with much of the same information (specifically on birds), and it is open access here.
Now, it should be noted that the limits on Str mentioned above only apply to cruising - that is, the animal is moving steadily at its efficient, long-distance gait. Burst performance is different, and on average, the Str will be higher during things like rapid climbs (say, just after takeoff) or bursts after prey. Nonetheless, we can get a good idea of how extinct animals worked by using Str. I'll post more on how to use Str, and how to combine it with other equations to solve for multiple variables, soon.