I've actually been pondering that question for quite a while. After doing some calculations, however, I've been able to reach a conclusion.
First of all, by comparing to other species with similar wingspan to bodymass ratios, the frequency and amplitude of an unladen swallow's flight could be estimated. This is assuming, of course, that we are dealing with a
European Swallow, and not an African Swallow, because information on the African Swallow is much more difficult to come by. Also, we must calculate under the assumption that our swallow is going at average cruising speed, because the top speed will likely vary from population to population, based on genetic makeup and mutations.
So you're probably thinking that since the swallow has to maintain it's air velocity, it must beat its wings at about 43 times a second. While it is easy to see how you came upon that conclusion, according to my calculations, is should be
15 beats per second. Now you're wondering how I found this out. Well, it's simple, really. I took the 3 species of birds with closest body masses, and then the 3 species of birds with similar wingspan. By closely observing their flight, I was able to discern their frequency of wing flaps. Averaging all 6 values, it became glaringly apparent that the European Swallow, unladen,
beats exactly 15 times a second.
Ok, so now we have frequency. What about amplitude? This was arguably the most difficult part of the process. All flying animals have a particular flight pattern. Observing an average European Swallow in flight, I was able to draw detailed diagrams. It seemed there were two extremes: a very efficient flight pattern and a very inefficient one.
Here is the efficient one. As you can see, the Strouhal Number in this flight pattern is a mere 0.2:
http://i.imgur.com/1FcG2KY.gif
Here is the ineffient one. As you can see, the Strouhal Number in this flight pattern is 0.4, which is double the first one!
http://i.imgur.com/1pufHPu.gif
After much thought, I determined the best way to get an accurate and precise amplitude of flight, I had to average the two Strouhal Numbers. Using several calculators, I found that 0.3 is the average Strouhal Number.
Finally, now that we have found the Strouhal Number, we can proceed to calculating airspeed. Using the simple forumula: (beats/s)*(meters/beat)=airspeed, I multiplied 15 beats per second * 0.73 meters per beat to get
11 meters/second.
This equates to
24 mph.
Any further questions, Snarg?