LogFAQs > #888328257

Skip a bit, Brother
Last months article on The Strouhal Number in Cruising Flight showed how simplified flight waveforms that graph amplitude versus wavelength can be useful for visualizing the Strouhal ratio (fA/U), a dimensionless parameter that tends to fall in the range of 0.20.4 during efficient cruising flight.

For a European Swallow flying with our estimated wingbeat amplitude of 24 cm, the predicted pattern of cruising flight ranges from a Strouhal number (St) of 0.2:

... to a less efficient 0.4:

If the first diagram (St = 0.2) is accurate, then the cruising speed of the European Swallow would be roughly 16 meters per second (15 beats per second * 1.1 meters per beat). If the second diagram (St = 0.4) is accurate, then the cruising speed of the European Swallow would be closer to 8 meters per second (15 beats per second * 0.55 meters per beat).

If we settle on an intermediate Strouhal value of 0.3:

We can estimate the airspeed of the European Swallow to be roughly 11 meters per second (15 beats per second * 0.73 meters per beat).

Three shall be the number thou shalt count
Airspeed can also be predicted using a published formula. By inverting this midpoint Strouhal ratio of 0.3 (fA/U 0.3), Graham K. Taylor et al. show that as a rule of thumb, the speed of a flying animal is roughly 3 times frequency times amplitude (U 3fA).5

We now need only plug in the numbers:

U 3fA
f 15 (beats per second)
A 0.22 (meters per beat)
U 3*15*0.22 9.9
... to estimate that the airspeed velocity of an unladen European Swallow is 10 meters per second.

Oh, yeah, I agree with that
With some further study, it became clear that these estimates are accurate, though perhaps coincidental.

An actual study of two European Swallows flying in a low-turbulence wind tunnel in Lund, Sweden, shows that swallows flap their wings much slower than my estimate, at only 79 beats per second:

Compared with other species of similar size, the swallow has quite low wingbeat frequency and relatively long wings. 7
The maximum speed the birds could maintain was 1314 meters per second, and although the Lund study does not discuss cruising flight in particular, the most efficient flapping (7 beats per second) occurred at an airspeed in the range of 811 meters per second, with an amplitude of 90100 (1719 cm).

And there was much rejoicing
Averaging the above numbers and plugging them in to the Strouhal equation for cruising flight (fA/U = 7 beats per second * 0.18 meters per beat / 9.5 meters per second) yields a Strouhal number of roughly 0.13:

... indicating a surprisingly efficient flight pattern falling well below the expected range of 0.20.4.

Although a definitive answer would of course require further measurements, published species-wide averages of wing length and body mass, initial Strouhal estimates based on those averages and cross-species comparisons, the Lund wind tunnel study of birds flying at a range of speeds, and revised Strouhal numbers based on that study all lead me to estimate that the average cruising airspeed velocity of an unladen European Swallow is roughly 11 meters per second, or 24 miles an hour.
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hi there :3
1264-1315-8952 | Anna