The Swallow is an avian being, or bird. It is passernine, meaning that it is a pearching bird. Being of a cosmopolitan distribution, the swallow can be found nearly anywhere around the world; they've even been rumored to nest in the beards of Dwarves. Not many aside from bird watchers and druids care much about the facts of swallows. However, what tends to be a very enigmatic and somehow important question across the world is:

"What is the average airspeed velocity of an unladen swallow?" Edit

A riddle that has fooled many a man into an untimely demise, this question must be met with equal mental prowess if an adventurer wishes to continue on his quest.

African or European? Edit

To begin with, one needs basic kinematic data on African and European swallow species. Although Africa and Europe are continents of another realm of existence, the African and European Swallows are still present across Etan. Two species of the bird are named after Africa: the West African Swallow (Hirundo domicella) and the South African Swallow (Hirundo spilodera), also known as the South African Cave Swallow.

Kinematic data for both African species is difficult to find, but the Barn or European Swallow (Hirundo rustica) has been studied intensively, and kinematic data for that species is readily available.

It's a Simple Question of Weight Ratio Edit

A 54-year survey of 26,285 European Swallows finds that the average adult European swallow has a wing length of 12.2 cm and a body mass of 20.3 grams.

Because wing beat frequency and wing amplitude both scale with body mass, and flight kinematic data is available for at least 22 other bird species, it should be possible to estimate the frequency (f ) and amplitude (A) of the European Swallow by a comparison with similar species. With those two numbers, it will be possible to estimate airspeed (U).

In order to maintain airspeed velocity, a swallow needs to beat its wings forty-three times every second, right? Edit

Actually, wrong. By comparing the European Swallow with bird species of similar body mass, we can estimate that the swallow beats its wings 18 times a second with an amplitude of 18 cm:

Species Body Mass Frequency Amplitude
Zebra Finch 13 g 27 Hz 11 cm
European Swallow 20 g ≈18 Hz ? ≈ 18 cm ?
Downy Woodpecker 27 g 14 Hz 29 cm
Budgerigar 34 g 14 Hz 15 cm

Note that even the tiny Zebra Finch flaps its wings no more than 27 times a second while cruising.

If we ignore body mass and look only at bird species with a similar wingspan, we can estimate an average frequency of 14 beats per second and an amplitude of 23 cm:

Species Wingspan Frequency Amplitude
Budgerigar 27 cm 14 Hz 15 cm
European Swallow ≈ 28-30 cm ≈14 Hz? ≈23 cm?
Downy Woodpecker 31 cm 14 Hz 29 cm
European Starling 35 cm 14 Hz 26 cm

By averaging all 6 values, we can estimate that an average European Swallow flies at cruising speed with a frequency of roughly 15 beats per second, and an amplitude of roughly 22 cm.

Skip a Bit Brother Edit

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 value (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 value (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 Edit

Airspeed can also be predicted using this 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).

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 Edit

With some further study, it became clear that these estimates are accurate, though perhaps coincidental.

An actual study of two European Swallows flying in low-turbulence shows that swallows flap their wings much slower than the original estimate, at only 7–9 beats per second:

The maximum speed the birds could maintain was 13–14 meters per second, and although the study does not discuss cruising flight in particular, the most efficient flapping (7 beats per second) occurred at an airspeed in the range of 8–11 meters per second, with an amplitude of 90–100° (17–19 cm).

And There Was Much Rejoicing Edit

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 0.2–0.4.

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 study of birds flying at a range of speeds, and revised Strouhal numbers based on that study all lead to an estimate that the average cruising airspeed velocity of an unladen European Swallow is roughly 11 meters a second, or 24 miles an hour.

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