Estimating the Airspeed Velocity of an Unladen Swallow

After spending some time last month trying to develop alternate graphic presentations for kinematic ratios in winged flight, I decided to try to answer one of the timeless questions of science: just what is the airspeed velocity of an unladen swallow?

What do you mean, an African or European Swallow?

To begin with, I needed basic kinematic data on African and European swallow species.

	South African Swallow (Hirundo spilodera)	European Swallow (Hirundo rustica)

Although 47 of the 74 worldwide swallow species are found in Africa,¹ only two species are named after the continent: the West African Swallow (Hirundo domicella) and the South African Swallow (Hirundo spilodera), also known as the South African Cave Swallow.

Since the range of the South African Swallow extends only as far north as Zaire,² I felt fairly confident that this was the non-migratory African species referred to in previous discussions of the comparative and cooperative weight-bearing capabilities of African and European swallows.³

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

It’s a simple question of weight ratios

A 54-year survey of 26,285 European Swallows captured and released by the Avian Demography Unit of the University of Capetown finds that the average adult European swallow has a wing length of 12.2 cm and a body mass of 20.3 grams.⁴

Because wing beat frequency and wing amplitude both scale with body mass,⁵ and flight kinematic data is available for at least 22 other bird species,⁶ 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?

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

Last month’s 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 0.2–0.4 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 7–9 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 13–14 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 8–11 meters per second, with an amplitude of 90–100° (17–19 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 0.2–0.4.

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 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.

What is the capital of Assyria?

For those looking for additional answers, the four capitals of Assyria were Ashur (or Qalat Sherqat), Calah (or Nimrud), the short-lived Dur Sharrukin (or Khorsabad), and Nineveh.⁸ The ruins of all four ancient cities fall within the modern state of Iraq.

References

1. Chris & Tilde Stuart
   Birds of Africa: From Seabirds to Seed-Eaters
   MIT Press (1999)
    
2. G. L. Maclean
   Roberts’ Birds of Southern Africa
   John Voelcker Bird Book Fund, Cape Town, South Africa (1985)
    
3. Graham Chapman, John Cleese, Eric Idle, Terry Gilliam, Terry Jones, Michael Palin
   Monty Python and the Holy Grail
   Python (Monty) Pictures Ltd. (1975)
    
4. Avian Demography Unit
   SAFRING results of the European Swallow (Hirundo rustica)
   Department of Statistical Sciences, University of Cape Town (2002)
    
5. Graham K. Taylor, Robert L. Nudds, Adrian L. R. Thomas
   Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency
   Nature 425, 707–711 (October 16, 2003)
    
6. Email correspondence with Graham K. Taylor of the University of Oxford Zoology Department (October 22–23, 2003)
    
7. Kirsty J. Park, Mikael Rosén, Anders Hedenström
   Flight kinematics of the barn swallow (Hirundo rustica) over a wide range of speeds in a wind tunnel
   The Journal of Experimental Biology 204, 2741–2750 (2001)
    
8. Ashur Cherry
   Assyrian History
   The Mesopotamian Encyclopedia (2001)
   

May we please have a moment of silence for a fallen friend who strapped on a ZOT! belt and blew himself up in a crowded thread...



Xeno, Paradise awaits you!

1,028 posted on 05/17/2006 1:37:37 PM CDT by BJClinton

---

---

Internet Explorer Download page:

http://www.microsoft.com/windows/ie/downloads/def ault.mspx

---

Cut and paste for a proper "sarcasm tag": </sarcasm>

---

BJClinton's Official Thread Hall of Fame
The Post	the Undead Thread
The Origin of Stuned Beeber	Unnngh..
Cheese	hugh
Series, vey series	PAt downs
History of FreeRepublic	The List
I Demand An Explanation From God	Heoo Dolly
dssssss	suck emergencies
Sir Mix-A-Lot's "Baby Got Back" translated into Latin	Why Do My Fingers Smell Funny?
DRUDGE: Unnamed Senior White House source: Cyborg and Petronski to be married...	please discover the reality (zot!!! distroy the troll, steel his oil)
can someone please interpret this drem for me	Can anyone else look at the sun and see anything
Potential Republican Crack-Up (Spawn of the Undead Thread)	Statuary Rape
I am a Bad Republican	I love a good og story
How Have We Become a Nation of Dumbies?	Clinton Enron Nexus
DID I ASK TO BE ON YOUR PING LIST?	Operation removes lightbulb from Mohammed's anus
Behind the Scenes of a ZOT!	Am I Logged In???

---

Top 10 things likely to be overheard from a Klingon Programmer

10. Specifications are for the weak and timid!
9. You question the worthiness of my code? I should kill you where you stand!
8. Indentation?! - I will show you how to indent when I indent your skull!
7. What is this talk of 'release'? Klingons do not make software 'releases'. Our software 'escapes' leaving a bloody trail of designers and quality assurance people in its wake.
6. Klingon function calls do not have 'parameters' - they have 'arguments' - and they ALWAYS WIN THEM.
5. Debugging? Klingons do not debug. Our software does not coddle the weak.
4. A TRUE Klingon Warrior does not comment on his code!
3. Klingon software does NOT have BUGS. It has FEATURES, and those features are too sophisticated for a Romulan pig like you to understand.
2. You cannot truly appreciate Dilbert unless you've read it in the original Klingon.
1. Our users will know fear and cower before our software! Ship it! Ship it and let them flee like the dogs they are!

---

1. Men are not mind readers.

1. Learn to work the toilet seat. You're a big girl. If it's up, put it down. We need it up, you need it down. You don't hear us complaining about you leaving it down.

1. Sunday sports are like the full moon or the changing of the tides. Let it be.

1. Shopping is NOT a sport. And no, we are never going to think of it that way.

1. Crying is blackmail.

1. Ask for what you want. Let us be clear on this one:
Subtle hints do not work!
Strong hints do not work!
Obvious hints do not work!
Just say it!


1. Yes and no are perfectly acceptable answers to almost every question.

1. Come to us with a problem only if you want help solving it. That's what we do. Sympathy is what your girlfriends are for.

1. A headache that lasts for 17 months is a problem. See a doctor.

1. Anything we said 6 months ago is inadmissible in an argument. In fact, all comments become null and void after 7 days.

1. If you won't dress like the Victoria's Secret girls, don't expect us to act like soap opera guys.

1. If you think you're fat, you probably are. Don't ask us.

1. If something we said can be interpreted two ways and one of the ways makes you sad or angry, we meant the other one

1. You can either ask us to do something, or you can tell us how you want it done. Not both. If you already know best how to do it, just do it yourself.

1. Whenever possible, please say whatever you have to say during commercials.

1. Christopher Columbus did NOT need directions, and neither do we.

1. ALL men see in only 16 colors, like Windows default settings. Peach, for example, is a fruit, not a color. Pumpkin is also a fruit. We have no idea what mauve is.

1. If it itches, it will be scratched. We do that.

1. If we ask what is wrong and you say "nothing," we will act like nothing's wrong. We know you are lying, but it's just not worth the hassle.

1. If you ask a question you don't want the answer to, expect an answer you don't want to hear.

1. When we have to go somewhere, absolutely anything you wear is fine. Really.

1. Don't ask us what we're thinking about unless you are prepared to discuss baseball, the shotgun formation, or golf.

1. You have enough clothes.

1. You have too many shoes.

1. I am in shape. Round IS a shape!

1. Thank you for reading this. Yes, I know, I have to sleep on the couch tonight.