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Please don't zot me for asking this, but what is a "click"? Such as "two clicks down that road"?

Posted on 08/05/2007 1:40:04 PM PDT by Cringing Negativism Network

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To: spokeshave
...and depth in fathoms.....

But the touchy feely measurement is 1 Atm for every 33 feet of water depth. Or it can be measured by volume reduction and/or salt content calculated against geographic location. :-)

41 posted on 08/05/2007 4:52:52 PM PDT by JoeSixPack1
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To: donna

PINK!

42 posted on 08/05/2007 4:54:31 PM PDT by JoeSixPack1
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To: JoeSixPack1

The bear was white; the only place you can walk south, east and north and end up where you started is at the north pole so it had to be a polar bear.


43 posted on 08/05/2007 4:59:08 PM PDT by donna (The United States Constitution and the Koran are mutually exclusive.)
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To: Cringing Negativism Network; JRios1968

A click is a bunch of snotty people who hang out together.


44 posted on 08/05/2007 5:13:53 PM PDT by Enterprise (I can't talk about liberals anymore because some of the words will get me sent to rehab.)
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To: donna

OK,,, wanna get tough eh?...

“Polar bears are not actually white. Their hairs are hollow transparent tubes, similar to a straw. The bears black skin attract the suns heat and her hair help trap the heat. The sunlight bouncing off these hairs is what gives a polar bear her color.”

http://www.panix.com/~teej/zoo/


45 posted on 08/05/2007 5:25:19 PM PDT by JoeSixPack1
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To: JoeSixPack1

Shapeshifter!


46 posted on 08/05/2007 5:34:29 PM PDT by donna (The United States Constitution and the Koran are mutually exclusive.)
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To: donna

:-)


47 posted on 08/05/2007 5:59:21 PM PDT by JoeSixPack1
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To: JoeSixPack1

(-:


48 posted on 08/05/2007 6:00:49 PM PDT by JoeSixPack1
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To: Cringing Negativism Network
I guess that pretty much ends this thread. :)

Nope, we need to move on to bigger things.

Estimating the Airspeed Velocity of an Unladen Swallow

Hashing out the classic question with Strouhal numbers and simplified flight waveforms.
by Jonathan Corum

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.

ItÂ’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

Thank to everyone who has written in with comments and questions. Responses are posted here, along with a revised estimate from Dr Graham K. Taylor, and some alternate theories.
  1. Chris & Tilde Stuart
    Birds of Africa: From Seabirds to Seed-Eaters
    MIT Press (1999)
     
  2. G. L. Maclean
    RobertsÂ’ 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)

49 posted on 08/05/2007 6:16:20 PM PDT by BJClinton (VickÂ’s only hope now is an all-cat jury. ~BlazingArizona)
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To: Daffynition

That pic reminds me of a house of tards


50 posted on 08/05/2007 6:48:31 PM PDT by al baby (Hi mom)
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To: humblegunner
You don't scare me, you damned, inhuman gray
51 posted on 08/05/2007 6:50:26 PM PDT by unspun (FREEP Bill O'Reilly about anything you think he needs)
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To: Cringing Negativism Network

I always wondered, too.


52 posted on 08/05/2007 7:51:55 PM PDT by ukie55
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To: humblegunner; Lost Dutchman
What is "opps"? Anything like "oops"?

Probably in FRese; kind of like "series' and "huge"

53 posted on 08/05/2007 8:07:06 PM PDT by ukie55
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To: Cringing Negativism Network

My old Grandpaw used to have multiple “clicks” when he talked with those loose dentures in his mouth. It was a rare occurrence for him to wear them except at chow time. I used to make clicks for wind adjustments on my gun. No, that was a weapon or rifle. My gun did not have an adjustment.


54 posted on 08/05/2007 8:21:01 PM PDT by CHEE
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To: Cringing Negativism Network
Is this a dumb question? :)

The real question is why have we still not adopted the metric system? I know those damn French invented it! Still, it makes sense!!!

Damn you Jimmy Carter!

When I read Metrics Are For Us in the 3rd grade, I had high hopes! I'm really tired of dividing pounds by 2.2 to tell my Ukrainian wife how many kilos I weigh.

Metric system now! Revolution!!!

55 posted on 08/05/2007 8:28:59 PM PDT by Drew68
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To: BJClinton

Are you saying that coconuts migrate?

Mark


56 posted on 08/05/2007 8:36:53 PM PDT by MarkL (Listen, Strange women lyin' in ponds distributin' swords is no basis for a system of government)
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To: donna

More importantly, where did the bear go poop?


57 posted on 08/05/2007 9:09:49 PM PDT by JRios1968 (Faith is not believing that God can. It is knowing that God will. - Ben Stein)
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To: JoeSixPack1

LOL, I just got that.


58 posted on 08/05/2007 9:13:01 PM PDT by donna (The United States Constitution and the Koran are mutually exclusive.)
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To: Cringing Negativism Network
Mispronunciation. The word is "clucks" and denotes the distance a chicken travels when crossing the road. For whatever reason.
59 posted on 08/05/2007 11:35:46 PM PDT by Jeff Chandler (A man who will not defend himself does not deserve to be defended by others.)
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To: humblegunner

Instead of opps, or oops anymore...

I’m going to start using “Oh crap”...”Crape” if I want to sound french...


60 posted on 08/06/2007 5:13:28 AM PDT by stevie_d_64 (Houston Area Texans (I've always been hated))
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