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What is the airspeed velocity of an unladen swallow?
"This was certainly a tricky question to say the least. Lots of physics involved that I have pushed to those dusty corners in my mind. Not to mention you need to know a little bit about swallows.
Leave it to Marion to make me think this hard…
Let’s start with what an unladen swallow is. The simple answer, it’s a bird. The more complicated answer is that it’s a bird with 74 distinct species of swallow. Some found in Africa, others in Europe.
What is air speed velocity? It’s the relative velocity between some object, in this case the swallow, and the air.
In order to calculate the airspeed you have to take the difference between ground speed and the wind speed. Ground speed is the speed in which an object moves relative to some reference point on the ground. Wind speed is the speed in which the air moves relative to some reference point on the ground.
If there was a case in which a day had absolutely no wind, the ground speed is equal to the wind speed. Of course this is highly unlikely to ever happen.
This definition applies best to planes. When dealing with animals is a little different. To find the airspeed velocity of a bird, one must calculate the Strouhal number. The Strouhal number is usually used in the calculation of speed of fish in water. In that case, it is the ratio of frequency of the tail moving and the forward speed of the animal. A man named Graham K. Taylor discovered the same principle can be applied to birds and other animals that can fly.
For birds, the Strouhal number is the frequency multiplied by the amplitude of the wings divided by the animal’s speed through the air. The frequency is the number of times the bird beats its wings a second and the amplitude is the distance the wing travels in one beat.
To get an approximate airspeed, Taylor said to invert the midpoint Strouhal number (which is 0.3). This means that the airspeed about 3 times the product of the frequency and the amplitude.
There is a very detailed blog on style.org that discusses all the fun mathematical details of the Strouhal Number if you are interested. Here’s a link:
The Strouhal Number in Cruising Flight
Now, in the case of the swallow, the Strouhal number is actually less than the average so it doesn’t work right out of the box. For all the details, see:
Estimating the Airspeed Velocity of an Unladen Swallow
In the end, it’s concluded that the airspeed velocity of a (European) unladen swallow is about 24 miles per hour or 11 meters per second."
Reference:
https://www.saratoga.com/how-should-i-know/2013/07/what-is-the-average-air-speed-velocity-of-a-laden-swallow/