Knapek, M. (May 27, 2001). Personal communication.

Mojmir Knapek from the Czech Republic responded to the editor's personal request for a reaction to an interview published by Diane Martindale (May, 2001), the introduction to which follows:

Why don't planes fall out of the sky? If you believe Boeing, Airbus and just about every textbook on the subject, it's because air travels faster over the "hump" of a wing, which creates lift. But Fermilab physicist David Anderson is convinced they're all wrong. Forget the fancy fluid dynamics, he says. Newton's three laws of motion are all you need. In his quest for the truth, he learned to fly, and has co-written a new book claiming to set the record straight. So, will pilots and engineers have to be retrained? And will tomorrow's aircraft look any different? Diane Martindale asked Anderson if he thinks the Wright brothers got it wrong . . .

The Reply

My reaction to this interview is somewhat reserved. To be clearer, my attitude to this matter as it refers to swimming technique is:

"The Bernoulli Principle is unable to explain the main propulsive forces in swimming!"

Regarding the interview and its implication for swimming, I am stimulated to consider this:

"What is Bernoulli's Principle? It is only a special case of Newton's Laws. As well, if the Reynolds number around a wing is under the critical limit of Re = 200,000 - 250,000, Bernoulli's Principle really is inappropriate, but mainly Newton's Third Law is."

There is the possibility that the interview does not fully cover the contents of Mr. Anderson's book. However, it does provoke consideration of lift and drag force production in swimming propulsion. It is possible to very roughly estimate the role of lift forces in swimming propulsion by using measures that are critical for estimating lift force production from Bernoullian assumptions.

Here are some general approximations, assumptions, and calculations.

A rough estimate of the speed of a swimmer's hand motion in water is about 30 - 75 cm/s (do not think of the speed of the body!). The diameter of a man's palm is approximately 10 cm, the wrist approximately 6 cm, and the forearm to the elbow is approximately 8 cm. An approximate Re number can be calculated as follows:

If this Re number is compared to the Re numbers suitable for a good lift, this is 5 - 10 times less than is needed to attain a critical Re number. [Remember, a critical Re number varies from approximately 200,000 for the best wing profiles to 300,000 for poor wing profiles. Circle and elliptical profiles, such as those for the human hand and forearm, have critical Re numbers ranging from 350,000 to 380,000 if significant lift force is to be produced.]

Therefore, Bernoulli's Principle is inappropriate for describing the forces around swimmers' hands and forearms. If you want to increase the lift of a hand, you have to increase the Re number around the hand. This leads to the following question: "If the best swimmers are able to increase the Re number [could this be a better feel for the water], is that achieved by exhibiting a better hump?" [aeronautical curvature on the top of an airfoil]

My primary intention with this reply has been to clear up some points about the shapes of surfaces, the production of lift, and the roles of lift and drag forces in swimming propulsion. Because of the slow speeds and poor aerodynamic shapes of human arms, lift force is unimportant for propulsion but drag force production in accordance with Newton's Laws is.

I hope this explanation is helpful.

Best regards,

Mojmir Knapek
Czech Republic

[Ed. Mr. Knapek graduated from the Technical University of Brno in the Czech Republic with a degree in engineering. He is assistant-coach of the Czech National Team of Finswimming.]


Martindale, D. (May 05, 2001). Taking flight. New Scientist Magazine. [https://www.newscientist.com/ns/20010505.html]

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