NEWTON'S LAWS ARE BETTER THAN BERNOULLI'S THEORY FOR UNDERSTANDING SWIMMING

Sprigings, E. J., & Koehler, J. A. (1990). The choice between Bernoulli's or Newton's Model in predicting dynamic lift. *International Journal of Sport Biomechanics, 6,* 235-245.

In swimming there has existed a controversy over whether the propulsion that is derived from swimming is caused by Bernoulli's theorem (that explains lift forces) or Newton's principles (that explain both lift and drag forces).

Noted swimming scientists such as Counsilman in the early 1970s, Hay in the late 1970s, and Maglischo in the early 1980s, reverently postulate that Bernoulli's theorem and the generation of lift explains the propulsive forces of swimming. However, this theorem provokes the image of an asymmetrical wing, the shape being the major ingredient for developing lift. Small changes in shape should cause large changes in lift. However, even in aeronautical engineering, this principle is not particularly important for aircraft performance. In swimming it is obvious that the shape of the hand and forearm are constant and somewhat symmetrical and therefore, are not good objects for producing significant *"Bernoullian lift."* One only has to look at his/her own hand and forearm to witness that there is little useful foil shape for producing lift. For Bernoulli's theorem to be applicable, increased lift has to be derived from changes in shape, something which in not possible given the set shapes of hands and forearms with which swimmers are endowed. **Thus, attempting to explain swimming forces because of Bernoullian lift is inappropriate. Ascriptions to the shape of a swimmer's hand surface as being an airfoil are misleading.**

What is added to explanations for swimming forces is the angle of attack or "pitch" of the hand and forearm (something which is not accommodated by Bernoulli's theorem). It is contended that this feature is more significant for accounting for propulsion than is aerodynamic lift. This contribution to propulsion can be adequately explained by Newton's third law of motion (popularly expressed as* "To every action there is an equal and opposite reaction"*). What happens is that as a surface is angled and moved, the fluid it encounters is deflected, forced away, and it slows. That creates a force or pressure that acts upon the surface in an equal and opposite direction. The increased pressure propels the body past the hand-forearm surface that is creating the force.

Lift forces in swimming are primarily caused by the pitch (angle of attack) of the hand, not shape. Thus, Bernoulli's principle is not appropriate for explaining the major forces in swimming propulsion but Newton's are.

What happens when a swimmer presses a hand against the water to propel the body forward is as follows.

- Initially, there is backward drift or slipping that decreases as the force on the water is increased through friction. During this
*"compression,"*very little forward acceleration in the body occurs. - As friction increases, the hand slows as the water mass encountered increases and its location is changed. Because of Newton's second law, it is known that a force has been applied to the water for the hand to have slowed.
- The hand-forearm will receive an equal and opposite force back on itself (Newton's third law). It is this reaction back on the hand-forearm that produces the main propulsive force in swimming and consequently, the body is propelled forward.
- The maximum force is developed when the hand-forearm is at right angles to the intended line of progression (in swimming terms, the hand must face backwards to derive the greatest efficiency for forward propulsion but because of accommodations to anatomical restrictions this is not always possible).

Bernoulli's theorem only explains lift while Newton's principles explain lift and drag. Lift is only part of the total force *"package"* and does not always point in the direction of intended travel. *"Thus, to dwell exclusively on the lift component without any attention to the drag component would be an analytical blunder" *(p. 238). Swimmers are propelled primarily by drag forces and assisted by some lift.

**Implication.** It is more appropriate to explain and understand swimming forces by invoking Newtonian principles than by using Bernoulli's theorem. The fact that the forearm and hand cannot change shape to accommodate different speeds is the weakness in the Bernoulli argument. As well, the speeds attained in swimming are quite low and not conducive to good Bernoullian lift, even if shape alterations were possible.

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