The biomechanics of swimming

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The biomechanics of swimming boil down to two major concepts:

Streamlining: optimization of form for reduction of drag.

Displacement: ability to move water so that it will function as reaction mass for propulsion.

Drag: the resistance to movement of a body through a fluid, occurs in two varieties:

The relationship of form and frictional drag is represented by the Reynolds Number.

Easy to calculate, but where, exactly, are form and friction drag represented?

Since density & viscosity are essentially constant within an environment, they essentially cancel out, leaving:

Ultimately, the Reynolds number addresses the behavior of the boundary layer that surrounds an object moving through a viscous fluid. That layer is influenced by the viscosity of the fluid and the speed of the object.

Consider the familiar example of raindrops on a moving car:

Of course, the faster the car goes, the thinner the boundary layer gets and the more things poke out of it. When they do, they cause frictional drag in the surrounding medium. SO... objects operating at higher Reynolds numbers inherently experience more frictional drag than objects at lower Reynolds numbers.

As a first order approximation, the Reynolds number in water is a function of velocity and length. So.....

Large or speedy swimmers operating at higher Reynolds numbers (greater than 10,000) have a greater need for streamlining than smaller or slower ones operating at lower values (less than 100). E.G.:

Water displacement: But how do we accelerate an animal to the point that we need to think about Reynolds numbers in the first place? By water displacement. All swimmers use displaced water as a reaction mass to move their bodies forward (Newton's third law of motion.) This happens in three general ways:

Recoil locomotion

Familiar examples include:

High speed water jets provide momentum according to the equation:

momentum=mass * velocity

We noticed a difference in the jellyfish and Nautilus's performance. Why?

Velocity is proportional to the reciprocal of the cross-sectional area of the nozzle. Thus the Nautilus with its low-area nozzle, accelerates excurrent water to a greater velocity than the jelly.

As stated previously, the big disadvantage of recoil locomotion is that if the creature is already moving, the reaction mass must be carried along inside the cavity (i.e. accelerated forward) for some interval before being expelled backwards.

Appendicular locomotion

Appendages are used to displace water. This takes two general forms:

Axial locomotion

Many creatures, especially chordates, use the sides of their torso to displace water during axial undulations in which the body is thrown into a series of S-curves that propagate rearward. If living primitive chordates like Branchiostoma, hagfish, and lampreys are any guide, the ancestral chordate's body was probably long and sinuous, and most of it was used in propulsion. From this ancestral state, axial locomotion has been variously derived in vertebrates.

Two major trends are apparent:

Naturally a creature can combine these modes of propulsion. E.g.

The biomechanical constraints of swimming give us robust criteria for rejecting hypotheses of ancient creatures' life habits. E.G.: