Question 13 of 13: Drafting: Cyclists vs. Swimmers

Question 13 — Drafting: Cyclists vs. Swimmers (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Momentum-theory view of drafting. Any body moving through a fluid imparts momentum to that fluid, leaving behind a wake — a region of reduced velocity relative to the body (a "momentum deficit"), whose magnitude by a momentum-integral control-volume analysis equals the body's own drag force: the leader does work on the fluid at a rate F_drag·V, permanently leaving a lower-relative-velocity column of fluid behind it. A trailing body positioned inside that momentum-deficit column experiences a reduced local relative flow velocity, and since drag scales with the square of relative velocity, its own drag force (for the same ground speed) is reduced — this is the shared mechanism behind BOTH cyclist and swimmer drafting; the question is whether it survives the very different force balance of each case.

Cyclists. At typical cycling speeds (∼8–15 m/s) aerodynamic (pressure/form) drag in air dominates the rider's total resistance, because muscular power is limited while drag grows with V² and air, though low in density, is displaced at high speed. A drafting cyclist sitting in the lead rider's low-pressure wake experiences a substantially reduced relative wind and can maintain the same ground speed for markedly less power (commonly cited savings of order 30%). Illustrative Reynolds number (body length scale ∼0.5 m, V∼10 m/s, air ν∼1.5×10⁻⁵ m²/s): $$Re_{cyclist} = \frac{VL}{\nu} = \frac{(10)(0.5)}{1.5\times10^{-5}} = \boxed{3.3\times10^5}$$

Swimmers. A swimmer's resistance is a mix of skin-friction (viscous) drag, form drag, and — unique to surface swimming — wave-making drag from the free surface, which is often the dominant term at typical human swim speeds (much lower Froude numbers than a planing boat, but still surface-wave-significant). Water's much higher density means absolute drag forces are far larger than in air at the same relative velocity, but swim speeds (∼1.5–2 m/s) are far lower than cycling speeds; using the same illustrative scaling (V∼1.5 m/s, water ν∼1.0×10⁻⁶ m²/s): $$Re_{swimmer} = \frac{(1.5)(0.5)}{1.0\times10^{-6}} = \boxed{7.5\times10^5}$$ Despite the much lower speed, the swimmer's Reynolds number is actually HIGHER than the cyclist's, because water's kinematic viscosity is roughly 15 times smaller than air's — both flows are solidly turbulent, and a genuine wake momentum-deficit region does form behind a swimmer, just as behind a cyclist.

Conclusion. Yes, the same drafting mechanism DOES apply to swimmers — a trailing swimmer positioned in the lead swimmer's wake genuinely experiences reduced relative flow and can realise an energy saving, and documented studies confirm a measurable (though generally smaller than cycling's ∼30%) reduction for a closely-trailing swimmer. The effect is smaller and less reliable for three reasons distinguishing the two force balances: (1) the swimmer's wake includes a chaotic, unsteady surface-wave train in addition to the momentum-deficit region, so the "calm" drafting zone is narrower and less predictable than a cyclist's steady aerodynamic wake; (2) water's higher viscosity dissipates the momentum deficit over a shorter distance than air does, shrinking the usable drafting window; and (3) a trailing swimmer who mis-positions in the turbulent/wave portion of the wake (rather than the calmer momentum-deficit column) can actually experience INCREASED resistance and disrupted stroke timing, making drafting a net disadvantage if done poorly. So the answer is a qualified yes: the same physics applies, the potential benefit is real but smaller and more position-sensitive than for cyclists.