Where watts matter most in a time trial: power, CdA and speed

contrarrelojJuly 23, 20267 min readBorja Alfaraz

Time trial

17 W

Power-equivalent of a 0.015 CdA reduction on a flat time trial (43.6 km/h).

On a 6% climb (19.7 km/h), the same reduction is worth only 2 W. Computed with the AthletePro physics engine.

Abstract. This article analyses, with a physical model, the chronometric sensitivity of power and of the aerodynamic coefficient CdA as a function of speed. Two interventions of roughly equivalent effort are compared in a flat and in a climbing scenario, concluding that speed determines which variable —aerodynamics or power— constitutes the dominant performance lever.

A recurring question in time-trial preparation is where to invest the effort: in producing more watts, in reducing CdA, or in lightening the system. There is no single answer, because it depends on a variable that is often overlooked: speed.

Physical framework

The power required for forward motion is distributed among three resistances: aerodynamic, rolling and gravitational.

P = ½ · ρ · CdA · v³ + Crr · m · g · v + m · g · sin(θ) · v

The aerodynamic term grows with the cube of speed; the rolling term, linearly; and the gravitational term depends on the gradient. As a result, the distribution of resistance —and therefore the most rewarding lever— changes radically with the speed at which one rides.

Marginal analysis: two scenarios

We compare two interventions of roughly equivalent effort: increasing power by 15 W, or reducing CdA by 0.015 m² (a realistic position or fabric improvement). They are solved with the AthletePro physics engine in two opposing scenarios.

Scenario	Speed	+15 W	−0.015 CdA	−0.015 CdA in W
Flat · 40 km · 0%	43.6 km/h	−58 s	−67 s	≈ 17 W
Climb · 10 km · 6%	19.7 km/h	−72 s	−8 s	≈ 2 W

+15 W of power−0.015 m² of CdA

Flat · 40 km · 0% (43.6 km/h)

58s

67s

Climb · 10 km · 6% (19.7 km/h)

72s

Figure 1. Seconds saved by each intervention, computed with the AthletePro physics engine (rider-bike mass ≈ 75-78 kg, Crr 0.004-0.005, ρ 1.2 kg/m³). On the flat, aerodynamics dominates; on the climb, power does.

Interpretation

On the fast flat, the CdA reduction saves more time than 15 W of power: those 0.015 m² are equivalent to roughly 17 W of additional power. The reason is the cubic term: at 43 km/h aerodynamics consumes most of the power, so acting on it multiplies the effect.

On the 6% climb, the situation reverses. At 20 km/h air resistance is small, and the same CdA reduction saves barely 8 s —equivalent to about 2 W— while power and, above all, weight come to dominate: in that same scenario, shedding 1 kg saves close to 18 s. Aerodynamics does not vanish, but it ceases to be the principal lever.

Speed as the criterion

The operational conclusion is that speed determines which variable to prioritise:

Flat, fast time trial (>40 km/h): aerodynamics (position, helmet, suit, wheels) is the dominant lever.
Climbs and ramps (<25 km/h): power and power-to-weight prevail; aerodynamics is secondary.
Mixed courses: the priority changes segment by segment, and the optimal effort distribution depends on where each second is won or lost.

This is why the analysis should not be performed over the whole course, but segment by segment and at each segment's real speed. AthletePro breaks the course down and shows, segment by segment, where a watt or a tenth of CdA yields the greatest return, before the start.