Weight or aerodynamics: from what gradient a kilo less is worth more than a lower CdA
Crossover gradient
2.5 %
Gradient above which dropping a kilo saves more time than lowering CdA by 0.005 m², for a 300 W rider.
Model calculation over 40 km: at 0 % the kilo is worth 2 s and the CdA 22; at 6 %, the kilo 73 s and the CdA 11.
At 300 W over 40 flat kilometres, a kilo less saves 1.9 seconds and lowering CdA from 0.240 to 0.235 m², which is what a well-chosen helmet or leg covers give, saves 22. On a 6 % climb, the kilo saves 73 seconds and the CdA 11. In between there is a point where both improvements are worth the same, and it is much lower than most people think.
Where is the crossover?
The curves cross between 2 and 2.5 %. Below that, aerodynamics wins; above it, weight. The reason is speed: at 2.5 % the example rider goes 31.5 km/h, and at that speed air is already less than half of total resistance2. At 6 % they go 19.8 km/h and air barely counts.
The crossover moves with power. A more powerful rider goes faster on every gradient, air matters more and the crossover rises; a 200 W rider has it lower. And on a 10 km climb at 7 %, which takes 34 minutes at 300 W, the kilo is worth 22 seconds and the CdA only 2.
What to buy for your course?
- Flat or rolling time trial (average under 2 %): everything into aerodynamics. A kilo on the TT bike is almost irrelevant; 0.005 m² of CdA is 20 seconds over 40 km3,4.
- Race with climbs of 5 % or more: here weight rules, and the weight that counts most is the rider's, not the bike's. A kilo of fat and a kilo of frame save the same on the climb, but the first one is free.
- Mixed course: average gradient misleads. What matters is how much time you spend above 2.5 %, because on the descents neither weight nor aero gives back what they took.
Rule of thumb: if your course averages under 2 % and you spend less than a quarter of the time climbing, every euro yields more in aerodynamics than in weight.
What is known and what is not
The physics of the crossover is solid and matches what reviews recommend on where to spend time and money3. What the calculation leaves out is that mass also costs on every acceleration, which favours weight a little more on twisty courses, and that a heavier rider has a somewhat larger CdA because of their size5, which favours them on the flat.
Frequently asked questions
From what gradient does weight matter more than aerodynamics?
Around 2.5 % for a 300 W rider: there a kilo less and a CdA 0.005 m² lower save the same, about 20 seconds over 40 km.
How much is a kilo worth on a climb?
At 6 %, about 73 seconds over 40 km, or 22 seconds on a 10 km climb at 7 %. On the flat, barely 2 seconds over 40 km.
References
- Martin JC, Milliken DL, Cobb JE, McFadden KL, Coggan AR. Validation of a mathematical model for road cycling power. J Appl Biomech. 1998;14(3):276-91. doi:10.1123/jab.14.3.276
- Swain DP. A model for optimizing cycling performance by varying power on hills and in wind. Med Sci Sports Exerc. 1997;29(8):1104-8. doi:10.1097/00005768-199708000-00017
- Jeukendrup AE, Martin J. Improving cycling performance: how should we spend our time and money. Sports Med. 2001;31(7):559-69. doi:10.2165/00007256-200131070-00009
- Crouch TN, Burton D, LaBry ZA, Blair KB. Riding against the wind: a review of competition cycling aerodynamics. Sports Eng. 2017;20(2):81-110. doi:10.1007/s12283-017-0234-1
- Swain DP, Coast JR, Clifford PS, Milliken MC, Stray-Gundersen J. Influence of body size on oxygen consumption during bicycling. J Appl Physiol. 1987;62(2):668-72. doi:10.1152/jappl.1987.62.2.668
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