Notes — Variable CdA

Commentary, references and provenance for Variable CdA. Each note is addressed by name so it can be cited from anywhere in the Knowledgebase. Working draft, 2026-09-22.

Sphere and cylinder transitions

For smooth bodies the drag crisis falls at about Re = 2–5×10⁵ for a circular cylinder in crossflow (Achenbach 1971) and about 3.7×10⁵ for a sphere (Achenbach 1972). Roughness moves both earlier by a similar amount (Achenbach 1971; Achenbach 1974). The Cd levels differ (about 1.2 against 0.47 on the subcritical plateau), but the Reynolds number range of the transition is of the same order, which is all the article relies on.

Referenced from: Everything will be treated as a cylinder

The wind tunnel data

Grappe, F. (2009), Cyclisme et optimisation de la performance, 2nd ed., De Boeck; data as reproduced in Debraux, Grappe, Manolova & Bertucci (2011), Sports Biomechanics 10(3), 197–218, doi:10.1080/14763141.2011.592209. One cyclist in a static position, 15 to 100 km/h in 5 km/h steps, 18 points. The tunnel’s turbulence intensity, blockage and tare corrections are not stated in the source (ReynoldsData/cylinder_drag_sources_and_caveats.html).

Table 2. The 18 wind tunnel points of Figure 4.details

Speed (km/h)Air speed (m/s)CdA (m²)Re, 30 cm cylinder
154.170.4358.5e+04
205.560.3971.1e+05
256.940.3941.4e+05
308.330.3831.7e+05
359.720.3802e+05
4011.110.3702.3e+05
4512.500.3772.5e+05
5013.890.3782.8e+05
5515.280.3843.1e+05
6016.670.3813.4e+05
6518.060.3843.7e+05
7019.440.3903.9e+05
7520.830.3954.2e+05
8022.220.3924.5e+05
8523.610.4074.8e+05
9025.000.3955.1e+05
9526.390.4245.3e+05
10027.780.4265.6e+05

Referenced from: What do wind tunnel results show?

Reading the wind tunnel points

CdA values read from the figure in ReynoldsData/cylinder_drag_composite_model.html to about ±0.002 m². The Reynolds column is for a 0.30 m diameter at ν = 1.48×10⁻⁵ m²/s.

Not yet referenced.

Auxiliary documents

The documents behind this entry. They stay in the entry folder and are the audit trail for every number.

ReynoldsData/cylinder_drag_composite_model.html — the cylinder curves and the wind tunnel points (source of Figures 2 and 4 and Table 2), and a composite cylinder model of the Grappe data that is no longer used in the article.

ReynoldsData/cylinder_drag_sources_and_caveats.html — sources, provenance and known problems behind every number in the cylinder model; read before reusing any value out of context.

field cda variability/CdA_variability.md — “The constant that isn’t”, the field measurements and the constant-pair algebra, with anna_constant_pair_fit.py and cda_variability_fig.py.