Computational settings and parameters
The CFD simulations were performed at full scale. The cyclist and motorcycle geometry were identical to those of the WT models apart from the WT model bottom plate, the vertical reinforcement bars in the cycling wheels (Fig. 2c-d) and the geometrical scale (1:1 versus 1:4). Δy was 1.3 m. The rectangular computational domain had dimensions length x width x height = 60 × 32 × 24 m3. The blockage ratio was about 0.1%, which is below the recommended maximum of 3% for CFD simulations [17,18,19,20].
The computational grids were hybrid hexahedral–tetrahedral grids based on grid convergence analysis (not reported here) and on grid generation guidelines [16,17,18,19,20,21,22,23,24]. They had a wall-adjacent cell size of 20 µm (= 0.02 mm) and 40 layers of prismatic cells near the cyclist and motorcycle surfaces to accurately resolve the thin boundary layer including the laminar sublayer (Fig. 5). The dimensionless wall unit y* had values that were generally below one and always below five. The cell size in the area between motorcycle and cyclist was 0.03 m. Figure 5 shows the grid resolution on the surface of the cyclist, motorcycle and in the vertical plane through the cyclist. The total cell count was 53.2 × 106.
The computational settings are identical to those in  and are summarized here for completeness. At the inlet, a uniform velocity of 15 m/s was imposed that represented the riding velocity. As in the WT tests, it was assumed that there was no crosswind, no head wind and no tail wind. The inlet turbulence intensity was set to 0.5% to obtain the same approach-flow value of 0.3% in the region directly upstream of the motorcycle as in the wind tunnel. This was required because the turbulence intensity decayed from 0.5 to 0.3% from the inlet of the computational domain to the position of the motorcycle model. At the outlet, zero static gauge pressure was set. The bottom, side and top surfaces of the domain were slip walls. The surfaces of the motorcycle and cyclist were no-slip walls, where the cyclist body and the motorcycle had a surface roughness with equivalent sand-grain roughness height kS = 0.1 mm and the bicycle kS = 0 mm.
Scale Adaptive Simulations (SAS)  were performed involving the Shear Stress Transport (SST) k-ω model  with curvature correction. Pressure–velocity coupling was performed by the PISO algorithm. Pressure interpolation was second order, gradient interpolation was conducted with the Green–Gauss node-based scheme. Bounded central differencing was used for the momentum equations and second-order discretization for the turbulence model equations. Time discretization was bounded second-order implicit. The simulations were performed with the commercial CFD code Ansys Fluent 16.1 . The time step of 0.002 s was selected such that the Courant–Friedrichs–Lewy (CFL) number was equal to unity or below unity in the area between the motorcycle and the cyclist. A time step convergence analysis confirmed the suitability of this time step . The number of time steps required to obtain a constant moving average of the sampled drag values was 8000.
The computed isolated cyclist drag area (CdA) was 0.231 m2 while that of the cyclist in parallel arrangement with the motorcycle was 0.248 m2, yielding about 7.5% drag increase, in line with the WT result at Δx = 0 (Fig. 3).
Figure 6 presents contours of air speed in a horizontal plane at 0.8 m above ground, for the parallel arrangement compared with the isolated cyclist. Figure 6a,b shows the time-averaged results, while Fig. 6c-j shows instantaneous results at time intervals of 0.12 s. The presence of the motorcycle increased the size of the high-speed areas (red color) wrapping around the cyclist’s waist. These areas partly interacted with similar areas around the front part of the motorcycle, yielding a high-speed jet in between the cyclist and motorcycle (see Fig. 6a). Due to the presence of the motorcycle, the velocity in the wake behind the cyclist increased, the wake behind the cyclist widened and slightly curved towards the wake behind the motorcycle.
Figure 7 depicts contours of pressure coefficient Cp in a horizontal plane at 0.8 m above ground. For the isolated cyclist, a clear over-pressure area (red/orange) in front and under-pressure areas (blue) on the side and behind the cyclist body were present, where the latter was distorted over time by periodic vortex shedding. For the parallel arrangement, the large over-pressure area in front of the motorcycle partly merged with that in front of the cyclist. Also the large under-pressure area behind the motorcycle partly merged with that behind the cyclist. As a result, the size of the most intense under-pressure areas wrapping around the waist of the cyclist increased substantially, as did the size of the under-pressure area behind the cyclist and the overall absolute value of the pressure coefficient in the wake behind the cyclist. The larger under-pressure areas on the side were in line with the faster air speed around the sides of the cyclist in Fig. 6.
Figure 8 displays contours of mean CP on the surface of the cyclist and motorcycle. While Fig. 8a,b only shows minor differences in terms of the positive CP values, Fig. 8c-f clearly shows larger under-pressure on the sides and torso of the cyclist as well as on the bicycle rear wheel due to the presence of the motorcycle.
Animations of the SAS-SST k–ω simulations are provided in (Supplementary Material 1, 2, 3, 4).