Acknowledgement

We wish to express our gratitude to the San Diego Wind Tunnel and the Wind Tunnel at the University of Washington for the sharing of data.

Chapter 6

Predictive Model of Time Saved on

Descents in Road Cycling Achieved

Through Reduction in

Aerodynamic Drag Area

Abstract

This chapter presents simulation results of descent time to completion in road cy- cling. A mathematical model is formulated to predict time saved on road cycling descents where a cyclist’s position is static through manipulation of Aerodynamic Drag Area, system parameters and initial conditions. Road cyclists often adopt dras- tic static riding positions on long descents in order to minimise aerodynamic drag and optimise performance measured as race time to completion. In those riding po- sitions bicycle control is compromised and the risk of fall and injury increases. The aims of this study were to investigate the effect of the difference on time to com- pletion of road descents associated with the ’Top-Tube’ descending riding position compared to ’Normal’ descending riding position. Based on Newtonian-Lagrangian equations of motion of the cyclist-bicycle system, an analogue mathematical model as a non-linear Riccati ordinary differential equation was developed to enable pre- diction of velocity and time to completion of a road cycling course descent of known length and gradient as measures of performance for an athlete of known mass and drag area in a descending position. Previously proposed models of cycling perfor- mance have been based on physiological, anthropometric, and mechanical power output. No general closed form time to completion mathematical model for cycling was found in the literature. Analytical solutions allow for a concise investigation of a dynamical system model’s behaviour that is not as readily available with a numer- ical solution. The analytical solution to the non-linear Riccati differential equation showed large time savings as a result of reduction of drag area can be made on road cycling race descents. In the example scenario simulated here, 29.2sec may be saved on a 5km descent of 10% gradient with 25% reduction in aerodynamic drag area (CdA). We conclude that the ’Top-Tube’ riding position is associated with large

reduction in aerodynamic drag area in road descents compared to conventional de- scending riding position. Our model enables the prediction of time to completion on descents. This may assist cyclists to assess the trade off between undertaking in- creased risk associated with drastic rider descending position and the potential for improved performance in the context of race tactics and strategy.

6.1

Introduction

The performance of cyclists in road racing as measured by the time to completion of a race course is significantly affected by the cyclist’s aerodynamic properties [140]. Three types of external forces act on the bicycle/cyclist couple, being the system’s weight, aerodynamic drag force and contact forces between the road and the bicycle tyres [38] At racing speeds greater than 14m/s, aerodynamic drag force account for more than 90% of the total resistive forces acting on the cyclist/bike system [106, 140, 141], of which up to 70% are attributed to the cyclist [39, 64, 141]. The aerodynamic drag of a cyclist, as typical to bluff bodies, is dominated primarily by form drag associated with the geometrical shape of the bike-cyclist system and the vortical wake contribution [48]. This is in contrast to highly streamlined airfoil bodies, the aerodynamic properties of which are dominated by viscous drag com- ponent due to the velocity slow down in the boundary layers and associated skin friction [25]. The form drag can be reduced mainly by modifications to the geo- metrical shape of the bike-cyclist system through changes to cyclist’s riding position [11, 25]. Given the large potential of improved cycling performance, past research focused on reduction of aerodynamic drag through modification to riding position [48, 62, 64, 97, 106, 128, 139, 179, 226] or equipment [3, 11, 14, 25, 25, 28, 38, 138, 142]. Grappe et al. [106] reported up to 27% reduction in drag area in the O’bree posi- tion compared to upright, dropped and aero positions, which indicate the possibility for rider position optimisation for reduction in aerodynamic drag. Similarly, Garcia- Lopez14 reported reference values of aerodynamic drag of professional cyclists as measured in a wind tunnel in five riding positions under static and dynamic condi- tions. They showed that modifications to riding position can reduce the drag area of the system by up to 14%. However, the modifications in rider positions were achieved through manipulation of peripheral equipment (bicycle type, handlebar height and elbow pads location). Hence, the kinematic variables used to describe each position showed large variations and are participant and trial specific and are not consistent or reproducible. Defraeye et al. [64] attempted to control for the variability in rider position using a physical constraints positioning system. They studied three rider po- sitions and attempted to characterise the wake flow field using CFD, but only achieve moderate agreement with wind tunnel empirical data. The majority of past research focused on aerodynamic optimisation for flat surface or quasi-flat surface cycling such as time trial or track pursuit events [106, 226]. Grappe et al. [106] showed 7.8% and 12.4% reduction in drag area (CdA) in the dropped and aero positions respec- tively relative to an upright position. Underwood and Jermy [226] showed a small

§6.1 Introduction 93

(0.6+/-0.4N) reduction in aerodynamic drag for arrow-style hand position with no loss in power output. This also corresponded with reduction in estimated time to completion of a 250m lap of individual pursuit effort at assumed zero wind and gra- dient conditions. Chowdhury et al. [46] showed the CdA in a time trial position was lower than dropped position or the upright position, but failed to control the shape of the cyclist or the kinematic characteristics of the cyclist’s position. Despite the increased proportional effect of aerodynamic drag on total resistive forces acting on the cyclist-bicycle system, which exceeds 90% at 14m/s [140], no studies were found that measured or reported aerodynamic drag in cycling descents where the velocity of the cyclist may exceed 25m/s. This chapter will present first reference empirical values for aerodynamic drag of cyclists in descending riding position. The effect of reduced aerodynamic drag through modification of riding position on cycling performance is difficult to determine. Previous studies report a trade off between aerodynamic drag reduction achieved through adoption of aerodynamic favourable position and the ability of the cyclist to deliver the same power to the system. Savel- berg et al. [203] showed that changes to trunk angle influences muscle recruitment pattern and limb kinematics. This may be due to reasons relating to either the abil- ity of the neuro-muscular system to produce muscular effort in those positions [13] or the motor pattern specificity in trained participants, who are unable to execute a modified pattern in a position different to that they are trained in. Irrespective of the reason, this limits the ability to infer cause and effect relationship between reduction of aerodynamic drag achieved through modification of riding position and cycling performance. In cycling descents, however, cyclists regularly assume static position with the aim of increasing velocity through reduction of aerodynamic drag, in which case there is no cyclist’s muscular effort input that influences propulsion. In this specific case where propulsion is dominated by gravity, the direct effect of reduction in aerodynamic drag through changes in riding position on cycling performance can be studied. For this reason, this chapter will use cycling descent to estimate the ef- fect of reduced aerodynamic drag achieved through changes to riding position on simulated cycling performance.