1. automotive and vehicles
2. bicycles and accessories

Bicycle Aerodynamics, or:
How to lose the Tour de France.
Duncan Sutherland
ΣUMS
Duncan Sutherland
Bicycle Aerodynamics
Background
1989 Tour de France final stage. Greg LeMond (right) beat
Laurent Fignon (left) by 8 seconds. The closest margin in Tour de
France history.
Duncan Sutherland
Bicycle Aerodynamics
From Wikipedia: “ Fignon, who rode after LeMond, lost 58
seconds during the stage, and although he became third in the
stage, he lost the lead to LeMond. It was calculated afterwards
that if Fignon had cut off his ponytail, he would have reduced his
drag that much that he would have won the Tour.[McCann]”
Jolly good, but how is such a problem approached? Paper by
Thijis Defraeye, et al. “Aerodynamic study of different cyclist
positions: CFD analysis and full-scale wind-tunnel tests.” Journal
of Biomechanics, v43, i7, pp 1262-1286 (2010).
Duncan Sutherland
Bicycle Aerodynamics
Streamlined and bluff bodies
I
Streamlined bodies: flow follows the contours of the body.
Example: airfoils.
I
Bluff bodies: flow around the body separates and vorticies are
formed by rolling up of shear layers. Example: A brick.
I
Cyclists are combinations of these types of body. Areas such
as the helmet may be quite streamlined, but areas such as the
torso may be bluff bodies.
(a) Airfoil
Duncan Sutherland
(b) Brick
Bicycle Aerodynamics
Resistance
I
A cyclist’s performance is affected by the resistance, eg, drag,
friction and gradients
I
At the highest speeds 50kms/h and above, most of the
resistance is aerodynamic drag, mostly accounted for by the
position of the cyclist’s body.
I
Two sources of drag: form drag contributes more than 90% of
the drag and viscous drag, caused by roughness on the surface
of the cyclist.
Duncan Sutherland
Bicycle Aerodynamics
Dimensional analysis and the drag equation
Dimensional analysis is way of deriving an equation for an unknown
quantity without thinking too hard:
I Take variables of interest: drag FD , velocity u, density ρ, area
L2 and viscosity ν
I Write
fa (FD , u, ρ, L2 , ν) = 0
I
and note that 0 is dimensionless, thus the function must be
dimensionless.
Rearranging into dimensionless groups
FD uL
,
=0
fb
ρL2 u2 ν
I
since only FD is unknown:
FD = 21 ρL2 u2 fc (Re), Re =
CD = fc (Re). CD ≈ 0.23.
Duncan Sutherland
uL
ν
and then define
Bicycle Aerodynamics
Fluid Dynamics
Fluid mechanics is basically concerned with solving the
Navier-Stokes equation and the continuity equation
∂Tij
∂ui
∂p
∂ui
+ uj
=−
+
ρ
∂t
∂xj
∂xi
∂xi
∂uj
∂ρ
∂ρ
+ uj
+ρ
=0
∂t
∂xi
∂xj
i
Simplifying assumptions: incompressibility, ∂u
∂xi = 0; Newtonian
∂u
∂ui
+ ∂xji These are complicated and we want to
fluid, Tij = µ ∂x
j
use a computer. Problems are cost, stability and accuracy.
Duncan Sutherland
Bicycle Aerodynamics
Reynolds Averaged Navier Stokes
For an incompressible, viscous, Newtonian fluid, we may
decompose velocity, ui into the time averaged part Ui and the
fluctuating part, with zero mean, u
˜:
ui = Ui + u˜i
pi = Pi + p˜i
Tij = T¯ij + τij
This gives the RANS equation:
∂Ui
∂Ui
∂P
∂ ¯
+ Uj
=−
+
(Tij − ρh˜
ui u
˜j i)
ρ
∂t
∂xj
∂xi ∂xj
Turbulence Closure Problem: use models of turbulence to
determine h˜
ui u
˜j i.
Duncan Sutherland
Bicycle Aerodynamics
Free pizza
Duncan Sutherland
Bicycle Aerodynamics
Large Eddy Simulation
Low-pass filter applied to the Navier-Stokes equation.
Z ∞Z ∞
¯ t) =
ϕ(x,
ϕ(r, t0 )G(r − x, t − t0 )dt0 dr
−∞
−∞
∂τijr
∂
1 ∂ p¯
∂ ¯
∂ u¯i
+
(¯
ui u
¯j ) = −
+ 2ν
Sij −
∂t
∂xj
ρ ∂xi
∂xj
∂xj
Sij is the rate of strain tensor. The residual stress tensor
τijr = Lij + Cij + Rij Lij represents interation of large scales, Cij
cross scale interations and Rij is subscale stress.
(c) Direct sim- (d) LES sim- (e) LES simulation
ulation ∆ = ulation ∆ =
L/32
L/16
Duncan Sutherland
Bicycle Aerodynamics
Finite Element Method
FEM is a means of approximating the solution to a PDE on a
mesh, using certain basis functions eg: peicewise polynomials. The
mesh can cope with complicated geometries and the computation
is relatively cheap.
Duncan Sutherland
Bicycle Aerodynamics
Defraeye paper
I
Comparison of the area drag L2 CD , of different cyclist
positions.
I
Wind tunnel experiments and a comparison of LES and RANS
calculations based upon the cyclist’s position alone.
I
Experimental setup of a bicycle was photographed, digitised
and the cyclist was smoothed into a mesh suitable for finite
element computations.
Duncan Sutherland
Bicycle Aerodynamics
Meshing
The mesh is generated by a 3D laser scanning and digitising
system. The bicycle, stand and other pieces of experimental
equipment were omitted from the computational domain.
(f) Computational (g) Experimental
domain
setup
Duncan Sutherland
Bicycle Aerodynamics
Comparison of simulation and experiment
Duncan Sutherland
Bicycle Aerodynamics
Conclusion
Maurice Garin, disqualified in 1904 for catching a train.
Duncan Sutherland
Bicycle Aerodynamics