14th International Symposium on Particle Image Velocimetry – ISPIV 2021
August 1–5, 2021

Aerodynamics of a cycling wheel in crosswind by
coaxial volumetric velocimetry

C. Jux1∗, A. Sciacchitano1, F. Scarano1

1 Delft University of Technology, Dept. of Aerospace Engineering - Aerodynamics, Delft, The Netherlands
∗ C.Jux@tudelft.nl

Abstract
The aerodynamic characteristics of a modern road cycling wheel in crosswind are studied through force
measurements and 3D velocimetry in TU Delft’s Open Jet Facility. The performance of the 62 mm deep
rim is evaluated for two tire profiles, and yaw angles up to 20◦. All measurements are executed at 12.5
m/s (45 km/h) freestream- and wheel-rotational velocity. The wheel’s rim-tire section in crosswind is found
to behave similar to an airfoil at incidence, ultimately resulting in a reduction of the wheel’s aerodynamic
resistance with increasing yaw angle magnitude. This trend, also referred to as the sail-effect, is limited by
the stall angle of the tire-rim profile. The stall angle is found to be dependent on the tire surface texture and
varies between 14◦ and 20◦.

1 Introduction
Aerodynamic drag is the major resistance a cyclist needs to overcome at speeds of 40 km/h and beyond.
In fact, the aerodynamic drag accounts for approximately 90% of a rider’s total resistance in this speed
regime which is typical for road racing (Kyle and Burke, 1984). The wheels contribute to about 10% of the
total aerodynamic drag (Greenwell et al., 1995), making them a crucial element in any cycling-performance
optimization.

Focusing on road cycling, a rider is exposed to a variety of wind conditions, affecting the perceived yaw
angle. The concept of wind-averaged drag (WAD, Cooper, 2003) accounts for the statistically anticipated
yaw-angle distribution experienced by a ground vehicle. The higher the vehicle velocity, the smaller the
maximum yaw angle perceived for a given wind speed. For professional road cycling speeds, the probability
of exceeding 20◦ yaw angle is reported to be less than 10% (Brownlie et al., 2010; Barry, 2018). Vice versa,
a rider spends 90% of the time at yaw angles below 20◦.

Aerodynamically designed wheels used in road racing (thus, excluding time-trial and triathlon specific
multi-spoke and disc wheels) are characterized by a 40-80 mm deep rim section, that connects via a multi-
tude of thin spokes to a cylindrical hub. In comparison to classical, shallow rim profiles, the deep-section
rim fulfills two functions: on one hand, it streamlines the tire shape, effectively reducing the tire-rim drag
coefficient. On the other hand, it generates —similar to a sail —a side force perpendicular to the relative
wind direction. A component of this force points in the riding direction, effectively “pulling” the wheel for-
wards and thereby further reducing its drag coefficient for non-zero yaw angles. The latter effect is known
as the “sail-effect” in literature, and it can result in a negative net drag force for wheels at high yaw angles
(Lukes et al., 2005; Barry et al., 2012; Malizia and Blocken, 2020a).

Designing a wheel for optimal performance is, however, not solely about minimizing (wind-averaged)
drag. As Barry et al. (2012) point out, large side forces on wheels yield strong steering moments and can
be a concern of maneuverability. Similar concerns can be expressed when discussing the stall behavior for
wheels at large yaw angles.

In addition to the rim-geometry, the aerodynamic characteristics of a wheel depend on the interaction of
rim and tire. Crane and Morton (2018) investigate this interaction with specific attention to tire width relative
to the rim. Besides tire width, data from wheel manufacturers suggests that the tire profile is equally decisive
for the rim-tire interaction, because the tire’s surface texture conditions the boundary layer development for
the flow over the wheel (Cant, 2014). Complementing the analysis of Crane and Morton (2018), this work
includes the comparison of a slick tire to a slightly profiled tire for a fixed tire width.



In the discussion of cycling wheel aerodynamics it is common practice to study wheels in isolation.
Experimental studies in the field focus predominantly on balance measurements (e.g. Zdravkovich, 1992;
Greenwell et al., 1995; Tew and Sayers, 1999), whereas flow topology data remains undocumented to the
best of the authors’ knowledge. Such data is readily available from computational fluid dynamics (CFD)
analysis, which presents an active line of research in the context of cycling wheel aerodynamics (Godo
et al., 2010; Malizia et al., 2019; Malizia and Blocken, 2020b). Authors developing numerical tools for the
aerodynamic analysis of cycling wheels, however, have to rely on the experimentally documented force data
for validation of their simulations. This practice becomes problematic when reported drag measurements
for the same wheel show variations of up to 300%, as observed by Godo et al. (2010). The large force
sensitivity is ascribed to variations in the experimental setup, including tire choice, free-stream turbulence,
wheel support design and wind tunnel blockage.

In view of the gaps and discrepancies in literature, the present work provides an experimental analysis
of the flow topology on a state-of-the-art bicycle wheel in crosswind by means of coaxial volumetric ve-
locimetry (CVV, Schneiders et al., 2018). The change in flow topology with yaw angle and tire selection is
documented. Additionally, the hypothesized “sail-effect” theory is scrutinized by analysis of the pressure
distribution near the rim-tire surface.

2 Definitions & terminology
Prior to presentation of the experimental apparatus and procedures in the subsequent section, we provide
clear definitions of the relevant variables and coordinate systems. The provided definitions largely follow
the work of Tew and Sayers (1999).

Figure 1: Definition of axes systems, flow angles and velocities for a cyclist moving at a velocity Vbg relative
to the ground (left). Relation of forces in wind and bike reference frames, illustrated on a bicycle wheel in
top view (right).

Figure 1 (left) shows a cyclist moving at a velocity Vbg relative to the ground. The direction of travel
defines the main reference frame Xb, pertaining to the bicycle, with the x-axis pointing opposite to the
motion direction. In an external environment, the wind velocity Vext and its direction (γ, the crosswind
angle) relative to the cyclist’s direction of motion are relevant for the definition of the aerodynamic problem.
The vector difference of external wind Vext and bicycle ground velocity Vbg determines the relative wind
velocity Vrel experienced by the cyclist. The angle between the cyclist’s motion axis and the relative wind
velocity defines the yaw angle β. Let us define a second coordinate system Xwt whose x-axis is aligned
with Vrel . The subscript ‘wt’ signals that this reference frame pertains to the wind-tunnel when testing in a
laboratory environment, where the x-axis is always aligned with the relative wind direction.

Figure 1 (right) illustrates the resistive and lateral forces acting on a bicycle wheel. Classically, the drag
force D acts parallel to the free-stream direction defined by Vrel , whereas the lift force L points perpendicular
to it, combining to the resultant force Ftot . More relevant for a cyclist, however, are the force components
in the reference frame Xb connected to the direction of motion. The side force Fs and the axial force Fa are
expressed as geometrical projections of L and D:

Fa = Dcos(β)−Lsin(β) (1)

Fs = Dsin(β)+Lcos(β) (2)



It follows that a situation can arise in which Lsin(β) > Dcos(β), resulting in a thrusting force which sup-
ports the cyclist’s motion —the sail effect. In the remainder of this work, forces are always provided and
discussed in the bicycle reference frame.

3 Experimental apparatus and procedures
Wind tunnel measurements are conducted at TU Delft’s Open Jet Facility, an open jet, atmospheric wind
tunnel with a 2.85×2.85 m2 exit section. All measurements are executed at a freestream velocity of 12.5 m/s
(45 km/h). The turbulence intensity in the test section, with a large-scale PIV seeding system installed in
the settling chamber, is reported with 0.8% by Giaquinta (2018). An overview of the test setup is provided
in Figure 2.

Figure 2: Experimental setup in the Open Jet Facility (left). Details of the mechanical systems installed in
the wind tunnel, with surrounding floor plates removed (right).

3.1 Wheel model & mechanical setup
A DT Swiss ARC 1100 Dicut DB 62 front wheel is installed in the test section. The 28” (700 mm diameter
with tire fitted) wheel features a 62 mm deep and 27 mm wide carbon rim. While the wheel is designed to
run with disc brakes, no brake discs were installed during the wind tunnel test. The clincher rim is fitted
with a 25 mm tire, inflated at 7 bar. A Continental GP 5000 tire featuring a mild periodic surface pattern
is chosen as a baseline tire, which is compared to a slick tire, a Continental GP TT. The difference in tire
profile is shown in Figure 3. The grooved texture element on the baseline tire model is approximately 35
mm long, and 12 mm wide, with a 35 mm gap along the circumference between two subsequent elements.

The wheel is connected to the support structure using a standard 12×100 mm through axle. The single-
sided support holding the wheel from the left hand side is designed to enhance optical access for the ve-
locimetry measurements.

The tire rests on two 70 mm diameter (60 mm width) rollers embedded in the wooden ground plate. The
rearward roller is driven by a variable speed DC motor to control wheel rotation. The wheel rotational speed
is kept constant at 348 rpm, matching a ground velocity (Vbg) of 12.5 m/s equal to the freestream velocity.
Wheel rotational speed and freestream velocity are both maintained constant at all times, and only the yaw
angle is adjusted during the measurements.

The wheel branding is covered by black adhesive foil to limit background reflections in the PIV acqui-
sition. A few circular (2 mm diameter) targets on the rim serve as reference markers to locate the model in
the PIV data, as well as a means to verify the wheel rotational speed.



(a) Baseline tire, Continental GP 5000, with approximate
indication of texture element size.

(b) Option tire, Continental GP TT

Figure 3: Fotographs of the tested tires mounted on the wheel.

3.2 Force measurement system
The wheel model including the mechanical support and drive mechanism is installed on a 6-axis force
balance situated underneath the ground plate. The balance acquires data at a frequency of 2 kHz, and its
accuracy is reported with 0.06% (0.15 N) of its full 250 N load capacity (Alons, 2008). Force data is acquired
and averaged over 20 s. The balance is placed on a turntable that controls the yaw angle. As such, the force
measurements delivered by the balance system pertain to the bicycle wheel reference frame (Xb). The yaw
angle is varied in a range of β between -22◦ and +22◦ in steps of 2◦. The arrangement of the components is
illustrated in Figure 2 (right).

Prior to force measurements on the wheel, the forces on the isolated support are recorded for all yaw
angles of interest. This data is subsequently subtracted from the measurements with the wheel installed to
identify the forces generated by the wheel only.

3.3 Velocimetry system
Three-dimensional (3D) particle image velocimetry data is acquired by a coaxial volumetric velocimetry
(CVV, Schneiders et al., 2018) system. A LaVision MiniShaker Aero CVV probe acquires image quadruples
of 640×476 px2 at a frequency of 821 Hz. 16,400 images are acquired for each yaw angle, equaling an
acquisition period of 20 s. The velocimeter is mounted on a Universal Robots UR5 robotic arm, allowing to
keep a similar imaging position and distance relative to the wheel for all yaw angles.

Neutrally-buoyant helium filled soap bubbles (HFSB, Scarano et al., 2015) of 300 - 500 µm diameter
serve as tracer particles, which are provided by a 0.6×0.8 m2 seeding rake installed in the wind tunnel
settling chamber. The measurement domain spans a 30×20×20 cm3 volume near the most upstream section
of the wheel. Data is only acquired on the leeward, respectively, the suction-side of the rim.

3.3.1 Velocity measurement

The wheel rotation results in unsteady reflections which are filtered from the particle images by means of a
Butterworth frequency filter (Sciacchitano and Scarano, 2014), followed by a directional minimum filter on
a local 5×5 px2 kernel. Pre-processed images are analyzed by the 3D Lagrangian particle tracking algorithm
“Shake-The-Box” (STB, Schanz et al., 2016) as implemented in Davis 10.1. The scattered STB tracks are
subsequently ensemble averaged by a linear fit of the velocity data in ellipsoidal cells of 6×6×30 mm3

(x× y× z), analogous to the approach presented by Agüera et al. (2016). Anisotropic cells are selected to
enhance spatial resolution in the horizontal directions, where velocity gradients are anticipated be stronger
as compared to the vertical direction, for the section of the wheel imaged by the velocimetry system. The
grid spacing is maintained constant at 1.5 mm in all axes.



3.3.2 Pressure evaluation

Based on the time-averaged velocity data, the static pressure is evaluated following a dual-model approach
previously presented by the authors (Jux et al., 2020). In the region of irrotational flow, Bernoulli’s equation
provides the local pressure and the necessary Dirichlet condition for the subsequent spatial integration of
the pressure gradient in the rotational flow domain. Lastly, the static pressure in the flow is mapped onto rim
and tire surface, using the local pressure gradient information.

4 Results and discussion
The analysis of the measurement data starts with the force measurements. Subsequently, the velocimetry
data is analyzed, leading to the discussion of the pressure distribution.

4.1 Force measurement
Figure 4 compares the axial and lateral forces as function of yaw angle for the two tested tire options. The
side force Fs in Figure 4a features a linear trend of decreasing force magnitude with increasing yaw for
moderate angles within |β| ≤ 10◦. In this range, the lateral force reduces by approx. 0.85 N/◦, independent
of the selected tire. Interestingly, the point of zero side force is found at a small positive yaw angle of about
2◦. For large yaw angle magnitudes beyond 10◦, the slope tapers off with a clear difference between the tires:
the (slick) option tire reaches higher side force magnitudes for both, large negative and positive yaw angles,
whereas the side force for the (profiled) baseline tire tapers off at slightly smaller yaw angle magnitudes.
This trend is well illustrated around β = 14◦ where the force curves cross each other.

(a) Lateral force (b) Axial force

Figure 4: Force measurements on the isolated wheel versus yaw angle.

The axial force Fa in Figure 4b indicates a plateau of maximum resistance for small yaw angles (-
2◦ ≤ β ≤ 6◦). The peak resistance of 1.12 N is found at 2◦ yaw, corresponding with the location of zero
side force in Figure 4a. Outside the indicated range, the axial force rapidly reduces for increasing yaw angle
magnitudes. For negative yaw angles the tires behave similarly, with the axial force decreasing until -10◦
yaw, where a negative resistive force is measured, meaning the wheel is generating a propulsive force in this
condition, albeit small in magnitude with about 0.1 N. The trend of decreasing axial force is stagnating in
the range of -14◦ ≤ β ≤ -10◦, before the axial force rapidly increases again for even lower yaw angle values.
This suggests that the flow over the wheel separates around β = -12◦. For yaw angles below -10◦ the (slick)
option tire shows a lower axial force as compared to the baseline tire.

Differences between the two tire options are stronger for large positive yaw angles. The baseline tire
initially shows a steeper reduction of the axial force with increasing yaw until β = 12◦, where the trend turns,
and the resistive force increases again for β > 14◦. For positive yaw angles, the resistive force on the wheel
with the baseline tire is always positive. In contrast, the axial force on the wheel with the option tire keeps
reducing until β = 18◦, although at a slightly slower rate. An increase in axial force is only observed for the
highest tested yaw angle of 22◦. Negative resistance is observed for 18◦ ≤ β ≤ 20◦.



Despite the differences between the tire configurations, both cases show an asymmetric behavior against
yaw angle: (1) the point of maximum axial force and minimum side force is found at β = 2◦ rather than
0◦. (2) Minima in axial force are different in magnitude and occur at different yaw angle magnitudes when
comparing behavior in negative and positive yaw. Potential sources of this asymmetry are the non-symmetric
wheel support, holding the wheel only from the left-hand-side (LHS); the blockage caused by the support
structure of the PIV system on the wheel’s right-hand-side (RHS); and the asymmetric design of the wheel’s
hub and spokes to accommodate a (centerlock) brake disc on its LHS.

The above analysis of the force data suggests nonetheless that the aerodynamic performance of the
wheel is strongly dependent on the tire choice. The two tires behave similarly in the range of -10◦ ≤ β ≤
10◦, whereas for larger yaw angles the option tire features lower axial resistance, which even becomes
negative, and thus acts as a (small) propulsive force. The lower resistive force of the option tire comes with
an increase in lateral force, which is approximately 10% higher as compared to the wheel with the baseline
tire for |β| > 14◦. In the following we scrutinize the velocimetry data to link the observed differences to
changes in the flow topology.

4.2 Time-average velocity field
For analysis of the flow topology, we extract slices of the 3D velocimetry data in a horizontal plane at hub-
height (z = 342.5 mm). The data shown in Figure 5 contains the velocity field upstream and past the leeward
(suction) side of the rim. The velocity contours show the normalized axial velocity component in the bicycle
wheel reference frame Xb,

u∗
b =

ub

ub∞

=
ub

uwt∞ cos(β)
(3)

where the subscript ‘∞’ indicates free-stream conditions upstream of the wheel. The velocity contours are
complemented by streamlines in the 2D planes. Additionally, for each yaw angle, the aerodynamic effect of
the tire is illustrated by plotting the difference in the axial velocity component between the baseline and the
option tire.

In straight ahead conditions (β = 0◦, Figure 5a) the inflow decelerates towards the most upstream point of
the tire. While one would expect the streamwise velocity component to stagnate at the tire surface, the finite
velocity measurement reduces only to u∗

b ≈ 0.6, which is attributed to spatial resolution effects. Alongside
the rim-tire profile the flow accelerates reaching streamwise velocities in excess of u∗

b = 1.2 at the thickest
section of the rim. The wake of the rim is not well captured by the velocimetry data. The streamlines,
however, suggest the presence of a separated wake zone just downstream of the rim. The differences between
the tire options are very mild at 0◦ yaw, in line with the balance data discussed previously.

The region of accelerated flow past the wheel gains in size and magnitude as the yaw angle increases.
Consider e.g. Figure 5c (β = 8◦) where for both cases the axial velocity exceeds 130% of the inflow velocity
as it passes the wheel. Comparing back to the straight ahead case in Figure 5a it is also noted that the
location of maximum velocity moved upstream, approximately to the junction of rim and tire, whereas at
0◦ yaw the maximum velocity is observed further downstream at the thickest point of the rim. Likewise,
the zone of decelerated flow upstream of the wheel rotates towards the windward side as the yaw angle
increases. The latter is seen well by following the unity contour of axial velocity (u∗

b = 1) which follows a
counter-clockwise motion with increasing yaw angle.

The described trend continues for both tire cases until β = 12◦ (Figure 5d). For greater yaw angles there
is a substantial difference in the flow topology for the different tire options. Comparing the data in Figures 5e
and 5f, the streamlines pertaining to the (slick) option tire in the right-hand-side plots suggest that the flow
follows the largest part of the wheel contour. Instead, for the (textured) baseline tire in the left-hand-side
plots, the streamlines only bend slightly around the tire but continue diverging from the rim surface as the
flow passes the wheel. The different behavior is also visible in the delta plot in Figure 5f, which indicates
that the flow around the wheel with the option tire attains far greater axial velocity. While flow data closer
to the rim surface is lacking for the baseline tire at these high yaw angles, the streamlines indicate that the
flow separates from the tire, similar to a leading edge separation on aeronautical airfoil profiles at high angle
of attack. Such leading edge separation results in a loss of lift (here, side force) and a simultaneous increase
in drag (here, axial force) which is in line with the observations from the force data above.



(a) β = 0◦

(b) β = 4◦

(c) β = 8◦

(d) β = 12◦

Figure 5: Time-average velocity contours in xy-planes at hub height (z = 342.5 mm), along with 2D surface
streamlines. Velocity contours show the normalized axial velocity component in the bicycle wheel reference
frame. (Left) Baseline tire. (Right) Option tire. (Center) Delta = ubaseline −uoption. (Continues on next page)



(e) β = 16◦

(f) β = 18◦

Figure 5: (Continued) Time-average velocity contours in xy-planes at hub height (z = 342.5 mm), along
with 2D surface streamlines. Velocity contours show the normalized axial velocity component in the bicycle
wheel reference frame. (Left) Baseline tire. (Right) Option tire. (Center) Delta = ubaseline −uoption.

4.3 Pressure data
Following the analysis of the velocity data, we briefly investigate the pressure distribution over tire and
rim profile. Similar to the previous assessment, the analysis starts in a horizontal xy-plane at hub height
(z = 342.5 mm). Because both tire options behave similar for moderate yaw angles, and data close to the

Figure 6: CP profiles over the tire-rim surface at hub-
height (z = 342.5 mm) for the option tire (GP TT).

surface is lacking for high yaw angles on the
baseline tire, we limit ourselves to the study
of the (slick) option tire here.

Figure 6 shows the pressure profiles on
the leeward side of the wheel for β = [0,
8, 16]◦. The pressure profiles are charac-
terized by a steep pressure reduction over
the upstream tire section. As the yaw an-
gle increases, the pressure reduction gains in
magnitude, signifying greater suction with in-
creasing yaw angle. The location of mini-
mum CP moves downstream as the yaw an-
gle grows. At 0◦ yaw the minimum pressure
of CP = -0.7 is recorded at x/c = 0.06, before
approaching an approximately constant value
of CP = -0.5 further downstream. At 8◦ yaw
instead, the minimum pressure coefficient ex-
ceeds a value of -1, and it is obtained slightly
further downstream (x/c = 0.13). Increasing
the yaw angle further to 16◦, the pressure co-
efficient drops to a minimum of CP = -1.75 at



x/c = 0.26, followed by an adverse pressure gradient approaching CP = -0.5 at x/c = 0.6.
Complementing the above pressure profiles in the wheel center plane, 3D iso-surfaces of pressure co-

efficient are shown for the three selected cases in Figure 7, along with axial velocity contours on the upper
and lower boundary of the measurement volume. For each case, two iso-surfaces are plotted: the first, at CP
= 0.35 (red) indicates the volume of increased pressure resulting from the flow deceleration upstream of the
wheel. The second, at CP = -0.6 (blue) is selected to visualize the volume of reduced pressure induced by the
flow acceleration alongside the wheel. Comparing the latter iso-surface for the three yaw angles confirms
the growth of the low-pressure region with increasing yaw angle, signaling a likewise increase in side force.

Figure 7: Axial velocity contours in horizontal planes at z = [242.5, 442.5] mm along with 3D pressure
iso-surfaces of CP = 0.35 (red) and -0.6 (blue). Data shown for wheel fitted with option tire at β = 0◦ (left),
8◦ (center) and 16◦ (right).

The observed trend is qualitatively in line with the force data presented in Section 4.1 which indicated a
monotonically increasing side force magnitude with increasing yaw angle in this range. It further supports
the theory that the tire-rim profile in crosswind indeed behaves like an airfoil at incidence, thereby making
the wheel work like a sail.

5 Conclusions
The aerodynamic characteristics of a state-of-the-art road cycling wheel in cross wind have been assessed
experimentally by means of force measurements and a full-scale 3D velocimetry investigation. Additionally,
the interaction of rim and tire is studied by comparison of a textured and a slick tire. The resistive force on
the isolated wheel is highest at moderate yaw angles of β = 2◦ ± 4◦. Outside this range, the aerodynamic
resistance of the wheel is reduced as the yaw angle magnitude increases. Analysis of the velocimetry data
confirms that the reduction in resistance measured by a force balance is indeed a consequence of the “sail-
effect”, resulting from a substantial side-force on the wheel at yaw incidence. The benefit of this effect is
limited by the stall angle of the tire-rim combination, which is found to be dependent on the tire choice.
The two tested tires behave similarly for negative yaw angles, with the flow separating around β = -14◦. For
positive yaw angles, the slick tire performs significantly better, increasing the separation angle from 14◦ to
20◦ with respect to the profiled baseline tire.

Acknowledgements
We thank Thomas Koep on behalf of DT Swiss for providing the wheels for the study. Likewise, we thank
Dennis Bruikman, Peter Duyndam and Frits Donker Duyvis for the invaluable technical support. This
research is supported by LaVision GmbH.



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	Introduction
	Definitions & terminology
	Experimental apparatus and procedures
	Wheel model & mechanical setup
	Force measurement system
	Velocimetry system
	Velocity measurement
	Pressure evaluation


	Results and discussion
	Force measurement
	Time-average velocity field
	Pressure data

	Conclusions