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Assessment of bike handling during cycling individual time trials with a novel
analytical technique adapted from motorcycle racing
Andrea Zignoli1,2,3,*, Francesco Biral1, Alessandro Fornasiero3, Dajo Sanders4, Teun Van Erp5,
Manuel Mateo-March6,7, Federico Y. Fontana8, Paolo Artuso9, Paolo Menaspà10, Marc Quod11,
Andrea Giorgi12,13, Paul B. Laursen14
1. Department of Industrial Engineering, University of Trento, Trento, Italy
2. Prom Facility, Trentino Sviluppo, Trento, Italy
3. CeRiSM Research Centre, University of Verona, Trento, Italy
4. Department of Human Movement Science, Faculty of Health, Medicine and Life Sciences,
Maastricht University, Maastricht, Netherlands
5. Division of Orthopaedic Surgery, Department of Surgical Sciences, Faculty of Medicine and
Health Sciences, Stellenbosch University, Tygerberg, South Africa
6. Spanish Cycling Federation, Madrid, Spain
7. Movistar Team, Abarca Sports, Pamplona, Spain
8. Team Novo Nordisk professional cycling team, Atlanta, USA
9. Team Bahrain McLaren, Manama, Bahrain
10. School of Medical and Health Sciences, Edith Cowan University, Perth, Australia
11. Mitchelton-Scott Cycling Team, Adelaide, Australia
12. Androni Giocattoli-Sidermec Professional Cycling Team, Medical Staff, Italy
13. Internal Medicine, Specialists Medicine and Rehabilitation Department. Functional Recovery
and Re-education Unit. USL Toscana south-east
14. Sport Performance Research Institute New Zealand (SPRINZ), Auckland University of
Technology, Auckland, New Zealand
*Corresponding author:
Andrea Zignoli
Mail to: CeRiSM Research Centre, via Matteo del Ben 5b, 38068, Rovereto, Trento, Italy
Mob: +39-340-8117956
email: andrea.zignoli@unitn.it
ORCID ID: 0000-0003-1315-5573
Please cite as: Zignoli, A., Biral, F., Fornasiero, A., Sanders, D., Erp, T.V., Mateo-March, M.,
Fontana, F.Y., Artuso, P., Menaspà, P., Quod, M. and Giorgi, A., 2021. Assessment of bike handling
during cycling individual time trials with a novel analytical technique adapted from motorcycle
racing. European journal of sport science, pp.1-23.
DOI: https://doi.org/10.1080/17461391.2021.1966517
Abstract
A methodology to study bike handling of cyclists during individual time trials (ITT) is presented.
Lateral and longitudinal accelerations were estimated from GPS data of professional cyclists (n=53)
racing in two ITT of different length and technical content. Acceleration points were plotted on a plot
(g-g diagram) and they were enclosed in an ellipse. A correlation analysis was conducted between
the area of the ellipse and the final ITT ranking. It was hypothesized that a larger area was associated
to a better performance. An analytical model for the bike-cyclist system dynamics was used to
conduct a parametric analysis on the influence of riding position on the shape of the g-g diagram. A
moderate (n=27, r=-0.40, p=0.038) and a very large (n=26, r=-0.83, p<0.0001) association were found
between the area of the enclosing ellipse and the final ranking in the two ITT. Interestingly, this
association was larger in the shorter race with higher technical content. The analytical model
suggested that maximal decelerations are highly influenced by the cycling position, road slope and
speed. This investigation, for the first time, explores a novel methodology that can provide insights
into bike handling, a large unexplored area of cycling performance.
Introduction
In road cycling, the individual time trial (ITT), nicknamed the ‘race of truth’, is an event
where riders perform alone against the clock (Earnest et al., 2009). Professional ITT specialists are
distinguished by exceptionally high values of power output at the onset of blood lactate accumulation
(Padilla et al., 1999) and by their ability to maintain these high power output values for prolonged
periods of time in the aero-position (Gnehm et al., 1997). In addition, many authors recognised the
importance of bike handling or ‘technical’ skills in high-speed courses with sharp corners
(Jeukendrup et al., 2000) and technical content (e.g. technical descents), either from a safety (Fonda,
Sarabon, Blacklock, et al., 2014; Fonda, Sarabon, & Lee, 2014) and a performance perspective
(Phillips & Hopkins, 2020). In spite of its popularity among the community of coaches and sport
scientists, bike handling still lacks a precise definition and an objective assessment methodology that
can be used to differentiate, discriminate and characterize technical skills in races.
To appreciate the influence of different riding positions and environmental (e.g. wind,
altimetry profile) and physiological factors on ITT performance, several cycling locomotion models
(Olds, 2001) have been used (Jeukendrup & Martin, 2001). However, the vast majority of the existing
locomotion models (e.g. those inherited from the seminal work of P.E. Di Prampero (di Prampero et
al., 1979) such as (Martin et al., 1998)), are mono-dimensional as they only equate propulsive and
resistive forces in the longitudinal direction to compute how the power flows from the spinning legs
of the rider to the rear wheel of the bike (Ingen Schenau & Cavanagh, 1990). In reality, the forces
available to the riders in their control of the bike are derived at the tyre-road interface, and they act
in both the lateral and the longitudinal direction (Kooijman & Schwab, 2013). Indeed, substantial
lateral forces arise when a rider is negotiating a curve, and they constitute the centripetal force needed
to make the rider follow the curved trajectory.
The magnitudes of the forces generated at the tyre contact patches are the product of the
vertical load acting on the single tyre and a tyre-road friction coefficient (Muller et al., 2003). If the
product of the vertical load and the tyre-road friction coefficient actually exceeds a maximal limit of
adherence, then the interested tyre loses the grip on the road surface. This means that physics imposes
limits to the maximal longitudinal and lateral forces that can be generated at the tyre-road interfaces
and hence to the longitudinal and lateral accelerations that the rider can sustain. These limits are
influenced by a multitude of uncontrollable factors like road condition (e.g., wet vs. dry), but also by
riding position and riding style. On this note, the rider with better bike handling abilities is thought
to be the one who can tolerate higher accelerations and push the bike to the limits to gain competitive
advantage. However, at the moment, these considerations remain anecdotal. In a recent simulation
study, it has been suggested that riders who can sustain larger lateral accelerations and have a better
bike control, can complete corners at higher speeds and deliver lower power output levels to restore
the cruise speed after a turn (Zignoli, 2020). Therefore, to make a step forward in the assessment of
real and ‘curvilinear’ ITT performance bringing to light the influence of bike handling, models of
cycling locomotion that can take into account forces acting along both the longitudinal and the lateral
direction are needed (Zignoli & Biral, 2020).
In the world of racing motorcycles, bike-handling received so much more attention
(D’Artibale et al., 2018; Tanelli et al., 2014). Nevertheless, given that bicycles and motorcycles are
both single-track vehicles with similar dynamics (Kooijman & Schwab, 2013), inductive reasoning
suggests that a number of concepts can be transferred between the two disciplines. For example, the
g-g diagram (Rice, 1973) (i.e. a graph where the lateral acceleration points are plotted against the
longitudinal acceleration points) is extensively used racing motorcycles (Biral & Lot, 2009) to
express the acceleration limits imposed by the tyre-road interaction using the friction circle, defined
by the equation:
!
"!
#$
%
"&
!
"#
#$
%
"' (
Where ax and ay are the longitudinal and lateral accelerations, µ is the tyre-road friction
coefficient, and g is the constant of gravity. If the lateral and longitudinal accelerations experienced
by the riders fall in the friction circle, then it means that the tyres are working safely within their grip
limits. Conversely, if the accelerations are close to the limits of the friction circle, then the tyres are
close to their grip limits.
Interestingly, in the g-g diagram of Fig. 1A, lateral and longitudinal accelerations during
performance riding in 125cc and 1000cc engine motorcycles, and individual time trial (ITT) cycling
are compared and can be used to assess how the rider combines braking and steering (Biral et al.,
2010, 2005; Rice, 1973). For example, if riders exhibit a cross-like shape of the g-g diagram, it means
that they have the tendency to brake and then turn with two distinct actions. On the contrary, a more
elliptical shape of the g-g diagram, express strong brake and steer actions at the same time. Since
most of the braking action occurs at the front wheel, steering and braking at the same time engages
the front tyre closer to its limit, with less margin to correct disturbances and increasing the risk of
falling. In Fig. 1A, an important difference with the motorsports can be highlighted. In fact, by their
nature, motorcycles exhibit larger combination of accelerations/decelerations, and this is because they
can deliver high power outputs while cornering by using the accelerator throttle with no need to spin
the pedals. To express the distribution of the acceleration in a single metrics and promote easier
comparisons between riding styles, it is convenient to enclose the acceleration points in an
approximating ellipse (Fig. 1A) (where axes are given by multiples of the SD of the accelerations in
the two directions) and to use the area of this ellipse to evaluate how close the riders operate to the
limits imposed by the friction circle.
Figure 1A: The g-g diagrams' basic concept is to plot longitudinal (ax) versus lateral (ay) accelerations of a vehicle, scaled with
respect to gravity. Here, the the g-g diagram for representative 125cc motorcycles, 1000cc motorcycles and time trial bicycles is
provided as a reference. Motorcycle data kindly donated by F. Biral. Cyclist data from the present study.
As previously mentioned, by changing their body positions the riders can greatly affect the
load transfer between the bike tyres and have direct influence on force and acceleration limits.
However, the position of the rider is not the only determinant of the load transfer. In fact, inertial
components and aerodynamic resistive forces also play a large role. During normal ITT cycling (Fig.
2A(A)), cyclists position their arms on aero-bars and pedal in a streamlined position, balancing
between comfort, efficiency and aerodynamics (Gnehm et al., 1997). In the upright position (Fig.
2A(B)), riders position their hands on the handlebars, hence raising the system’s centre of gravity. In
some cases (Merkes et al., 2019), riders stand out of the saddle (Fig. 2A(C)), holding onto the
handlebars, in order to deliver high power outputs (Bouillod & Grappe, 2018) and allow for higher
longitudinal accelerations (positive portion of the g-g diagram). In this position, riders place a high
weight on the front tyre, and also incur high air resistive forces. In the tucked position (Fig. 2A(D)),
riders move downward and backward, placing their hands on the lateral handlebars. This movement
transfers substantial weight to the rear tyre therefore allowing higher tyre-road friction forces at the
rear allowing higher maximal deceleration values (negative portion of the g-g diagram). In the
‘Froome’ downhill position (Blocken et al., 2018) (Fig. 2A(D)), riders move down and forward,
almost placing their chests on the aero-bars. In this position, substantial weight is placed on the front
wheel and, while air drag forces are minimised, limiting the maximal deceleration values.
Interestingly, the ‘Froome’ position has been recently banned by the cycling governing body (UCI)
for safety reasons (Rider Safety New Regulations in 2021: Explanation Guide for Organizers, Teams
and Riders, 2021)).
Figure 2A: Most used riding positions during an individual time trial: normal (A), upright (B), standing (C), tucked (D) and ‘Froome’
downhill (E).
The riding positions shown in Fig. 2A are commonly used during professional ITT.
However, ways to objectively evaluate the influence of these positions on bike handling during races
are not known, neither we have ways to evaluate how close the riders go to the limits imposed by the
friction circle. Therefore, this study aimed at using the g-g diagram (Rice, 1973) and a model of
lateral and longitudinal cycling locomotion (Zignoli & Biral, 2020) to address these unresolved
issues. In particular, it was hypothesised that the area of ellipse enclosing the acceleration points in
the g-g diagram was correlated with the final performance time in professional ITT.
Methods
Professional racing data
GPS data were collected in professional cyclists during two ITT Giro d’Italia stages with
different technical content: A) a stage with limited technical content: 16th stage on 22nd May 2018 in
Rovereto and B) a stage with relevant technical content: 21st stage on 2nd Jun 2019 in Verona. During
the Rovereto stage, 27 riders (weight: 65.5(5.9) kg, height: 1.79(0.08) m) contributed with data
providing the fit GPS and power output files (Garmin Edge 520, 720, 1030, or Sigma Rox 11, 12, 1
Hz of sampling frequency). The Rovereto stage counted a total of 161 participants (winner’s time: 44
min and 0 sec) and was raced on dry asphalt and dry weather conditions (wind: ~2.6 m/s N/S, Temp:
24-28 °C). The Rovereto stage had almost no vertical gain, limited downhill sections and a reduced
number of 90-deg or hair-pin turns. During the Verona stage, 26 riders (weight: 66.6(6.8) kg, height:
1.79(0.06) m) contributed with data. The Verona stage counted a total of 142 participants (winner’s
time: 22 min and 7 sec) and was raced on dry asphalt and dry/hot weather conditions (wind: ~2.7 m/s
NE/SW, Temp: >30 °C). The Verona stage had 200 m of vertical gain and a 5 km -6.5% downhill
section, characterised by a number of 90-deg and hair-pin turns. In both races, clothoids (Bertolazzi
et al., 2005) were used to fit the GPS data every 0.25 m.
This is an observational study conducted retrospectively. All the cyclists gave their written
informed consent to let the head-scientists using the GPS fit data files for scientific purposes. All the
data files were anonymised prior to the inclusion in the dataset and for the modelling analysis. The
study conforms to the Code of Ethics of the World Medical Association (Declaration of Helsinki).
The study has been conducted in agreement with the guidelines of the Ethical Committee of the
University of Trento (n. 2021-010). The same data collection procedure is routinely performed by the
riders during races and training sessions; therefore, it could not cause any harm to the riders nor to
their safety and performance.
The analytical model
A bi-dimensional cycling locomotion model was used in this study to estimate the
longitudinal and lateral accelerations during the races and to interpret the g-g diagrams. The model
consists in a simplified inverted-pendulum rider-bike model (Fig. 3A) already adopted to predict
racing trajectories in ITT races (Zignoli, 2020; Zignoli & Biral, 2020). The main difference between
this and other relevant mono-dimensional models available from the cycling literature (di Prampero
et al., 1979; Ingen Schenau & Cavanagh, 1990; Martin et al., 1998), is that this model takes into
account both longitudinal and lateral forces on the road plane. The longitudinal forces are constituted
by the propelling (i.e., the power output reproduced at the rear tyre) and resistive (i.e., braking,
aerodynamic, rolling and gravitational) forces, and their balance determines how the riders
accelerate/decelerate forward in the anterior-posterior direction (which is perpendicular to the frontal
plane of the rider). The forces acting in the lateral direction (which is perpendicular to the sagittal
plane of the rider) sum up to build the centripetal forces that make the rider follow a curved trajectory.
The rider-bike model adopted here involve multiple actions from the rider, who needs to deliver a
power output and to act on the steering angle to complete the curves. To estimate the actions of the
rider, we adopted an optimal control approach, which is a state-of-the-art framework for the
simulation, the tracking and the prediction of cycling locomotion (De Jong et al., 2017; Gordon, 2005;
Wolf et al., 2019; Zignoli & Biral, 2020). In our optimal control problem, a solver for dynamic
optimisation problems (Biral et al., 2015) was asked to find the power output and the steering angle
distributions, so the differences between the experimental and simulated trajectories (in the least-
square sense) were minimised. The Maple software (Maplesoft, ver. 2018) was used to write (R Lot
& Da Lio, 2004) and manipulate the equations of motion, which were used to generate the simulated
trajectories. They are reported with greater level of details elsewhere (Zignoli, 2020; Zignoli & Biral,
2020)). A custom written Maple package called XOptima (Biral et al., 2015) was used to numerically
solve the dynamic optimisation problem. A set of curvilinear coordinates (Roberto Lot & Biral, 2014)
were used in the description of the position along the trajectory of each cyclist, and hence a curvilinear
abscissa was used as independent variable.
Figure 3A: The simplified rider-bike model used to examine the influence of rider position, velocity and road conditions on the
performance envelop. The position of the centre of gravity is defined by parameters a, b and h. The length of the bike is defined as
the sum of a + b. We assume that: 1) the air drag-resistive forces (Fw) are applied to the centre of mass; 2) the breaking forces Sf
and Sr are applied to the front and rear contact points, respectively; 3) the normal forces Nf and Nr are applied at the front and rear
contact points, respectively; 4) the lateral forces Ff and Fr are applied at the front and rear contact points, respectively; 5)
longitudinal and lateral acceleration components (i.e. m
•
ax and m
•
ay) are applied to the centre of mass of the system together
with the weight component (i.e. m
・
g, always vertical). The roll angle ɸ represent the roll angle, which is the angle between the
vertical line connecting the centre of mass and the point in the middle between the two contact points. The angle ɸb represents the
roll angle of the bike, which might be different from ɸ, especially in turns.
One of the advantages of this model is that a direct relationship between the roll angle and
the lateral acceleration can be derived for steady turns. The values of the tyre-road friction coefficient
directly provide the maximal roll angles that the system can sustain: fMAX=atan(µ) (i.e. ~42 deg in
dry conditions (Muller et al., 2003) with µ=1). It is worth noting that the roll angle does not indicate
the angle between the bike frame and the road surface (ɸb, Fig. 3A), but the angle that the centre of
gravity creates with the road surface.
Assessing the breaking limits
The model presented in the previous section, was used to estimate the braking limits of the
different riding positions. In Fig. 3A Sf and Sr are the forces developed at the front and rear tyre
contact patches in the longitudinal direction; while Ff and Fr are the forces developed at the front and
rear tyre contact patches in the lateral direction. Both the lateral and longitudinal forces are a product
of the vertical loads acting on the tyres (i.e., Nf and Nr) and the road friction coefficient. It follows
that, for a given normal load, the tyre provides some amount of force before losing grip. The
magnitude of the normal loads on the tyres are largely determined by the position of the centre of
gravity and by the forces acting on the system (i.e., inertia, gravitational, aerodynamic and rolling
resistive forces). After computing the lateral and the longitudinal acceleration values (see previous
Section), the area of the ellipse that enclosed the data could be computed as (Schubert & Kirchner,
2014):
")*"+*,,-./* 0 1 2+3$%&'(" 2
4
5)25"
+
Where c0.95,2 is the value of the inverse of the c-square cumulative distribution function with
2 degrees of freedom at the 95% probability (i.e., ~5.99), and l1 and l2 are the eigenvalues of the
covariance matrix computed from the lateral and longitudinal accelerations. The riding positions
depicted in Fig. 2A are characterised by different values of the position of the centre of gravity
(described by the three parameters: a (the distance from the front wheel), b (i.e., the distance from
the rear wheel) and h (i.e., the distance from the midline between the contact points), Fig. 2A and
Tab. 1). These values were used to compute the limits to the maximal longitudinal deceleration (axmin)
of the different riding positions.
To compute these limits as a function of the lateral acceleration, the following equation was used:
"!*+, 0678
9
:
;
<=-<>< ?
>2
@
(&"#
"
A
$%'
BC>
Where β is the slope of the road and FW is the aerodynamic force component (Martin et al.,
1998) (computed as 0.5・ρ・CDA・v2, with ρ air density of 1.23 kg/m3 and CDA values (Tab. 1)
according to the literature) (Barry et al., 2015; Blocken et al., 2018; Crouch et al., 2017; Merkes et
al., 2019) and L is the wheelbase (i.e., sum of a and b in Fig. 3A). This equation can be obtained from
the equation of motion, imposing Nr=0, i.e.: when the load on the rear wheel is zero and there is no
chance to stop the bike acting on the friction force at the rear wheel, i.e., Sr (Fig. 3A). Restricting
limits are computed for different velocities and different road slopes and maximal deceleration values
cannot exceed these limits. When cycling downhill (β<0), the maximal deceleration values are
reduced by the action of gravity. Conversely, at higher speeds, the aerodynamic force can help with
the braking action. Only the positions adopted while braking (B-D-E, Fig. 2A) were considered for
the analysis of the braking limits.
Statistics
After assumption verifications (normality, linearity and homogeneity of variances), the
Pearson’s correlation coefficient (r) was calculated along with the coefficient of determination R2
between the area of the ellipse enclosing the acceleration points and three variables expressing the
final ITT performance, i.e.: 1) the final time (computed as the difference with the winner’s time) 2)
the final ranking at each stage and 3) the log-transformed final ranking (Phillips & Hopkins, 2017).
Statistical analyses were conducted separately for the two ITT stages classified by technical content.
The following criteria were adopted to interpret the magnitude of the correlation r between the
measures: < 0.1 trivial, 0.1-0.3 small, 0.3-0.5 moderate, 0.5-0.7 large, 0.7-0.9 very large, and 0.9-1.0
almost perfect. Regression lines were bootstrapped 1000 times to calculate 95% confidence intervals
[CI] and to provide further information on the dispersion of the regression coefficient around its
expected value (Cumming, 2014). Statistical significance was declared when p < 0.05. All analyses
were conducted with GraphPad software (ver. 6). In the Results, data are presented as mean (SD).
Results
The g-g diagram (Fig. 4) indicates that, on average, cyclists perform very close to the limits
imposed by the physics of the system on the lateral accelerations (x-axis of the g-g diagram). The
same experimental values are repeated in the three panels of Fig. 4. However, in the three different
panels, the limits to the maximal deceleration values computed from the equation of motion (as
previously detailed) are also reported for different road slopes and longitudinal velocities. These
limits are shown in Fig. 4 for the different riding positions and are reported in Tab. 1 in the case of
no lateral accelerations (i.e., ay=0).
Figure 4: The g-g diagram collectively presents the resulting lateral (ay) and longitudinal (ax) normalised accelerations for all riders
in our sample (grey open small circles). The background shaded-grey area represents the limits imposed by the friction coefficient μ.
The outer line (dashed grey) indicates the limits of adherence for a dry road (Muller et al., 2003) that approximatively results in a
maximal roll angle of ~42 deg and a maximal lateral acceleration of aymax=±1
・
g. In each panel adherence limits are given for the
‘Froome’ descending position (left), for the seated position (centre) and for the ‘tucked’ braking position (right). An analytical model
was used to compute the safety margins (i.e.: the limits to the braking actions in different conditions): downhill slope of -6.5% at 30
km/h (black thin line), downhill slope of -6.5% at 60 km/h (black thin dashed line), flat road at 30 km/h (black thick continuous line)
and flat road at 60 km/h (black dotted line).
Centre of mass position and CDA
Position
a (%L)
b (%L)
h (%L)
CDA (m2)
Regular TT (A, Fig. 1)
40%
60%
160%
~0.24
Seated (B, Fig. 1)
60%
40%
180%
~0.28
Standing (C, Fig. 1)
30%
70%
200%
~0.34
Tucked (D, Fig. 1)
80%
20%
140%
~0.21
‘Froome’ (E, Fig. 1)
20%
80%
120%
~0.19
Maximal deceleration values
Position
60 km/h -6.5%
30 km/h -6.5%
60 km/h 0%
30 km/h 0%
‘Froome’
0.09・g
<-0.01・g
0.25・g
0.19・g
Seated
0.25・g
0.20・g
0.36・g
0.32・g
Tucked
0.43・g
0.38・g
0.6・g
0.52・g
Tab. 1: Position of the centre of gravity has been defined by means of three parameters: a (i.e., the distance from the front wheel),
b (i.e., the distance from the rear wheel) and h (the distance from the midline between the contact points). All the values are given
as a percentage of the wheelbase L (with L=a+b). An average value of L=0.852 m was used. Five different riding positions were
considered, and different values of CDA for those positions were reported.
Maximal normalised deceleration values for the different riding positions, different speeds and different road slopes. Absolute
values are given in multiples of the constant of gravity g.
The correlation analysis (Fig. 5) resulted in a moderate significant negative association
between the area of the enclosing ellipse and the final ranking in the Rovereto stage. A very large
negative significant association was found between the area of the enclosing ellipse and the final
ranking in the Verona stage. Results of the statistical analyses are summarised in Tab. 2.
Figure 5: Correlation between the area of the ellipse (g2) that encloses the experimental accelerations and the logarithm of the final
ranking in Rovereto (A) and in Verona (B) stage.
Stage
Final time
(difference
with the
winner)
Final time
(percentage
difference
with the
winner)
Final
rank
Area ellipse
Correlation
with final
rank
Correlation with
log of the final
rank
Correlation with
final time
(difference with
the winner)
Rovereto
(n=27)
227(89) s
9.4(3.7) %
84(48)
0.026(0.003) g2
-0.40[-0.67 to -
0.02] (R2=
0.161,
p<0.038)
-0.44[-0.70 to -0.08]
(R2= 0.2, p<0.0187)
-0.45[-0.71 to -0.09]
(R2= 0.2,
p<0.0.0175)
Verona (n=26)
90(48)
6.8(3.7) %
52(35)
0.069(0.006) g2
-0.83[-0.91 to -
0.66] (R2=
0.69,
p<0.0001)
-0.81[-0.91 to -0.62]
(R2= 0.66,
p<0.0001)
-0.86[-0.94 to -0.70]
(R2= 0.74,
p<0.0001)
Tab. 2: Results of the statistical analyses (mean(SD)). Results of the correlation analyses are presented as: r [CI] (R2, p-value).
Discussion
Bike handling or ‘technical skills’ are often listed in the determinants of the cycling
performance (Jeukendrup et al., 2000; Phillips & Hopkins, 2020), but they have been poorly
investigated and they have not been taken into account in the existing mono-dimensional cycling
locomotion models. In this work, we adopted a methodology borrowed from motorcycle racing to
provide an objective evaluation of bike-handling during ITT races. We hypothesised that the area of
ellipse enclosing the acceleration points in the g-g diagram was correlated with the final performance
time in professional ITT. According to our hypothesis, we found meaningful correlations between
the area of the ellipse in the g-g diagram and the final performance time and ranking in two
professional ITT races.
The g-g diagram (Fig. 4) can be used to spot maximal acceleration values that the riders
sustained during the races. Results suggest that the magnitude of the maximal longitudinal
deceleration was smaller than 0.2・g. These values are close to the limits imposed by physics (i.e.,
rear wheel lift) and estimated by the analytical model for the seated position (Tab. 1 and central
panel, Fig. 1). In the lateral direction, maximal acceleration values were around 0.9・g, meaning that
in the examined races, riders could reach roll angle values of ~38-40 deg. The adopted analytical
model (Fig. 3A) suggested that the maximal deceleration values could improve if: 1) cyclists move
their body down and backwards, 2) they are cycling on a flat road and 3) they are travelling at very
high speeds (>60 km/h). This means that, if cyclists were riding downhill in ‘Froome’ position and
they were approaching a corner, they could move in a seated position and use their upper body as an
air brake before moving in a tucked position and pull the brake levers. In fact, Tab. 1 and Fig. 4
highlight that maximal deceleration values (i.e., safety margins) improve by changing position from
‘Froome’ to seated, and from seated to tucked. In a tucked position, the low centre of mass reduces
the tendency of the rear wheel to lift off during hard braking actions. Recently, the cycling governing
body (UCI), in a published safety guide (Rider Safety New Regulations in 2021: Explanation Guide
for Organizers, Teams and Riders, 2021) has banned the ‘Froome’ position. The narrow braking
limits presented in Tab. 1 and Fig. 4, might be partly used to support and discuss this choice.
As expected, the association between the area of the ellipse and the final ITT performance
was larger in the race with greater technical content (i.e., Verona) (Tab. 2). In the longer and less
technical stage (i.e., Rovereto) the absolute values of the ellipse area were smaller, and only
moderately associated with the ITT performance (Tab. 2). However, we adopted a method (Schubert
& Kirchner, 2014) that preserves the area of ellipse regardless the sample size (i.e. the length of the
course), which means that the area of the ellipse should be independent from the length of the stage.
This may suggest that during longer ITT stages, cyclists do not race close to the limits of handling,
most probably because the expected time gains are irrelevant if compared to the total duration of the
race. It is important to highlight that not all riders were motivated to perform the stage at all costs,
due to energy preservation strategies or other reasons (Jeukendrup et al., 2000). However, the results
suggest that the cyclists who wanted to be in front at the end of the stage were willing to brake and
turn at the limits of what was physically possible.
The applicability of the results of this study is hindered by assumptions and limitations. First,
accelerations were computed from GPS data, not from inertial measurements (e.g., inertial
measurement unit) which are usually adopted to collect experimental inertial data. However, a
validated mathematical model of the longitudinal and the lateral dynamics of a cyclist (Zignoli &
Biral, 2020) was used to fit the experimental speed and trajectory. As a consequence, realistic and
smooth signals for the accelerations along the longitudinal and lateral direction could be obtained.
Second, there was no direct information on a number of parameters, i.e.: the actual cycling position,
the drag coefficient CD and the frontal area Af. Values were retrieved from the literature or estimated
with equations fitting experimental data. Third, the analytical model adopted is a simplified
representation of reality, where the mass of the bike-cyclist system is collapsed into a point mass (but
the roll inertia is included). This is, of course, an important assumption made in the attempt to reduce
the mathematical complexity and obtain a simple equation for maximal deceleration values.
This research work is innovative in two main aspects: 1) it adopts a bi-dimensional state-of-
the-art cycling model (Zignoli & Biral, 2020) to estimate longitudinal and lateral accelerations from
GPS data during races, and 2) it applies the principle of the g-g diagram (Rice, 1973) for the first time
in ITT races to study bike handling. Guided by the results of the present performance analysis (i.e.,
g-g diagram and analytical model), riders can learn how the different body positions, road slopes and
aerodynamic resistive forces impact bike handling and the handling limits imposed by physics.
Conclusions
Recent advances in numerical optimisation techniques, modelling capabilities and GPS
technologies, are giving researchers new tools to fit and interpret GPS data collected during cycling
races. The focus of this work was the interpretation of the racing g-g diagram (a concept borrowed
from the world of racing motorcycles) during two professional ITT with different technical content.
We showed that there was a meaningful correlation between the area of the ellipse enclosing the
longitudinal and lateral accelerations of a rider during a race and its final ranking. The underlying
association was especially large in the ITT with greater technical content. We also showed that, by
means of an analytical model of cycling locomotion, it is possible to objectively evaluate the braking
limits of different cycling positions. This study therefore can provide new insights into bike handling
and cycling performance.
Disclosure statement
No potential conflict of interest was reported by the authors.
Data availability statement
Data associated to this manuscript will not be shared.
References
Barry, N., Burton, D., Sheridan, J., Thompson, M., & Brown, N. A. (2015). Aerodynamic
performance and riding posture in road cycling and triathlon. Proceedings of the Institution
of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, 229(1),
28–38. https://doi.org/10.1177/1754337114549876
Bertolazzi, E., Biral, F., & Da Lio, M. (2005). Symbolic–numeric indirect method for solving
optimal control problems for large multibody systems. Multibody System Dynamics, 13(2),
233–252.
Biral, F., Bertolazzi, E., & Bosetti, P. (2015). Notes on Numerical Methods for Solving Optimal
Control Problems. IEEJ Journal of Industry Applications, 5, 154–166.
Biral, F., Da Lio, M., & Bertolazzi, E. (2005). Combining safety margins and user preferences into
a driving criterion for optimal control-based computation of reference maneuvers for an
ADAS of the next generation. IEEE Proceedings. Intelligent Vehicles Symposium, 2005.,
36–41. https://doi.org/10.1109/IVS.2005.1505074
Biral, F., Da Lio, M., Lot, R., & Sartori, R. (2010). An intelligent curve warning system for
powered two wheel vehicles. European Transport Research Review, 2(3), 147–156.
https://doi.org/10.1007/s12544-010-0033-2
Biral, F., & Lot, R. (2009). An interpretative model of gg diagrams of racing motorcycle.
Proceedings of the 3rd ICMEM International Conference on Mechanical Engineering and
Mechanics, 21–23.
Blocken, B., van Druenen, T., Toparlar, Y., & Andrianne, T. (2018). Aerodynamic analysis of
different cyclist hill descent positions. Journal of Wind Engineering and Industrial
Aerodynamics, 181, 27–45. https://doi.org/10.1016/j.jweia.2018.08.010
Bouillod, A., & Grappe, F. (2018). Physiological and biomechanical responses between seated and
standing positions during distance‑based uphill time trials in elite cyclists. Journal of Sports
Sciences, 36(10), 1173–1178. https://doi.org/10.1080/02640414.2017.1363902
Crouch, T. N., Burton, D., LaBry, Z. A., & Blair, K. B. (2017). Riding against the wind: A review
of competition cycling aerodynamics. Sports Engineering, 20(2), 81–110.
https://doi.org/10.1007/s12283-017-0234-1
Cumming, G. (2014). The New Statistics: Why and How. Psychological Science, 25(1), 7–29.
https://doi.org/10.1177/0956797613504966
D’Artibale, E., Laursen, P. B., & Cronin, J. B. (2018). Human Performance in Motorcycle Road
Racing: A Review of the Literature. Sports Medicine, 48(6), 1345–1356.
https://doi.org/10.1007/s40279-018-0895-3
De Jong, J., Fokkink, R., Olsder, G. J., & Schwab, A. (2017). The individual time trial as an
optimal control problem. Proceedings of the Institution of Mechanical Engineers, Part P:
Journal of Sports Engineering and Technology, 231(3), 200–206.
di Prampero, P., Cortili, G., Mognoni, P., & Saibene, F. (1979). Equation of motion of a cyclist.
Journal of Applied Physiology, 47(1), 201–206.
Earnest, C. P., Foster, C., Hoyos, J., Muniesa, C., Santalla, A., & Lucia, A. (2009). Time trial
exertion traits of cycling’s Grand Tours. International Journal of Sports Medicine, 30(04),
240–244.
Fonda, B., Sarabon, N., Blacklock, R., & Li, F. (2014). Effects of changing seat height on bike
handling. Journal of Science and Cycling, 3(2), 19.
Fonda, B., Sarabon, N., & Lee, F. (2014). A new test battery to assess bike handling skills of
experienced and inexperienced cyclists. Journal of Science and Cycling, 3(2), 18.
Gnehm, P., Reichenbach, S., Altpeter, E., Widmer, H., & Hoppeler, H. (1997). Influence of
different racing positions on metabolic cost in elite cyclists. Medicine and Science in Sports
and Exercise, 29(6), 818–823.
Gordon, S. (2005). Optimising distribution of power during a cycling time trial. Sports Engineering,
8(2), 81–90. https://doi.org/10.1007/BF02844006
Ingen Schenau, G. J. van, & Cavanagh, P. R. (1990). Power equations in endurance sports. Journal
of Biomechanics, 23(9), 865–881. https://doi.org/10.1016/0021-9290(90)90352-4
Jeukendrup, A. E., Craig, N. P., & Hawley, J. A. (2000). The bioenergetics of world class cycling.
Journal of Science and Medicine in Sport, 3(4), 414–433.
Jeukendrup, A. E., & Martin, J. (2001). Improving cycling performance. Sports Medicine, 31(7),
559–569.
Kooijman, J. D. G., & Schwab, A. L. (2013). A review on bicycle and motorcycle rider control with
a perspective on handling qualities. Vehicle System Dynamics, 51(11), 1722–1764.
https://doi.org/10.1080/00423114.2013.824990
Lot, R, & Da Lio, M. (2004). A symbolic approach for automatic generation of the equations of
motion of multibody systems. Multibody System Dynamics, 12(2), 147–172.
Lot, Roberto, & Biral, F. (2014). A curvilinear abscissa approach for the lap time optimization of
racing vehicles. IFAC Proceedings Volumes, 47(3), 7559–7565.
Martin, J. C., Milliken, D. L., Cobb, J. E., McFadden, K. L., & Coggan, A. R. (1998). Validation of
a Mathematical Model for Road Cycling Power. Journal of Applied Biomechanics, 14(3),
276–291. https://doi.org/10.1123/jab.14.3.276
Merkes, P. F. J., Menaspà, P., & Abbiss, C. R. (2019). Reducing Aerodynamic Drag by Adopting a
Novel Road-Cycling Sprint Position. International Journal of Sports Physiology and
Performance, 14(6), 733–738. https://doi.org/10.1123/ijspp.2018-0560
Muller, S., Uchanski, M., & Hedrick, K. (2003). Estimation of the maximum tire-road friction
coefficient. Journal of Dynamic Systems, Measurement, and Control, 125(4), 607–617.
Olds, T. (2001). Modelling human locomotion. Sports Medicine, 31(7), 497–509.
Padilla, S., Mujika, I., Cuesta, G., & Goiriena, J. J. (1999). Level ground and uphill cycling ability
in professional road cycling: Medicine & Science in Sports & Exercise, 31(6), 878–885.
https://doi.org/10.1097/00005768-199906000-00017
Phillips, K. E., & Hopkins, W. G. (2017). Performance Relationships in Timed and Mass-Start
Events for Elite Omnium Cyclists. International Journal of Sports Physiology and
Performance, 12(5), 628–633. https://doi.org/10.1123/ijspp.2016-0204
Phillips, K. E., & Hopkins, W. G. (2020). Determinants of Cycling Performance: A Review of the
Dimensions and Features Regulating Performance in Elite Cycling Competitions. Sports
Medicine - Open, 6(1), 23. https://doi.org/10.1186/s40798-020-00252-z
Rice, R. S. (1973). Measuring car-driver interaction with the gg diagram (No. 0148–7191). SAE
Technical Paper.
Schubert, P., & Kirchner, M. (2014). Ellipse area calculations and their applicability in
posturography. Gait & Posture, 39(1), 518–522.
https://doi.org/10.1016/j.gaitpost.2013.09.001
Tanelli, M., Corno, M., & Savaresi, S. M. (Eds.). (2014). Modelling, Simulation and Control of
Two-Wheeled Vehicles: Tanelli/Modelling, Simulation and Control of Two-Wheeled
Vehicles. John Wiley & Sons, Ltd. https://doi.org/10.1002/9781118536391
Rider Safety New Regulations in 2021: Explanation Guide for Organizers, Teams and Riders,
(2021). https://www.uci.org/docs/default-source/default-document-library/2021-uci-guide-
safety-en.pdf
Wolf, S., Biral, F., & Saupe, D. (2019). Adaptive feedback system for optimal pacing strategies in
road cycling. Sports Engineering, 22(1), 6.
Zignoli, A. (2020). Influence of corners and road conditions on cycling individual time trial
performance and ‘optimal’ pacing strategy: A simulation study. Proceedings of the
Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and
Technology, 175433712097487. https://doi.org/10.1177/1754337120974872
Zignoli, A., & Biral, F. (2020). Prediction of pacing and cornering strategies during cycling
individual time trials with optimal control. Sports Engineering, 23(1), 13.
https://doi.org/10.1007/s12283-020-00326-x
