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In¯ uence of tyre pressure and vertical load on coe cient of
rolling resistance and simulated cycling performance
F. GRAPPE²*, R. CANDAU², B. BARBIE R², M. D. HOFFMAN³, A. BEL LI²and
J.-D. ROUILLON²
²Laboratoire des Sciences du Sport, UFR-STAPS de BesancË on, 2 Place Saint
Jacques, 25030 BesancË on cedex, France
³Sports Performance and Technology Laboratory and Department of Physical
Medicine and Rehabilitation, Medical College of Wisconsin and VA Medical
Center, Milwaukee, WN 53295, USA
Keywords: Extra loading; Rolling resistance; Hysteresis loss; Elasticity;
Performance simulation.
The coe cient of rolling resistance (C
r
) for pneumatic tyres is dependent on
hysteresis loss from tyre deformation which is aŒected by the vertical force
applied to the tyres (F
v
) and the tyre in¯ ation pressure (P
r
). The purpose of this
paper was to determine the relative in¯ uence of ® ve diŒerent levels of P
r
and four
diŒerent levels of F
v
on C
r
and to examine the relationships of C
r
with P
r
and F
v
during cycling locomotion. F
v
was modi® ed through carriage of additional mass
by the subject. C
r
was determined with the coasting deceleration method from
measur ements performed in a level hallway. Iterations minimizing the sum of the
squared diŒerence between the actual deceleration distance and a predicted
deceleration distance were used to determine C
r
. This latter distance was
computed from a derivation based on Newton’s second law applied to the forces
opposing motion. C
r
was described by a hyperbolic function of P
r
(C
r
=0.1071
P
r
Ð
0.477
,r
2
=0.99, p<0.05), decreasing 62.4% from 150 kPa (C
r
=0.0101) to
1200 kPa (C
r
=0.0038). F
v
was related to C
r
by a polynomial function
(C
r
=1.92
.
10
Ð
8
F
v
2
Ð2.86
.
10
Ð
5
F
v
+ 0.0142, r
2
=0.99, p=0.084), with an added
mass of 15 kg (C
r
=0.0040) resulting in an 11.4% increase in C
r
compared with
no added mass (C
r
=0.0035). From this study, it is concluded that the
relationships of P
r
and F
v
with C
r
for cycling are non-linear. Furthermore, a
simulation model shows that changes in P
r
and F
v
of the magnitude examined
here have an important eŒect on competitive cycling performance.
1. Introduction
Decreases in rolling resistance (R
r
, N; see appendix for the list of abbreviations)
have been a major contributing factor to the improvements in cycling
performance observed during the past 20 years. R
r
has been reduced through
the development of tyres allowing higher in¯ ation pressures (P
r
, kPa) and lighter
bicycles which have reduced the vertical force applied to the tyres (F
v
, N). It has
been established that the major source of R
r
in a pneumatic tyre is from
hysteresis, or non-elastic deformations, occurring to the tyre when compressed on
a solid surface (Tabor 1955, Schuring 1980, Kauzlarich and Thacker 1985,
*Author for correspondence.
ERGONOMICS, 1999, VOL. 10, 1361± 1371
Ergonom ics ISSN 001 4-0139 print/ISSN 1366-5847 online Ó199 9 Taylor & Francis Ltd
http://www.tandf.co.uk/JNLS/erg.htm
http://www.taylorandfrancis.com/JNLS/erg.htm
Me nard 1992). The magnitude of this deformation determines the tyre coe cient
of rolling resistance (C
r
, unitless). The two main factors that aŒect tyre
deformation are P
r
and F
v
. When rolling, some slippage also occurs, but its
contribution to the total R
r
is negligible. Other energy-dissipating mechanisms
such as adhesion between the tyre and roadway, air pumping in the tyre cavity,
and road deformation are generally estimated as insigni® cant relative to the
hysteresis phenomenon (Schuring 1980).
In contemporary cycling, the main force opposing motion of the cyclist is from
aerodynamic drag (R
a
, N), while R
r
represents a minor part of the total resistance
(R
T
, N). At a typical race speed (V
c
) of 14 m
.
s
Ð
1
,R
r
constitutes only 10% of R
T
,
although at a lower V
c
(7 m
.
s
Ð
1
), R
r
could reach 30% of R
T
(Pugh 1974, Kyle and
Edelman 1975, Di Prampero et al. 1979, 1986, Gross et al. 1983, Me nard et al.
1990, Me nard 1992, Capelli et al. 1993, Grappe et al. 1997). In most previous
studies, R
r
has been reported to be independent of V
c
and equal to the product of
C
r
and F
v
(Pugh 1974, Di Prampero et al. 1979, Kyle and Burke 1984, Davies
1980, Me
Ânard et al. 1990, Me
Ânard 1992, Capelli et al. 1993, Grappe et al. 1997,
Candau et al. 1999):
Rr5CrFv,(1)
where F
v
=Mg, where M=transported mass (kg) and g=acceleration due to
gravity (9.81 m
.
s
Ð
2
).
A recent laboratory study conducted on cycling reported a positive linear
relationship between C
r
and F
v
, and an inverse linear relationship between C
r
and P
r
(Me nard 1992). However, an earlier study conducted in the ® eld using a tricycle
reported C
r
to be inversely, but not linearly, related to P
r
(Kyle and van
Valkenburgh 1985). Moreover, previous laboratory and ® eld studies conducted on
passenger car tyres have reported C
r
to be related to P
r
and F
v
by numerous
empirical equations (Schuring 1980).
It has been reported that a decrease in C
r
of as little as 0.02% would have
important impacts on racing performance (Kyle and van Valkenburgh 1985). This
magnitude of change in C
r
could result from an increase in P
r
from 680 to 750 kPa.
Yet, a recent laboratory study concluded that alterations in P
r
from 550 to 960 kPa
were too small to be detected by metabolic measurements (Ryschon and Stray-
Gundersen 1993). Thus, changes in P
r
or F
v
could have important impacts on cycling
performance without being detectable through physiological measurements.
Additionally, to the best of our knowledge, it appears that no study has been
conducted during actual cycling locomotion to determine the mathematical
relationships for C
r
with P
r
and F
v
, or to determine the eŒect of changes in P
r
and F
v
on cycling performance.
Thus, the purpose of this paper was to examine the relationships of C
r
with P
r
and F
v
during actual cycling locomotion by using a previously described ® eld
method (Candau et al. 1996, 1999). In addition, the in¯ uence of changes in P
r
and F
v
on cycling performance during a 1 h event were estimated using a mathematical
simulation model.
2. Method
2.1. General procedure
One trained male cyclist participated in this study. All of the risks associated with the
experimental procedures used in this investigation were explained thoroughly during
1362 F. Grappe et al.
his ® rst visit to the laboratory, and he provided written informed consent. The age,
mass and height of the subject were 32 years, 66.2 kg and 1.72 m respectively.
The subject performed testing under two diŒerent conditions. For the ® rst, the
eŒect of ® ve diŒerent levels of P
r
(150, 300, 600, 900, 1200 kPa) on C
r
was tested.
Classical 32-spoked wheels were equipped with tubular tyres (Victoria Corsa Cx
22 mm, 220 g; Italy). P
r
was adjusted and controlled with a classical foot pump
(Silca, Italy; accuracy 620 kPa). For the second test condition, the eŒect of four
diŒerent levels of F
v
on C
r
was tested. Classical clincher wheels were equipped with
clincher tyres (Techno Kevelar 23 mm, 250 g, Vittoria). P
r
was maintained constant
at 1000 kPa while F
v
was modi® ed by loading the subject with additional mass (0, 5,
10, 15 kg) in a backpack. To maintain a constant eŒective frontal area for the cyclist
(AC
d
, m
2
), the size of the backpack was kept constant (perimeter of trunk and
backpack =1.1 m) by the insertion of light foam plastic material into the backpack.
Since the maximal change in backpack dimensions was kept to <0.5 cm, AC
d
was
assumed to be constant. For all tests, a classical racing bicycle of 9.8 kg was used.
2.2. Determination of C
r
C
r
was determined through coasting deceleration tests. The reproducibility (mean
absolute error =0.70% ; coe cient of va riation =0.59% ) and the sensitivity of this
method have been previously reported (Candau et al. 1996, 1999). To eliminate
disturbances due to variations in weather conditions, testing was performed on a
level 60 m indoor hallway with tiled ¯ ooring. Acceleration was achieved during the
® rst 40 m of the hallway. The cyclist then decelerates while maintaining a constant
upright position (the hands on the upper part of the handlebars) while rolling across
three timing switches. To simulate actual cycling conditions with turbulence induced
by movement of the lower limbs, the subject continued to pedal without transmitting
propulsive force to the rear wheel during each coasting trial. The timing switches
were linked to a chronometer system with an accuracy of 30 ls (Electronique
Informatique du Pilat, Jonzieux, France) from which the time (T
initial
) to travel
between the ® rst two timing switches (D
initial
=1 m) and the time (T) to travel
between the second third timing switches (D =20 m) were determined. The system
included speci® c software, an interface and a PC-like computer. Each timing switch
was 51 mm wide, with the central 15 mm measuring 1.5 mm thick and the remainder
being 1 mm thick.
Two marker strips separated by 0.5 m were placed on the ¯ oor between the
timing switches for the cyclist to use as guides to maintain straight tracking
during deceleration. The strips helped the cyclist avoid steering corrections which
could cause the tyres to side-slip and elicit a slight braking force that would
elevate the measured C
r
. When tracking was not straight, the trial was discarded.
One test procedure consisted of 30 acceptable coasting decelerations across
diŒerent initial velocities (v
0
) ranging from 2.5 to 12.8 m
.
s
Ð
1
. For the ® rst test
conditions, ® ve test procedures were performed (i.e. 5 ´30 =150 trials), and for
the second test conditions, four test procedures were performed (i.e. 4 ´30 =120
trials).
C
r
was calculated using techniques previously detailed (Candau et al. 1999).
Calculations w ere ba sed upon a derivation from Newton’ s second law describing the
two forces opposing motion of the cyclist, and iterations minimizing the sum of the
squared diŒerence between the actual deceleration distance (D) and a calculated
deceleration distance (D*):
1363
Tyre pressure and vertical load in cycling
D*(m0,T)51/(2b).1n 1 1tan ab.T2atan(b/a.v0)2/11(b/a).v02,
(2)
where a=Ðg C
r
and b=ÐqAC
d
/2M, and
v05V(Dinitial,Tinitial )5a/b.cos(ab.Tinitial)2eb.Dinitial /sin(ab.Tinitial).(3)
2.3. Simulations
The in¯ uence of changes in P
r
and F
v
on simulated cycling performance during 1 h
of cycling was estimated using a simulation model to compute the mean V
c
sustained
(V
c
). Simulations were performed by considering an elite cyclist riding in an aero-
posture (aerodynamic position) on a covered track velodrome with no wind, a mean
external mechanical power output (P
ext
) of 400 W and air density (q) of
1.19 kg
.
m
Ð
3
. In the conditions of the simulation, the two forces opposing motion
of the cyclist are R
a
and R
r
. Thus, P
ext
can be described by:
2Pext 5Ra
2Vc1Rr
2Vc,(4)
where the ® rst and second terms represent the mean power outputs to overcome R
a
(P
Ra
, W) and R
r
(P
Rr
, W) respectively.
R
a
was calculated from R
a
=0.5 qAC
d
V
c
2
and based on results from previous
studies (Kyle and Burke 1984, Me nard 1992, Grappe et al. 1997). AC
d
=0.2 m
2
was
used in the calculations. Then, according to equation (1), V
c
was computed by
iterations of the following equation:
2Pext 50.5 qACd
2
Vc31CrMg2Vc.(5)
2.4. Statistical analysis
The data are presented using ordinary descriptive statistics of mean and SD. A
power regression and a second-order polynomial regression were used to describe the
relationships of P
r
with C
r
and F
v
with C
r
respectively. These types of regressions
were chosen according to their better r
2
and level of statistical signi® cance. The level
of statistical signi® cance was ® xed at p<0.05.
3. Results
3.1. In¯ uence of changes in P
r
on C
r
The relationship between C
r
and P
r
is presented in ® gure 1. C
r
was 0.010160.0003,
0.006960.0004, 0.005060.0005, 0.004060.0003 and 0.003860.0003 with increasing
P
r
levels of 150, 300, 600, 900 and 1200 kPa respectively. C
r
was well described
(r
2
=0.99, p<0.05) as a function of P
r
by the hyperbolic power equation:
Cr50.1071 P20.47 7
r.(6)
In the present study, C
r
decreased by 62% between 150 and 1200 kPa. The greatest
decrease (50% ) was observed between 150 and 600 kPa. Between 600 and
1200 kPa, the magnitude of the decrease was 24% . Within the range of P
r
levels
usually used by road cyclists (i.e. between 600 and 900 kPa), C
r
could vary by
20% . For track cycling , where P
r
usually ranges from 900 to 1200 kPa, C
r
could
vary by 5% .
1364 F. Grappe et al.
3.2. In¯ uence of changes in F
v
on C
r
The additional loads of 0, 5, 10 and 15 kg resulted in F
v
=743, 794, 843 and 892 N
respectively. Thus, the overloads of 5, 10 and 15 kg involved 22.7, 30.3 and 37.8%
increases in F
v
from the unloaded condition. The relationship between C
r
and F
v
is
presented in ® gure 2. C
r
increased from a baseline value of 0.003560.0004 to
Table 1. Mean cyclist speed sustained during 1 h (V
c
) at diŒerent tyre pressures (A) and
loads (B) predicte d from the sim ulation model. Als o reported are assoc iated values for the
coe cient of rolling resistance (C
r
) and mean power output to overcome aero-
dynamic drag (P
R a
) and rolling resistance (P
R r
). For all simulations, it was assumed
that there was no wind, the eŒective frontal area of the cyclist was 0.2 m
2
, the mean
external mechanical power provided (P
e x t
) was 400 W, and air density (p) was
1.19 kg
.
m
Ð
3
.
(A)
Pressure (kPa) 1.5 3 6 9 12
C
r
0.0101 0.0069 0.0050 0.0040 0.0038
P
R a
(W)
P
R r
(W)
V
c
(km
.
h
Ð
1
)
298
102
48.9
328
72
50.5
347
53
51.5
357
43
52.0
359
41
52.1
(B)
Overload (kg) 0 5 10 15
C
r
0.0035 0.0036 0.0037 0.004
P
R a
(W)
P
R r
(W)
V
c
(km
.
h
Ð
1
)
362
38
52.2
359
41
52.0
355
45
51.9
350
50
51.6
Figure 1. Coe cient of rolling resistance (C
r
) as a function of tyre in¯ ation pressure.
Brackets=1 SD.
1365
Tyre pressure and vertical load in cycling
0.003660.0002, 0.003760.0001 and 0.00460.0003 with the overloads of 5, 10 and
15 kg respectively. The relationship between C
r
and F
v
was well described (r
2
=0.99,
p=0.084) by the second-order polynomial equation:
Cr51.92.1028Fv222.86.1025Fv10.0142. (7)
A Spearman test indicated that there was no signi® cant linear relationship between
C
r
and F
v
(r
2
=0.91, p=0.084).
3.3. In¯ uence of changes in P
r
and F
v
on cycling performance
The in¯ uence of alterations in C
r
on V
c
during a 1 h ride under the diŒerent
experimental conditions of this study are summarized in table 1. Changes in C
r
were
associated with large variations in P
Ra
and P
Rr
. As compared with a P
r
=150 kPa,
P
r
of 300, 600, 900 and 1200 kPa resulted in an estimated increase in distance that
would be travelled during 1 h of 1600, 2600, 3100 and 3200 m respectively. With
overloads of 5, 10 and 15 kg, the predicted distance that would be covered during 1 h
decreased by 200, 300 and 600 m respectively. At 150 kPa, P
Rr
was predicted to
represent 25.5% of P
ext
. At 150, 300, 600, 900 and 1200 kPa, P
Rr
was predicted to
represent 25.5, 18, 13.2, 10.7 and 10.2% of P
ext
respectively.
4. Discussion
The most important ® ndings of this study are that the eŒects of P
r
and F
v
on C
r
are
non-linear in nature. C
r
decreased curvilinearly with increases in P
r
and increased
curvilinearly with increases in F
v
. The simulation model demonstrates that small
changes in P
r
and F
v
can have large aŒects on cycling performance.
4.1. Comparisons of C
r
with previous studies
The C
r
observed here were in line with those reported previously (table 2) when
considering a similar surface, tyre, P
r
and F
v
. Table 2 shows that C
r
have been found
to range between 0.001 and 0.0081. This C
r
variability is partly explained by
Figure 2. Coe cient of rolling resistance (C
r
) as a function of the total vertical force applied
to the bicycle tyres. Brackets=1 SD.
1366 F. Grappe et al.
Table 2. Summary of previously reported values for rolling resistance (R
r
) and coe cient of rolling resistance (C
r
) in cycling according to the type of
surface, tyre in¯ ation pressure and vertical load.
Studies R
r
(N) C
r
Place and type of surface Type of tyre
In¯ ation
pressure (kPa)
Vertical load
(kg)
Pugh (1974) 6.9 0.0081 aerodrome, asphalt surface tubular 220 g 630 86
Kyle and E delman (1975) N A* 0.0019 ± 0.0039 NA diŒerent tu bulars NA NA
Di Prampero et al. (1979) 3.2 0.0046 car track, asphalt surface NA 700 70
Davies (1980) 0.76 0.001 treadmill, linoleum surface NA NA 79
Gross et al. (1983) NA 0.0030 ± 0.0045 NA NA NA NA
Kyle and B urke ( 1984) NA 0.0016 ± 0.035 hallway, smooth surface diŒerent tu bulars 500 ± 1100 NA
Kyle and van Valkenburgh (1985) NA 0.0017 ± 0.0043 road, smooth asphalt diŒerent tubulars 540 ± 1500 NA
clincher 400 ± 82 0
Me
Ânard (1992) 1 ± 3 0.0028 ± 0 .0058 treadmill diŒerent tu bulars 300 ± 500 20 ± 61
Capelli et al. (1993) 2.43 0.0031 indoor velodrom, wood surface NA 1000 ± 1100 80
Grappe et al. (1997) 1.95 0.0030 outdoor velodrom,
synthetic surface
tubular Corsa Cx section,
22 mm
800 78
Present study
(changes in in¯ ation pressure)
7.5 ± 2.8 0.010 ± 0.0038 hallway, tiled ¯ oor tubular Corsa Cx 150 ± 1200 76
Present study
(change in weight added)
2.6 ± 3.5 0.0035 ± 0.0039 hallway, tiled ¯ oor clincher
Techno kevlar
1000 76 ± 91
*Data not reported.
1367
Tyre pressure and vertical load in cycling
variations in the surface compactness and roughness, the tyre material properties, P
r
and F
v
. The measurement methods used to determine C
r
must also be taken into
account. C
r
has been previously determined in cycling locomotion through the
dynamometric technique (Di Prampero et al. 1979, Capelli et al. 1993), coast-down
tests (Kyle and Edelman 1975, Gross et al. 1983, Kyle and Burke 1984, Kyle and van
Valkenburgh 1985), direct measurement of power input to the rear wheel (Grappe et
al. 1997) and indirectly through metabolic measurements (Pugh 1974, Davies 1980).
C
r
has also been previously measured in the laboratory (Shuring 1985, Me nard
1992). The dynamometric technique involve air turbulence set up by the towing
vehicle and alterations in weather conditions, especially wind, can aŒect the results
with this technique. The precision of the direct measurement appears limited by poor
linearity of the transducer (mounted in the hub of the rear wheel), and the eŒects of
alterations in ambient conditions. In the indirect measurement methods the
determination of C
r
is di cult and, thus, can give rise to measurement errors. With
the coasting deceleration method, some variables can degrade the test precision to
the point where repeat tests have shown variations of >10% (Candau et al. 1999).
The potential error sources could be due to: (1) irregular grades; (2) behaviour of the
subject during the deceleration test. Indeed, in our study, the simulation of actual
cycling conditions with turbulence was induced by movement of the lower limbs, the
subject continuing to pedal without transmitting propulsive force to the rear wheel
during each coasting trial; (3) the cyclist to use as guides to maintain straight
tracking during deceleration. In this study, two marker strips separated by 0.5 m
were placed on the ¯ oor between the timing switches to help the cyclist avoid steering
corrections during deceleration. That allows the reduction of the braking force that
would elevate the measured C
r
; and (4) the procedure to take into account a coasting
deceleration. In our study, when tracking was not straight, the trial was discarded
and the cyclist performed another deceleration. Previously, it has been observed that
when all the above parameters are not well controlled that could involve signi® cant
changes in C
r
.
4.2. In¯ uence of changes in P
r
on C
r
The decreases in C
r
with increases in P
r
observed in this study were in line with those
previously reported by Kyle and van Valkenburgh (1985). They reported a 27%
decrease in C
r
between 540 and 1080 kPa for silk road tubular tyres, a 37% decrease
in C
r
between 680 and 1500 kPa for kevlar track tubular tyres, a 23% decrease in C
r
between 400 and 820 kPa for touring wired-on tyres and a 15% decrease in C
r
between 540 and 950 kPa for cotton utility tubular tyres.
In the present study, C
r
was inversely and hyperbolically related to P
r
(® gure 1).
Equation (6) describing this relationship was similar to empirical equations reported
in previous studies conducted on passenger car tyres (Schuring 1980). Thus, the eŒect
of P
r
on C
r
in cycling appears similar to that which has been observed for passenger
cars. To the best of our knowledge, no previous study conducted in actual cycling
locomotion has reported such a relationship between C
r
and P
r
. However, through
coast-down tests with a loaded tricycle, Kyle and van Valkenburgh (1985) found a
curvilinear decrease in C
r
with increases in P
r
. In contrast, from a laboratory study,
Me
Ânard (1992) reported that C
r
for road cycling tyres was well described as an
inverse linear relationship with P
r
.
It has been reported that C
r
is dependent on the characteristics of the tyre material
at energy dissipation (Schuring 1980, Me nard 1992). For a given F
v
, the tyre bulges
1368 F. Grappe et al.
and its de¯ ection produces a `footprint’ (Schuring 1980, Me nard 1992). The leading
part of the footprint stores energy, whereas the trailing part dissipates this stored
energy (Kauzlarich and Thacker 1985, Schuring 1980, Me
Ânard 1992). As the tyre
material is not perfectly elastic, some of the stored energy is lost due to hysteresis, the
extent of which varies with the strain and stress on the tyre and the elastic properties
of the tyre material (Tabor 1955, Schuring 1980, Me nard 1992). The hyperbolic
relation between C
r
and P
r
observed in this study is probably accounted for by the
manner in which P
r
aŒects the tyre footprint and the elastic properties of the tyre
material, and in turn alters the amount of energy loss due to hysteresis.
4.3. In¯ uence of changes in F
v
on C
r
In the present study, a 15 kg overload added to the 66 kg cyclist and 9.8 kg bicycle
resulted in an 11.4% increase in C
r
. This result indicates that C
r
for an 81 kg cyclist
would be 11.4% greater compared with a 66 kg cyclist using the same bicycle. Thus,
the in¯ uence of F
v
on C
r
cannot be neglected in cycling.
C
r
was well described by F
v
with a second-order polynomial equation (equation
7; ® gure 2). As was the case for the relationship of P
r
with C
r
, the relationship
observed between F
v
and C
r
was similar to that previously reported for passenger car
tyres (Schuring 1980). In contrast, previous studies of cycling have described the
relationship between C
r
and F
v
as linear (Kyle and Burke 1984, Kyle and van
Valkenburgh 1985, Me
Ânard 1992).
The non-linear increase in C
r
with F
v
observed in this study could be similarly
explained by the hysteretic loss phenomenon proposed to account for the eŒect of
changes in P
r
on C
r
. Indeed, the tyre footprint is aŒected by F
v
, and therefore the
extent of energy loss due to hysteresis would also be expected to be aŒected by F
v
.
Furthermore, changes in F
v
could alter the elastic properties of the tyres. It has been
reported that the tyre elastic input energy per unit distance is proportional to the
load to the four-thirds power (Schuring 1980). Thus, the non-linear increase in C
r
relative to F
v
observed in this study could be accounted for by the eŒects of F
v
on the
tyre footprint as well as the elastic properties of the tyre.
4.4. In¯ uence of changes in C
r
on cycling performance
Table 1A and B demonstrates that during a 1 h ride, cycling performance can be
improved from decreases in C
r
produced through increases in P
r
. Furthermore,
cycling performance can be adversely aŒected from increases in C
r
produced through
elevations in F
v
. For a given load, a 300 kPa increase in P
r
from 900 to 1200 kPa
would predict a 100 m increase in the distance travelled during 1 h. For a given P
r
, a
5 kg load increase from 76 to 81 kg would predict a 200 m reduction in performance.
These ® ndings indicate that P
r
and the weight of both the bicycle and the subject are
important factors aŒecting performance.
Kyle and van Valkenburgh (1985) have previously estimated that for a cyclist
travelling 48.3 km during 1 h, increases in C
r
of 10 and 20% would result in
reductions in the distance travelled of 377 and 754 m respectively. According to the
simulation model used in the present study (equation 5), it appears that the aŒect
reported by these authors is slightly overestimated. The present model predicts that
the distance travelled would be reduced by close to 200 and 400 m for increases in C
r
of 10 and 20% respectively.
The results of this study demonstrate that within the P
r
range usually used by
road cyclists, an increase in P
r
from 600 to 900 kPa could result in an improvement
1369
Tyre pressure and vertical load in cycling
in performance of 0.5 km
.
h
Ð
1
. Recognizing the important impact of P
r
on
performance, the 1984 US Olympic team reportedly used a tyre pressure of
950 kPa in the 100 km time trial on the road (Kyle and van Valkenburgh 1985).
Interestingly, within the P
r
range used by track cyclists, an increase from 900 to
1200 kPa would be predicted to improve performance by 0.1 km
.
h
Ð
1
. These results
indicate that variations within higher levels of P
r
result in smaller improvements in
performance. Nevertheless, the 1984 US Olympic cycling team reportedly used
pressures of 1500 kPa in their tyres for track cycling (Kyle and van Valkenburgh
1985). When ® rst and second places are determined by <1 s, even such relatively
small eŒects on performance are important.
C
r
has previously been reported to be on the order of 0.0001 for trains (Schuring
1980). This is due to the minimization of hysteresis loss that occurs through steel
rolling against steel. It is interesting to consider how such a low C
r
might aŒect
cycling results. The present simulation model predicts that an elite cyclist could
maintain an average speed of 53.9 km
.
h
Ð
1
for 1 h with C
r
=0.0001. This could
determine a gain of 1800 m during a 1 h ride compared with a C
r
of 0.0038
correspondent to a P
r
of 1200 kPa. Thus, it is apparent that considerable gains in
cycling performance are conceivable through further reduction in C
r
.
4.5. Conclusions
This study demonstrates that the relationships of C
r
with P
r
and F
v
for cycling are
similar to those previously reported for passenger cars. The non-linear eŒects of P
r
and F
v
on C
r
probably result from the manner in which these variables alter the tyre
footprint and elastic properties of the tyre material. The tyres used for the two
experimental conditions of this study were `standard’ tyres, and it is possible to
generalize the ® ndings of the eŒect of tyre pressure and load on these tyres. The
simulation model used in this study shows that the eŒect of P
r
and F
v
on cycling
performance cannot be neglected.
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Appendix. Glossary of abbreviations
AC
d
eŒective frontal area (m
2
)
C
r
coe cient of rolling resistance (unitless)
Ddistance between the second a nd third timing sw itches =20 m
D* calculated distance between the second and third timing switches
D
initial
distance between the ® rst and second timing switches =1 m
F
v
vertical load applied on the tyre (N)
gacceleration due to gravity =9.81 m
.
s
Ð
2
Mtransported mass of the bicycle (kg)
P
r
tyre in¯ ation pressure (kPa)
P
ext
mean external mechanical power provided by the cyclist (W)
P
Ra
mean power output to overcome aerodynamic drag (W)
P
Rr
mean power output to overcome rolling resistance (W)
R
a
aerodynamic drag (N)
R
r
rolling resistance (N)
R
T
total resistance opposing motion of a cyclist (N)
Ttime to travel between the second and third timing switches (s)
T
initial
time to travel between the ® rst and second timing switches (s)
V
c
cyclist speed (m
.
s
Ð
1
)
V
c
mean cyclist speed (m
.
s
Ð
1
)
v
0
initial speed of the cyclist between the ® rst and second timing switches (m
.
s
Ð
1
)
qair density (kg
.
m
Ð
3
)
1371
Tyre pressure and vertical load in cycling