NEUROMUSCULAR-STEERING DYNAMICS: MOTORCYCLE RIDERS VS CAR DRIVERS
M. Massaro
Department of Industrial Engineering
University of Padova
Via Venezia, 1
Padova 35131, Italy,
matteo.massaro@unipd.it
ABSTRACT
The neuromuscular dynamics affect the response and stability
of the driver-vehicle system. This paper addresses the most recent
findings on driver steering neuromuscular properties, both for
two-wheeled vehicles and four-wheeled vehicles. An analysis of
the effect of neuromuscular dynamics on the stability of the
driver-vehicle system is included.
NOMENCLATURE
a distance from the vehicle c.g. and the front contact point
b distance from the rear contact point and the vehicle c.g.
ca arms damping coefficient
cs steering damping coefficient (reduced to the steering wheel)
cy rider’s lateral damping coefficient
c
ct
dp
Cf
Cr
h
H
H2w
H4w
Hb
Hf
Hr
Hs,v
ig
Ja
rider’s roll damping coefficient
torso damping coefficient
car pneumatic trail
front tire cornering stiffness
rear tire cornering stiffness
height of the upper rider c.g. from the roll axis
transfer function (steering angle/steering torque)
motorcycle-rider transfer function (steering angle/steering
torque)
car-driver transfer function (steering angle/steering torque)
transfer function (steering torque/steering angle) related to
the intrinsic muscle passive response
forward model of the muscle and vehicle system
transfer function (steering torque/steering angle) related to
the reflex response
transfer function of the vehicle (output/steering torque)
car steering ratio
arms and hands inertia reduced to the steering wheel
D.J. Cole
Department of Engineering
University of Cambridge
Trumpington Street
Cambridge CB2 1PZ, UK
djc13@eng.cam.ac.uk
Js steering inertia (reduced to the steering wheel)
Jt arms and torso inertia reduced at the torso
Jxxr roll moment of inertia of motorcycle rider’s upper body
ka arms stiffness
kc motorcycle structural stiffness
ks steering stiffness (reduced to the steering wheel)
kt torso stiffness
ky rider’s lateral stiffness
k rider’s roll stiffness
K brain path following block
m car mass
mr rider mass
mr,u upper rider mass
NMS
Neuro Muscular System
s Laplace variable
T steering torque
Tb steering torque (intrinsic muscle passive component)
Tm steering torque (brain component plus reflex component)
x vehicle state
yp target path


f
b


t

steering torque generated by brain
driver cognitive response (whole)
driver cognitive response (feedforward component)
driver cognitive response (feedback component)
expected steering angle generated by brain
steering angle
rider’s torso rotation
relaxation length
INTRODUCTION
Few papers on the interaction of a driver's neuromuscular
system (NMS) with the steering system while driving two or fourwheeled vehicles have been published so far. Nevertheless the
NMS dynamics affect the response of the driver-vehicle system
and in the case of single-track vehicles significant effects on
stability have been documented [1]. In addition, theoretical
understanding of human steering control behavior is essential
when using numerical simulation to develop sophisticated
systems that actively modify the steering angle and torque in fourwheeled vehicles [2].
One of the earliest attempts to understand the role of NMS
dynamics in the driver–vehicle–steering system dated back to
1993 [3]. The NMS system of the driver’s arms was represented
using a second-order low-pass filter, a pure delay related to
human signal processing time and two first order transfer
functions representing the feedback of variables related to the
motion of the human limbs and muscles to the steering action.
In 2004 a fixed-base car driving simulator with a torque
feedback steering wheel was used to identify the passive
properties of the driver’s arms [4]. The experiments involved the
test subject holding the steering wheel with both hands whilst a
random torque signal was sent to the steering system. The test
subject was asked to hold the steering wheel with just enough
force to prevent their hands from slipping as the wheel moved,
but not to actively resist the wheel's movement in order that only
the passive arm dynamics were measured. Subsequently, the
stiffness and damper values of the driver-steering wheel system
identified on the car simulator were also used to model the driverhandlebar system of a motorcycle [5], and vehicle stability was
addressed. It should be noted that different muscles are involved
when riding a motorcycle, and so different transfer functions may
be involved. However no motorcycle related data were published
at the time.
In 2007 [6] further results on the dynamic properties of a
driver's arms holding a steering wheel were reported. The
identified values for damping and stiffness appeared to show little
dependence on torque amplitude in comparison with the variation
seen among test subjects.
In 2011 the identification of the rider-handlebar properties
were identified on a motorcycle simulator [7]. The experiments
involved the test subject holding the handlebar with both hands
whilst a sine swept signal was sent to the steering system. The test
subjects were asked to hold the handlebar with just enough force
to prevent their hands from slipping as the handlebar moved, but
not to actively resist the handlebar's movement in order that only
the passive arm dynamics were measured. Afterward, the
identified driver properties were used to evaluate the motorcycle
weave stability and compared with road tests, giving good
correlation results [1].
The objectives of the present paper are to: summarize and
compare the most recent findings on driver NMS dynamics; to
provide a reference for NMS data to be used in the driver-vehicle
modeling and simulation; and to analyze the effect of the NMS
dynamics on the stability of two- and four-wheel vehicles.
MODELING OF NMS-STEERING DYNAMICS
There are mainly three components characterizing the driver
steering response: (i) the cognitive response of the brain, (ii) the
stretch reflex response and (iii) the pure passive (intrinsic)
response.
The cognitive response is mainly related to the driver path
following task and comprises two parts: a feedforward steering
action based on the previewed road path and the expected vehicle
behavior (an internal model of the vehicle dynamics that the
driver has learnt through experience); and a feedback steering
action based on the sensed motion of the vehicle. From the
control point of view, the use of a receding horizon strategy with
both LQ preview and MPC approaches have been shown to be
effective for the simulation of the path following task. Indeed the
action of these controllers can be considered to consist of a
feedforward component f and a feedback component b:
α  α f  αb
(1)
where  is a vector consisting of the driver steering action, the
throttle position, the braking action, etc. Examples of applications
are reported in [8] and [9] for car and motorcycle respectively. It
is worth stressing that while the feedforward component is an
openloop component, whose frequency content can reach
significant values, the feedback component has a limited
bandwidth (1-2Hz), due to the brain cognitive processing time
[11]. Finally, it is likely that the vehicle driver combines the noisy
sensed signals to estimate the current vehicle state (and then
properly generate the feedback control); an attempt at modeling
the effect of human sensory noise on path following steering
control has been reported in [12].
While a satisfactory modeling framework exists for the
cognitive response to the path following task (i), the driver stretch
reflex response (ii) and the passive response (iii) remain open and
challenging research issues. Nevertheless they are important when
it comes to both the vehicle stability (especially in the case of
two-wheeled vehicles) and to the study of sophisticated steering
systems (especially in the case of four-wheeled vehicles).
Measurements carried out recently at the University of Cambridge
[4],[6] and at the University of Padova [7] were aimed at
identifying NMS-steering dynamics. Given the test procedures,
the cognitive activity (i) was assumed to be almost null (the driver
has no task to accomplish during the test with the exception of
preventing the hands from slipping), while both the reflex (ii) and
the passive component (iii) were assumed to be excited.
Both tests were aimed at measuring the transfer function
between the steering torque T and the steering angle :
H (s) 
 (s)
T ( s)
(2)
From the inspection of the experimental transfer functions, it was
apparent that, in the frequency range of interest (up to 10Hz), the
driver-car system exhibits one resonance while the ridermotorcycle system presents two resonances. In practice, in the
case of car a single degree of freedom system is sufficient (the
TABLE 1. AVERAGE DRIVER & RIDER PARAMETERS
4-wheeled
(relax)
4-wheeled
(tense)
parameter
2-wheeled
(relax)
0.094
0.094
Ja[kgm2]
-
0.59
1.12
ca[Nms/rad]
19.28
3.4
59.6
ka[Nm/rad]
1053.4
FIGURE 1 DRIVER (LEFT) VS RIDER (RIGHT)
H 2 w ( s) 
 ( s)
T (s)
 ( s)
T ( s)


1
J a s 2  ca s  ka
J t s 2   ct  ca  s   kt  ka 
J s
t
2
 ct s  kt   ca s  ka 
(3)
(4)
Note that the steering torque is computed at the interface between
the steering wheel/handlebar and the driver's hands, i.e. the inertia
of the steering system is not included in Eq. (3),(4). Moreover, in
Eq. (3) all the driver inertia involved in the vibration (mainly that
of the arms and hands) is accounted for in Ja, which experiences
the steering rotation , while in (4) all the rider inertia involved in
the vibration (mainly the torso) is accounted in Jt, which
experiences the torso rotation t. Average driver properties are
available for both cases (derived from [6],[7]), both in relaxed and
tensed condition for the car-driver, and only in the relaxed
condition for the motorcycle-rider: Table 1 and Figure 2.
When comparing the transfer functions, it is evident that
both systems have a spring-like behavior at low frequency, though
the static gain (1/ka=1/3.4 (relaxed) to 1/ka=1/59.6 (tensed) for
car-driver and (kt+ka)/ktka=1/70.7 for motorcycle-rider) are
significantly different, that of the car driver in tensed condition
being close to that of the motorcycle rider in relaxed, or normal,
condition. The difference between the static gains of the car driver
in the relaxed configuration and the motorcycle driver in normal
configuration may seem surprising at a first glance. However it
should be noted that different muscles are involved in the
systems: the car-driver in mainly excited in the roll axis, while the
motorcycle-rider is mainly excited in the yaw axis (see Figure 1).
In addition, for the results reported, the car drivers applied the
hands to a steering wheel with a radius of 0.16m , while during
the motorcycle-rider tests the distance between the hand’s grip on the handlebar and the steering axis was 0.34m. Given this
difference in radii, higher static gains for the motorcycle rider are
expected. Finally, the rider's arms are close to a kinematic
singularity (forearm and upper arm aligned). As regards the
position of the H(s) main resonance, the car driver has the
-
Jt[kgm ]
0.644
-
-
ct[Nms/rad]
4.79
-
-
kt[Nm/rad]
75.8
0
Magnitude (dB)
H 4 w ( s) 
-
resonance at a damped frequency of 0.81Hz when relaxed, and at
3.89Hz when tensed, while the motorcycle rider has a resonance
at a damped frequency of 1.62Hz. It can be concluded that
different models and parameter values should be considered when
adding the NMS to four- and two-wheeled vehicles.
The next step is to split the stretch reflex response (ii) from
the passive response (iii). Indeed, it is evident that when the
driver is completely relaxed there is no control on the limb
dynamics (one may think of an unconscious person whose arms
can be moved without significant intrinsic resistance). From the
mechanical point of view, there is no significant intrinsic muscle
stiffness. On the contrary, a conscious person is able to control
limb position, thus providing the required stiffness, by activating
the cognitive response and the stretch-reflex response. In
particular the reflex response is related to the difference between
the expected limbs configuration and the current one, with a
limitation in the maximum frequency of about 3Hz, see [11].
It is herein assumed that the reflex response is activated by
the difference between the expected steering angle and the actual
steering angle. In addition, the investigation of [11] highlighted
that the passive (intrinsic) muscle response is essentially damperlike. Putting aside the cognitive control, it is assumed that all of
the spring-like response of the
limb arises from stretch-reflex
Bode Diagram
action (i), while all the complement is considered pure passive
-20
-40
2w (relax)
-60
4w (relax)
4w (tense)
-80
0
-45
Phase (deg)
steering rotation being the only significant degree of freedom),
while in the case of motorcycle a two degrees of freedom system
is necessary (the degrees of freedom being the steering rotation
plus the rotation of the torso about the spine, see Figure 1).
The following transfer functions were found for the four-wheeled
vehicle (H4w(s)) and the two-wheeled vehicle (H2w(s)):
2
-90
-135
-180
-1
10
0
10
Frequency (Hz)
FIGURE 2 H2W VS H4W
1
10
TABLE 2. CAR STEERING DATA
FIGURE 3 DRIVER-VEHICLE SYSTEM
(ii). The resulting scheme is depicted in Figure 3 and is adopted in
the rest of this paper as the general structure for the driver-vehicle
system.
In more detail, the brain generates the steering torque signal
 through the block K, from the target path yp and the current
state x (K usually calculated using LQ preview or MPC
approaches) and the related expected steering angle  (generated
through the block Hf which is a forward model of the musclevehicle system) according to mechanism (i). When the current
steering angle  does not correspond to the expected angle  a
stretch-reflex torque is generated through the block Hr according
to mechanism (ii), which adds to the brain torque  to give the
torque Tm. Finally the pure passive (intrinsic muscle) torque Tb
(iii) adds to the whole torque applied by the driver on the steering
wheel/handlebar which is the input of the vehicle (block Hs,v). In
other words, the driver has to balance the resistance of the muscle
passive behavior: the torque is applied to the muscles which have
their own dynamics. Note that the presented approach is suitable
for arbitrary maneuvers, whereas the models reported in [6],[7]
are not, since they generate a reflex torque whenever the steering
angle is not zero, and are thus suitable only for straight-motion
simulation.
Summarizing, when simulating a maneuver with no driver
unexpected disturbance, the stretch-reflex dynamics Hr (ii) are not
involved, and the passive dynamics Hb (iii) and brain K (i) are
only involved. When unexpected motion and vibration are
present, the stretch-reflex response is involved.
Finally, additional blocks can be included to account for the
limited bandwidth and/or delay of the brain Dc (typical delay
0.5s) the stretch-reflex Dr (typical delay 0.04s), the motor neurons
plus muscle activation/deactivation and tendon dynamics Da (first
order lags with typical time constants 0.03s, 0.02s and 0.05s
respectively), [2],[11],[12]. When including these blocks, the
passive muscle response remains the only high-bandwidth
component of the NMS.
parameter
value
ig
15.8
Js [kgm2]
0.02
ks [Nm/rad], cs [Nms/rad]
2
dm, dp [m]
0.038, 0.037
VEHICLE MODELS
Two vehicle models are used to analyze the effect of the
driver-vehicle dynamics on the four-wheeled vehicles and two
wheeled vehicles stability.
The car model is of the general form reported in [14] (degrees
of freedom: position on the road, yaw and roll of the chassis,
steering angle) and the data are those of the five doors passenger
vehicle identified in [14] and extended to include the additional
steering and tire parameters of Table 2. More precisely, the input
is the driver’s steering torque which is applied to the steering
wheel and then to the tire through a steering system having an
inertia Js and a transmission ratio ig. The model includes also the
damping of the steering system cs as well as a spring term ks due
to the self-centering effect. Finally, the steering system has a
mechanical trail dm and the tire has a pneumatic trail dp.
The motorcycle model is of the general form reported in [15]
(degrees of freedom: position on the road, yaw, roll and pitch of
the chassis, steering angle) and the data are those of the street
motorcycle of [16] extended to include the rider’s mobility and
structural chassis flexibility parameters of Table 3. In more detail,
the modeling of the motorcycle rider is more complex when
compared with the car driver because the ratio of rider to vehicle
mass is usually in the range 0.25-0.50 (0.33 for the current
vehicle) and so the related inertia effects must be considered in
the multibody model. Therefore, the rider is divided in two
bodies: lower body (from feet to hip) and upper body (from hip to
head). The lower body moves laterally with respect to the chassis,
while the upper body yaws and rolls with respect to the lower
body. The roll axis of the upper body with respect to the lower
body passes in the neighborhood of the rider’s hips and the yaw
axis passes through the upper body c.g. (see Figure 4). The lateral
motion and the roll motion are restrained by spring/damper
TABLE 3. MOTORCYCLE & RIDER DATA
parameter
value
mr, mr,u [kg]
75.2, 40
h[m]
0.35
2
FIGURE 4 RIDER MODELING
Jxxr [kgm ]
3.5
ky[Nm/rad], cy[Nms/rad]
45433, 1161.1
k[Nm/rad], c[Nms/rad]
671.6, 65.5
kc [kNm/rad]
45
elements tuned to give an upper body roll frequency of 1.27Hz
with a damping ratio of 0.489 (k, c), and a whole body lateral
frequency of 4.0Hz with a damping ratio of 0.321 (ky, cy),
according to [1],[18]. To account for the NMS steering dynamics,
a spring damper element restrains the yaw motion of the upper
body with respect to the lower body (kt, ct), and an additional
spring-damper element connects the upper body with the
handlebar to account for the arm effects (ka, ca). The parameters
for the NMS are from Table 1. Finally, the chassis flexibility is
considered by including the torsion of the front frame with respect
to the chassis, with a lumped stiffness element at the steering head
[19].
The NMSs are modeled using the Hr and Hb blocks.
According to the previous section, Hr consists of ka and Hb
consists of ca. Note that, in addition to the torque between the
driver’s upper body and the steering wheel or handlebar, in the
case of the motorcycle there is also the spring/damper element
between the torso and the lower body (kt, ct).
STABILITY ANALYSIS
This section aims at highlighting the effect of reflex (ii) and
passive (iii) NMS dynamics on the stability of the driver-vehicle
system. The vibration modes of the system are computed for
speeds from 5 to 50m/s (straight-motion) and analyzed. Both
relaxed and tensed driver properties are considered for the drivercar system (from Table 1), while relaxed properties are considered
for the rider-motorcycle system (from Table 1) and an estimated
set of parameter values for the tensed rider-motorcycle are
derived and analyzed (no measured data are currently available
for the tensed case). Since the analysis aims at the effect of the
reflex and passive dynamics on the stability, it is assumed =0
(the expected steering angle is null) and =0 (the brain steering
torque demand is null), according to the scheme of Figure 3. In
other words, the driver is placing his hands on the steering and
letting the vehicle travel with no cognitive path following control.
None of the additional delay/filter blocks Dc ,Dr, Da are
considered because the parameters used were identified without
any of these blocks. In other words, the related dynamics are
embedded in the identified parameters.
Figure 5 depicts the root-locus of the driver-car system for
the (understeering) passenger vehicle under investigation in four
different conditions: with the steering locked (red circles); with
the driver’s hands off the steering wheel and the steering free to vibrate (blue squares); with the hands of the driver on the steering
wheel in relaxed condition (green diamonds); and with the hands
on in tensed conditions (black crosses). When the steering is
locked the system has three main vibration modes: two of them
are oscillatory (complex conjugate pair of roots) at all speeds. The
higher frequency mode is in the range 2-3Hz, while the lower
frequency mode is in the range 1-2Hz and is always the less
damped mode. The third mode is oscillatory up to 20m/s then
splits into two real roots. This is the well known behavior of the
so-called car-bicycle model including tire relaxation behavior
[17], with the exception that here also the roll of the sprung mass
is included (natural frequency 1.85Hz) according to the
identification of [14]. When considering the steering free to rotate
(i.e. hands off configuration), the two oscillatory modes are
affected and the third mode becomes non-oscillatory at a higher
speed (40m/s). When the hands are placed on the steering wheel
in a relaxed manner, all modes remain oscillatory in the whole
speed range, while when a tensed condition is considered the
system behavior gets closer to that of the locked steering. Figure 7
show the real part of the less damped mode as a function of speed,
being the mode that affects the response most. It is clear that the
most stable configuration is that with the steering locked,
followed by the tense, the relaxed and the hands off. Therefore, in
the case of poorly damped vibration, it is suggested to co-contract
and thereby tense the muscles to stabilize the vehicle response.
It is interesting to consider also the case of an oversteering
passenger car: in this condition there exists a critical speed above
which the system is known to be unstable [17]. For this reason
most passenger cars are designed to be understeering, however
there may be conditions where an understeering vehicle turns into
an oversteering one because of reduced rear cornering stiffness,
e.g. as a consequence of the longitudinal tire force in rear wheel
drive vehicles. For the purpose of simulation, an oversteering
behavior is derived by reducing by one third the rear cornering
stiffness and doubling the front tire cornering stiffness. In this
condition, the critical speed of the vehicle with the steering
locked (neglecting roll dynamics and considering instantaneous
tire behavior) has the following analytical expression [17]:
vcr 

C f Cr  a  b 
2
m C f  a  d p   Cr  b  d p 

(5)
which is 37m/s for the current vehicle. Figure 9 shows the real
part of the less stable mode as a function of speed for the four
configurations. Note that when the steering is locked, the critical
speed is 37m/s (according to the value computed with Eq. (5)):
above this speed the system is unstable because of a nonoscillatory mode. When the steering is free to vibrate (hands off)
the critical speed rises to 43m/s, and the instability is oscillatory.
When the driver places his hands in a relaxed manner the critical
speed further rises to 46m/s (still oscillatory) while when the
tensed condition is considered no critical speed is observed at all.
In other words, only a tensed driver can stabilize the oversteering
vehicle. Note that no damping is effective in this sense, because
the stabilization effect arises mainly due to the driver’s stretchreflex spring-like contribution added to the steering system.
25
steering locked
hands off
hands on (relax)
hands on (tense)
3
15
2
speed
freq[Hz]
imag[rad/s]
20
10
1
5
40m/s
10m/s
20m/s
0
0
-30
-25
-20
-15
-10
-5
0
5
real[rad/s]
FIGURE 5 CAR-DRIVER ROOT LOCUS
70
10
60
imag[rad/s]
wobble
40
6
30
4
20
fixed rider
hands off
hands on (relax)
hands on (tense 1)
hands on (tense 2)
10
weave
2
0
0
-30
-25
-20
-15
-10
-5
real[rad/s]
FIGURE 6 MOTORCYCLE-RIDER ROOT-LOCUS
0
5
freq[Hz]
8
50
1
1
0
0
-1
-0.6
-4
-5
10
20
30
speed[m/s]
40
-0.2
-2
-0.4
-3
-0.6
-4
-5
-0.8
steering locked
hands off
hands on (relax)
hands on (tense)
-6
real[rad/s]
real[rad/s]
-0.4
-3
0
-1
-0.2
-2
-7
0
-6
-1
-7
50
-0.8
steering locked
hands off
hands on (relax)
hands on (tense)
10
20
30
speed[m/s]
40
-1
50
FIGURE 7 CAR-DRIVER (UNDERSTEERING)
(DRIVER IS STABILIZING AT ALL SPEEDS
WHEN COMPARED WITH FREE-STEER SCENARIO)
FIGURE 9 CAR-DRIVER (OVERSTEERING)
(TENSE DRIVER CAN STABILIZE
THE HIGH SPEED FREE-STEER INSTABILITY)
To account for the NMS dynamics of the motorcycle rider, a
spring-damper element restrains the yaw motion of the upper
rider’s body with respect to the rider’s lower body (kt and ct in
Figure 1), and an additional spring-damper element connects the
rider’s upper body with the handlebar to account for the arms effects (ka and ca in Figure 1). The parameter values of the rider
model are those reported in Table 3.
Figure 4 depicts the root-locus of the rider-motorcycle system
for the street bike under investigation. The configuration with the
steering locked is not considered, because the bike turns into an
inverted unstable pendulum in that condition and so it is not
relevant. The following five conditions are analyzed: with the
rider’s body rigidly fixed to the chassis (red circles); with the
rider’s hands off the handlebar (blue squares); with the hands of
the rider on the handlebar in relaxed condition (green diamonds);
with the hands in “tensed 1” condition (black crosses); and with
hands in “tensed 2” condition (magenta triangles). Since no
measured tensed parameter values are currently available for the
motorcycle rider, two tentative sets of values are assumed:
“tensed 1” where the ratio between the NMS stiffness in tensed
and relaxed condition is 7, while the ratio between the damping
coefficients is 1.5, and “tensed 2” where the ratio between the NMS stiffness in tensed and relaxed condition is 15, while the
ratio between the damping coefficients is 2. It is worth stressing
that these are estimated values, derived from the ratio of the
corresponding parameters in the car-driver conditions, which
should be checked against measured data as soon as it is
available. However, in general when moving from a relaxed to a
tensed condition, much higher stiffness and slightly higher
damping are expected.
The root-locus of Figure 4 highlights the two well-known
weave and wobble vibration modes. Weave mode is a fishtailing
of the whole vehicle with frequency rising with speed up to 3-4Hz
[17], usually poorly damped at high speeds. Wobble is mainly a
front assembly oscillation about the steering axis with frequency
in the range 5-10Hz, usually poorly damped at low to medium
speeds depending on the vehicle structural flexibility [19]. Both
modes can even become unstable in certain motion and/or loading
condition. Figure 8 shows the real part of the weave mode at
different speeds in the five analyzed conditions. For speeds
higher than 25m/s the less-damped configuration is that with the
rider rigidly fixed to the chassis (red circles), which has been
0
0
-2
-4
real[rad/s]
real[rad/s]
-5
-6
fixed rider
hands off
hands on (relax)
hands on (tense 1)
hands on (tense 2)
-8
-10
10
20
30
40
-10
fixed rider
hands off
hands on (relax)
hands on (tense 1)
hands on (tense 2)
-15
50
speed[m/s]
FIGURE 8 MOTORCYCLE-RIDER WEAVE
(RIDER IS DESTABILIZING AT HIGH SPEEDS
WHEN COMPARED WITH FREE-STEER SCENARIO)
-20
10
20
30
speed[m/s]
40
50
FIGURE 10 MOTORCYCLE-RIDER WOBBLE
(RIDER IS STABILIZING AT MID-SPEEDS
WHEN COMPARED WITH FREE-STEER SCENARIO)
reported because it is often assumed for simulating the motorcycle
dynamics. However the experimental evidence highlights that
during weave oscillations the rider rolls and moves laterally on
the saddle as a consequence of the vehicle motion [18]. When
considering this effect, i.e. the rider with hands off the handlebar
but passively vibrating on the saddle (blue squares), the weave
stability improves for speeds higher than 20m/s when compared
with the fixed rider case. In practice, the main contribution is that
of the rider who rolls almost in anti-phase with respect to the
motorcycle roll, and stabilizes the system. When the NMS is
considered, namely the rider places his hands on the handlebar in
a relaxed condition (green diamonds), the weave stability worsens
when compared with the hand off scenario. Some experimental
evidence confirming this tendency has been reported recently [1]
using a different vehicle and two different riders. Finally, when
considering the tensed conditions (black crosses and magenta
triangles) the weave stability at high speeds (higher than 40m/s) is
in between the hands off and the hands on relaxed cases.
Summarizing, the effect of reflex-passive dynamics worsens the
stability of the vehicle: the rider’s hands on handlebar, although
necessary, have a de-stabilizing effect on the weave mode.
Figure 10 shows the real part of wobble mode as a function
of speeds for the five configurations considered. Again the fixed
rider (red circles) is reported because this assumption is
considered in several studies. When considering the rider’s vibration on the saddle (blue squares) the wobble mode has the
minimum damping at medium speeds (30-40m/s). When
considering the effect of the hands on the handlebar (reflex and
passive component of the steering NMS) the wobble stability
improves, as confirmed by experimental findings, where most of
the wobble instability appears only without the rider’s hands on the handlebar. However, above a certain speed (43m/s) the hands
on effect is no more stabilizing. When the rider turns to a tensed
condition (black crosses and magenta triangles), the improvement
in the wobble stability with the respect to the hands off condition
is reduced when compared with that arising from the relaxed
condition. In addition, the tensed condition worsens the wobble
stability above 45m/s. Summarizing, the reflex-passive NMS
stabilizes the wobble mode in the speed range where it is less
damped.
CONCLUSION
The modeling of the driver-car and rider-motorcycle systems
has been addressed, similarities and differences have been
analyzed and reference parameter values provided. The effect of
the reflex and passive NMS dynamics on the vehicle stability
have been analyzed in car (both understeering and oversteering
cases) and in motorcycle. In particular, the car driver stabilizes the
less damped mode of an understeering vehicle and can increase
significantly the critical speed of an oversteering vehicle. The
effect of reflex and passive NMS dynamics on the motorcycle are
to increase the stability of wobble and reduce the stability of
weave. Future work will include identification of the rider’s NMS
dynamics in tensed condition and further comparison to on road
tests.
ACKNOWLEDGMENTS
This work was partially supported by the University of Padova,
Grant agreement MAS1PRGR10. Part of the work was performed during
Dr. Massaro's period (Jan-Mar 2012) at Cambridge University
Engineering Department.
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