ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT
AZOJETE March 2020. Vol. 16(1):92-99

Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria.
Print ISSN: 1596-2490, Electronic ISSN: 2545-5818

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ORIGINAL RESEARCH ARTICLE

ROLLOVER STABILITY MODELS FOR THREE-WHEELED VEHICLE DESIGN

S. J. Ojolo, O. O. Ajayi and G. A. Asuelinmen*
(Department of Mechanical Engineering, University of Lagos, Lagos, Nigeria)

*Corresponding author’s email address: asuegeo@gmail.com

1.0 Introduction
The tricycle, called trike or three-wheeler, is a three-wheeled vehicle (TWV). In African and Asian
countries, they are used mainly for commercial purposes (Gawade et al., 2004) as shown in
Figure 1.

Figure 1: Three-wheeled vehicle (TWV)

The vehicle is safer when compared with commercial motorcycle, and cheaper and able to
manoeuvre through heavy traffic in urban environments when compared with four-wheeled
vehicles. It is fuel efficient and generates about 33% of green gases per rider when compared
with cars and jeeps as a result of weight difference (Goodarzi et al., 2015). All this have
accentuated its usage.
However, there are some safety problems associated with the usage of these TWVs. They are
more accident prone when compared to four wheeled vehicles. The stakeholders of three-

ARTICLE INFORMATION ABSTRACT

The current commercial three-wheeled vehicles (TWVs) in the market
are rollover unstable, with adverse effects on life and property. This
places limitation on their speed and usage, even though they are fuel
efficient, cheap and generate about 33% of green gases per rider when
compared with four-wheeled vehicles.This work derived mathematical
models for the analysis of the stability of the three-wheeled vehicle
(TWV). Based on these models, the test method for rollover stability was
adopted. Rollover test was carried out on a TWV on Nigerian road. The
results showed that the vehicle is unstable with respect to rollover
stability. The test procedure if adopted and legislated upon, would
significantly enhance safety of life and property of the population.
Moreover, the speed and usage of the vehicle for both private and
commercial purposes will be enhanced.

© 2020 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved.

Submitted 20 September, 2019
Revised 06 December, 2019
Accepted 08 January, 2020

Keywords:
Three-wheeled vehicle
rollover stability
safety of life and properties
test method.

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Arid Zone Journal of Engineering, Technology and Environment, March, 2020; Vol. 16(1) 92-99. ISSN 1596-2490;
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wheeled vehicles attested to it that the vehicle can tip-over when negotiating a bend, even
though their maximum speed is about 60km/h. This places some limitations on their usage.
The development of the TWV was based on the old scooter motorcycles without much stability
considerations. The upright sitting positions of occupants result in high centre of gravity
(Mukherjee et al., 2007). Considering also that the vehicle is narrow and cannot lean inwards
when negotiating a bend to counter the effect of centrifugal force, there are bound to be
instability problems (Berote et al., 2008; Dardaine et al., 2008). Consequently, there are
challenges posed by the TWV especially in the area of safety of life and property, due to this
instability. However, Huston et al. (1982) and Valkenburgh et al. (1982) asserted that it is
possible to engineer a TWV that can be safe as the four-wheeled ones. Therefore, the aim of this
study is to generate mathematical models and to investigate the rollover stability of TWV, in
order to enhance safety of life and property on the roads.

2. Materials and Methods
2.1 Rollover Stability Model under Static Condition
Figure 2 shows the static model for TWV on a banked road for the determination of rollover
stability factor and height of centre of gravity h. Where θ is the angle of inclination of the
vehicle to the horizontal plane. The basic assumptions of the model are: load distribution is
symmetrical about x- axis when on horizontal plane and the effect of depression of tyre due to
load transfer is negligible.

Figure 2: Three-wheeled vehicle on a banked road

The governing equations are derived by vertical and horizontal resolution of forces about the
plane of motion:

FRI + FF + FRO = mg sin θ (1)
RRI + RF + RRO = mgcos θ (2)

FF =
L2
wB
mgsin θ (3)

RF =
L2
WB
mgcos θ (4)

FRI + FRO =
L1
wB
mgsinθ (5)

RRI + RRO =
L1
wB
mgcos θ (6)

WhereWB is wheelbase andWT is the wheel-track
Taking moment about centre of gravity:

h(FRI + FF + FRO) =
WT
2
(RRI − RRO) (7)

Substituting equation (1) and (6) in (7) to eliminate RRO:

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Ojolo et al: Rollover stability models for three-wheeled vehicle design. AZOJETE,16(1):92-99. ISSN 1596-2490; e-ISSN
2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: asuegeo@gmail.com 94

h(mg sinθ) = WT
2
(RRI − ( − RRI +

L1
wB
mgcos θ ) (8)

Rearranging equation (8):

RRI =
L1
2WB

mgcosθ + h
WT
mgsinθ (9)

Similarly, substituting equation (1) and (6) in (7) to eliminate RRI:

h(mg sin θ) = WT
2
( − RRO + ( − RRO +

L1
wB
mgcos θ ) (10)

Rearranging equation (23):

RRO =
L1
2WB

mgcos θ − h
WT
mgsinθ (11)

If the vehicle does not slide or is blocked from sliding as θ is increased, at limit of rollover, RRO
will become zero, therefore equation (11) becomes:

L1
2WB

mgcosθ = h
WT
mgsin θ (12)

Or:
L1
2WB

cos θ = h
WT
sin θ (13)

Therefore, the Static Stability Factor (SSF) for the three wheeled vehicle is defined as:
tanθ = l1

WB

WT
2h

(14)
The equation is basically the same as that of Huston et al., (1982) only that a different
methodology of derivation was adopted.
Rearranging equation (14), where h is height of centre of gravity of the vehicle:

h = L1
WB
x WTE
2tanθ

(15)
Equation (15) can be used to determine the height of centre of gravity h for a TWV, using
rollover angle, since other parametric values can be accessed or determined.

2.2 Rollover Stability Model under Dynamic Condition
Figure 3 shows the model of three wheeled vehicles moving in circle of radius R. The basic
assumptions of the model are: that the vehicle is moving in horizontal plane with constant
tangential velocity V, the effect of aerodynamic drag force is not significant, load distribution is
symmetrical about x-axis and the effect of depression of tyre due to load transfer is negligible.
Mathematical models were developed from the model to determine dynamic behaviour of TWV
as it affects the Rollover Stability, using force and torque equations.

Figure 3: Rollover dynamic stability model

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Arid Zone Journal of Engineering, Technology and Environment, March, 2020; Vol. 16(1) 92-99. ISSN 1596-2490;
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The centrifugal force acting at the centre of gravity (C.G) of the vehicle in the direction of y-axis
is balanced by lateral frictional resistance from the three wheels (FRI + FF + FRO ) if there is no
slide, while the rear wheels reactions due to the weight of the vehicle is given as L1

WB
(mg).

Therefore, the force equations are:
mV2

R
= FRI + FF + FRO (16)

RRO + RRI =
L1
WB
(mg) (17)

Taking moment about centre line A-O (along x-axis) to eliminate RF the equation becomes:
mV2

R
h = WT

2
(RRO−RRI) (18)

Substituting equation (17) in (18):
mV2

R
h = WT

2
L1
WB
mg− RRIWT (19)

At the limit of rollover stability the reaction at inner wheel will be zero (RRI = 0), therefore:
mV2

R
h = WT

2
L1
WB
mg (20)

Where V is now the critical or rollover velocity (VR) and a is the centrifugal acceleration
VR
2

R
= a = WT

2h
L1
WB
g (21)

Rearranging Equation (6):
a
g
= WT

2h
L1
WB

(22)

Equation (22), which is dimensionless, is the dynamic stability factor. The equation is basically
the same as that: static stability factor for TWV as seen in Equation (14); and Valkenburgh et al.,
(1982), except for the methodology of derivation.
The lateral friction coefficient (µ) is in the opposite direction to dynamic stability factor. If the
dynamic stability factor is less than the lateral friction coefficient, such that:

a
g
= WT

2h
L1
WB

< µ (23)

then vehicle will rollover since the lateral friction force will stop the vehicle from sliding, which is
not what is desirable in vehicle design. It is easier to handle sliding challenges under emergency
situation than rollover (Huston, et al., 1982).
If however, the dynamic stability factor is greater than the lateral friction coefficient, then the
vehicle will slide before rollover based on Equation (24), which is the desirable option in vehicle
design.

a
g
= WT

2h
L1
WB

> μ (24)

The rollover velocity (VR) is defined in Equation (25) based on Equation (21):

VR = (WT
h

L1
WB
gR)

1
2 (25)

The other dynamic reactions that may be incorporated into the basic Equation (22) are: dynamic
reactions due to acceleration and deceleration (Huston, et al., 1982) aerodynamic reactions due

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Ojolo et al: Rollover stability models for three-wheeled vehicle design. AZOJETE,16(1):92-99. ISSN 1596-2490; e-ISSN
2545-5818, www.azojete.com.ng

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to drag force (Sachdeva and Kamiyo, 2015; Rajamani, 2012); gyroscopic couple and Coriolis
force. These reactions put together will change the value of L1 to L1A . Since other factors are
constant, the final equation becomes:

a
g
= WT

2h
L1A
WB

(26)

2.3 Test Method for Rollover Stability Determination of TWV
There are various test methods for rollover stability. The following are some of the standard
methods for vehicle testing: The tilting test, constant cycle test, slowly increasing steer (SIS),
NHTSA (National Highway Traffic Safety Administration’s) J-turn and Road edge recovery (PER).
For the purpose of testing the vehicle for stability, tilting test method is adopted based on
Equations (14) and (15). Moreover, it is less involving and easy to implement in a developing
country. 0.8 is taken as minimum rollover stability factor or 39° minimum tilting angles
(Mukherjee et al., 2007).

Briscoe Garage UNILAG Service Centre was used for the test with fairly flat horizontal surface.
Items used for the test were: TWV, Long jack, Protractor with attached pendulum, Camera and
Engineering Tape. The vehicle was placed on the floor of the Garage with attached protractor
and a pendulum at the back of vehicle. The vehicle was jacked up from left or right until it
reached the rollover point as shown in the Figure 4.

All necessary readings were taken. Other values that involved loads were obtained through
analysis (Swearingen, 1962) , since it will be very involving to obtain standard human weights
with average centre of gravity.

Dimensions taken from the vehicles were: Wheelbase, wheel-track, horizontal distance from the
ground centre of front axle driver back support, horizontal distance from the ground centre of
front axle to the passenger back support, vertical distance from the to the top of driver seat and
vertical distance from the ground to the top of passenger seat.
For the purpose of this work, 72kg average weight for an adult was adopted based on the
random survey that was carried out at Ogun State Property and Investment Cooperation (OPIC)
Estate Agbara, Nigeria for one hundred adults.
Shown in Figure 4 is the picture of the vehicle during the tilting test.

Figure 4: Tilting of TWV to Rollover Angle

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3. Results and Discussion
3.1 Rollover Tilting Test Results
The Rollover dynamic stability factor determination was based on angle of tilt, which is tan θ
(Equation 14). Table 1 shows the values of rollover angles that were obtained through the tilting
test that was carried out at Briscoe Garage UNILAG Service Centre with the centre gravity of
humans taken into consideration (Swearingen, 1962) for a TWV on Nigerian roads.

Table 1: Rollover stability report
Item Occupants Rollover

Angle
Actual

Rollover
Angle
Minimum
Standard

Variance
a - b

Compliant (C) /
Non-compliant
(NC)

A B c D e
1 0 390 390 00 C
2 1 = Driver 340 390 -50 NC
3 2 = Driver + 1 Passenger 340 390 -50 NC
4 3 = Driver + 2 Passengers 300 390 -90 NC
5 4 = Driver + 3 Passengers 280 390 -110 NC

Figure 5 shows the TWV rollover stability simulations.

Figure 5: Rollover stability angle versus occupants

From Table 1 and Figure 5, it can be deduced that the vehicle itself without any occupant is
rollover stable. With the driver alone, the vehicle became unstable. The reason is quite obvious.
The weight of the driver shifted more load to the front wheel than the rear. This reduced the
value of L1 and also increased the overall height of C.G. since centre C.G. of vehicle is lower than
that of the driver. The two factors combined together brought down the value of rollover
stability below the minimum required based on Equation (14). The result is in line with that of
literature (Mukherjee et al., 2007; Karanam et al., 2012). However, with the first passenger at rear
seat, more loads were transferred to the rear wheels than the front wheel because of the
position of C. G. of the vehicle (Karanam et al., 2012). One would have expected rollover stability
to increase but the height of C. G. of the passenger nullified the effect of increase in stability.
Moreover, with more passengers, the effect of the height of C. G. of passengers took over since

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Ojolo et al: Rollover stability models for three-wheeled vehicle design. AZOJETE,16(1):92-99. ISSN 1596-2490; e-ISSN
2545-5818, www.azojete.com.ng

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there were no more backward movements. This made the vehicle to become more and more
rollover unstable. Therefore, the non-compliance of the vehicle, in terms of rollover stability is
mainly due to the high C. G. of occupants. It can be deduced from the variances that the vehicle
itself is rollover stable and it will suffer rollover instability with one occupant and above.

From equations (14) and (22) it can be seen that the factors that affect rollover stability are:
wheel-track (WT), horizontal distance from centre of front wheel to the C. G. of vehicle (L1 ),
height of C. G. (h) and wheelbase (WB). Deceleration will transfer more load to the front wheel
thereby increasing rollover instability and should be taken into account in vehicle design
stability. Outward cambering of rear wheels will increase rollover stability since wheel-tract is
increased (Ihueze and Ebisike, 2018). In case of the redesign of the vehicle, the effect cambering
of the wheels should be taken into consideration, including suspension, and roll resistance.
There are other factors such as steering compliance, gyroscopic couple due to road bumps,
Coriolis force due to curvilinear motion, etc. that could impact negatively on lateral stability. All
these factors should be taken into consideration in a major modification of the vehicle at the
initial stage of its design to be rollover stability compliant based on Equation (26), so that newer
models of the vehicle will be rollover stable.

4. Conclusions
This study came up with mathematical models and tilting test method for the determination of
the rollover stability of TWVs and for the design and regulation of the vehicle in developing
countries, in order to enhance safety of life and property.

The test method was used in the determination of the rollover stability of one of the
commonest TWV on the Nigerian road. The vehicle was found to be rollover unstable with one
occupant and above. However, this instability could be minimised on the current TWV by
increase in the wheel-track of the vehicle relatively to wheelbase and lowering seat heights of
the occupants. The ultimate solution lies in redesigning of the vehicle to take care of the
problem.

The TWST currently being used by developing countries is not too safe in terms of rollover
stability due basically to the high centre of gravity of occupants. Therefore, the following
recommendations are made to ensure its rollover stability:
That the Rollover Stability Factor should not be less than 0.8 which amounts to 390 rollover
angle, taken into consideration all the loadings through redesign and modifications.
Developing countries should at least adopt the Tilting method of vehicle testing for the design,
regulation and importation of TWV.

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Corresponding author’s e-mail address: asuegeo@gmail.com 99

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