ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT
AZOJETE, September 2019. Vol. 15(3) 628-637

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

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638

ORIGINAL RESEARCH ARTICLE

EFFECT OF NUMBER OF PASSENGERS [LOADING] ON CENTRE OF GRAVITY OF A
THREE WHEELED VEHICLE [KEKE-NAPEP]

B. Sunday1*, U. Thomas1, I. S. Ityokumbul2, A. Nasir3
(1Department of Mechanical Engineering, Nuhu Bamalli Polytechnic, Zaria, Nigeria
2Department of Mechanical Engineering, Kaduna Polytechnic, Kaduna, Nigeria

3Department of Mechanical Engineering, Federal University of Technology, Minna, Nigeria)
* Corresponding author’s email address: s2bako@yahoo.com

ARTICLE INFORMATION

Submitted 22 November, 2018
Revised 7 March, 2019
Accepted 10 March, 2019

Keywords:
CG Analysis
CG of Four Wheeled Vehicle
CG of Three wheeled Vehicle
Effects of Loading on CG
Static Stability Factor

ABSTRACT
In order to combat insecurity and to reduce the rate of accidents
caused by commercial motorcyclist; many States Government in
Northern Nigeria have substituted the use of motor cycles commonly
known as Okada, with the use of three wheeled vehicle commonly
known as keke-napep. The Static and dynamic characteristics of these
vehicles are not as those of the usual vehicles. Therefore, the need to
know more about the effects loading on these vehicles is highly
needed by Nigerians in order to ensure good road and passengers’
safety. This paper uses simple approach to highlight the effects of
number of passengers (loading) on the position of Centre of Gravity
(CG) of the three wheeled vehicles. It will serve as a measure for
ensuring safe riding and reducing road clashes. As the load on the
three wheeled vehicle increases from 3505N to 5410N, the Static
Stability Factor decreases. This reduces the safety margin against
rollover of the three wheeled vehicles compared to those of the four
wheeled vehicles. The keke-napep is a rear wheel drive vehicle with rear
engine and rear passenger arrangement. It subjects the vehicle to high
weight transfer during braking. This causes the change in position of
Centre of Gravity and the instability of the three wheeled vehicles.
Therefore, it is hereby recommended that the wheelbase, track length,
loading space and the Centre of Gravity position should be given a
critical consideration during chassis design in order to improve the
static and dynamic stability of these vehicles. Also, Components such as
the engine and transmission system should be rearranged to obtain a
more reliable position of the Centre of Gravity.

© 2019 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved.

1.0 Introduction
Three wheeled vehicles are automobiles with three wheels; having one or two wheels at the front
for steering while the other one(s) for power transmission (Saeedi and Kazemi, 2013). These
vehicles are commonly known as: Tuk-tuk in Kenya, Bajaj in Somalia, Tok-tok in Egypt, Rasha in
Sudan, Baby Taxi in Bangladesh and Keke-napep in Nigeria. Having one wheel at the front and
two at the rear the vehicle is known as the delta configuration. The second type of three wheeled
vehicles is called the tadpole or reverse trike which is the opposite of the delta type (Palash et al.,
2014). Figure 1 shows the Delta type of three wheeled vehicle commonly use in Nigeria for
commercial transportation. The vehicle has many advantages over two wheeled vehicles. They

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offer, more comfort, more luggage space, more distance between fill-ups and an increased
safety. Having three wheels on the ground, they are naturally more stable than two wheeled
vehicles. They combine the comfort and safety of a four wheeled vehicle (car) (Berote et al.,
2008). It has the disadvantage of instability compared to four wheeled vehicles. The presence of
three wheels indicates that the vehicles would have different static and dynamic characteristics
compared to those of other vehicles. This paper shows how the number of passengers (loading)
effects the position of Centre of Gravity (CG) of the three wheeled vehicles, thereby affecting its
static and dynamic characteristics.

One of the crucial vehicle properties is the location of its position of Center of Gravity and if it is
properly located, the vehicle would be stable (Starr, 2006)). The Centre of Gravity position of the
three wheeled vehicle changes with inclusion of more passengers (Mukherejee, 2007). This
happens as the result of loading on the vehicle. Overloading is a safety hazard that has leads to
loss of lives, properties and deterioration of our roads which results in increase of maintenance
and transportation cost. In the fight against road accident; the Federal Road Safety Commission
incorporate campaigns against overloading. This fight can only be successful if the riders and
public knows the impact and effects of overloading on the vehicles. This paper tends to highlight
the effects of passengers (loading) on the position of Centre of Gravity of the three wheeled
vehicles. The concept of this paper would help to educate the riders and the general public on
effects of loading on the stability of these vehicles. This would help to monitor the static and
dynamic characteristics of these vehicles thereby improving its service life and to ensure good
road and passengers’ safety.

Figure 1: A Delta Type of Three Wheeled Vehicle Commonly use in Nigeria

2.0 Materials and Method
The materials used in this paper are: three wheeled vehicle technical specifications, literatures,
Microsoft excel (2007) and AutoCAD (2010) engineering drawing software. Data obtained from
the three wheeled specification and literatures were utilized using equations to calculate the
position of Centre of Gravity (CG) from; the rear wheel, front wheel and from the roll over lines.
The data were also used to calculate the height of the Centre of Gravity from the road surface
and Static Stability Factor (SSF) of the three wheeled vehicles under different loading conditions.
This was done in order to investigate the effect of number of passengers (loading) on the Centre
of Gravity of the three wheeled vehicles. All the calculated results were presented inform of
graphs using Microsoft excel (2007) and the results were discussed. The AutoCAD (2010)
engineering drawing software was used for drawing purpose to illustrate the position of Centre
of Gravity on the three wheeled vehicles.

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Sunday, et al: Effect of number of passengers [loading] on centre of gravity of a three wheeled vehicle [keke-napep].
AZOJETE, 15(3):638-647. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: s2bako@yahoo.com 640

3.0 Centre of Gravity (CG) Analysis
It was noted in Raipput (1991) and Abbott (1984) that the weight of all parts of a body are
directed toward the centre of the earth and the point through which all the weights act is called
the Centre of Gravity (CG). Palash et al. (2014) and Abbott (1984), also noted that the centrifugal
force (CF) is exerted at the Centre of Gravity (CG) and is directed toward the centre (turning
point) in order to keep a body moving in a circular path.

3.1 Centre of Gravity Analysis for Four Wheeled Vehicle
Consider a four wheeled vehicle as shown in Figure 2 (a). If the vehicle is in a curve towards the
left, the Centrifugal Force (CF) tends to roll the vehicle over towards the right, around an
imaginary point (black spot under the right tyre in Figure 2 (b)), while the Gravitational Force (GF)
holds the vehicle back to avoid rollover. It’s as though the Centrifugal Force and the
Gravitational Force combined together into a resulting force exerted on the Center of Gravity to
turn it around this imaginary point (Palash et al., 2014).
Mukhejee (2007), states that the ratio of half-track width (half the distance of the centre of the
two rear tyres) to the height of Centre of Gravity (h) is called the State Stability Factor (SSF), and
this plays a crucial role in determining the stability against rollover of a four wheeled vehicle.

(a) (b)
Figure 2: Position of Centre of Gravity (Developed from; (Palash et al. 2014). (a) Top view of Four

Wheeled Vehicle. (b) Rear view of Four wheeled Vehicle.

3.2 Centre Gravity Analysis for Three Wheeled Vehicles
In the case of three wheeled vehicles, another factor comes into play; unlike the four wheeled
vehicles, their structures are triangular in design. The slant sides from the front wheel to the rear
wheel are called the rollover lines. It is observed that the distance between the Center of Gravity
and the rollover line (Figure 3 (a)) is shorter than in the case of the four wheeled vehicles, even
though the Center of Gravity height (h), the base length (L) and the track (t) of the three wheeled
vehicle are the same as those of the four wheeled vehicles. The Center of Gravity height (h) is
therefore proportionately greater, which reduces its safety margin against rollover of the three
wheeled vehicles in curves. As it was shown for the four wheeled vehicles; they roll over around

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Arid Zone Journal of Engineering, Technology and Environment, September, 2019; Vol. 15(3):638-647. ISSN 1596-2490;
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641

the rollover line corresponding to the imaginary point. But in the case of a three wheeled vehicle,
it rather rolls over around the rollover line going from the single front wheel to one of the two
symmetrical rear wheels.

(a) (b)
Figure 3: Position of Centre of Gravity (Developed from Palash et al., 2014). (a) Top view of Three

Wheeled Vehicle. (b). Rear View of Three Wheeled Vehicle.

3.3 Effects Loading on Centre of Gravity (CG)
Kenneth et al., (1996) noted that the Centre of Gravity (CG) of a loaded vehicle ‘’A’’ would shift
rearward to point ‘’B’’ as shown in Figure 4 (a). As the Center of Gravity (CG) of the four wheeled
vehicles shift from ‘A’ to ‘B’ the distance At1 and At2 remains constant (At1=At2). While for the
three wheeled vehicles; distance increases (C1<C2) as shown in Figure 4 (b). The loading of the
four wheeled vehicles in this analysis leads no change in static stability. The loading of the three
wheeled vehicles did improve its static stability when change in CG height is neglected (Kenneth
et al., 1996).

(a) (b)
Figure 4: The Effects of Loading. (a). Four Wheeled Vehicle, (b) Three Wheeled Vehicle. (Adapted

from; Kenneth et al. 1996)

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Sunday, et al: Effect of number of passengers [loading] on centre of gravity of a three wheeled vehicle [keke-napep].
AZOJETE, 15(3):638-647. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: s2bako@yahoo.com 642

3.4 Effects of Loading on Centre of Gravity Position
From the technical specifications of three wheeled vehicles by Bajaj (2014); It was noted that the
three wheeled vehicles have a wheel base (L) of 2m and wheel track (t) of 1.3m. Mukherejee
(2007) shows that. The Centre of Gravity position, mass and moment of inertia changes with the
inclusion of more passengers (loads) on the Bajaj three wheeled vehicle. In order to calculate the
distance of the rollover line parallel to the Centre of Gravity (c’’) at various (number of
passengers) loading condition, the ‘x’ axis was rotated parallel to the roll over axis, as shown in
Figure 5.

Figure 5: Lateral distance from CG to rollover axis (Adapted from Azadeh, 2014)

Figure 6: Side-view of the vehicle showing the vertical force (weight).
According to Figure 5, θ can be determined from equation (1),
θ = tan−1

t
2L

(1)

To calculate the distance of Centre of Gravity (CG) from the Rollover line (c) from Figure 3 (a) and
Figure 5 (Azadeh, 2014);
c
T
2
=
a
L → c =

T × a
2L (2)

While,
c'' = ccosθ (3)
By substituting Equation (2) into Equation (3)
c'' =

T × a
2L ccosθ (4)

Equation (4) above is used to determine the position of Centre of Gravity from the roll over line
The Static Stability Factor (SSF) is defined as one half the track width (wheel track) divided by the
height of the Centre of Gravity (Narang, 2004). This is determine using equation (5) below;
SSF = t

2h
(5)

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643

According to Thomas (1992), when a vehicle sits statistically on a level ground, the weight
distribution on the front and rear wheels are related by equation (6) and (7) respectively;
Wf = W b

L
(6)

Wf = Weight at the Front Wheel (N)
W = Total Weight of the Vehicle (N)
The weight at the rear of the Three Wheeled Vehicle is given by;
Wr = W

a
L

(7)

Wr =Weight at the Rear Wheel (N)

4.0 Results and Discussion
The three wheeled vehicles use in Nigeria is design to carry the maximum of three passengers at
the rear seat, but the riders tend to carry four passengers in order to maximized profit. In the
case of carrying additional passenger at the front; the driver’s control and operating space are
reduced, escalating the chance of for accidents. In Table 1, the fourth passenger was computed
in order to show the effects of increase in (number of passengers) weight on the position Centre
of Gravity of the three wheeled vehicles.

From Table 1, as the number of passengers increases from 0 to 4, the weight at the front wheel
decreases, while the weight at the rear wheels increases. This also increases the weight transfer
from the rear wheels to front wheel during braking. Due to this effect and the presence of one
wheel at the front, makes the three wheeled vehicles unstable thereby leading to rollover
accident during braking. Also, from Table 1, as the vehicle total weight increases due to increase
in number of passengers, the distance of Centre of Gravity increases from 1.305m to 1.645m
along the base length (wheelbase) from the front axle, with an inverse reduction in length of
Centre of Gravity from the rear. This also leads to an increase in distance of Centre of Gravity
from the rollover line thereby increasing the rollover propensity of this vehicle. This increase in
weight as the result of increase in number passengers on the keke-napep also leads to an
increase in height of Centre of Gravity from the 0.602m to 0.828m. This inversely reduces the
Static Stability Factor (SSF) of the vehicle as indicated by the last column of Table 1.

Table 1: Effects Weights and Position of Centre of Gravity (CG).
(Developed from; Mukherejee, 2007)
Total No. of
Occupant
(= Driver + n)

Weight (N) CG Location (m) Static
Stability
Factor
(SSF)

At Front
Wheel
Wf

At Rear
Wheels
Wr

Total
W

From
Front
Axle
(a)

From
Rear
Axle
(b)

From
Rollover
Line
(c)

From
Rollover
Line
(c’’)

Height
(h)

1( = 1 + 0) 1221 2284 3505 1.303 0.697 0.423 0.402 0,602 0.540
2( = 1 + 1) 1349 2927 4276 1.369 0.631 0.445 0.423 0.661 0.492
3( = 1 + 2) 1474 3573 5047 1.416 0.584 0.460 0.438 0.701 0.464
4( = 1 + 3) 1600 4218 5818 1.450 0.550 0.471 0.448 0.731 0.444
5( = 1 + 4) 1179 5410 6589 1.642 0.358 0.534 0.508 0.828 0.393
n = Number of passengers

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Sunday, et al: Effect of number of passengers [loading] on centre of gravity of a three wheeled vehicle [keke-napep].
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Figure 7 (a), Shows that for every increase in weight (number of passengers), the distance of CG
from the front axle (a) are inversely proportional to the distance of CG from the rear axle (b). This
justified the work done by Kenneth et al. (1996), which states that if a vehicle is loaded, its
position of Centre of Gravity (CG) shifts to the rear. The three wheeled vehicle is a rear-engine,
rear-wheel drive vehicles and according to Dolan (1978), increase in weight at the rear of a rear-
engine, rear-wheeled drive vehicle tends to make the vehicle unstable at high speeds.

Palash et al. (2014), noted that if the Centre of Gravity height (h) is greater than half the track
length (t/2), the resulting force (R) (Figure 3 (b)) would align with the imaginary point (black spot
under the tyre) and will roll the vehicle over in a curve. From Table 1, the least value of the
Centre Gravity height (h) is 0.602m, while the half of the track length is 0.575m when the three
wheeled vehicle is loaded. This shows that the Centre of Gravity height (h) of the three wheeled
vehicle is proportionally greater than half its track length. This increases the rollover tendency of
the vehicles. Therefore, the higher the weight, higher the position of position of Center of
Gravity height (h) from the two symmetric wheels, and the longer the distance of the Centre of
Gravity from the rollover line (c and c’’) as shown in Figure 7 (d). This reduces the safety margin
against rollover of the three wheeled vehicles compared to the four wheeled vehicles.

The Static Stability Factor (SSF) is viewed as the ultimate measure of the rollover resistance of a
vehicle. Figure 7 (c), shows that the Static Stability Factor of the three wheeled vehicle decreases
with an increase in weight (number of passengers) on the three wheeled vehicles. This increases
the rollover propensity of the three wheeled vehicles. Therefore, the riders should not exceed the
recommended riding speed and should always maintain the recommended tyres pressure. The
three wheeled vehicles are rear-engine, rear-wheeled drive with rear passengers’ arrangement.
According to Dolan (1978), a rear-engine, rear-wheeled drive vehicles have tendency to over
steer (that is the wheels turn too sharply into the curve) and this can be corrected by turning the
steering in opposite direction.

(a) (b)

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(c) (d)
Figure 7: (a) CG from Front and Rear Wheel (b). CG from Roll Overline.

(c) Static Stability Factor (SSF). (d) Height of CG (h).

Under some riding conditions of the three wheeled vehicles, it is possible to have only two
wheels in contact with the road surface. This could occur during turning or tight maneuvers
whenever enough weight is transferred outside the rollover lines. This tendency requires careful
load and passenger positioning inside the vehicle (Motorcycle Operator Manual, 2017). If the
loads are not properly positioned on the vehicle, the weights will not be properly distributed at
each wheel. This would affect the position of Centre of Gravity and the static and dynamic
stability of the vehicle.

Consider the vehicle moving on a horizontal road (Figure 8). Giri (2010), noted that a vehicle
weight and its kinetic energy act through the Center of Gravity. This makes the vehicle to pitch
forward when the brakes are applied. As a result of this action, some weights are effectively
transferred from the rear wheel to the front wheels. Due to the rear-engine, rear-wheeled design
of the three wheeled vehicles and the rear position of passengers; the weight at the rear is more
than that of the front. This weight is transfer to the front during braking. This changes the
position of Centre of Gravity which affects the stability of the vehicle. Therefore, this problem of
weight transfer and instability of this vehicle can be improved by;
Designing the height of the Centre of Gravity to a minimum level toward the road surface.
Designing the length of the Centre of Gravity to a minimum distance from the two (2) rear
wheels.
Significant increase in length of the rear wheel track length.

Figure 8: Weight Transfer (Developed from; Giri (2010)).

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Sunday, et al: Effect of number of passengers [loading] on centre of gravity of a three wheeled vehicle [keke-napep].
AZOJETE, 15(3):638-647. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

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Overloading puts massive strain on vehicle tyres and chassis and also makes the vehicle less
sable, difficult to steer, takes longer time to stop and causes damages to the road and road
users. To reduce the number of road accidents; the government should set measures to regulate
the operation of these vehicles. The Federal Road Safety in conjunction with the Vehicles
Inspection Officers should enforce this illegal art.

5.0 Conclusion and Recommendations
The paper presents the effect of number passengers (loading) on the Centre of Gravity of a three
wheeled vehicle (keke-napep). This analysis shows that the inclusion of each passenger (load) on
the three wheeled vehicles, raises the Centre of Gravity (CG) height (h) and decreases the vehicle
Static Stability Factor (SSF). Also, the farther the position of Centre of Gravity (CG) from the two
symmetric wheels towards the single wheel, the shorter the distance (c) from the Center of
Gravity to the rollover line. This reduces the safety margin against rollover effect of the three
wheeled vehicles compared to the four wheeled vehicles. This implies that the three wheeled
vehicles with minimum number of passengers (loads) would be more stable in rollover condition
than a three wheeled vehicle with high number of passengers.

The keke-napep is a rear wheel drive vehicle with rear engine and rear passenger arrangement.
This makes the vehicle to have high load concentration at the rear wheels. This subjects the
vehicle to high weight transfer during braking. This affects the position of Centre of Gravity and
the instability of the three wheeled vehicles. Therefore, it is hereby recommended that the
wheelbase, track length, loading space and the Centre of Gravity position should be given a
critical consideration during chassis design in order to improve the static and dynamic stability
of these vehicles. Also, Components such as the engine and the transmission system should be
rearranged to obtain a more reliable position of the Centre of Gravity.
Finally, as the numbers of these vehicles increases as a means of commercial transportation in
Nigeria, the rate of traffic congestion, air pollution and road clashes would also increase.
Therefore, the Federal Ministry of Transport and Environmental should set aside future measures
to combat these phenomena.

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Arid Zone Journal of Engineering, Technology and Environment, September, 2019; Vol. 15(3):638-647. ISSN 1596-2490;
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