Real Driving on Under-inflated Rear Tire on Horizontal Curves:

A Road Experimental Study

Yasmany García-Ramírez

Civil Engineering Department, Universidad Técnica Particular de Loja, San Cayetano Street, Loja, Ecuador

Keywords: Under-inflated Rear Tire, Horizontal Curves, Experimental Study.

Abstract: An under-inflated tire represents a high risk of accidents for vehicle occupants and other users. Publications

have previously been directed toward monitoring tire pressure and its influence on several driving-controlled

experiences. However, little has been written about their impact on a real road trip, for example driving on

curves, grades, or unfavourable weather conditions. This study aims to evaluate the relationship between the

stability variables on the vehicle in curves of the road when driving on the under-inflated rear tire on wet

pavement. In this interesting experience, the left rear tire of a pickup truck was under-inflated to 10 psi (-

33%). The vehicle travelled more than 50 km of a mountain road. As a result, an average reduction in speed

(-6.5%) was found in the right curves and an average increase in lateral acceleration (+ 8.5%) in the right

curves in relation to the left ones. As a secondary result, the radius of the curve had a statistical relationship

on lateral acceleration and the grade had not. The results of this study, would help to create a new indirect

pressure method and in accidents reconstructions.

1 INTRODUCTION

Driving on under-inflated or deflated tires cause

damage very quickly. Inadequate tire inflation can

shorten the tire life or damage the rim, it may lead to

a tire blow-out, affect the passenger's comfort, or

even negatively affect the vehicle's stability (Motrycz

et al., 2021; Toma et al., 2018). Those effects could

induce the driver's loss of control and subsequent

vehicular accidents (Fancher et al., 1974; Liqiang et

al., 2018). A properly inflated tire that distributes the

vehicle weight could provide good contact with the

road, passenger comfort, responsive handling, and

uniform tire wear (Varghese, 2013). Nowadays,

modern vehicles are equipped with systems that

monitor vehicle safety problems.

The tire-pressure monitoring system (TPMS) is

one of those systems. There are two approaches to

perform this monitoring: direct and indirect. The first

method has higher precision but is more expensive.

While the second one has more errors but is cheaper

(Goharimanesh et al., 2016). The direct method uses

a tire pressure sensor to measure the tire pressure

directly. The indirect one, such as the rotation radius

procedure, employs effective tire rotation to monitor

https://orcid.org/0000-0002-0250-5155

the tire pressure (Liqiang et al., 2018). In both cases,

the idea is to warn drivers when the tire has lost air

pressure. For them to act, they need to know the

effects of driving with an under-inflated tire.

Under-inflated tires increase forward drag and

lateral steering effects on vehicles which are frequently

an issue in an accident reconstruction (Robinette et al.,

1997). Since the under-inflation tire increases the

contact patch length, the tire would have a higher

rolling resistance (Varghese, 2013). And with lower

speeds, the rolling resistance will be higher (AASHTO,

2011). Also, the tire pressure affects the vehicle

handling, such as lateral force, self-aligning moment,

and longitudinal force (Pacejka, 2012). What happens

if drivers, despite warnings or knowledge, do not act.

What would happen?

Several studies were conducted to answer this

question. One of the experiments had six passenger

cars and a pickup truck (Robinette et al., 1997). With

all four tires deflated to 10 psi, acceleration and

vehicle control results were similar to the tires'

pressure in the regular conditions. When one tire was

deflated (either the front or rear axle), the driver

controlled the vehicle. These results are applicable up

to 72 km/h (45 mph). Another investigation, between

324

García-Ramírez, Y.

Real Driving on Under-inﬂated Rear Tire on Horizontal Curves: A Road Experimental Study.

DOI: 10.5220/0011056900003191

In Proceedings of the 8th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2022), pages 324-330

ISBN: 978-989-758-573-9; ISSN: 2184-495X

5-7 km/h, found the tire pressure did not influence the

maximum braking rate (Toma et al., 2018). One study

using laboratory and field equipment found that a

decrease in inflation pressures reduces the cornering

and camber stiffness and increases the aligning

stiffness of the tire (Fancher et al., 1974). Based on

these results, well-adjusted mathematical

relationships have been carried out with simulators

for road accident reconstruction (Zȩbala et al., 2014;

Zebala & Wach, 2014).

Most of the studies carried out in the field have

not related the variables of the vehicle stability when

it has an under-inflated tire with geometric variables

on the road, such as a curve. In addition, they have

been in a relatively controlled environment, for

example, in good environmental conditions.

Therefore, the objective of this study is to evaluate the

relationship between the stability variables on the

vehicle on curves, when driving on an under-inflated

rear tire on wet pavement. It analyzed the speed,

lateral and longitudinal acceleration, the vertical

velocity with the radius of the curve and the grade.

To present these findings of this unique

experimental study, the materials and methods details

the selection of the road and the vehicle, measurement

tool. Also, it presents the road geometric design

estimation, and data collection procedure and data

processing. Then, the results are presented in section

3, where four analyses are performed: curve radii,

grade, descriptive statistics, and linear regression.

Each section discussed the influence of the geometric

features on speed, vertical velocity, and accelerations.

2 MATERIALS AND METHODS

2.1 Road Selection

The selected road for the study was in a mountainous

topography (see Figure 1). Considering its geometric

design limitations, this type of road allows it to have

a high number of horizontal curves. Also, combine

them with other geometric elements, such as steep

grades. The evaluated road section has a length of

more than 50 km. The longitudinal profile of the road

is shown in Figure 2. In this profile, the sections with

homogeneous grades have been shaded. This profile

was obtained from the GPS data of the VBOX tool.

The selected road is located in the Ecuadorian

Amazon between Palanda and Yangana town. This

road belongs to the "Eje Vial No. 4" that

communicates Ecuador with Peru. The road has a

rigid pavement roadway and has a lane width of 3.65

m. The road crosses several protected forests:

Podocarpus National Park and Tapichalaca Reserve.

The mountain forests and paramos of the region are

considered "super-humid" since rainfall over 6000

mm has been recorded (Richter, 2003).

Figure 1: Planimetry of the selected road for this

experimental study (Ecuador).

Figure 2: Road vertical profile of the selected road.

2.2 Test Vehicle Selection

The vehicle selected was a Chevrolet D-Max diesel

pickup. The truck has the characteristics shown in

Table 1. This car is practical in the case of small

landslides, small rock falls, among others, which are

frequently on these roads. The vehicle has ABS +

EBD brakes, traction control, and stability control.

2.3 Measurement Tool

The selected measurement tool was the Video VBOX

Lite. This device collects the following data: time,

Real Driving on Under-inﬂated Rear Tire on Horizontal Curves: A Road Experimental Study

325

distance, satellites, speed (km/h), heading (degrees),

latitude, longitude, height (m), vertical velocity

(km/h), longitudinal and lateral acceleration (m/s²).

Table 1: Technical specifications of the test vehicle.

Characteristic Condition

Motor 2,5L turbo diesel

Net Power (Hp @ rpm) 34 @ 3600

Torque (Nm @ rpm) 320 @ 1800

Traction 4x4

Front suspension

Independent Double

Wishbone Type

Rear suspension Rigid with Crossbow

Gross vehicle weight (kg) 2950

Front axle capacity (kg) 1350

Rear axle capacity (kg) 1870

Tire size 245/75/ R16

Rated press 30 psi

Height (mm) 1790

Width (mm) 1860

Length (mm) 5295

It allows recording geo-referenced digital images

through high-resolution cameras and the GPS

antenna. The antenna was placed on the roof of the

vehicle. The Video VBOX Lite has an accuracy of

0.05% for distance travelled, 0.2 km / h for speed, and

± 10 m for height. Accuracy acceleration: 0.50%

(resolution = 0.01 g and max = 20 g). The device has

a sampling frequency of 10 Hz.

2.4 Road Geometric Design Estimation

The VBOX Lite also collects the heading data. This

variable helped to estimate the horizontal geometry of

the road. The use of heading direction for recreating

the horizontal alignment of an existing road

(Camacho-Torregrosa et al., 2015) is well extended in

the field. The heading remains constant when

traveling along a tangent and varies its slope when

traveling along a horizontal curve. After this

procedure, a check of the radii of the curves was

carried out using the calculation method based on

three known points. With this procedure, 327

horizontal curves were determined. This value means

that there are 6.29 curves per kilometre. The radii of

these curves were between 20 to 558 m.

On the other hand, to determine the grades of the

section, the total length was divided into sub-sections

that have the same slope. In these homogeneous sub-

sections, the average slopes of each section were: -

9%, -8%, -7%, 2%, 4%, 5% and 8%.

2.5 Data Collection Procedure

The Video VBOX Lite was placed inside the test

vehicle, as seen in Figure 3. The device has a GPS

antenna and a high-resolution camera.

Figure 3: Details of data collection on the test vehicle.

The antenna was placed in the central part of the

vehicle roof, and the camera was placed on the front

windshield facing the road. Data were collected in

poor weather conditions: light rain, wet pavement,

and daylight. The test vehicle was unloaded. The

rated press of the tire suggested by the manufacturer

in the unloaded state is 30 psi. The air pressure of the

left rear tire was reduced to 10 psi. This value was

taken from the previous literature (Robinette et al.,

1997). A single trip was made considering the risk of

the test. As a precaution, emergency and mechanical

units were located in the middle and end of the route.

After finishing the experiment, the mechanical team

checked the tire and the operation of the entire vehicle

and its components. During the test, the driver was

always able to easily maintain control of the test

vehicles and steer them in the road test.

2.6 Data Processing

After the data collection, video and data were

obtained employing the VBOX Test Suite ® of the

equipment manufacturer. It eliminated all the

following data: the vehicle was not in free flow,

overtaking maneuverer, in an urban or suburban area,

or when the road deteriorated. The acceleration data

were subjected to a smoothing process using a

Figure 4: Example of lateral acceleration smooth.

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326

moving average with a window width of 7. Figure 4

shows as an example, the original and smoothed

profile of lateral acceleration. After this procedure,

the data was extracted in the midpoint of the

horizontal curve, also shown in Figure 4.

3 RESULTS

The number of satellites registered on the route was

between 6 and 13, with an average of 10. The

minimum speed was 5.03, and the maximum was

69.37 km/h. Previous studies reached 72 km/h

(Robinette et al., 1997). The under-inflated rear tire

could mainly affect the speed, vertical velocity,

longitudinal acceleration, and lateral acceleration. It

would have very little relevance to analyse all the

acceleration values without considering the geometry

of the road. Therefore, these are discussed below for

the road grades and the radii of the curves.

3.1 Road Grades Analysis

In order to analyse the variations of the variables

concerning the grade, the homogeneous sections with

similar slopes were grouped. Then, it calculated their

average grade in every section. Then, it plotted the

boxplots of the speed, vertical velocity, longitudinal

and lateral acceleration versus the grade of the road

(see Figure 5). In Figure 5, it can be seen just the

logical relationship between vertical velocity and

slope. Vertical velocity has a direction associated, is

positive when climbing, and is negative when

descending. Regarding speed, there are no significant

variations between positive or negative slopes that

have been reported in previous research (García-

Ramírez & Alverca, 2019). Previous studies found

higher speeds on descending slopes and lower them

on ascending slopes. This situation could be a result

of a mountain topography with consecutive curves,

where the grade could be less important than the

curvature itself.

3.2 Curve Radii Analysis

The scatterplot of the speed, vertical velocity,

longitudinal and lateral acceleration is seen in Figure

6. The scatterplot of the speed, vertical velocity,

longitudinal and lateral acceleration is seen in Figure

6. In this figure, when the radius of the curve is lower,

speeds go down, and vice versa. This relationship is

well documented in previous speed prediction

models. Regarding the vertical velocity, the Figure 5

does not show any trend with the grade or the radius

of the curve. On the other hand, the longitudinal

acceleration does not present any visible trend, unlike

the lateral acceleration, where the highest values are

found in the radii smallest and the lowest at the largest

radii. This relationship is consistent with the highway

geometric design philosophy (AASHTO, 2011).

In Figure 6, the direction of the curve has also

been placed. This was done because the driver, during

Figure 5: Boxplot of speed, vertical velocity, longitudinal

and lateral acceleration versus the grade of the road.

Real Driving on Under-inﬂated Rear Tire on Horizontal Curves: A Road Experimental Study

327

the test, reported skidding in the left curves. The

grade and vertical speed were discarded since there

were no significant differences. Table 2 shows the

average speed, acceleration, and radius. This table

confirmed the trends in Figure 6, and, other two

interesting elements appear, the speeds generally are

lower in the right curves; while the lateral

accelerations are lower in those curves. In the next

section, this element will be analysed in deep.

Figure 6: Scatterplot of the speed, longitudinal and lateral

acceleration versus the radius of the curve and considering

the direction of the curve.

3.3 Descriptive Statistics Analysis

Table 3 presents the descriptive statistics of the

variables previously detected. This table shows the

mean longitudinal acceleration in the right curve is

greater than in the left. The rest of the statistics are

very similar to each other, except for the minimum

value. Regarding the mean lateral acceleration, the

value of the right curve is also greater than the left.

Table 2: Descriptive statistics of speed and acceleration

with the ranges of the radii of the curves.

Radii of

curves

(m)

Mean

Speed

(km/h)

Mean long.

acc. (m/s

)

Mean lat.

acc. (m/s

)

All data

20-50 110 40.1 -0.233 3.518

51-100 123 48.9 -0.145 2.707

101-150 43 52.1 0.188 1.981

151-200 16 55.9 0.090 1.218

201-250 13 54.4 0.155 0.719

>250 22 57.4 -0.151 0.856

Right curves

20-50 66 39.7 -0.242 -3.461

51-100 52 48.0 -0.321 -2.671

101-150 16 51.6 0.144 -2.305

151-200 5 53.4 0.188 -1.382

201-250 5 52.2 0.336 -0.934

>250 13 55.5 -0.057 -0.980

Left curves

20-50 44 40.6 -0.219 3.604

51-100 71 49.5 -0.015 2.735

101-150 27 52.3 0.214 1.790

151-200 11 57.0 0.045 1.143

201-250 8 55.7 0.041 0.585

>250 9 60.2 -0.288 0.677

Regarding the speeds, in general, higher values

were obtained in the left curves than in the right

curves. The driver was expected to slow down in the

right curves since with the under-inflated rear tire, the

possibility of outward skidding was a consequence.

This behaviour does not occur on left curves. This

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particularity also impacts the lateral acceleration,

since although the left curves have higher average

speeds, they have lower lateral acceleration values

than the right ones. The same happens in longitudinal

acceleration. In conclusion, the presence of an under-

inflated left rear tire impacts a reduction in average

speed in left curves and an increase in average lateral

acceleration and average longitudinal acceleration.

The variations are -6.5%, + 8.5% and + 78% for

speed, lateral acceleration and average longitudinal

acceleration, respectively.

Table 3: Descriptive statistics of speed and acceleration for

the direction of the curve.

Variable

Curve

type

N Mean StDev. Min Max

Long.

acc.

(m/s

)

Right

157

-0.182

0.997

-4.320

2.98

Left

170

-0.040

0.942

-2.27

2.94

Lat.

acc.

(m/s

)

Right

157

2.729

1.420

0.000

6.360

Left

170

2.496

1.397

0.030

7.590

Speed

(km/h)

Right

157

45.803

8.166

20.110

64.840

Left

170

48.981

8.610

19.940

65.200

3.4 Linear Regression Analysis

Due the differences between the direction of the

curves, the following linear regression analysis was

carried out as shown in Table 4.

The regression analysis was done with the

Stepwise function of Minitab ® (State College,

2005). These equations are referential and should be

explored further in future research.

Table 4 shows the models for all the data, the right

curves, and the left curves. The lateral acceleration

was a dependent variable. The main predictors for

lateral acceleration are: the speed and the radius of the

curve. It used the R

-1

(inverse of the curve radii) in the

regression process, but it was not statistically

significant. The model that best fits is the one for the

Table 4: Linear regression models for the lateral

acceleration and the direction of the curve.

Predictor Coef.

Coef.

T-

value

P-

value

All data

Constant -2.20 0.92 -2.39 0.018

1.5

Speed

(

km/h

)

0.05 0.02 2.41 0.016

Right curves

Constant -3.49 0.14 -24.96 0.000

26.4

Curve

radii

(

)

0.09 0.00 7.94 0.000

Left curves

Constant 3.67 0.14 26.37 0.000

39.4

Curve

radii (m)

-0.01 0.00 -10.54 0.000

Coef.: model coefficients, SE Coef.: standard error of the

coefficient, T-value: ratio between the coefficient and its

standard error, P-value:

robability that measures the

evidence against the null hypothesis, R

adj.: adjusted R-

squared.

left curves. This outcome was expected because the

under-inflated tire did not have a meaningful effect on

these curves. The real impact is in the right curves,

where the coefficient of determination is low. And

this also affects the fit of the general model, so the R

adjusted is very low.

4 CONCLUSIONS

This article aimed to investigate the influence on the

stability variables of the vehicle in curves of the road

when the vehicle driving on the under-inflated rear

tire on wet pavement. After analysing the results, the

following conclusions are presented:

The speed and acceleration were the variables that

were mainly affected because of a left under-inflated

rear tire. However, the influence was only present in

curves on the opposite side of the under-inflated rear

tire. Speed decreases in these curves, while lateral

acceleration increases. The radius of the curve was

also statistically significant; nevertheless, the grade of

the road was not. That is why equations were

calibrated with this variable, where, as a result of the

presence of the under-inflated tire, the right curves

had less regression fit than the left curves. It is

necessary to mention that differences in lateral

acceleration in left or right curves are not only to the

flat tire but it could also have been caused by the

driver, for whom a left curve differs from a right

Real Driving on Under-inﬂated Rear Tire on Horizontal Curves: A Road Experimental Study

329

curve since he/she sits on one side of the vehicle. This

could be analysed in future studies.

This study has several limitations. First, this study

employed a single vehicle and a single under-inflated

rear tire. Additionally, just one trip was conducted in

the experiment, with 10-psi tire pressure. Both

conditions could differ in other vehicles, another tire

or air pressure, or driving several trips. It did not

repeat the trip due to an accident hazard. It would be

interesting to compare at least 3 cases: 1) current case,

2) normal case (all tires inflated to 30 psi) 3) the right

rear tire reduced to 10 psi, and other combinations.

This study focused on the kinematics effects of an

under−inflated tyre; therefore, we don’t know what

are the causes of this behaviour: rolling resistance, the

contact area tyre, among others. These causes could

be modelled as seen in Varghese (2013). With this

procedure, it could predict the effect of more

under−inflated tires and complement the presented

experiment that involves only one under−inflated tire.

Despite these limitations, the present study helps

to extend the knowledge of the consequences of an

under-inflated rear tire, and their relationship with the

road geometric variables. Data in this study belonged

to the actual driving on more than 50 km in the

mountainous road. This context was not previously

analysed. Although modern vehicles include direct

monitoring of the tire pressure, the present outcomes

can be the basis for a new indirect pressure method in

accidents reconstructions, which can be analysed in

future studies.

ACKNOWLEDGEMENTS

The author acknowledges the support of the National

Secretariat of Higher Education, Science,

Technology and Innovation (SENESCYT) and

Universidad Técnica Particular de Loja from the

Republic of Ecuador.

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