A fundamental experimental approach for optimal design of speed bumps

A fundamental experimental approach for optimal design of speed bumps

Accident Analysis and Prevention xxx (xxxx) xxx–xxx Contents lists available at ScienceDirect Accident Analysis and Prevention journal homepage: www...

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Accident Analysis and Prevention xxx (xxxx) xxx–xxx

Contents lists available at ScienceDirect

Accident Analysis and Prevention journal homepage: www.elsevier.com/locate/aap

A fundamental experimental approach for optimal design of speed bumps ⁎

A. Hakan Lava, , Ertugrul Bilginb, A. Hilmi Lavb a b

Koc University, Istanbul Turkey Istanbul Technical University, Istanbul Turkey

A B S T R A C T Speed bumps and humps are utilized as means of calming traffic and controlling vehicular speed. Needleless to say, bumps and humps of large dimensions in length and width force drivers to significantly reduce their driving speeds so as to avoid significant vehicle vertical acceleration. It is thus that this experimental study was conducted with the aim of determining a speed bump design that performs optimally when leading drivers to reduce the speed of their vehicles to safe levels. The first step of the investigation starts off by considering the following question: “What is the optimal design of a speed bump that will − at the same time − reduce the velocity of an incoming vehicle significantly and to a speed that resulting vertical acceleration does not jeopardize road safety? The experiment has been designed to study the dependent variables and collect data in order to propose an optimal design for a speed bump. To achieve this, a scaled model of 1:6 to real life was created to simulate the interaction between a car wheel and a speed bump. During the course of the experiment, a wheel was accelerated down an inclined plane onto a horizontal plane of motion where it was allowed to collide with a speed bump. The speed of the wheel and the vertical acceleration at the speed bump were captured by means of a Vernier Motion Detector.

The optimal width was found by testing speed bumps with widths ranging from 1 to 10 cm with 1 cm increments, while keeping height constant at 1 cm. The optimal height was determined by using test heights ranging from 0.7-3.4 cm with 0.3 increments, while the width was kept constant at 5 cm. The simultaneous use of motion detectors and computer software enabled the measurement of two important mechanical factors affecting the performance of speed bumps: namely velocity reduction, which is the measure of decrease in velocity of the wheel, and the peak vertical acceleration, which is believed to be one of the main factors affecting passenger comfort. The gathered raw data were then refined for each speed bump and a Speed Bump Coefficient of Performance (SBCP) was introduced to compare the speed bumps. The study focusing on optimal width determination provided evidence of the existence of a parabolic relationship between the width of the speed bump and the reduction in velocity. Within these conditions, the optimal speed bump dimensions were found to be 5.0 cm in width and 2.8 cm in height, scaled up to 30.0 cm in width and 16.8 cm in height at real conditions. 1. Introduction Traffic engineers use a variety of methods in their efforts to control vehicle speeds and to prevent accidents caused by speeding. One of the



most common methods used is the placement of traffic calming devices, of which speed bumps and humps are popular types. These speed bumps and humps are obstacles that are placed across various roads to reduce the velocity of incoming vehicles. The utilization of speed bumps allows both for a steady flow of traffic on private roads and vehicular speed management in parking lots (Kramberger 2010). Despite their popular use, however, little consideration has been paid for the design of these devices and this haphazard approach oftentimes leads to incorrect constructions. It is especially important that speed bumps are built correctly, as even the slightest deficiency may lead to such problems as damage to vehicles; strong jolts caused by excessive vertical acceleration, which have the potential of causing passenger discomfort, and, in severe cases, injuries; and insufficient velocity reduction due to inefficient designs, etc. (Hessling et al., 2008). Hence, it is critical and necessary to investigate the optimal design for a speed bump that will both reduce the velocity of an incoming vehicle while also keeping peak vertical acceleration at an acceptable level, since severe vertical acceleration levels also endangers traffic safety. Because the primary interactions being observed are collisions and accelerations caused by either gravity or macroscopic object interaction, this study is also closely related to the field of classical mechanics. More specifically, the Principles of Momentum and Newton’s Laws of

Corresponding author. E-mail address: [email protected] (A.H. Lav).

http://dx.doi.org/10.1016/j.aap.2017.05.022 Received 14 February 2017; Received in revised form 23 May 2017; Accepted 25 May 2017 0001-4575/ © 2017 Elsevier Ltd. All rights reserved.

Please cite this article as: Lav, A.H., Accident Analysis and Prevention (2017), http://dx.doi.org/10.1016/j.aap.2017.05.022

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Another study found that a lower ramp of speed humps having specific other profiles lead the vehicle to gently cross the hump at a straddle, which at the same time forces the driver to reduce the speed to a degree at which a catastrophic jump over the road pavement will be avoided. This study’s analysis of drivers’ responses to installation of such raisings shows that users prefer larger humps since they are more comfortable in terms of jolts perceived inside the car (Pau and Angius, 2001). The year 2008 marked the introduction of a new approach to the shape optimization of speed humps. Based on multi-objective genetic optimization of the hump profile, this approach takes into consideration the separation phenomenon that occurs when the front tires of the vehicle momentarily lose contact with the road surface. The results of the same research have shown that longer humps do not necessarily perform better in terms of speed reduction, a conclusion that is somewhat different from those previously reported by others (Ardeh et al., 2008). In 2009, a similar study of shape optimization of speed hump based on a multi-objective optimization technique called “GAM,” which was first proposed by Gembicki in 1974, was also carried out. The main objective of the study was to minimize vehicle response functions below the hump crossing speed limit and to maximize them above the speed limit. This study concluded that the commonly used sinusoidal, circular, and parabolic profiles do not perform well in terms of hump efficiency requirements and that polynomial and trapezoidal profiles tended to produce better results. (Başlamışlı and Ünlüsoy, 2009). While frequent exposure to speed humps has been found to cause back discomfort in both drivers and passengers, and despite the importance of speed humps as a traffic device, a review of the literature demonstrates that very little research has been carried out to investigate their design. This lack of suitable study shows that there is a real need to identify an effective, suitable design that is less hazardous to cars driving at an acceptable speed on residential streets (Zainuddin et al., 2014). In 2015, two different investigations towards the design of a “Simple Harmonic Hump” and “Polynomial Hump” were published. In these studies, a ride comfort diagram was created by using the “MATLAB” simulation. This work led to the design of simple harmonic hump and polynomial hump for any desired hump crossing speed in the range of 5–30 km/h (Hassan, 2015a, 2015b).

Motion are key to predicting an overview of the interaction. This issue was investigated here with a study based on an experimental approach. As a first step, a basic model for the interaction between a vehicle wheel and a speed bump was created. This model supports experimental procedures by providing a precise projection and stable contact between the projectile and the speed bump. A scaled environment was constructed as a means of testing various speed bumps under controllable conditions. The horizontal velocity and vertical acceleration of the wheel during the interaction were monitored to measure both the velocity reduction and peak vertical acceleration of the wheel. The collected data were analyzed to assign an efficiency level to each speed bump tested, and to determine the most optimal speed bump. 2. Literature review These speed humps and bumps have been playing vital roles as traffic calming devices for the past several decades and this utilization has catalyzed the publishing of a wide number of studies on this subject, a development that began to significantly increase in the mid 1980′s and that continues to date. These investigations have been published as scientific articles in many journals, as reports, and as MSc and PhD theses, etc. While many of these scientific research studies on this subject have been conducted globally, most have originated thus far from the United States of America, Canada, Great Britain, and Australia. Some of these studies have concluded that, for instance, as compared to speed bumps, speed humps provide a much smoother and more gradual flow of vehicle speeds (Namee and Witchayangkoon, 2011). Other studies have dealt with various aspects of speed humps and bumps. Among these were the first attempts at determining the kinds of designs needed for speed humps (Watts and Seminol Profiles). This design, which has become the most common speed hump design, was created by Watts in 1973 and has been termed the ‘Watts Profile’ or circular hump (Weber, 1998). As a response to this design, concerns over the abruptness of Watts Profile humps at higher speeds in Seminole County, Florida resulted in the creation of a design called the Seminole Profile Hump. These latter humps are similar in profile to trapezoidal humps with the difference that they are circular rather than straight ramps (Nicodemus, 1991). Further concerns about the designs of these early humps led to efforts that began in the mid 1990s towards the creation of a design of a profile to serve as an optimum speed hump. To this end, the maximum acceleration of the driver at a speed specified by the hump design was selected as the objective function for the optimization of the humps. In addition to this aim, the maximum acceleration of the driver at a speed that exceeded that specified by the hump design served as the objective function for the optimization of the suspension. These efforts led to a method proposed to create an optimum hump design that would minimize these two objective functions (Maemori, 1995). The Transportation and Road Research Laboratory (TRRL) of Great Britain conducted extensive laboratory research on test tracks investigating the outcomes of vehicles travelling at various speeds over various hump size and shapes. In these studies, the British researchers concluded that the ideal speed hump is 12 feet long and 3–4 inches high. It was as a result of these experiments that the parabolic shaped speed hump used throughout Europe, Australia and New Zealand were developed by TRRL (Smith and Giese, 1997). A Canadian MSc thesis entitled, Towards a Canadian Standard for The Geometric Design of Speed Humps was developed with the aim of determining a set of geometric design standards for speed humps in Canada. In this study, accelerations were recorded for vehicles travelling over several of on-road Watts and Seminole Profile wooden speed humps, and those records were compared to discomfort criteria. This study concluded that precisely designed speed humps could reduce automobile and heavy vehicle speeds, produce acceptable levels of discomfort for vehicle occupants, result in no vehicle damage, maximize overall road safety, and minimize vehicle noise (Weber, 1998).

2.1. Flat top trapezoidal humps and raised pedestrian crosswalks (Speed tables) Another study (Vejdirektoratet, 1991) concluded that flat top trapezoidal humps are particularly useful when combined with pedestrian crossings. In response to this, Australia prefers to use these trapezoidal humps, and does so even on bus routes (Jarvis, 1992). A study completed in 2009 investigated the optimization of crosssection dimensions of raised pedestrian crosswalks (RPC) in Qazvin, Iran. This research concluded that the second ramp length ranks as the highest impact variable. This is followed by the first ramp length, top flat crown length, before-RPC spot speed, height and street width, in order of magnitude (Mohammadipour and Alavi, 2009). 2.2. Optimization of speed hump spacing A further study considered the optimization of the speed hump spacing (Abaza et al., 2012). Effects of Speed Humps in Reducing Various Type of Crashes, Pedestrian Injuries and Fatalities in Residential Areas A study carried out in Oakland, California with the purpose of determining the effectiveness of speed humps in reducing child pedestrian injuries in residential areas concluded that the presence of block of speed humps within the boundaries of a neighborhood significantly reduces (53% to 60% reduction) the odds of being struck and injured by 2

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speed hump was crossed. But while this is obviously a negative implication and a setback for their use, it should not be considered as an isolated variable. Any assessment of speed bump efficacy should consider total relevant implications, such as the speed reduction achieved and the resulting increase in safety levels (Silva et al., 2010).

an automobile (Tester et al., 2004). Another study demonstrated that since motor vehicle speeds were low on pedestrian crossings irrespective of distance between cushion and crossing, distances of two-car lengths (app. 10 m) between such bumps had shown positive effects concerning mobility for vulnerable road users. The study thus suggested the use of this distance when installing speed cushions. These researchers also emphasized that a longer distance would also make it easier − especially for children and the elderly − to distinguish if a driver was going to stop or not, a factor that increases both safety and mobility (Johansson et al., 2011). Another investigation recommended that median separation, speed humps, and road lighting be incorporated into road design and construction, as such inclusion significantly reduces pedestrian accidents and the likelihood of hit-and-run incidents (Aidoo et al., 2013). The performance of 13 different type of countermeasures, including the speed humps that had been installed in New York City during the past 20 years by New York City Department of Transportation (NYCDOT), were also evaluated. This study concluded that speed humps have only a limited impact on crashes, including injurious and fatal crashes, which does not meet with their expected performance (Chen et al., 2013).

2.7. Dynamic simulation of speed Humps/Bumps to investigate the dynamic response of vehicles In 2006 and 2007 two similar MSc theses prepared by Gürer and Sözen respectively considered the dynamic simulations of speed bumps and speed humps under traffic loading, and their vibration effects on vehicles. These studies measured the vertical accelerations of vehicles while passing over a speed hump, derived the frequency analysis of the vibration on the vehicle, and obtained the frequencies of vibration at different locations (Gürer, 2006). In these studies, the researchers used the Matlab/Simulink method to analyse and compare/contrast wheel acceleration, vehicle acceleration, the change of the location of the wheel, and change of the location of the (Sözen, 2007). Other researchers investigated the dynamic responses of vehicles on different types of speed humps using the kind of multibody simulation package which is popular in the automotive industry and found that the dynamic performance of the recommended two sinusoidal type profiles had significantly better performance than that of conventional humps; i.e. parabolic, sinusoidal and four types of flat-topped humps (speed table). The authors expected the results of their study to be useful in the future geometric design of speed humps (Molan and Kordani, 2014).

2.3. Studies of design of speed humps utilized in rural areas Although speed humps and speed tables have been shown to be effective in reducing vehicle speeds, the majority of these studies have been conducted in large urbanized areas. Little information as to how these devices function in smaller or more rural cities is available in the literature. Smith et al’s study was one of the rare and useful examples for their use in such kinds of residential areas. The results of this study led the authors to conclude that speed humps − especially speed tables − effectively reduce the number of the vehicles exceeding the speed limits in those particular areas (Smith et al., 2002). Practical applications have also demonstrated that on highways located in mountainous areas, the use of appropriate speed control humps situated on the downhill slopes can lead drivers to actively control their vehicular speed, improve the operational safety of large vehicles, and effectively reduce traffic accidents (Jianbo et al., 2010).

2.8. Effects of speed humps on pavement condition Yet another study looked at the effects of speed bumps on the pavement itself and concluded that the presence of improper speed humps significantly and negatively affects pavement condition by reducing the PCI (Pavement Condition Index) value (Bekheet, 2014). 3. The model In this study, a model of the interaction between a vehicle and a speed bump was created by replicating some properties involved in collisions. This model only looks at one wheel, for such an investigation is sufficient in providing data about the speed bump performance. The interaction can be described according to three main phases: pre-collision, during collision, and post-collision, as follows:

2.4. Studies on the design of bicycle and motorcycle friendly humps Early uncertainty about the effects of humps on vehicle stability initially restrained the use of humps. Despite this, time has shown that the use of humps has relatively little negative effect on vehicles, including even motorcycles, and this is offset by their effectiveness in controlling vehicle speed (Kjemtrup and Herrstedt, 1992). Speed hump can also be especially designed to be bicycle friendly. Local authorities can adjust their use for cyclists by changing their hyperbolic design, tapering the edges, and providing a one meter gap at the curb lane side (Jacobs, 2004).

3.1. Pre-Collision In this phase, the wheel is moving towards a speed bump as shown in Fig. 1. Several factors impact the motion of the wheel in this part of the investigation. Firstly, the wheel displaces over time parallel to the plane of motion. This means that it has a certain mass (m), has a velocity (v1), kinetic energy, and momentum (P). The momentum is equal to the product of the mass of the object and its velocity;

2.5. Studies on the design of emergency vehicle and public transportation friendly speed humps One study included the search for ways to solve those problems arising from the passing of public transportation and emergency vehicles over speed humps. This study of speed bumps located in several countries over the face of the globe demonstrated that if speed bumps are designed and executed correctly such problems as vehicle damage or driver’s loss of control can be effectively eliminated (Zaidel et al., 1992).

Momentum (P ) = mv

(1)

According to Newton’s 2nd Law of Motion, the net force acting on an object is equal to the rate of change in momentum within the direction of the force. The law can be represented as a derivation equation;

F= 2.6. Predicting the environmental effects of speed humps in residential areas

dP dmv = dt dt

(2)

Given that the mass of the wheel (m) remains constant throughout the motion, it can be excluded from the derivation by the constant factor rule in differentiation.

According to the preliminary findings of a research study conducted in 2010, a significant increase in tail pipe emissions was noted after the 3

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Fig. 1. System Prior to Collision.

F=

dP ΔP dv Δv = =m =m dt Δt dt Δt

(3)

Lastly, by refining Eqn. (3), a final equation can be deduced for the mechanical variables;

F Δt = ΔP = mΔv



(4)

Eqn. (4) states that if a force was to act on the wheel during a time interval, the wheel’s momentum and hence velocity would change. In this study, Eqn. (4) is vital as it explains the relationship between the speed bump design and change in the mechanical properties of the wheel (further explained in System During Collision). Additionally, wheel slippage has been controlled, and rolling resistance has been neglected in this study.



3.2. System during collision

• Although the wheel and the speed bump are elastic objects, in rea•



lity they can be assumed to be rigid as their elasticity is negligible. This assumption enables us to provide a model of the collision as given in Fig. 2. As the two objects come into contact, the wheel starts to exert a force on the speed bump. According to Newton’s 3rd Law of Motion, the speed bump exerts an equal and opposite force on the wheel. The direction and the magnitude of the forces exerted vary with time over the duration of the collision. Nevertheless, a representation of the averages of the forces exerted is made by FC in Fig. 2. The speed bump is stationary and attached to the ground, and therefore, the forces acting on it have no effect and will not cause

• 4

the speed bump to move. On the other hand, because the wheel is not stationary, the forces acting on the wheel will cause a change in its horizontal velocity and vertical acceleration. The force exerted by the speed bump can be investigated in two component force vectors: FC┴ and FC║. FC║is the component vector which is parallel and opposite to the momentum of the wheel. As already deduced in Eqn. (4), the overall force of FC║ during the time of contact decreases the momentum of the wheel as the direction of the force opposes the wheel’s momentum. The reduction in the net momentum acts to decrease the velocity of the wheel. Hence, FC║ is important as it is the force governing the velocity reduction. FC┴ is the component vector which is normal to the motion of the wheel. Although FC┴ does not have any effect on the horizontal momentum, it is the force that causes change in the vertical axis of the wheel. Gravitational force is exerted on the center of the wheel throughout its motion. During the time of collision, FC┴ is the force acting on the wheel opposite to W. However, while W can be assumed constant, FC┴ changes significantly over a short period of time. Therefore, during collision, the drastic change in the net vertical force will affect the vertical acceleration of the wheel. The vertical acceleration of the wheel has been observed in this study because the peak vertical acceleration is one of the important factors affecting passenger comfort. Since the duration of passing the speed bump is roughly constant, the peak acceleration indicates the degree of jolt that occurs in the interaction between the wheel and the speed bump. Additionally, the friction of the speed bump and back slope acceleration by the wheel are also accounted for in this study (Fig 3).

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Fig. 2. System During Collision.

parabolic. This means that this investigation into the design ignores the curvature of the speed bump, for its parabolic shape is the determining factor of a what defines a speed bump (Fig 4). In order to achieve the greatest reduction in velocity reduction and the least vertical acceleration, the height and width of the speed bump must be optimized for the best ratio of force components. The experiment conducted within this investigation is an attempt to find the optimal values.

3.3. Post-Collision system This phase is similar to the pre-collision system. However, following the collision the wheel moves through the plane of motion slower than it had prior to the collision. Eqn. (5) can then be deduced by considering the final velocity (v2) measured in this phase: FΔt = ΔP = m(v_2-v_1) (5) The final velocity will always be smaller than the initial velocity as FC║ acts opposite to the direction of motion. For this reason, the change in overall velocity will always be a reduction in velocity. From the theory, two dependent variables are deduced, as follows:

3.3.4. Initial velocity The initial collision velocity of the wheel affects the force exerted. However, this variable is controlled in this experiment to focus on the shape of the speed bump.

3.3.1. Velocity reduction This variable is the change in velocity caused by the collision. As seen in Eqn. (4), this factor is proportional to the average parallel force exerted during the time interval of collision. Therefore, velocity reduction depends on the magnitude and duration of the force exerted while the wheel collides with the speed bump.

4. Experiment setup The experiment conducted in this study was designed to study the dependent variables and collect data in order to propose the optimal design for a speed bump. Here, a wheel is accelerated down an inclined plane onto a horizontal plane of motion where it collides with a speed bump. The wheel in the experiment is a 1/6th scale replica of an actual wheel. It has a diameter of 1.05 × 10–1 ± 0.05 × 10–1 m and a mass of 1.550 × 10-1 ± 0.001 × 10–1 kg. To carry out the experiment a wheel of such size and mass was available and it satisfied acceptable accuracy and precision. The curvature of each speed bump was parabolic, which means their highest point was located midway between the width. Finally, Vernier Motion Detectors were used to measure the horizontal velocity and vertical acceleration of the wheel. Fig. 5 represents the setup of the experiment. As seen in Fig. 5, the Vernier Motion Detector was placed on the same level of motion as the wheel, or above the speed bump. The device acts by sending ultrasonic waves and analyzing the reflections bouncing back from the objects in the path of the waves to determine the distance of a particular object. To meet the purposes of this experiment, the data need to be collected very quickly; to achieve this, the data collection

3.3.2. Peak vertical acceleration Humans are not disturbed by high accelerations while travelling in a vehicle (e.g. sports cars accelerating at great rates); however, a sudden change in acceleration causes human discomfort as a result of the jolting effect (e.g. bumpy car rides). When a wheel passes over a speed bump, the peak vertical acceleration should indicate an accurate estimate of the jolt that was experienced by the wheel. This variable is a means of optimizing speed bump designs to be more passenger-friendly and comfortable. The dependent variables are affected by the following independent variables: 3.3.3. Shape of the speed bump The shape of a traffic calming device is determined by three distinct elements: curvature, height, and width parallel to the traffic flow. The term speed bump is used for vertical traffic calming devices that are 5

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Fig. 3. System After Collision.

provides reliable data for the purposes of this experiment. Additionally, the uncertainties of the results of these tests are used as a measure of uncertainty for the raw data of the main experiment.

speed was set at 20 Hz or 20 samples per second. The motion detector was connected to the computer via Vernier Lab Pro. The Lab Pro converts the measurements from the motion detector into appropriate data which can be processed into Logger Pro 3.6.1 computer software. The simultaneous use of these devices enables the collection of displacement, horizontal velocity, and vertical acceleration of the wheel.

6. Experiment procedure The analytical approach used in this study focused on acquiring sets of data points that could lead to a determination of the possible functions, which can then be used to predict the optimal dimensions for speed bumps. The second purpose of the study was to discover the most appropriate functions that could describe the relationships between

5. Calibration and accuracy tests The calibration tests have shown that the Vernier Motion Detector

Fig. 4. Theoretical Change in Force of Collision (FC) By The Change of Speed Bump Design.

6

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Fig. 5. Experiment Setup.

8. Analysis of the test results

independent and dependent variables. The width and height of speed bumps were investigated separately and their results were combined to find the optimal speed bump dimensions. A scale of 1:6 scale was used to reflect both the weight and the velocity of the wheel through a dimensional analysis and similarity (Geometric and Kinematic Similarity). Individual speed bumps were constructed for each trial and the wheel was placed at the release point as shown in Fig. 5. As the wheel approached the speed bump, the data collected from Logger Pro 3.6.1 software was processed to obtain the change in velocity and maximum vertical acceleration of the wheel. Examples of the positions and vertical acceleration of the wheel travelling over the speed bump are given in Fig. 6 and Fig. 7, respectively.

The data collected from the study are presented in figures in order to analyse the relationships between the dependent and independent variables, and are given as follows: As indicated in Fig. 8, there is a parabolic relationship between velocity reduction and width of the speed bump. This shows that there is an optimal width dimension that provides the highest degree of velocity reduction. During testing, it was observed that the back-slope acceleration played a major role in forming a parabolic relationship between these two variables. That velocity reduction increases as the width of the speed bump increases is a logical outcome since the retarding forces acting on the wheel would be exerted for a longer duration. However, as the width of the speed bump increased after a certain point, the intensity of the collisions decreased and the wheel was able to attain a greater amount of velocity from rolling down the back slope of the speed bump. This outcome explains the lesser values of velocity reduction for longer speed bumps. This argument can be supported by comparing the maximum velocity reduction and back slope velocity increase caused by the speed bump as indicated in(Table 3) Fig. 9. As seen in Fig. 10, although the maximum velocity reduction remained roughly the same for longer speed bumps, the velocity gained from the back slope increased quite significantly. This would explain the parabolic relationship in Fig. 8 and why longer speed bumps failed to provide the most velocity reduction. Fig. 11 shows a correlation coefficient of 0.05, thus appearing to be little or no correlation between width and peak vertical acceleration. It is possible that since the height of the speed bump remained constant, the wheel could only be elevated to a certain level which limited the possibility of a more abrupt or controlled freefall. Hence, the peak acceleration remained roughly the same for all widths. This assumption can be supported by analyzing the height and peak vertical acceleration data to check if there is any correlation between those two variables. As shown in Fig. 12, a correlation coefficient of 0.99 indicates a

7. Test results The raw logger pro data was interpreted and then presented in a table format. The reduction in velocity (-Δv) and the peak acceleration data were extracted from the Logger Pro software and these are given in Tables 1 and 2. It is important to note that the investigations on width (Table 1) and height (Table 2) are shown separately. Also, the value of the dimensions of the speed bumps were recorded in centimeter notation (cm, 10–2 m) for easier comprehension; the uncertainties for the dimensions can be assumed negligible since they are relatively extremely small compared to the values themselves (10–5 m uncertainty for a value of around 10–2 m, nearly a difference of 103 m). Repeated trials were conducted to reduce any random uncertainties that might have occurred during testing. The average of 3 trials is accepted as the value of the measurement. The constant height dimension for the tested widths was 1 cm, while the constant width dimension for the tested heights was 5 cm. This selection was based on the fact that these scaled height and width fall in the ranges published in such manuals as Pennsylvania’s Traffic Calming Handbook and DDOT (2010) Speed Hump Request Procedures and Engineering Guidelines. 7

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Fig. 6. Interpretation of Raw Vertical Position Graph of 5 cm Width, 1.9 cm Height Speed Bump.

Fig. 7. Interpretation of Raw Vertical Acceleration Graph of 5 cm Width, 1.9 cm Height Speed Bump. Table 1 Width Data with respect to Reduction in Horizontal Velocity and Peak Vertical Acceleration. Width of Speed Bump cm/(negligible)

1 2 3 4 5 6 7 8 9 10

Reduction in Horizontal Velocity ms−1/ ± 0.01

Peak Vertical Acceleration ms−2/ ± 0.1

Trial 1

Trial 2

Trial 3

Avg.

Trial 1

Trial 2

Trial 3

Avg.

0.10 0.12 0.17 0.19 0.20 0.19 0.18 0.15 0.12 0.12

0.10 0.15 0.17 0.17 0.19 0.19 0.18 0.15 0.14 0.13

0.11 0.13 0.17 0.18 0.19 0.18 0.18 0.18 0.15 0.12

0.10 0.13 0.17 0.18 0.19 0.19 0.18 0.16 0.14 0.12

6.5 6.3 6.6 6.5 6.2 6.1 6.4 6.8 6.0 6.5

6.2 6.3 6.7 6.4 6.2 6.5 6.3 7.1 6.1 6.5

6.2 6.2 6.6 6.0 6.3 6.2 6.3 7.0 5.9 6.3

6.3 6.3 6.6 6.3 6.2 6.3 6.3 7.0 6.0 6.4

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Table 2 Height Data with respect to Reduction in Horizontal Velocity and Peak Vertical Acceleration. Height of Speed ump cm/(negligible)

0.7 1.0 1.3 1.6 1.9 2.2 2.5 2.8 3.1 3.4 a

Reduction in Horizontal Velocity ms−1/ ± 0.01

Peak Vertical Acceleration ms−2/ ± 0.1

Trial 1

Trial 2

Trial 3

Avg.

Trial 1

Trial 2

Trial 3

Avg.

0.13 0.19 0.20 0.23 0.26 0.32 0.38 0.39 N/Aa

0.13 0.18 0.20 0.23 0.27 0.32 0.38 0.47

0.14 0.18 0.19 0.23 0.27 0.31 0.38 0.43

0.13 0.18 0.20 0.23 0.27 0.32 0.38 0.43

5.8 5.2 5.1 5.0 4.8 4.4 4.3 4.0

5.5 5.5 5.1 5.0 4.5 4.0 4.3 3.9

6.0 5.5 5.2 5.0 4.1 4.2 4.3 3.6

5.8 5.4 5.1 5.0 4.5 4.2 4.3 3.8

The wheel could not pass over the speed bump.

Fig. 8. Width Against Reduction in Horizontal Velocity. Table 3 First Trial Data of Width with respect to Maximum Reduction in Horizontal Velocity and Velocity Gain from Back Slope. Width of Speed Bump cm/(negligible)

Maximum Reduction in Horizontal Velocity ms−1/ ± 0.01

Velocity Gain from Back Slope ms−1/ ± 0.01

1 2 3 4 5 6 7 8 9 10

0.10 0.14 0.18 0.22 0.23 0.24 0.22 0.24 0.22 0.23

0.00 0.02 0.01 0.03 0.03 0.05 0.04 0.09 0.10 0.11

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Fig. 9. Raw Horizontal Velocity Graph of 5 cm Width, 1.6 cm Height Speed Bump.

Fig. 10. Comparison of Reduction in Horizontal Velocity, Maximum Reduction in Horizontal Velocity and Velocity Gain from Back Slope.

it can be assumed that these two variables are also inversely correlated in the context of the study on height. This assumption has been more thoroughly investigated in “Full-scope Analysis” with respect to the hypothesis made about the effect of speed bump dimensions on the components of the force exerted on the wheel in Fig. 4.

strong positive correlation between height and velocity reduction. In Fig. 13, a correlation coefficient of −0.98 suggests that there is a strong negative correlation between height and peak vertical acceleration. It seems that the correlation of velocity reduction and peak vertical acceleration with regard to the same independent variable (height) is of an opposite nature (positive and negative), and therefore

10

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Fig. 11. Width Against Peak Vertical Acceleration.

Fig. 12. Height Against Reduction in Horizontal Velocity.

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Fig. 13. Height Against Peak Vertical Acceleration.

Fig. 14. Width of The Speed Bump and Component Forces.

9. Full-scope analysis

The test results on width did not, however, provide the kind of correlation described in the hypothesis. It may be that the independent variable width has either slight or no effect on the force components of the force exerted by the speed bump. Fig. 14 displays this outcome. The investigation on height provided evidence of an inverse correlation between the dependent variables with respect to height. This relationship might support the hypothesis as presented in Fig. 15. Furthermore, as shown in Table 6, it was observed that the wheel could not pass over the speed bump after a certain height. This can also

The previous section hypothesized that there might be a relationship between the shape of the speed bump and the force components of the force exerted on the wheel. Based on this assumption, then the dependent variables (velocity reduction and peak vertical acceleration) would be inversely correlated because the magnitudes of the component forces governing each of the two dependent variables are negatively correlated. 12

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Fig. 15. Height of The Speed Bump and Component Forces.

Fig. 16. Height at which The Wheel Fails to Pass the Speed Bump.

be shown as an evidence that supports the hypothesis on force components, since the hypothesis can be used to explain the existence of such an observations as seen in Fig. 16.

Ideally, the optimal speed bump would provide the most velocity reduction and the least peak vertical acceleration. Therefore, the performance of a speed bump is positively proportional to the velocity reduction and inversely proportional to the peak vertical acceleration;

9.1. Speed bump coefficient of performance (SBCP)

SpeedBumpPerformance ∝ VelocityReduction

The aim of this study is to determine the design of an optimal speed bump with respect to both velocity reduction and peak vertical acceleration. The Speed Bump Coefficient of Performance (SBCP) is a value introduced to compare the performance of both of these variables as they affect speed bumps.

SpeedBumpPerformance ∝

1 PeakVerticalAcceleration

(6)

Combining these two relationships; VelocityReduction SpeedBumpPerformance ∝ PeakVerticalAcceleration (7) Hence, to compare the tested speed bumps in this investigation, 13

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10. Evaluation of testing

Table 4 Width of Speed Bump with respect to SBCP and Uncertainty in SBCP. Width of Speed Bump cm/(negligible)

SBCP/unit value

Uncertainty in SBCP/unit value

1 2 3 4 5 6 7 8 9 10

1.5 × 10−2 2.1 × 10−2 2.6 × 10−2 2.9 × 10−2 3.1 × 10−2 3.0 × 10−2 2.8 × 10−2 2.3 × 10−2 2.3 × 10−2 1.9 × 10−2

± 0.2 × 10−2 ± 0.2 × 10−2 ± 0.2 × 10−2 ± 0.2 × 10−2 ± 0.2 × 10−2 ± 0.2 × 10−2 ± 0.2 × 10−2 ± 0.2 × 10−2 ± 0.2 × 10−2 ± 0.2 × 10−2

The speed bump with the dimensions of 5 cm in width and 1.0 cm in height was tested twice, in both width and height investigations. The values of the two trials can be compared to evaluate the accuracy of testing as represented in Table 6. It appears that the results for velocity reduction and SBCP lie within the uncertainty range of the corresponding investigations results; therefore, it can be assumed that the testing and results of these two dependent variables were quite accurate. However, the comparison of peak vertical acceleration data shows that there is a significant discrepancy between the two results. This discrepancy is likely an indication of a systematic error because the repeated trials should have been able to reduce random errors to a point where the discrepancy would be lower. One possible cause of this error may be that the curvature of the speed bump in the width investigation was incorrectly reconstructed in the height investigation. This error can be eliminated by building a more sophisticated construction system.

Table 5 Height of Speed Bump with respect to SBCP and Uncertainty in SBCP. Height of Speed Bump cm/(negligible)

SBCP/unit value

Uncertainty in SBCP/unit value

0.7 1.0 1.3 1.6 1.9 2.2 2.5 2.8 3.1 3.4

2.2 × 10−2 3.3 × 10−2 3.9 × 10−2 4.6 × 10−2 6.0 × 10−2 7.6 × 10−2 8.8 × 10−2 11.3 × 10−2 N/A*

± 0.2 × 10−2 ± 0.2 × 10−2 ± 0.3 × 10−2 ± 0.3 × 10−2 ± 0.4 × 10−2 ± 0.4 × 10−2 ± 0.4 × 10−2 ± 0.6 × 10−2

11. Conclusion and further recommendations The purpose of this study was to determine the optimal design for a speed bump that can best reduce the velocity of an incoming vehicle the most, while not causing a vertical acceleration that jeopardizes road safety. This study found that the optimal dimensions of a speed bump are 5.0 cm in width and 2.8 cm in height. Keeping in mind the scaled environment is of 1:6 ratio, these values are scaled up to: 20 cm width 16.8 cm height

SBCP is defined as; VelocityReduction SpeedBumpCoefficientofPerformance = PeakVerticalAcceleration (8) Example For Trial 1 of 1 cm width, 1 cm height speed bump; VelocityReduction 0.10 SBCP = PeakVerticalAcceleration = 6.5 = 0.015 Uncertainty (Percentage uncertainties are added);

The investigation that focused on optimal width provided evidence of a parabolic relationship that exists between the width of the speed bump and velocity reduction. However, it failed to support the hypothesis on force components. On the other hand, the investigation that focused on optimal height supported the hypothesis by presenting both a negative correlation between dependent variables and an explanation as to why the wheel could not pass over some of the speed bumps. The main limitation in this experiment was related to the ability to control the initial velocity of the wheel. Because the apparatus used to project the wheel had an uncontrollable friction, a consistent collision velocity could not be established for every trial. This limitation can be improved by using a smoother apparatus. Another limitation was the use of only one projection speed for the wheel. A more reliable investigation could be achieved if the speed bumps are tested for a variety of initial velocities. Although significant manuals like MUTCD (2009) and SCDOT (2006) focus on the placement and shape of speed hump and bump signs, other manuals such as DDOT (2010) and Pennsylvania’s Traffic Calming Handbook (2012) only briefly mention recommended ranges of height and width of speed humps. Therefore, the scaled height and width selected in this basic experimental study complies with the ranges given in those above-mentioned manuals. Lastly, possible further investigations relevant to the topic may include investigations related to the optimal spacing for speed bumps and the effect of the shape and curvature of the speed bump on their performance.

0.01 0.1 ⎞ x 0.015 = ± 0.002 ± SBCP = ⎛ + 6.5 ⎠ ⎝ 0.10 The full SBCP; 16.1 × 10−2 ± 0.2 × 10−2 unit value

9.2. Optimal dimensions The optimal dimensions for a speed bump found by modelling the SBCP values for width and height are given in Tables 4 and 5 as functions and calculating the values that yield the greatest SBCP within the range of the test data (Figs. 17 and 18). Calculated Value: 2.8000000 cm Accepted Value: 2.8 cm Optimal Speed Bump; 17.1 cm width, 2.8 cm height

Table 6 Average Reduction in Horizontal Velocity, Peak Vertical Acceleration and SBCP comparison for The Two Trials of 5 cm Width and 1.0 cm Height Speed Bump. The Investigation

Reduction in Horizontal Velocity ms−1/ ± 0.01

Peak Vertical Acceleration ms−2/ ± 0.1

SBCP unit value/ ± 0.2 × 10−2

Width Height

0.19 0.18

6.2 5.4

3.1 × 10−2 3.3 × 10−2

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Fig. 17. Width Against SBCP.

Fig. 18. Height Against SBCP. Bekheet, W., 2014. Short term performance and effect of speed humps on pavement condition of alexandria governorate roads. Alexandria Eng. J. 53 (4), 855–861. Chen, L., Chen, C., Ewing, R., McKnight, C.E., Srinivasan, R., Roe, M., 2013. Safety countermeasures and crash reduction in new York city-Experience and lessons learned. Accid. Anal. Prev. 50, 312–322. DDOT, 2010. DDOT Speed Hump Request Procedures and Engineering Guidelines. pp. 19. https://comp.ddot.dc.gov/Documents/Speed%20Hump%20Request%20Procedures %20and%20Engineering%20Guidelines.pdf. Gürer, M., 2006. Hız Tümseklerinin Taşıt Titreşim Tekniği Açısından İncelenmesi. https://hdl.handle.net/11527/3810. handbook, 2012. Pennsylvania’s Traffic Calming Handbook. Pennsylvania Dept. Of Transportation (109 p).

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