Physics IA rolling resistance

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PHYS 100

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Mechanical Engineering

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Dec 6, 2023

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pdf

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Relationship between the air pressure of a bike and the Coef±icient of rolling resistance 1.0 Introduction Because I live in the Netherlands it is very common for people to use bikes as a way of transportation as bike paths are very common and new urban development is surrounded around making bike lanes safe and ef±icient to reduce CO 2 emissions. When I was younger I used to compete in biking marathons with my father, where I began to ±ind a passion for biking. I did competitions from age 15-16, however now I use my bike on a day-to-day basis to get to school which was approximately 4km each way, and then bike to Basketball practice which was 11km each way. I would constantly have to pump my tires as they would commonly go ±lat due to the age of my bike, therefore I began to notably see a difference in how much force I had to exert to bike faster when my tires were lower rather than when I would have recently pumped them up. During Bike marathons, my father would vary the pressure of our bikes depending on the terrain and weather. Consequently, I began to wonder what the most practical pressure is for biking the distances I do on a daily would be. Therefore throughout the report, I will be investigating the relationship between the change in the pressure of the bike tire and the coef±icient of rolling resistance (C sr ). 1.1 Research question How is the Coef±icient of rolling resistance (dimensionless), of a bike tire affected by the variation of its pressure (60psi, 80psi, 100psi, 120psi, 140psi 2% )? ± 2.0 Scienti±ic Context & theory Through this Lab report I will be investigating the effect that a change in the pressure of a bike tire has on the coef±icient of rolling resistance. The property inherent to the tire, based on factors affecting the resistance of the tire, force acting opposite to the motion of the cyclist is the coef±icient. Although pressure has an impact, factors such as surface characteristics for instance roughness, tire characteristics for example tire material/tread and the supported weight are likewise relevant factors which would in±luence the magnitude of resistive force, therefore re±lecting variations in the coef±icient. The equation of rolling resistance is expressed as, F=C sr N (Ryan Johnson). The friction experienced by the E-bike tire due to rolling on a surface is F ,

where the coef±icient property of the tire is C sr , and the weight of the E-bike body supporting the tire being equal to the Normal force N. The Normal force ( N ) can likewise be expressed as mg, m being the mass of the body and g being equal to the constant of Earth's gravitational acceleration (9.81 m/s 2 ). To make the coef±icient property of the tire ( C sr ) the subject, C sr = F/W , therefore expressing C sr as the force of rolling resistance on the tire per unit force of weight as W=mg. Consequently, for 0.5kg of weight (4.45N) to oppose the resistant force of rolling resistance and accelerate in a forward direction more than 0.5kg of force (4.45N) must be acquired. As there is an inverse relationship, The coef±icient of rolling resistance will inversely increase with the pressure of the tire (Greg Kopecky). From biking, it's known to me that an individual has to exert more force on the pedals when the tires have lower pressure, causing acceleration to be more dif±icult in the forward direction. This, therefore, demonstrates force opposite to velocity is larger. Intuitively, as the pressure of a tire decreases, and the surface area of the tire increases as it hits the ground, therefore more force is necessitated to move the tire. This occurs as the structural properties of a tire are affected by the pressure of the tire. As air is pumped into the tire, there's correspondingly an increase in air molecules, causing the volume to ultimately increase. The vacuity of the tire decreases, as the increasing number of molecules, occupy it. The pressure is increased as a result of a higher force exerted by the greater momentum change when molecules interact with the wall and collide at a more rapid rate. As pressure is equal to the perpendicular force per unit area (Aakanksha Gaur), As pressure decreases, the number of molecules would decrease, resulting in a lower density. Correspondingly fewer molecules will collide against the wall and the tire becomes less ±irm increasing the tire's contact with the surface, and increasing the frictional property (Kevin Shen). 3.1 Independent Variables The variation in the pressure of the E-Bike tire which I will investigate is (4.14 x 10 5 Pa,5.52 x 10 5 Pa,6.89 x 10 5 Pa,8.27 x 10 5 Pa, and 9.65 x 10 5 Pa). I shall be measuring the pressure of the bike tire through a pressure gauge in psi where 1 psi is equal to 6894.76Pa. The selected values were determined by the accuracy of the pump measurements. The measurement markings between 10 were indistinct and therefore values which have the highest accuracy were selected. As preliminary experiments demonstrated a signi±icant difference from 60psi to 140psi, it can be deduced that the selected range was suf±icient. In cogitation with section 2, the surrounding temperature of the tire might vary the accuracy of the E-bike when gauging the pressure within it if there's a sudden change in temperature. 3.2 Dependant variable

Due to the coef±icient of rolling resistance being dimensionless, initially the raw data will consist of measuring the deceleration (m/s 2 ) of the tire in relation to the varying pressure (Pa). The experimental set-up (section 4.2), was done with 5 trials to reduce the uncertainty through random error. The coef±icient will then be calculated through data processing ( section 5.1). 3.3 Controlled variable Controlled Variables Justi±ication why I chose this variable Method to control this variable Initial velocity of the bike tire (m/s) It's crucial to keep the initial velocity constant as through the experimental process the coef±icient will be discovered through measuring the acceleration of the tire. Acceleration is equal to the velocity over time therefore accurately measuring acceleration will require a constant initial velocity. I conceptualised that to accurately measure the velocity a tire is moving, and repeat this process with the exact identical constant initial velocity, I could use an electric bike (Sparta ultra M5B conversion kit on an X-treme bike frame). The electric bike has various settings where the speed can be controlled through a throttle which accelerates the bike's front tire at a constant force. I chose setting 1 which was 8km/h, which is 2.23m/s ± 0.1 Tire (Wanlihu), tire tread (mountain bike), and tire material (natural rubber) Controlling the tire used is essential to only measure the dependent variable varies when altering the pressure (Pa) within the bike tire. If the thickness of the tire is varied as a re±lection of the gauge pressure, the shape might alter and the tire might have more/less surface area touching the ground. Different tires would correspondingly have distinct designs which This will simply be controlled by using the exact same tire as a constant for all trials. The bike tire used is a 26-inch Wanlihu mountain bike tire made from natural rubber and has a mountain bike tread.

affect the traction. Temperature ( °C ) Variations in temperature in±luence the pressure in a tire. This is as the gas particle's kinetic energy increases in correlation with an increase in temperature, causing them to move with greater energy and increasing their collisions with each other and the surface. However small changes in temperature should theoretically not signi±icantly skew the results. The air pressure of a bike is increased by 1.8% for every increase in degree celsius (Floadmin) To minimize the variation in temperature, the experimental procedure will be conducted in an ef±icient manner where all results can be collected within a 30min time period to reduce the probability of a change in weather. This will be monitored to be around 19 ± 1 °C Surface of the tire is tested on Changes in the surface would correspond to changes in its frictional properties of it. Rougher surfaces have higher friction because there are more irregularities, causing interlocking, therefore the force of kinetic friction against the bike tire will be greater. Conducting the experimental procedure will be done on a smooth stone. To control this variable by keeping the surface being used constantly at the same location Mass supported by the tire The mass of the bike frame supported by the tire can affect the resistance exerted onto the bike tire. The larger the mass in which the tire supports, the larger the kinetic frictional force between the wooden ±loor and the tire, due to the irregularities colliding against each other with a greater force. Controlling To control this variable, I will simply use the same E-bike and due to the bike having 2 tires the mass is distributed fairly evenly.

this will make sure the data collected is valid and reliable as the resistance force exerted on the tire remains constant. (Table 1 - controlled variables) 4.1 Equipment - Bike stand (28-inch double kickstand) - Air compressor (with pressure display in increments of 20) - Presta Valve - Stopwatch - Electric Bike ( Bosch ultra M5B conversion kit on X-treme bike frame) - Pressure Gauge 4.2 Experimental set up (Figure 1 - Method set up) 4.3 Experimental methods

1. First, set the bike to suspend the front motorised tire, by using the double kickstand. 2. Secondly, attach the Presta valve onto the air compressor, then de±late the tire. 3. Following that, when the front tire is de±lated, use the air compressor to in±late the tire to 60psi 4. Whereafter by using the pressure gauge, inspect that the tire is at 60psi for increased accuracy 5. Before conducting the experiment, ensure to conduct the experiment at a monitored temperature (19 °C ) and to execute the experiment on the same surface for each trial. 6. Henseforce set the bike to setting 1 (8km/h) by using the arrows above and below the display and stand by until the bike displays 8km/h and has reached the maximum Velocity. 7. Next, release the throttle and place the front tire on the ground (make sure not to push down onto the bike resulting in a greater force exerted down onto the wheel). 8. As soon as the wheel makes contact with the ground surface, use the stopwatch to record the time taken for the tire to reach 0m/s and come to a complete stop. 9. Subsequently repeat steps 3-7, 5 different times, to have multiple trials 10. Finally repeat steps 3-8 for the various pressures (80psi,100psi,120psi and 140psi) 4.4 Risk assessment To ensure the E-Bike is secure and won't potentially cause damage to itself or harm to the individual conducting the experiment through falling, when mounting the bike caution should be taken. Although there are no signi±icant risks when conducting this experiment, to some degree the individual will have involvement with sharp points as well as fast-moving components such as the bike chain, spokes and gears. Gloves are suggested to avoid cuts and ensure the individual's safety. Comprehensively, the experimental procedure has minor safety concerns and no ethical or environmental issues and therefore are not applicable to this investigation. 6.0 Raw Data Time taken to decelerate from 2.24m/s to 0.00m/s (s) ±0.01 Pressure of the Tire (psi) Trial 1 (s) ± 0.17 Trial 2 (s) ± 0.17 Trial 3 (s) ± 0.17 Trial 4 (s) ± 0.17 Trial 5 (s) ± 0.17 60.0 ±1.22 3.43 3.98 3.50 4.02 3.62

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