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How does the sinkage depth of a tyre affect its rolling resistance ?

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How Does Sinkage depth of a tire affect its rolling resistance ?


Ashish    Raj


ABA An IB world school

Word Count :- 3691 words

Table of contents

Abstract                                                                                           3

Introduction                                                                                           4

Theory                                                                                         5

Mathematical Modelling                                                                         7

Method of Investigation                                                                         8

Results                                                                                         9

Evaluation                                                                                         11

Conclusion                                                                                        14

Limitations in the model                                                                         15

Bibliography                                                                                         16


The exploration is a laboratory experiment intended to explore relationship between rolling resistance of a tire and its sinkage depth .

The research question that was established from the introduction  is How does the sinkage depth of a tire affects the rolling resistance the tire faces ?

The modus operandi of this exploration involved allowing a bicycle with training wheels to roll down a slope inclined 45° into a smoothened sand bed. The sinkage depth of the tires on the sand that rolled on the sand bed was recorded . The tires of the bicycle had the radius of 27 cm and the width of the tire was 4cm. The range of the air pressure that were tested on the tire varied from  0 kPa to 196.16 kPa . The trials that were conducted varied on a value of 49.08 kPa . Using these values of sinkage depth obtained from the air pressure the rolling resistance for the tire was calculated.

We established a trend between the sinkage depth and the rolling resistance ; as the sinkage depth increased the rolling resistance force increased.  

The lowest values for the rolling resistance were observed when the tires were filled 50% to its full potential. The final values that were calculated for the rolling resistance had low percentage uncertainty hence this indicates that the values we obtained were likely precise values. The low uncertainty in the data allowed a quantitative generalization of the rolling resistance due to the sinkage depth.

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Crr or the rolling resistance force for a pneuamatic tire can be defined by the equation ( Hibbeler, R.C. 2007)

Crr = image00.png

The experimental rolling resistance is defined in the equation below

Fr = N x b / r                                                                        - 1)

N stands for the normal force acting on the bicycle , b stands for the rolling resistance coefficient with the dimension of length .

B = image00.png


In the equation above where b is the rolling resistance coefficient , z is the sinkage depth and d is the diameter of the wheel .

Fr = N x (image00.png


IN the experimental frictional force equation above the frictional force Frr is the function of the normal force N required to push the wheel forward . Other variables such as the sinkage depth , radius and diameter will be defined variables of the tire based on the air pressure in the tire.

Method of investigation

The method of investigation was designed in a way to reduce the possibilities of errors to its lowest potential while at the same time keeping in mind the attainment of highest accuracy of the results . The method involved allowing a bicycle with training wheels to roll down an inclined ramp 45° to a smoothened softened sand bed. On the trail of sand bed approximately 750cm3 of tap water had been added to reduce the elasticity of the sand and to make sure that the sand retains the tire tracks after the bicycle was dragged though the sand.

The air pressure of the tires that were used on a trial varied from 0kPa to 246 kPa with an interval of 49kPA in each trial which was measured by an analogue air pressure gauge.

The bicycle was allowed to roll down the inclined ramp. The force of the bicycle was a result of the accelerating force acting on the bicycle.

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The experiment was performed on in the outdoors during the day . The heat of sunlight was transferred to these materials used in the experiment , but since these materials have different thermal absorption capacitates their temperature might have varied. an abrupt increase in temperature induces a transient friction response similar to that induced by a step decrease in velocity ( Chester , 2012 ) . Since sand has a higher thermal capacity than wood the change in the temperature might cause a discrepancy . in order to control this variable we could have performed the experiment indoors with the temperature controlled by an air conditioner at 25ᵒC .


Silliman, Benjamin (1871) Principles of Physics, Or Natural Philosophy, Ivison, Blakeman, Taylor & company publishers

Calculating proper rolling resistance: A safer move for material handling | Plant Engineering. (n.d.). Plant Engineering provides strategic manufacturing knowledge to help the plant manager operate efficiently, effectively and safely. | Plant Engineering. Retrieved October 16, 2013, from http://www.plantengineering.com/single-article/calculating-proper-rolling-resistance-a-safer-move-for-material-handling/82fa156f91ea516c6b08be3bc595db65.html

Hibbeler, R. C., Fan, S. C., & Schiavone, P. (2007). Engineering mechanics: statics - dynamics (11th ed., ed.). Singapore: Prentice Hall/Pearson Education.

Rolling Resistance | Schwalbe North America. (n.d.). Schwalbe North America | Schwalbe North America. Retrieved October 16, 2013, from http://www.schwalbetires.com/tech_info/rolling_resistance

Tire Rolling Resistance Part 2: Defining Rolling Resistance. (n.d.). Tire Rack. Retrieved September 9, 2013, from www.tirerack.com/tires/tiretech/techpage.jsp?techid=175

Tires and passenger vehicle fuel economy: informing consumers, improving performance. (2006). Washington, DC: Transportation Research Board.

Rolling Resistance | Schwalbe North America. (n.d.). Schwalbe North America | Schwalbe North America. Retrieved October 16, 2013, from http://www.schwalbetires.com/tech_info/rolling_resistance#why>.

Kutz, M. (1986). Mechanical engineers' handbook. New York: Wiley.

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