The field of rolling resistance has been widely researched and analyzed. The most common laboratory test measures the force required to rotate a tire at the speed of 50mph against large diameter steel drum. Multiple samples of each tire /size are tested to establish an average rolling resistance value. The rolling resistance in a tire typically declines moderately as the tire temperature rise from cold to normal operating conditions during the first 30 minutes of driving every time the vehicle is used.
Theory
Rolling resistance is the force that resists the rolling of a wheel or other circular object along a surface caused by deformations in the object and/or surface. Generally the force of rolling resistance is less than that associated with kinetic friction. (Silliman. 1891)
Rolling resistance is the force that resists the rolling of a wheel or other circular object along a surface caused by deformations in the object and/or surface. Generally the force of rolling resistance is less than that associated with kinetic friction. Typical values for the coefficient of rolling resistance are 0.001. One of the most common examples of rolling resistance is the movement of motor vehicle tires on a road, a process which generates heat and sound as by-products. (Silliman. 1891)
The bicycle has tires made out of rubber i.e. the bicycle has pneumatic tires. The primary cause of rolling resistance in the pneumatic is hysteresis . Hysteresis is a property that is unique to all the elastic products in which energy is lost during the recovery of the elastic from the stress it is put under.
When the cycle rolls down the ramp it loses energy due to hysteresis property of the pneumatic tires. Since the bicycle loses energy because of hysteresis , less work has to be done by the cycle . But the bicycle has to travel the same distance , which means that the there is a reduction in force that is required by the bicycle to do the work . This reduction in the force is caused by the rolling resistance.
The theory stated above involves the rolling resistance faced by a bicycle on all surfaces . When we talk about the rolling resistance the tire faces on sand , it is important to remember that sand is a loose surface and the tire has the ability to sink in the sand .
If a tire sinks in more than its usual sinkage depth . The tire needs to do more work inoder to overcome the rut it has sunk in the opposite direction of the force . Since the force is constant , this work done by tire acts counter-effective to the work that needs to be done in order to cover the distance , and hence the force is degraded . The degradation in the force is caused by the increased rolling resistance due to the sinkage depth .
(bedenbender , 2012)
As the tire roates under the weight of the vehicle , the tire experiences continuous cycles of deformation and recovery . As the tires recovers from the deformation , energy is lost in the tires due to hysteris.
In the diagram above R refers to the rolling resistance acting on the wheel , r is the radius of the wheel , W is the force acting on the wheel , F is the towering force applied on the axle in this case it is the force due to the acceleration due to gravity .
( Dressel , 2011)
Mathematical modeling
The rolling resistance force in simple ways can be defined by a mathematical equation in which the rolling resistance force is a function of force that the tire undergoes . (National research council of reseach academies Washington D.C , 2006 )
Fr = Crr x N
Where Fr stands for rolling resistance force or rolling resistance , Crr stands for rolling resistance coefficient , and N stands for the normal force that acts on the bike .
Crr or the rolling resistance force for a pneuamatic tire can be defined by the equation ( Hibbeler, R.C. 2007)
Crr =
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 =
-2)
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 (
)/r
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. The inclined ramp was used in order to ensure that a constant force acts on the bicycle due to the accelerating force on the bicycle. The training wheels have been installed in order to guide the bicycle on the ramp and to prevent the bicycle from falling off the ramp.
For each value of air pressure , the bicycle was allowed to ride down the ramp and the sinkage depth of the tire on the sand was measured and 5 trials were performed for each . The main independent variable in this experiment is the sinkage depth of the tire whereas the dependent variable is the rolling resistance the tire faces due to the sinkage depth.
From the experiment performed values necessary for calculation were recorded and the calculations was performed.
Error calculation
Absolute error of the vernier caliper = ± 0.005cm
Absolute error of the weighing scale = ± 0.01 kg
Percentage error in the mass of the bicycle = (uncertainity /mass) x100
= (0.01/15.80)x100
= 0.06 %
Percentage error in the radius of the tire = (uncertainty / radius ) x100
=( 0.005/27.5 ) x100
= 0.02%
Percentage error in the diameter of the tire = 0.01 %
Percentage error in the sinkage depth = (uncertainty / sinkage depth ) x100
=(0.005/0.98) x100
= 0.51%
Percentage error in the rolling resistance coefficeient = (sum of the percentage of error sinkage depth and diameter ) /2
= (0.51+0.01)/2
= 0.26%
Overall percentage error = Sum of the percentage errors of the values involved in the formula
= 0.06% + 0.26% + 0.02%
= 0.34%
Therefore absolute uncertainity in the rolling resistance = ±0.00255
Results
The table below shows sinkage depth of tire in the sand when the air pressure was restricited to 49.04 kPa
The table below shows the sinkage depth of the tire in the sand bed when the air pressure was restricted to 98.08 kPa
The table below shows the sinkage depth of the tire when the air pressure of the tire was restricted to 147.12 kPa .
The table below shows the sinkage depth of the tire when the air pressure was restricted to 196.16 kPa
The table below shows the sinkage depth of the tire when the air pressure was restricted to 245.20 kPa
The table below shows the the rolling resistance faced by the tire due to its sinkage depth
The table below show the rolling resistance and its absolute error
Evaluation
Relationship of frictional force related to the sinkage depth
The graph above shows the data that establishes the relationship between rolling resistance of the bicycle and the sinkage depth of the tire on the sand bed. The relationship is found to be linear and is the only linear relationship in the whole experiment . As the sinkage depth of the tire increases the rolling resistance of the tire also increases . This shows that rolling resistance is directly proportional to sinkage depth . As we saw above the relationship between sinkage depth and the air pressure of the tire is varied and at the best can be explained by a polynomial trend . Arriving at the final conclusion for the rolling resistance based on the sole evidence of the sinkage depth on behalf of the air pressure of the tire. We can state that in order to determine the best possible value for the least resistance we would have to arrive at the a value offers the least sinkage depth for a given air pressure in order to attain the least rolling resistance the tire faces and optimize the force efficiency .
Rolling resistance in this case is primarily caused due to a characteristic of a deformable material such that energy of deformation is greater than the energy of recovery . In this case the rubber component of the tire causes hysteresis , a property characteristic to elastic tires . The hysteresis causes the tire tire to lose energy due to the constant stretch and recovery .
Looking at the results obtained from the experiment and the trends observed it can be stated that the primary cause that has affected the rolling resistance by the tire due its sinkage depth is the compressibility of the sand and the elasticity of the tire .
The compressibility of the sand or compaction resistance is usually produced in this case by the work done by the cycle in making a rut of the depth .
Another factor affecting the rolling resistance due to the sinakge depth is the amount of sand displaced by the tire in displacing the soil. The wheel compresses in the sand pushes out the sand from its original place. Hence as the work done by the bicycle increases in order to remove the sand from the original place the rolling resistance increases. The bulldozing resistance is mitigated by the fact that a portion of the soil is pushed to the sides of the wheel.
The results from the experiment show polynomical trend rather than a linear trend . the most desirable data for the rolling resistance would be the sinkage depth as the rolling resistance force is directly proportional to the sinkage depth . The graph starts off with a sinkage depth of 0.98 cm due to 49.04 kPa and decreases until it reaches 0.2 cm from which the value of the sinkage depth starts to increase .
At 147.12 kPA the tire has a considerable amount f air inflated . The amount of the air inflated is between the range of the air pressure classified as underflated an overflated. The ideal air pressure which in this case is 147.12 kPa increases the thread area of the tire on the sand bed , increasing the width of the tore on the sand which causes the force of the tire on the sand to be spread out in the surface rather actually penetration the sand bed .
At 49kPa and 98kPa there the tire is almost mildly inflated .With the tires fully inflated capacity being 320.26kPA , these two pressure allow the tire to be inflated just 15.3% and 30.6% of their maximum capacity respectively . While pedaling the bicycle because of the lack of the air pressure of the tire and bicycle frame comes in close contact and force the sidewalls of the tire to flex due to the force that is being applied and pushes the bicycle deep into the sand bed due to this flexing phenomenon .
From the above data we cannot establish linear relationship between air pressure and sinkage depth . There are many factors that affect the sinkage depth of a tire due to the air pressure . The air pressure of the tire causes the tread material in the tire to expand as it is partially filled and when the tread material is on the sand it adjusts the frame and the tread in a suitable manner . However as the air pressure in the tire increases and the tire is capacity for the air pressure reduces , the air that is present in the tire has less freedom to move around so as to adjust the frame and the tread of the tire in order to efficiently place itself . Hence as the air pressure in the tire begins to fill the tire up completely the sinkage depth in the tire increases . The air pressure in the tire limits the thread from spreading out the force on the sand and hence on a surface area of the sand as the force increases because it can’t be spread out the pressure on the sand increases and the tire sinks in deeper .
.
Conclusion
Our research question which formed the basis of the essay was How does change in Sinkage depth of a tire affect the rolling resistance . The main of this experiment was to establish a relationship between sinkage depth of the tire and the rolling resistance it faces .
The experiment involved allowing a bicycle , with specific air pressure which was measured using an air pressure gauge , with trainers to roll down a wooden ramp of length 5 meters and width 3 metres inclined at an angle of 45° to the ground . The bicycle after rolling down from the ramp rolled on a sand bed that was smoothened and softened by hand . The sand was wetted by adding 250cm3 of tap water in a linear manner , in order to make the sand retentive of the sinkage marks made by the tire. The reading of the sinkage depth was measured with the help of a vernier caliper. Consequently, the rolling resistance was calculated using these values .
At the end of the experiment we successfully derived a linear relationship between the sinkage depth of the tire and the rolling resistance. The rolling resistance that the tire faces is directly proportional to the sinkage depth of the tire. Hence as the sinkage depth of the tire increases so does the rolling resistance 9it faces . In order to find the air pressure of the tire propagates the rolling resistance , we have to find the air pressure which has the least rolling resistance value .
The absolute uncertainties that were obtained in our experiment for the rolling resistance were low , this shows that the values that we have obtained are precise . Performing this experiment at a small scale makes the rolling resistance negliblie. The devices that were used to measure the numerical values had a low least count . From the results that have been , there is a high possibility of the presence of random errors since the values that have been recorded show an inconsistency at unlikely events during the experiment.
The experiment involved focusing on a variable and its outcome on a particular event . At best this approach can be considered incomplete as there are others factors present in the experiment that might affected the rolling resistance equally if not partially . There is a high possibility that the temperature also a major impact on the experiment and hence further areas for research include involving temperature as a variable in deciding if sinkage depth alone affects the rolling resistance linearly .
Another area left for research and investigation is to find a quantitative data for the rolling resistance coefficient. In the experiment we found several data for the rolling resistance co-efficient , however we couldn’t compare this to a literature value due to a lack of research of bicycles on sand .
Limitations in the model
The limitations in the experiment that has been performed mainly arises from the various assumptions that have been made .
The sand that was used as for the sand bed was procured from an open sea beach. Although the sand was smoothened and sieved there is a high possibility that the sand contained minute impurities such as small fragments of shell which might have had an counter-effect on the compressibility of the sand. It is also possible that the there was a high content of salt deposits on the sand as the sea water contained salt and the water from the sand had evaporated leaving behind salt deposits on the sand . We could have instead used soil instead as a surface bought from the market as this would be possibly have more uniformity than the sand .
As mentioned in the method of investigation , the cycle had trainers attached to them while it rolled down the ramp in order to balance the cycle as it rolled down and prevent it from falling over . Since the trainers are wheels it is possible that they too contributed to the rolling resistance that the bicycle faced . However since all the quantitative values were recorded when the cycle was attached with trainers , the trainers have uniformly affected the rolling resistance in each trial and hence has no overall effect on the trend .
The experiment also involved pouring a specific amount of water on the sand in order to increase the retentive ability if the sand . However , what has not been established in the experiment is the right amount of water that should be added to sand in order to increase the retentive ability . An increased amount of water in the sand will reduce the elasticity of the sand even though increasing the retentive ability of the sand. This will be detrimental to the experiment the actual sinkage depth of the tire will be reduced . Also , water was poured on the sand only once during the experiment . there is also a possibility that the water evaporated during the experiment , hence reducing the retentive ability of the sand and causing a discrepancy in the values obtained.
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 .
Bibliography
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.
by
crysisfreak69 (student)
