Hard Rubber Friction Coeffs

*Corresponding author. Tel.: 001 817 264 3590; fax: 001 817264 3802.

Applied Ergonomics 30 (1999) 235—245

Factors affecting minimum push and pull forces of manual carts

Khaled W. Al-Eisawi!,*, Carter J. Kerk", Jerome J. Congleton#, Alfred A. Amendola#,Omer C. Jenkins$, Will Gaines%

!SABRE Technology Solutions, 1 East Kirkwood Blvd. MD 7385, Southlake, TX 76092, USA"South Dakota School of Mines and Technology, Industrial Engineering Program, Rapid City, SD 57701-3995, USA

#Safety Engineering Program, Department of Nuclear Engineering, Texas A&M University, College Station, TX 77843-3133, USA$Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA

%Scott & White, Department of Occupational Medicine, 1600 University Drive East, College Station, TX 77840, USA

Received 18 February 1997; accepted 2 March 1998

Abstract

The minimum forces needed to manually push or pull a 4-wheel cart of differing weights with similar wheel sizes from a stationarystate were measured on four floor materials under different conditions of wheel width, diameter, and orientation. Cart load wasincreased from 0 to 181.4 kg in increments of 36.3 kg. The floor materials were smooth concrete, tile, asphalt, and industrial carpet.Two wheel widths were tested: 25 and 38 mm. Wheel diameters were 51, 102, and 153 mm. Wheel orientation was tested at four levels:F0R0 (all four wheels aligned in the forward direction), F0R90 (the two front wheels, the wheels furthest from the cart handle, alignedin the forward direction and the two rear wheels, the wheels closest to the cart handle, aligned at 90° to the forward direction), F90R0(the two front wheels aligned at 90° to the forward direction and the two rear wheels aligned in the forward direction), and F90R90 (allfour wheels aligned at 90° to the forward direction). Wheel width did not have a significant effect on the minimum push/pull forces.The minimum push/pull forces were linearly proportional to cart weight, and inversely proportional to wheel diameter. Thecoefficients of rolling friction were estimated as 2.2, 2.4, 3.3, and 4.5 mm for hard rubber wheels rolling on smooth concrete, tile,asphalt, and industrial carpet floors, respectively. The effect of wheel orientation was not consistent over the tested conditions, but, ingeneral, the smallest minimum push/pull forces were measured with all four wheels aligned in the forward direction, whereas thelargest minimum push/pull forces were measured when all four wheels were aligned at 90° to the forward direction. There was nosignificant difference between the push and pull forces when all four wheels were aligned in the forward direction. ( 1999 ElsevierScience Ltd. All rights reserved.

Keywords: Push and pull forces; Carts; Rolling friction

1. Introduction

Most of the ergonomics studies that have been per-formed on pushing and pulling, including the psycho-physical guidelines developed by Snook and Ciriello(1991) for the design of manual material handling tasks,report results in terms of hand force exertions. Whendesigning a cart pushing or pulling task, a job designermust determine the maximum weight with which to loadthe cart so that the hand forces needed to push or pull thecart do not exceed safe limits. In designing or selecting

a cart, one should select a wheel diameter that will keepthe hand forces exerted in pushing or pulling the fullyloaded cart below safe limits. This is not an easy taskbecause the hand forces required to push or pull a cartdepend on many factors such as wheel diameter, wheelorientation, floor material, and wheel material. Thisstudy attempted to facilitate the determination of handforces from factors that are easier to measure includingcart weight, wheel diameter, floor material, and wheelorientation.

The resistance between rolling wheels and the floorsurface is termed ‘rolling friction’. Its laws are not yetdefinitely established. A widely acceptable relationship isthat if ¼ is the total weight, r the wheel radius, and othe coefficient of rolling friction, then F is equal to the

0003-6870/99/$ — see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 3 - 6 8 7 0 ( 9 8 ) 0 0 0 1 9 - 2

resistance applied at the circumference of the wheel and isgiven by

F"o¼

r(1)

To keep the wheel rolling in uniform motion withoutslipping, an external force equal to F must be applied.

Notice that o has units of length while the coefficient ofstatic friction and the coefficient of sliding friction aredimensionless quantities. o/r is called the coefficient ofresistance to rolling (Kragesky et al, 1982). The deriva-tion of the above relationship can be found in Shames(1966). It is important to note that the above relationshiphas been derived analytically and not empirically, whichmeans that it is theoretically justified.

Kragelsky et al. (1982) provided a summary of theearlier research on rolling friction. Rolling friction istypically much smaller than sliding or static friction. Thisis why vehicles have wheels instead of runners, and ballbearings are used in some machines instead of sleeve-bearings. Reimann (1971) reported that rolling friction isalmost unaffected by the presence of lubricants and ex-plained rolling friction as the result of the inability of anelastically deformed body to retain its original shapeimmediately on release of the stress. The harder therolling wheel or ball, and the harder the surface overwhich it rolls, the less the force of rolling friction (White,1969).

Very little information is available about the values ofo for different materials. For wood on wood, the coeffic-ient of rolling friction is 0.152 mm while the coefficient ofstatic friction is 0.25—0.5 (Oberg et al, 1987). The coeffic-ient of rolling friction may be assumed to be 0.051 mmfor iron on iron, 0.216 mm for iron on granite, 0.381 mmfor iron on asphalt, and 0.559 mm for iron on wood(Oberg et al, 1987). Marks and Baumeister (1978) in-cluded a table for the coefficients of rolling friction forsteel and pneumatic tires on different surfaces. Car-michael (1950) provided a small table of the coefficient ofrolling friction for different materials, mainly wood andsteel.

Eq. (1) describes the force needed to keep a wheelrolling without slipping and not the initial force requiredto start a wheel rolling. One would hypothesize that theinitial force has to be higher than the force needed tomaintain uniform rolling. What is not known is whetherthe initial force has the same kind of relationship withtotal weight and wheel radius as the force needed tosustain rolling. If that is the case, the only differencewould be that the coefficient of rolling friction (o) wouldbe higher for the initial force than that for the sustainingforce. Since ergonomists focus on the causes of higherstresses, this study investigated only the initial force andits relationship to total weight and wheel radius underdifferent conditions.

When a cart is pushed or pulled from a stationaryposition, the applied force must overcome the rollingfriction at the wheels and the friction at the wheel bear-ings. Wheel bearings are typically well lubricated andprovide very little resistance to rolling as compared tothe friction between the wheels and the floor. This studyfocused on rolling friction between the wheels and thefloor and investigated the relationship between rollingfriction, cart weight, and wheel diameter for differentfloor materials.

2. Objectives

This study was divided into four experiments to ad-dress the following questions:1. Does wheel width have an effect on the minimum

initial cart pull forces? The relationship described inEq. (1) does not include wheel width, which impliesthat wheel width should not have an effect on theminimum force required to move a cart.

2. What is the effect of floor material? Floor materialaffects the coefficient of rolling friction, which is theconstant of proportionality o in Eq. (1). According toWhite (1969), harder surfaces are expected to yieldlower cart push/pull forces. The coefficients of rollingfriction were determined for a number of floor surfacesand one wheel material.

3. What are the effects of wheel diameter, wheel orienta-tion and their interaction? Eq. (1) has been derived forthe case where the force applied at the circumferenceof the wheels acts in the same direction in which thewheel rolls. Therefore, it is expected that the relation-ship in Equation 1 will hold when all four wheels arealigned in the forward direction (F0R0). It is expectedthat when one or more of the wheels is not oriented inthe forward direction, higher forces are required tomove the cart forward.

4. Is there a difference between cart push and cart pullforces for different wheel orientations? The basic lawsof statics necessitate that cart push and pull forces arethe same when all wheels are oriented in the forwarddirection. What remains unknown is how the relation-ship between cart push and pull forces changes forother wheel orientations.

3. Methods

A Wagner push—pull force gauge (Model FDL 100)with a maximum reading of 100 lb and an accuracy of$0.3% of full scale was used to measure the minimumcart push/pull forces required to initiate the movement ofa cart under the different conditions. The cart startedfrom a stationary position for each measurement. Theexperimenter attached the force gauge to the cart at

236 K.W. Al-Eisawi et al. / Applied Ergonomics 30 (1999) 235—245

Fig. 1. Illustration of the cart used in this study.

a point midway along its width and pushed or pulled it,increasing the force slowly and steadily without jerkinguntil the cart moved. The force gauge was perpendicularto the cart handle. For measuring pull forces, the forcegauge contacted the cart at the end of a fork-type hookattachment. For measuring push forces, the attachmentwas cylindrical with a diameter of 5 mm. The dial on theforce gauge recorded the force and stored it after therelease of the force. The force gauge was reset before thenext measurement. Each measurement was repeated sixtimes, each trial being at a different random location. Thefloor was level and of consistent quality.

The cart was a 4-wheel Rubbermaid plastic utility cart.Its external dimensions were: 610 mm wide, 1020 mmlong, and 820 mm high. The cart is illustrated in Fig. 1.The cart weighed 15.3 kg without the wheels. It hada handle along its width. Cinder blocks were used to loadthe cart. Each block weighed 9.1 kg. The cinder blockswere distributed evenly with respect to the center of thecart.

3.1. Effect of wheel width

Two types of wheels were tested: 25 mm wide, and38 mm wide. This was the widest range of wheel widthsavailable for the same wheel material, wheel diameter,type of bearing, and load capacity. In other words, wheelsare not available in all materials, diameters, bearings, andwidths. This is not a surprise because smaller diameterwheels with relatively small widths and soft materials aredesigned for light duty while the larger diameter, largerwidth, and harder material wheels are designed for heavyduty. Obviously, the cost also increases as one startsconsidering the heavier duty wheels. Therefore,a 25—38 mm wheel width range was the range that a cart

designer would most likely select for the type of cart usedin this experiment.

The two types of wheels were made of hard rubber andhad a diameter of 102 mm. The experiment was per-formed on smooth concrete and industrial carpet floors.

Cart load was increased from 0 to 181.4 kg in in-crements of 36.3 kg. All four wheels were maintained inthe forward direction (F0R0) throughout this part of theexperiment. All the measured forces were pull forces.

3.2. Effect of floor material

Minimum cart pull forces were measured using the102 mm diameter hard rubber wheels on smooth con-crete, tile, asphalt, and industrial carpet. These are sur-faces commonly seen in different industries. The asphaltfloor was free of cracks, bumps, or gravel. The carpetfloor was made of carpet tiles (heuga Flor S, 55% nylon,27.5% animal hair, and 17.5% rayon). The latter type offloor is common in large, open floor areas in ‘electronic’and modular design offices. All floors were level and ofconsistent quality. The orientation of the wheels wasmaintained in the forward direction. Cart load waschanged in increments of 36.3 kg from 0 to 217.7 kg. Onlypull forces were measured.

3.3. Effect of wheel diameter and wheel orientation

In this part of the experiment, four factors and all oftheir combinations were tested. The factors were: wheeldiameter, wheel orientation, floor surface, and cart load.Three wheel diameters were tested: 51, 102, and 152 mm.All wheels had the same width, 25 mm, were madeof the same material (hard rubber), and had the sametype of bearing. Only pull forces were measured. Wheel

K.W. Al-Eisawi et al. / Applied Ergonomics 30 (1999) 235—245 237

Fig. 2. Effect of wheel width on minimum cart pull forces.

Table 1Least squares regression lines attributes for wheel width data

R2 Slope 95% confidenceinterval on slope

1A wide, concrete 0.975 0.0419 0.0407—0.04301.5A wide, concrete 0.981 0.0429 0.0420—0.04391A wide, carpet 0.977 0.0894 0.0874—0.09151.5A wide, carpet 0.992 0.0894 0.0880—0.0908

orientation was tested at four levels: F0R0 (all fourwheels aligned in the forward direction), F0R90 (the twofront wheels, the wheels furthest from the cart handle,aligned in the forward direction and the two rear wheels,the wheels closest to the cart handle, aligned at 90° to theforward direction), F90R0 (the two front wheels alignedat 90° to the forward direction and the two rear wheelsaligned in the forward direction), and F90R90 (all fourwheels aligned at 90° to the forward direction). Allswiveling wheels had an offset swivel base. When alignedat 90° to the forward direction, the swiveling wheels facedthe same direction. Measurements were taken on bothsmooth concrete and carpet floors. Cart load was variedfrom 0 to 181.4 kg in increments of 36.3 kg.

3.4. Comparison of minimum push and pull forces

In this part of the experiment, both the minimum pushand pull forces required to initiate cart movement of thecart were tested. The cart was equipped with 102 mmdiameter hard rubber wheels. Three wheel orientationswere tested: F0R0, F90R0, and F0R90. Testing was con-ducted on a carpet floor.

4. Results


Fig. 2 illustrates the results of this part of the study.Each point on the graph represents the average of sixdata points. Cart weight is the total weight including the

weight of the empty cart, the cinder blocks, and thewheels. The graph shows that there was no significanteffect of wheel width on the minimum cart pull forces oneither floor. It is obvious that all four curves exhibita strong linear trend. Table 1 summarizes the R2 values,slopes, and 95% confidence intervals on the slopes of theleast squares regression lines fit to the data sets in Fig. 2.The analysis was done on the individual observations. Allregression lines were forced to pass through the originsince a y-intercept other than zero would mean that ittakes a force equal to the y-intercept value to move a cartof zero weight. This does not make sense from a physicalpoint of view. Conceptually, zero force is required tomove an object of zero weight.

Analysis of covariance to compare the two wheelwidths at the different loads was conducted on the min-imum pull forces on concrete and on carpet separately,with cart weight as the covariate. Table 2 summarizes thep-values of wheel width, cart weight, and their interac-tions. Although the effect on pull forces of wheel width onconcrete was statistically significant (p"0.0083), it was


Table 2p-values from ANCOVA to compare wheel widths

Concrete Carpet

Wheel width (¼) 0.0083 0.2367Cart weight (¸) 0.0001 0.0001¼]¸ 0.8867 0.5400

Fig. 3. Effect of floor material on minimum cart pull forces.

Table 3Least-squares regression lines attributes for the different floor materials

R2 Slope 95% confidenceinterval on slope

Concrete 0.975 0.0434 0.0422—0.0446Tile 0.990 0.0465 0.0458—0.0473Asphalt 0.956 0.0642 0.0618—0.0666Carpet 0.977 0.0894 0.0874—0.0915

Table 4Estimated coefficients of rolling friction for the different floor materials(mm)

Floor Coefficientof rollingfriction (mm)

95% confidenceinterval oncoefficient ofrollingfriction (mm)

Comparison withconcrete

Concrete 2.205 2.144—2.266 —Tile 2.362 2.327—2.403 7% higherAsphalt 3.261 3.139—3.383 48% higherCarpet 4.541 4.440—4.648 106% higher

obvious from the graph in Fig. 2 that it had no practicalsignificant effect on the minimum cart pull forces. In fact,the 95% confidence interval on the difference betweenthe means of the minimum pull forces for both wheelwidths was (0.07—0.42 kg).


Fig. 3 shows the means and the standard deviations ofthe minimum cart pull forces for the four surfaces testedin this experiment: concrete, tile, asphalt, and carpet.Least-squares regression lines were fitted to the data ofeach floor surface. The lines were forced to pass throughthe origin. Table 3 provides the R2 values, slopes, andconfidence intervals for these slopes. Multiplying theseslopes by the radius of the wheels (51 mm) gave estimatesof the coefficients of rolling friction for hard rubberwheels on the different floor materials. This informationis presented in Table 4, which also shows how the differ-ent floor materials compared to concrete.


Figs. 4 and 5 show that increasing wheel diametercaused the minimum cart pull forces to decrease on boththe concrete and carpet floors when all four wheels werealigned in the forward direction (F0R0). Fig. 6 is a plot of


Fig. 4. Effect of wheel diameter on minimum cart pull forces on concrete floor with all wheels in forward direction.

Fig. 5. Effect of wheel diameter on minimum cart pull forces on carpet floor with all wheels in forward direction.

the minimum cart pull forces against the ratio of cartweight to wheel diameter for the concrete and carpetfloors with the wheels at the F0R0 orientation. The graphalso shows the least-squares regression lines fitted to theconcrete and carpet data. The least-squares regressionlines were forced through the origin. Table 5 summarizesthe attributes of the regression lines.

Least-squares regression lines were fitted to the min-imum cart pull forces as a function of cart weight for eachof the wheel diameters, wheel orientations, and floorcombinations. The lines were forced through the origin.All lines showed strong linear trends (R2'0.95). Estim-ates of the slopes are presented in Table 6. Table 7 showshow the different wheel orientations compare to the


Fig. 6. Minimum cart pull force versus ratio of cart weight to wheel diameter.

Table 5Attributes of least-squares regression lines describing the minimum cartpull forces as a function of the ratio of cart weight to wheel diameter

Floor R2 Slope(mm)

95% confidenceinterval on slope

Concrete 0.953 3.73 3.64—3.82Carpet 0.957 7.98 7.82—8.13

Table 6Estimated slopes of least-squares regression lines modeling minimumcart pull forces as a function of cart weight

Concrete Carpet

Orientation 51 mm 102 mm 153 mm 51 mm 102 mm 153 mm

F0R0 0.0685 0.0434 0.0237 0.145 0.0894 0.0584F90R0 0.0578 0.0514 0.0261 0.119 0.110 0.0772F0R90 0.0530 0.0586 0.0214 0.133 0.136 0.0843F90R90 0.0624 0.0787 0.0290 0.147 0.136 0.110

Table 7Comparison of slopes for F90R0, F0R90, and F90R90 wheel orienta-tions to slopes for F0R0 wheel orientation (within same wheel diameter)

Concrete Carpet


F0R0 1.00 1.00 1.00 1.00 1.00 1.00F90R0 0.84 1.18 1.10 0.82 1.24 1.32F0R90 0.77 1.35 0.90 0.92 1.53 1.44F90R90 0.91 1.81 1.22 1.01 1.53 1.90

Table 8Comparison of slopes for 102 mm and 153 mm wheel diameters withslopes for 51 mm wheel diameter (within same wheel orientation)

Concrete Carpet


F0R0 1.00 0.63 0.35 1.00 0.62 0.40F90R0 1.00 0.90 0.45 1.00 0.92 0.65F0R90 1.00 1.11 0.40 1.00 1.02 0.63F90R90 1.00 1.26 0.46 1.00 0.93 0.75

F0R0 wheel orientation for each wheel diameter on thetwo floor surfaces. For example, on the concrete floor,the minimum pull forces with the wheels at the F90R0were 1.18 times the minimum pull forces under F0R0wheel orientation and with all the other conditions beingthe same. Table 8 shows how the wheel diameters com-pare to the 51 mm diameter for each wheel orientation.

As the effect of wheel orientation seems to be inconsist-ent between the different wheel diameters, the minimumcart pull forces for all conditions within each of the wheelorientations tested were averaged and compared to theaverage force for the F0R0 wheel orientation. For


Fig. 7. Minimum cart pull and push forces for the F0R0 wheel orientation.

Fig. 8. Minimum cart pull and push forces for the F90R0 and F0R90 wheel orientations.

F90R0, the average force was 2.7% higher than that forF0R0. For F0R90, the average force was 13.1% higher;and for F90R90, the average force was 30.7% higher thanthat for F0R0.


Figs. 7 and 8 show the minimum cart pull and pushforces for the three wheel orientations: F0R0, F90R0, and


Table 9Slopes of least-squares regression lines for push and pull data

F0R0 F90R0 F0R90

Pull 0.0894 0.110 0.136Push 0.100 0.153 0.114

F0R90. The slopes of the least-squares regression linesfitted to each data set are shown in Table 9. The least-squares regression lines were forced through the origin.

Analysis of variance was conducted on the minimumforce to test for the significance of Task (pull versus push),Load, and their interaction for the F0R0 wheel orienta-tion. The p-values were 0.0003, 0.0001, and 0.0655 forTask, Cart Load, and Task]Cart Load, respectively.Since a statistically significant difference existed betweenpush and pull forces, a 95% confidence interval wasconstructed on the difference between the average pushforce and the average pull force for the F0R0 wheelorientation to test the practicality of the statistical signi-ficance. The confidence interval was (0.44!1.41 kg), theaverage push force being higher than the average pullforce. Thus, the maximum difference between push andpull forces could be as high as 1.4 kg, which attests that itis not a practically significant difference for ergonomicsdesign and evaluation purposes.

Analysis of variance was also conducted to comparethe pull forces with the F90R0 wheel orientation to thepush forces with the F0R90 wheel orientation. The p-values were 0.0659, 0.0001, and 0.0092 for Task, CartLoad, and Task]Cart Load, respectively, with Taskbeing pull with F90R0 versus push with F0R90 wheelorientation.

Similarly, analysis of variance was conducted to com-pare the pull forces with the F0R90 wheel orientation tothe push forces with the F90R0 wheel orientation. Thep-values were 0.0260, 0.0001, and 0.0041 for Task, CartLoad, and Task]Cart Load, respectively. Since Taskwas statistically significant, a 95% confidence intervalwas constructed for the difference between the averagepull force with F0R90 and average push force withF90R0 to investigate practical significance. The confid-ence interval was (0.10—1.22 kg) with the average pushforce being higher. Again, the confidence interval was notwide enough to conclude that the push-F90R0 and pull-F0R90 forces were significantly different for ergonomicsdesign and evaluation purposes.

5. Discussion

A significant finding of all four experiments, as evidentin the graphs presented in the previous section, is thestrong linear relationship between the minimum cartpush/pull forces and cart weight. This was evidenced in

the large R2 values (higher than 0.95) for all regressionlines described in the previous section. This strong linearrelationship existed for all floor surfaces, wheel dia-meters, and wheel orientations. Therefore, a linear rela-tionship exists between cart weight and the force toinitiate cart movement, similar to the linear relationshipbetween cart weight and the force to sustain wheel roll-ing, as described by Eq. (1). A similar linear relationshipbetween load weight and force was found by Strindbergand Petersson [9].


It was expected that a 50% increase in wheel widthwould not have a significant effect on the force needed toinitiate cart movement. The tables and graphs in theprevious section confirmed this hypothesis. Since wheelwidth does not appear in Eq. (1), it is known that it doesnot affect the force needed to sustain cart movement.Therefore, whether it is the force to initiate or sustaincart movement, wheel width does not have a signifi-cant effect. In fact, a result other than that would behard to explain physically. An analogy can be madehere with the well-known fact that area of contactbetween two objects does not affect translational frictionbetween them. It is surprising that Eastman Kodak(1986) stated that a wider tread increases the wheel’srolling resistance.

It is worth noting that since the 38 mm wide wheel was,as expected, heavier than the 25 mm wide wheel, totalcart weight at each cart load was not the same for the twotypes of wheels. This is why analysis of covariance andnot an analysis of variance had to be conducted withtotal cart weight as the covariate so as to filter outdifferences in cart pull forces that were merely due to cartweight difference for the two wheel types.


Cart pull forces were the lowest for concrete, thenincreased for tile, asphalt, and carpet surfaces. Drury etal. (1969) found a similar relationship between the forcesto push vehicles on hospital carpeted and hard floors.White (1969) stated that the harder the wheels and theharder the floor material, the less the force needed tosustain rolling. Among the tested floor surfaces, concreteis the hardest and carpet is the softest. Although asphaltmight be generally harder than tile, the rougher surface ofasphalt may be the cause for the higher forces measuredon asphalt as compared to tile.

Also, this experiment produced estimates of the coeffi-cients of rolling friction for initiating movement of hardrubber wheels on the four floor surfaces. Other wheelmaterials will certainly have different values for the coef-ficients of rolling friction. The reason the coefficients ofrolling friction reported in this study differ significantly


from those reported by previous researchers such asOberg et al. (1987) is that the wheel and surface materialsused in this study were different from those used inprevious studies. This attests to the significant impact ofwheel and surface materials on the coefficient of rollingfriction. Future research should establish a database ofthe coefficients of rolling friction for various wheel mater-ials, tires, and floor surfaces that exist in industry. Inorder to build this database, it would be imperative todevise a standard protocol for measuring the minimumforce required to initiate wheel rolling. It is recommendedthat the force exertion by the human experimenter bereplaced by a more automated technique to improvecross-study comparisons.


Figs. 4 and 5 and Tables 6 and 8 show that there wasa consistent drop in the minimum pull forces for theF0R0 wheel orientation as wheel diameter increased.Eq. (1) states that the force to sustain rolling is inverselyrelated to wheel radius. In order to test whether the samerelationship applies to the forces to initiate cart move-ment, the minimum cart pull forces measured in thisexperiment were regressed on the ratio of cart weight towheel diameter as illustrated in Fig. 6. The strong linearrelationship, evidenced by the high R2 values as shownin Table 5, suggest that the force needed to initiatecart movement is inversely proportional to wheeldiameter, or, in other words, directly proportionalto the ratio of cart weight to wheel diameter. Therefore,the relationship of cart weight and wheel diameter to theforce needed to sustain movement is the same as thatbetween those factors and the force needed to initiate cartmovement.

Drury et al. (1975) measured speed and pulse rate forpushing hospital vehicles of different wheel sizes. Pushingspeed was higher and pulse rate was lower for the largerwheel size. This result is congruent with the relationshipbetween wheel diameter and force that our study demon-strated.

It was expected that when the wheels are orientedaway from the forward direction, higher forces would berequired to move the cart. The results of this experiment,as shown in Tables 6 and 7, suggest that this hypothesiswas not supported consistently. The only cases that fol-lowed the expected trend were with the 102 mm diameterwheels, and the 153 mm diameter wheels on carpet. The51 mm diameter wheels showed obvious contradiction tothe expectations. This suggests a strong interaction be-tween wheel orientation and wheel diameter and betweenwheel orientation and floor surface. When such interac-tions exist, precise conclusions are typically difficult tomake.

It was known from the beginning that Eq. (1) does notapply except for the case when the wheels are all in the

forward direction because it was derived for the casewhen the direction of the applied force is the same as thatin which the wheel rolls. When the wheels are not alignedin the forward direction and the cart is pulled straight,factors other than the simple rolling friction come intoplay. Ideally, the wheels might be expected to align them-selves first in the forward direction and then start to roll.However, this did not occur consistently. What happenedwas that the cart started to turn with the wheels aligningthemselves as the cart turned. This might have con-taminated the measurement since the cart was alwayspulled straight backwards with the force gauge and whenthe cart turned the exerted force was no longer parallel tothe direction of the cart. The somewhat inconsistenteffect of wheel orientation warrants more research todevelop theories about what happens when the wheelsare not all aligned in the forward direction and to testthem in the lab.

It is worth noting that when all four wheels werealigned at 90° to the forward direction (F90R90) the pullforces were consistently higher than when only twowheels were aligned at 90° to the forward direction(F0R90 and F90R0).


It was expected that the minimum push and pull forceswould be the same for the F0R0 wheel orientation sincethe ultimate direction of the applied force was the samewhether it was a push or pull force. Although the resultstended to agree with the expectations, the smalldifferences detected might be attributed to the difficultyexperienced in applying pure push and pull forces.Applying a pure force that does not create a turningcouple necessitates applying a force strictly perpendicu-lar to the width of the cart at a point midway across thecart width. Applying a force that does not conform tothese rules will cause a force higher than the correctone to be measured and may cause the cart to turn.Applying pure push forces was slightly more difficultthan applying pure pull forces because in the case of pushforces, the force gauge contacted the cart at the end ofa small attachment that was 5 mm in diameter. In thecase of pull forces, the attachment was a fork-type hook.

The minimum pull forces at the F90R0 wheel orienta-tion were, on average, 28% less than the minimum pushforces. On the other hand, the minimum pull forces atthe F0R90 wheel orientation were, on average, 19%higher than minimum push forces. This suggests thatswiveling wheels are recommended in the front if thecart is primarily pulled, while the swiveling wheels arerecommended in the rear if the cart is primarily pushed.This recommendation is based entirely on the minim-um forces required to push or pull the cart forward anddoes not take into account the forces required to turnthe cart or maneuver it.


This experiment showed also that the pull-F90R0 for-ces were not significantly different from the push-F0R90forces. Similarly, the pull-F0R90 forces were not signifi-cantly different from the push-F90R0. This results sug-gests that pulling a cart with swiveling front wheelswould be the same as pushing a cart with swiveling rearwheels. Similarly, pulling a cart with swiveling rearwheels would be the same as pushing a cart with swivel-ing front wheels.

In more than one case, it appeared that the measuredforce values and the graphs suggested no practical signifi-cant difference, while statistical analysis produced a sig-nificant effect. One should be cautious not to concludehastily that a significant effect exists because smallvariances and large sample sizes make small differencesappear statistically significant. In such a case, a 95%confidence interval on the difference between the twotreatment means will help determine the practicality ofthe significant difference.

Concerning the question of whether the front or rearwheels should swivel, this study did not provide a definiteanswer since it did not investigate turning carts, andwheel orientation was found to have strong interactionswith wheel diameter and floor surface. This questionremains to be answered in future research. However, it isgenerally easier to turn a cart when the wheels closer tothe handles of the cart (rear wheels) are swiveling asopposed to when the front wheels swivel. In fact, turninga cart with swiveling front wheels requires the applica-tion of a couple at the cart handles; while turning a cartwith swiveling rear wheels requires the application ofa transverse force. However, controlling a cart with

swiveling rear wheels is generally harder. Therefore, wewould generally recommend having the wheels closer tothe cart handles swivel if the cart will have to go aroundcorners more often than be pushed or pulled straight.Based on this limited study, having all four wheels swivelis generally discouraged unless the cart is intended for usein very tight spaces and is not pushed or pulled for longdistances.

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Drury, C. G., Barnes, R. E., Daniels, E. B., Pedestrian operated vehiclesin hospitals. Proceedings of the American Institute of IndustrialEngineers, 26th Annual Conference and Convention, pp. 184—191.

Eastman Kodak, 1986. Ergonomic Design for People at Work. vol. 2.Van Nostrand Reinhold, New York.

Kragelsky, I. V., Dobychin, M. N., Kombalov, V. S., 1982. Friction andWear Calculation Methods. Pergamon Press, Oxford.

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Hard Rubber Friction Coeffs

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