hp50-2000

NUMBER 50, SPRING 2000

Summaries of articles in this issue; mast . . . . . . . . . . . . . . . . 2Contributions to Human Power . . . . . . . . . . . . . . . . . . . . . . . 2

ArticlesOn the efficiency of bicycle chain drives

James B. Spicer and others . . . . . . . . . . . . . . . . . . . . . . . . . 3Offset rims reduce the amount of dish

Vernon Forbes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Rolling resistance of bicycle tyres

John Lafford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Note on John Laffords paper and spreadsheet

Jim Papadopoulos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Reply to Jim Papadopoulos

John Lafford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Technical notesPower requirements for laid-back recumbents

Bert Hoge and Jeroen Schasfoort in HPV nieuwsReport and comment by Dave Wilson . . . . . . . . . . . . . . . . 18

My propeller theoryE. Eugene Larrabee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

ReviewsFeet on!: pedal-powered museum exhibit

Michael Eliasohn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Human power: the forgotten energy

Arnfried Schmitz, reviewed by Dave Wilson . . . . . . . . . . 22

EditorialCycle Vision, Ronald van Waveren . . . . . . . . . . . . . . . . . . . . 23

LettersUpdate, Anil Rajvanshi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Supplement to velocar variations, Arnfried Schmitz. . . . . 22Kudos, Chet Kyle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Number 50Spring 2000 $5.50

TECHNICAL JOURNAL OF THE IHPVA

HUMANPOWER

tions (Juden 1997). Without detailedanalysis of Kellers results, it appearsthat they do not wholly support the ideathat the efficiency is governed by fric-tion. Work by Kidd, Loch and Reuben(1998) has attempted to quantify driveefficiency in relation to models of drive-train performance based on chain con-tact forces. While static measurementsof these forces have agreed with mod-els, efficiency-measurement resultshave not appeared in the literature(Kidd et al. 1996).

In this work, the efficiencies of bicy-cle chain drives are investigated bothexperimentally and theoretically to iso-late factors associated with loss inthese systems. A computer-controlleddrive-train-testing system was designedto measure the performance of thechain, chain ring and rear cassette in aderailleur-type system. This system wasused to measure chain-drive perfor-mance under a variety of operatingconditions. Assuming that frictionalforces degrade the overall efficiency of

Human Power Number 50, Spring 2000 3

ABSTRACTThe efficiencies of bicycle drive

trains have been studied to understandenergy-loss mechanisms in these sys-tems. An analytical study of frictionalenergy loss along with a series ofexperimental efficiency measurementsof derailleur-type chain-drive systemsunder a range of power, speed andlubrication conditions are given toidentify loss mechanisms. These mea-surements of mechanical efficiency arecompared to infrared measurementsperformed during drive operation thatshow the heating of drive componentsresulting from frictional losses. Theresults of this study indicate that chaintension and sprocket size primarilydetermine chain-drive efficiency.

INTRODUCTIONWhen this study was performed, it

was hoped that through identificationof the loss mechanisms primarilyresponsible for limiting the efficiencyof bicycle chain drives, methods forimproving efficiency could be realizedby eliminating or decreasing the vari-ous losses. Unfortunately, as will beshown, definitive identification of thesemechanisms has not been successful.Rather, the results provide informationon the efficiency of chain drives and, atthe same time, lead to conclusionseliminating those mechanisms that donot dominate efficiency. We hope thatthe results here contribute to the over-all body of work on chain-drive effi-ciency and also to the on-going discus-sion of this topic (Cameron 1999; Wil-son 1999).

Even though design of chain drives isfairly well-understood (Vogwell 1994)the factors affecting efficiency havebeen considered only in passing as partof the design process. Generally designfactors that are considered includechain length, load ratings, roller impactvelocity, rotational forces, contactforces, chordal action and chain vibra-

tion (Tordion 1996). Since some of theseare dynamic effects, the work presentedhere was conducted on chain drivesduring operation.

Hollingworth and Hills (1986a) per-formed a detailed theoretical andexperimental study of chain contactforces during link articulation in heavy-duty chain drives and used theseresults to calculate the theoretical effi-ciency of chain drives assuming thatfrictional losses primarily affected effi-ciency (Hollingworth and Hills, 1986b).They found that the efficiency of thechain drive should increase with thenumber of sprocket teeth on each ofthe driver and driven sprockets. Unfor-tunately, no experimental results weregiven to verify their models.

In the work by Keller (1983) measure-ments of efficiency were made for dif-ferent transmission systems (derailleur,internally geared hub, fixed), usingchains exhibiting various conditions ofrepair (new, used, non-lubricated),under a variety of power-transfer condi-

On the efficiency of bicycle chain drivesJames B. Spicer,* Christopher J.K. Richardson, Michael J. Ehrlich and Johanna R. BernsteinThe Johns Hopkins University, Baltimore, Maryland 21218Masahiko Fukuda and Masao TeradaShimano Inc., Product Engineering Division, Sakai Osaka 590-77

Fig. 1. Experimental schematic of test stand showing elements of the driveassembly

2 Number 50, Spring 2000 Human Power

HUMAN POWERHUMAN POWERis the technical journal of theInternational Human Powered VehicleAssociationNumber 50, Spring 2000

EditorDavid Gordon Wilson21 Winthrop StreetWinchester, MA 01890-2851 [email protected]

Associate editorsToshio Kataoka, Japan1-7-2-818 Hiranomiya-MachiHirano-ku, Osaka-shi, Japan [email protected]

Theodor Schmidt, EuropeOrtbhlweg 44CH-3612 Steffisburg, [email protected]

Philip Thiel, Watercraft4720 - 7th Avenue, NESeattle, WA 98105 USA

ProductionJS Design & JW Stephens

IHPVAPaul MacCready, Honorary presidentChris Broome, USA, ChairBen Wichers Schreuer, The Netherlands,

Vice-chair,Open, Secretary/treasurer

PublisherIHPVAPO Box 1307 San Luis Obispo, CA 93406-1307 USAPhone: +805-545-9003; [email protected]

Human Power (ISSN 0898-6908) is pub-lished irregularly for the InternationalHuman Powered Vehicle Association, anon-profit organization dedicated to pro-moting improvement, innovation and cre-ativity in the use of human power gener-ally, and especially in the design anddevelopment of human-powered vehicles.

Material in Human Power is copyrightedby the IHPVA. Unless copyrighted also bythe author(s), complete articles or repre-sentative excerpts may be published else-where if full credit is given prominently tothe author(s) and the IHPVA. Individualsubscriptions and individual issues areavailable to non-IHPVA and non-HPVAmembers.

Number 50 Spring 2000 $5.50/IHPVA members, $4.00

IN THIS ISSUEBicycle chain transmissions

Jim Spicer and his associates at JohnsHopkins have written a paper that willchange minds, and design directions, onHPV transmissions. To give just oneexample: the losses associated with smallsprockets on the rear wheel make mid-drives or countershaft gears suddenlyattractive, and possibly hub gears too.They also find that chain lubricationdoesnt seem to reduce losses: that will beeven more controversial. (Your editor hashigh confidence in the data: he asked ChetKyle, IHPVA founder and one of theforemost researchers in bicycle perfor-mance in the world, to look at them beforepublication. He had done a proprietarystudy on the same topic, and has producedbroadly similar results.) Offset rims

Vernon Forbes gives us another of hiscareful studies of spoked-wheel construc-tion incorporating derailleur clusters orbrake disks that cause the wheel to bedished (spoked asymmetrically). Heshows that the use of rims that have off-center spoke holes brings about a consid-erable reduction in the difference in spoketensions that otherwise makes highlydished wheels prone to spoke failure andoccasionally to collapse.Rolling resistance

John Lafford has tested, on equipmentof his own design and construction, aprodigious number of bicycle tires, mostlyof a size particularly suited to the frontwheels of recumbent bikes. He measuredrolling resistance and power loss over arange of speeds and inflation pressures.Jim Papadopoulos wrote a commentary onthe results, and John Lafford responded,all in this issue.Power requirements for unfaired laid-back recumbentsBert Hoge and Jeroen Schasfoort wrote ashort but valuable technical note in the

beautifully produced Netherlandscounterpart to Human Power: HPVnieuws. They showed, by testing a rangeof Dutch recumbent bikes, that theaerodynamic drag decreases as the angleof reclining increases. My propeller theory

Gene Larrabee, whom Human Powernamed Mr. Propeller many years ago,summarizes his propeller theories and thedevelopments that have resulted fromthem. He also pays tribute to those whoinspired him and gave him the basictheories on which he built. Was IsaacNewton the first to state that we all standon the shoulders of giants? Feet-on! review

Mike Eliasohn writes a delightful reviewof what sounds to have been an equallydelightful and truly interactive museumexhibit devoted to human power.Human power: the forgotten energy

Your editor reviews a small fascinatingbook by Arnfried Schmitz, already well-known in these pages, on the origins ofHPVs in France, on the characters of theprotagonists, and (very modestly) on hisown part in the revival of interest in thesewonderful vehicles. Editorial from the Netherlands

Ronald van Waveren, chair of theNetherlands HPV association, writes aguest editorial about the astonishingnumbers of recumbent bicycles and HPVsin the Netherlands, and in particular aboutthe annual celebration known as CycleVision. Through delays in our publicationwe are too late to encourage you to visitthis exciting event this year, but we hopethat you will do so next year.Letters include kind words from ChetKyle; comments by Anil Rajvanshi on thepublication of his article on rickshaws inthe last issue (Human Power 49); andcomments and corrections by ArnfriedSchmitz on his article Velocar variations,also in the last issue.

CONTRIBUTIONS TO HUMAN POWERThe editor and associate editors (you may choose with whom to correspond) welcomecontributions to Human Power. They should be of long-term technical interest. News andsimilar items should go to HPV News or to your local equivalent. Contributions should beunderstandable by any English-speaker in any part of the world: units should be in S.I.(with local units optional), and the use of local expressions such as two-by-fours shouldbe either avoided or explained. Ask the editor for the contributors guide (available inpaper, e-mail and pdf formats). Many contributions are sent out for review by specialists.Alas! We cannot pay for contributions. Contributions include papers, articles, technicalnotes, reviews and letters. We welcome all types of contributions from IHPVA membersand from nonmembers.

These results indicate that configura-tion A should have 63% more power lossthan C and that configuration B shouldhave 28% more power loss. For exam-ple, if a test of efficiency indicated a 5%power loss in configuration C, then con-figuration A should suffer an 8.2% lossand B should have a 6.4% loss.

DESCRIPTION OF THE EXPERIMENTAL APPARATUS

To assess drive efficiency, a teststand was designed to measure theoverall or average mechanical efficien-cy of the chain drive from the frontchain ring to the rear transmissioncomponents. To assess the efficiency ofthe drive under various conditions, thepower input to the front chain ring wasmeasured and was compared to thepower that was output by the reardrive sprocket. The ratio of the outputpower to the input power was used toquantify the overall efficiency of thesystem. To determine the powers in thedrive and driven shafts, the torquestransmitted by the shafts were mea-sured along with the rotation rate ofthe drive shaft. Knowing the rotationrate of the drive shaft and the gearratio, the rotation rate of the drivenshaft could be calculated. The efficien-cy of the system was calculated usingthe following formula: (7)

where 1, 1 are the torque and theangular frequency, respectively, of thedrive shaft, and 2, 2 are the torqueand the angular frequency of the drivenshaft. To gather the data required forthe efficiency calculations, the teststand was automated using computercontrol. The essential elements of thetest stand are shown schematically infigure 1 (see page 3).

The drive shaft was driven by a vari-able-speed electric motor system con-nected to the drive shaft. The drive-shaft rotation rate from this systemcould be varied continuously undermanual control. However, once thedesired rotation rate was set, the ratewas not actively controlled and theactual rotation of the drive shaft was

measured using a speed sensor. Thedrive-shaft torque was measured usinga rotary transformer torque sensor.

The chain drive was configured to thegeometry found on bicycles with thedistance between the front chain ringand rear cassette being adjusted bymounting the entire output-shaft assem-bly on a translational platform.Mounting the output drive componentson this platform allowed for accurateadjustment of the cassette for distanceand offset from the front chain ring.Additionally, the derailleur unit(Shimano Dura Ace) could beadjusted independently to satisfy rec-ommended mounting conditions. Theoutput shaft torque was measured usinga second rotary torque sensor. Theentire drive system was loaded using anelectromagnetic brake mounted to theoutput shaft.

There are three signals that arerecorded under computer control in aLabView programming environ-ment: input and output torques andinput rotation rate. The torque-sensordifferential outputs were amplifiedusing low-noise instrumentation ampli-fiers. Since the torque-sensor outputswere harmonically varying signals withamplitudes proportional to the torque,the signals were measured using lock-in techniques to improve the signal-to-noise of recorded signal amplitudes.To relate thesesignals to actualtorque values,each of the torquesensors was cali-brated usingknown staticloads. Bymeasuring thetorque-sensorsignals as a func-tion of appliedtorque, a calibra-tion curve wasobtained thatrelated signal levelto the appliedtorque.

Finally, aninfrared-camerasystem was usedto acquire thermal

images of drive components while thedrive was in operation. Since frictionallosses result in heating of the drivecomponents, the infrared camera wasuseful in identifying those componentsthat had the highest temperature rises.The primary component of this systemis the infrared camera that operatedwith an InSb planar array sensitive inthe 35 m range. Again, usingLabView software to control thecamera and the image-acquisition-board operations, thermal images ofthe drive were acquired and stored foranalysis and display. For these opera-tions it was important to acquireimages of the drive so that the drivecomponent of interest occupied thesame position in the infrared imagefrom frame to frame. By acquiringimages in this manner, the heating ofan individual component, such as asingle chain link, could be trackedaccurately as a function of time.

EXPERIMENTAL PROCEDUREFour major areas for investigation wereidentified and were pursued. Time variation. Measurements of

efficiency were made over extendedrun periods (2 hours) to determinewhether or not efficiency varied as afunction of time during driveoperation.

Configuration. Efficiency was mea-


Figure 2. Measured chain-drive efficiency as a function of time forthree different drive configurations (5211, 5215 and 5221) inthe no-offset condition. Tests were run for two hours, but only thefirst 100 minutes are shown here. Note that efficiency is fairly con-stant during the entire time period.

% %Efficiency =

2 2

1 1100

the system, simple analytical modelsfor the losses of chain drives have beendeveloped to estimate and identify theprimary mechanisms of frictional loss.These models for drive losses havebeen used to interpret experimentalresults. Additionally, since losses dueto friction ultimately are manifested asheating of the drive components,infrared images of the operating chaindrive were taken.

THEORYIf it is assumed that friction between

contacting components performs workduring drive operation, then power loss-es from the drive necessarily reduceefficiency. The normal force producingfriction is related to the chain tension inthe link during articulation and engage-ment. An analysis for this tension canbe found in the work by Tordion (1996)and in the work by Kidd et al. (1998).Since the friction depends on chain ten-sion, there are perhaps two major loca-tions for loss in the drive that should beidentified beforehand since the chaintension is large and is transferred fromthe chain to the sprocket at these loca-tions. These include the surfacesbetween the inner link bushing andchain pin and between the sprockettooth, link roller and inner link bushing.Rather than derive in detail the func-tional form for the losses, the results ofmodels will be presented to give thereader a feeling for the anticipatedresults of experiment. The interestedreader can find the full derivation else-where (Spicer et al. 1999). Inner-link bushing and chain pin

Since the chain tension is large ononly one side of the drive, between thefront chain ring and the rear sprocket,this loss has significant contributionsonly at two points. One of these is atengagement on the front chain ring andthe other is at departure on the rearsprocket. Adding the contributionsfrom these two points, the total workresulting from friction can beexpressed as follows:(1)

where 1 is the coefficient of friction at

the pin/bushing interface, is the pinradius, T0 is the free chain tension, isthe pressure angle (for new chainsequal to [35120/N] where N is thenumber of teeth on the sprocket), and is the articulation angle (equal to360/N). The subscripts on the anglesrefer to the front chain ring, 1, and therear sprocket, 2. In deriving Eq. (1), itwas assumed that the pin and bushinghave a neat fit (all surfaces wereassumed to be in contact) and that thecoefficient of friction was a constant,independent of the chain tension.

The rate at which this work is per-formed represents the power lossresulting from friction, Pf . The averagepower dissipated per link by thissource is written using the period ofchain revolution (expressed in terms ofthe drive-sprocket angular frequency)along with Eq. (1). The resultingexpression must be multiplied by thenumber of links in the chain to obtainthe total power loss for this mecha-nism. The following result is obtained: (2)

Note that the functional dependenceof Pf1Total on the articulation angle and,consequently, on the number of teethon the drive and driven sprockets isnot clear owing to the form of Eq. (1).However, if the number of teeth on thesprockets is large such that the articu-lation angles are small, tan(/2) /2,then the expression can be simplifiedsuch that the total power dissipatedbecomes: (3)

A similar analysis can be carried outfor the effects of chain offset with theresult that the power lost as a result ofoffset has a form nearly identical tothat given for friction at the pin-bush-ing interface except that a factor of theoffset angle appears in the expressionfor offset losses. Since this angle issmall, the frictional effects of offsetshould be small compared withpin/bushing losses. Any effect wouldnecessarily appear in the largest offsetconditions.

Sprocket tooth, link roller and inner link bushing

A similar analysis for the losses atthe tooth/roller/bushing interfaces canbe performed with the followingresults: (4)

where 2 is the coefficient of friction atthe bushing/roller interface, rRi is theinner radius of the roller, and is theroller rotation angle (the angle throughwhich the roller executes no-slipmotion on the tooth). Since the pres-sure angle depends on tooth number, asimplified form for the variation of thepower loss with sprocket combinationis difficult to obtain from Eq. (4).

Since both of these loss mechanismsinvolved friction between elements ofthe chain, it can be assumed that thecoefficients of friction are approxi-mately equal such that a total powerloss can be written for the chain drive.This power loss is obtained by addingthe losses given as follows:(5)

where is the common coefficient offriction. It is noted that the total powerloss per sprocket is reciprocally relatedto the tooth number if the roller anglevanishes. Using this expression for thetotal power loss where N1 = 52, threeseparate configurations are examinedand are given as follows:

Configuration A: N2 = 11Configuration B: N2 = 15Configuration C: N2 = 21These configurations were chosen to

reflect situations that were realizedexperimentally in this study. Assumingthat the roller angle is 5.6 and alsoassuming that the geometrical pre-fac-tors for each of the losses are approxi-mately equal yields the followingresults: (6)


P N Wf fTotal1 1 1 1 2= /

P N TN N

f Total1 1 1 11 22

1 10 +

P T r N

N N N

f Ri

Total i

ii i

i ii

21

22 0

1 1

22 1 2 2

=

+ + +

=

cos sin cos sin cotn

P T N n

r n

fi

Rj

Total ii i

i i

i j j j j j j

=

+ ( ) ( ) ( ) ( ) +

+( ) ( +( ) + +( ) }=

=

01 1

2 21

1 2 21 2 2

1

1

2

1

2

sin tan / cot /tan / tan /

cos sin cos cot sin )

PP

ffTotalA

TotalC 1 63.

W T nf ii i

i ii1 1 0

21

1 2 21 2 21

2=

( )+ ( ) ( ) ( ) ( )=

sin tan / / tan /tan / tan / P

PffTotalB

TotalC 1 28.

and

efficiencies at high chain tensionsexceed 100% by a small amount (a fewpercent in the worst case).

Clearly, these data indicate that thefundamental operation of the drivemust be related to the chain tensionsuch that the efficiency increases withincreasing tension even though thefrictional losses should increase. Thisexperimentally measured dependenceof efficiency on chain tension can beexplained only in a limited sense usingthe models for loss developed previ-ously. For example, if the pressureangle changes with tension, then thecalculated losses will vary with tensionin a manner not considered previously.Measurements of link tension duringarticulation are currently beingpursued using noncontacting opticalmeasurement techniques to investigatethese effects. Lubrication

In this phase of the study, the chainwas thoroughly degreased/cleanedusing commercially available degreas-ing agents (Castrol Wrench ForceDegreaser and/or Simple GreenBike Cleaner/Degreaser) and was relu-bricated using one of three commer-cially available lubricants (CastrolWrench Force Dry Lube, Pedros SynLube or Generation 4 White Light-ning).

The results in table 2 indicate that

the previous trends for efficiency as afunction of configuration and as a func-tion of chain tension are still followed.However, these results also indicatethat the actual lubricant used has littleeffect on the overall performance ofthe drive under laboratory conditionsgiven the precision of the measure-ment. In addition, the chain used forthe lubrication study was fullydegreased and was re-tested for effi-ciency. This degreasing operation con-sisted of a five-minute scrub withkerosene followed by a cleaning withCastrol Degreaser. The measured effi-ciency of the de-lubricated chain forthe 5215 combination at 60 RPM and100 W was 90.3% and at 200 W was96.5%. These efficiencies are essentiallythe same as those measured for thechain in the re-lubricated condition.Infrared measurements during chain-drive operation

Infrared images of the chain driveduring operation aid the interpretationof the efficiency measurements thathave been presented and also supportaspects of the modeling of chain-driveloss since frictional losses should heatthe drive components. Simply put, thechain components responsible formechanical loss should heat the chainand cause its temperature to rise. Sincethe average heat deposition rate equalsthe average mechanical power loss, theheating should have a functionaldependence similar to that found forfrictional losses.

To acquire infrared images, the chaindrive was set initially to a low rotationrate and the components were allowedto reach a steady state in this mode ofoperation. The rotation rate and brakeresistance were then increased rapidlyto achieve the desired rate and powersettings (100 W 60 RPM, etc.). Infraredimage acquisition began prior to (orduring) the time of power and rotationincrease. Images were acquired at settime intervals (e.g., approximately 30seconds) for the duration of the testsuch that actual image acquisitionoccurred synchronously to a particularlink in the chain. Since pixel intensityis proportional to the infrared energyreaching the detector and the amountof infrared emission is proportional to


the temperature of the component, thepixel intensity is directly proportionalto temperature. This method for dataacquisition allows the temperature

Table 2. Efficiencies for different drive rotation rates and sprocket configura-tions (input power 100W)

2.1 Castrol Dry Lube

40 RPM 60 RPM 80 RPM

5211 92.8 89.4 84.2

5215 94.0 90.9 86.5

5221 95.2 92.0 88.3

2.2 Pedros Syn Lube


5211 93.6 89.9 85.6

5215 95.6 92.6 88.8

5221 95.3 92.6 89.0

2.3 Generation 4 White Lightning


5211

5215 94.2 91.1 87.2

5221

4:0

0 m

inut

es7:3

0 m

inut

es11:0

0 m

inut

es15:0

0 m

inut

es

Figure 4: Infrared images of chain drive dur-ing operation showing effects of frictionalheating.

5221: 60 RPM, 150W

sured as a function of gear ratio(5211 etc.) and the effects of offsetwere investigated to assess theeffects of drive configuration.

Power/rate. Efficiency variations withinput power and rotation rate weremeasured to determine if load orrate-dependent effects were present.

Lubrication. The effects of lubricationand de-lubrication on efficiency werequantified.

EXPERIMENTAL RESULTS AND ANALYSISTime variation of efficiency

A new chain used for these tests wascleaned using Simple Green BikeCleaner/Degreaser and was lubricatedusing Generation 4: White Lightningself-cleaning lubricant. These testslasted 120 minutes at 60 RPM 100W foreach of the following chain-driveconfigurations: 5211 no-offset, 5215no-offset and 5221 no offset. As isshown in figure 2, the efficiency for alllong-duration tests showed little-to-nolong-term efficiency variations duringthe tests. The measured efficienciesfor the three configurations are asfollows:

5211 no-offset: 91.4%5215 no-offset: 93.2%5221 no-offset: 95.0%

These values represent an averageover the duration of the test. As aresult of these long-duration tests,subsequent tests were run for no morethan 30 minutes to assess efficiency orefficiency variations. Configuration

The next series of tests investigatedthe effect of chain configuration onefficiency. These tests lasted 30minutes each and were conducted withthe 5215 combination in the no-offsetcondition. Consequently, the 5211 and5221 combinations were tested in anoffset condition as would occur for aproperly configured bicycle. Theresults of these tests are summarized


in Table 1.First, comparing the results here

with those in the long-duration tests,the effect of chain offset can be esti-mated. These data were obtained withthe 5211 and 5221 configurations inthe offset condition while those in thelong-duration tests were taken with nooffset. Comparing the data for 60 RPM100 W tests shows that the offset low-ers the efficiency by, at most, 0.5%when measurement precision is consid-ered. Additionally, if the efficiencies arenormalized by efficiencies measured inthe 5215 configuration (both sets ofdata were obtained with no offset),then it appears that the offset has anegligible effect on efficiency.

More importantly, in these mid-dura-tion tests, the efficiencies show a con-sistent dependence on rear sprocketsize where the larger the sprocket, thehigher the measured efficiency regard-less of the selected power or rotationrate. If the efficiency for 5221 is 95.2%(as is found for 50 RPM 100 W), thenthe previous modeling results predict adifference in efficiency of 2.6% betweenthe 5221 and 5211 combinations.From the data in the table, the mea-sured difference between the 5221and 5211 combination is 2.7%. Theseresults indicate that the primary mech-anism for chain-drive loss could be fric-tion at the pin/bushing interface andfriction at the bushing/roller interface.Power and rotation rate

To investigate theeffects of power androtation rate on drive-train efficiency, moreextensive measure-ments of efficiencyunder varying powersand rotation rateswere completed. Thechain was the same asthat used in the othertests and the lubrica-tion was not changed

with measurements of efficiency beingmade sequentially at 58 minute inter-vals. All recorded values for efficiencyhave a precision (due to short-termnoise) of 0.2% and a long-term preci-sion of 0.3% under normal operatingconditions.

Again, the efficiency results showedthat higher efficiencies are obtained forthose configurations that have largersprockets in combination. It was alsofound that the efficiency decreaseswith increasing rotation rate for con-stant power input and that efficiencyincreases with increasing power forconstant rotation rate. Both of thesedata trends can be related to the torqueapplied to the drive and ultimately tothe chain tension. Analyzing the effi-ciency as a function of tension showsthat the efficiency increases with chaintension regardless of input power orrotation rate. Additionally, for a givenchain tension, the efficiency was foundto be independent of drive rotation rate(between 40 and 80 RPM). The depen-dence of efficiency on chain tension isshown in figure 3 where the drive effi-ciency is shown as a function of thereciprocal chain tension.

This graph shows that for the ten-sions investigated in this study (76.2 to305 N) that the reciprocal of the ten-sion is linearly related to the drive effi-ciency. For each of the linear fits to theexperimental data, the correlation coef-ficient exceeds 0.996. The extrapolated

Table 1. Drive efficiencies for different chain configurations

50 RPM 60 RPM 70 RPM 60 RPM 60 RPM100 W 100 W 100W 150 W 175W

5211 92.5 91.1 88.7 94.6 95.55215 94.7 92.3 90.4 96.2 97.55221 95.2 93.8 92.0 97.4 98.2

Figure 3: Variation of chain-drive efficiency with the reciprocal ofthe chain tension. For this graph, chain tension has been calcu-lated using the measured torque values and the radius of thefront chain ring.


tested using three different chain lubri-cants under a variety of test configura-tions. No significant quantifiable effectof lubrication could be inferred fromthese tests.

Infrared measurements of drive com-ponents indicate that frictional lossesin the chain cause the chain tempera-ture to rise during operation. Thisincrease in temperature did not corre-late with measured efficiencies undervarious conditions of operation.Infrared measurements on lubricatedand delubricated chain links showedthat the frictional heating did notdepend on lubrication.

From the results of this study, itappears that the efficiency of the bicy-cle chain drive depends intimately onthe chain operation as it engages anddeparts from the sprockets on the high-tension part of the drive. Owing to thehigh efficiencies measured under highchain tensions, friction can account foronly a few percent of the overall losses.Most probably, mechanical losses thatare not converted to thermal energy inthe drive account for the remainder ofthe measured loss.

NOTESLabVIEW, National Instruments

Corporation is a computer softwareprogram useful for running scientific

instruments by computer. NationalInstruments Corp. Seehttp://www.ni.com/labview for ven-dor information.

REFERENCESCameron, A. 1999. Measuring drive-

train efficiency, Human Power46:57.

Hollingworth, N.E., and D.A. Hills.1986a. Forces in heavy-duty drivechain during articulation. InstnMech. Engrs, 200:C5, 367374.

Hollingworth, N.E., and D.A. Hills.1986b. Theoretical efficiency ofcranked link chain drive. Instn Mech.Engrs, 200:C5, 375377.

Juden, C. 1997. Measurements of effi-ciency of chain and shaft drives.http://www.soroos.net/hbs/chains/sn1_2_2.html, (1997).

Keller, J. 1983. Der Wirkungsgrad imFahrradantrieb. Radmarkt, 12:7173.

Kidd, M., N. Loch, and R. Reuben. 1996.Bicycle chain efficiency. TheEngineering of Sport, S. Haake, ed.Rotterdam: Balkema, 217220.

Kidd, M., N. Loch, and R. Reuben.1998. Experimental investigation ofbicycle chain forces. Submitted toExperimental Mechanics.

Spicer, J., M. Ehrlich, J. Bernstein,C. Richardson, M. Fukuda, andM. Terada. June 1999. Efficiency and

energy loss location in bicycle chaindrives. Submitted to the Journal ofMechanical Design.

Tordion, G.V. 1996. Chains. Mechanicaldesign handbook. H.A. Rothbart, ed.McGraw Hill, 25.125.12.

Vogwell, J. 1994. Chain drives. Rotarypower transmission design.K. Hurst, ed. McGraw-Hill Europe,7995.

Wilson, D.G.1999. Transmission effi-ciency, Human Power 48:2022.

*Corresponding author:

James B. Spicer, Associate ProfessorDept. of Materials Science &

EngineeringThe Johns Hopkins University, 3400 N. Charles St., Room 102

Maryland Hall, Baltimore, MD 21218, USA

[email protected]; 410-516-8524The Hopkins group pursues work in

pulsed and ultrafast (femtosecond)laser-based materials processing andcharacterization. In contrast, theexpertise of the Shimano participantsleans towards the design and manu-facture of cycling components. All ofthe authors express their gratitude tothe Baltimore Orioles for the use ofCamden Yards where many fruitfultechnical discussions about this workwere held.

SUMMARY OF EQUATIONS

W T nf ii i

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P N Wf fTotal1 1 1 1 2= /

PP

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ff

ff

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1 63

1 28

.

.

and

P N TN N

f Total1 1 1 11 22

1 10 +

P T r NN N N

f Ri

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i ii i

i21

22 0

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=

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% %Efficiency =

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1 1100

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i i

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+( ) ( +( ) + +( ) }=

=

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1

2

3

4

5

6

7

increases in various components to bemapped as a function of time afterimposition of the heat load.

Representative results are shown infigure 4 where a series of four infraredimages from efficiency tests for the5221 configuration are shown. At thebeginning of the test, the infraredimages showed only variations of emis-sivity since all components were inthermal equilibrium. From theseimages (taken at the times indicated)various qualitative observations aregiven as follows. 1. The chain pins rapidly heat on the

radial surfaces and reach nearsteady-state temperatures within 45minutes.

2. At high chain tensions and low rota-tion rates, both the guide and thetension pulleys heat primarily fromthe chain.

3. Steady-state temperature conditionsfor the chain drive are establishedwithin approximately 15 min-utes after the beginning of atest.These observations are in gen-

eral agreement with the proposedfrictional-loss mechanisms. Therapid heating at the radial pin sur-faces is consistent with heating atthe pin-bushing interface. At lowchain tensions, the frictional loss-es should be relatively low andthe temperature rise in the chainshould be low. At high chain ten-sions and low rotation rates, thefrictional losses in the chainshould be relatively high produc-ing large temperature rises in thechain. The pulley-bearing lossesshould be relatively low. Eventhough the infrared images pro-vide a wealth of qualitative infor-mation, quantitative analysis ofchain-drive heating must be per-formed using the temporal evolu-tion of pixel intensity.

In Fig. 5 the infrared pixelintensity for positions on a chainpin, on a pulley tooth and on thebody of the pulley (midwaybetween the bearing and the pul-ley teeth) are shown as a functionof time for different input powers.These data were taken at 60 RPM

in the 5221 configuration. Theseresults clearly show that the chain pinrises in temperature more rapidly thanthe other locations regardless of theinput power and indicate that heatingresults from frictional losses near thepin.

The data for the chain and the pulleytooth indicate that the component tem-perature rises with the input power.For the pulley tooth, at 50 W inputpower, the maximum pixel value isapproximately 23 units; at 100 W, 35units and at 150 W, 65 units. Theseresults are in rough agreement with theloss models presented previouslywhere the frictional losses are directlyproportional to the input power.

Unfortunately, the power loss ineach of these cases is not proportionalto the input power owing to the depen-dence of efficiency on chain tension.Using measured values for efficiencyunder the conditions for the data in

Fig. 5 (97.2% for 150 W, 94.4% for 100 Wand 85.5% for 50 W) indicates that 4.2W of power were lost at 150 W input;5.6 W at 100 W input and 7.3 W at 50 Winput. Obviously, for a lower powerloss, the temperature rise should belower if the lost power is convertedentirely to heat by frictional loss. Itwould be expected that the tempera-ture rise would be lowest for the 150 Winput test since the measured powerloss is lowest for this case.

DISCUSSION AND CONCLUSIONSTests of efficiency for the derailleur-

type chain drive indicate that the over-all efficiencies for the transfer ofpower from the front drive sprocket tothe rear sprocket range from 80.9% to98.6% depending on the conditions ofdrive operation. Primary factors affect-ing the efficiency include the sizes ofthe sprockets in the drive and the ten-sion in the chain.

It was found that larger sprocketsprovide more efficient transfer ofpower while smaller sprockets provedto be less efficient. Simple, frictionalloss models were developed that gavesprocket-size loss variations thatagreed with those variations measuredexperimentally. Typically, a 25% lossdifference was measured between the5211 and the 5221 sprocket combina-tions depending on the drive operatingconditions.

Experimental results indicated thatthe efficiency of the chain drive variedas a function of chain tension. It wasfound that the efficiency varied linearlywith the reciprocal of the averagechain tension with the highest efficien-cies occurring at high chain tensionsand lowest at low chain tensions. Forexample, the highest efficiency mea-sured in the study, 98.6%, was mea-sured at a chain tension of 305 N andthe lowest, 80.9%, at 76.2 N.

It was found that chain-line offsetand chain lubrication have a negligibleeffect on efficiency under laboratoryconditions. Calculations of frictionalloss resulting from offset indicate thatthis loss should be small compared tothose produced by other mechanisms.This was verified experimentally. Lubri-cation effects on chain efficiency were


Figure 5: Variation of infrared emission with timeduring chain operation for different drive compo-nents. At time equal to 0 s, the chain drive wasplaced under full power loading.


ever, this changes the chainline andunless the bottom bracket is alsowidened it can result in difficult shift-ing and premature chain wear. Anothersolution to the problem of the DS beingat a higher tension than the NDS is touse a dishless hub. A dishless hubmust be a narrower hub. It has the NDSflange moved in closer so that it is thesame distance from the rim center asthe DS flange. However dishless hubsthat are wider are known to be laterallystronger than narrow, dishless hubs.

Recently, offset rims (Ritchey, Bon-trager) have been developed that havethe spoke holes offset closer to theNDS (see figure 2). Both sides of thewheel are affected equally: the DSspokes are put at a steeper angle as theNDS spokes are put at a shallower one(see figure 1). This equalizes tension,reducing the failure rate of spokes onthe DS due to fatigue. The ability ofthese rims to reduce the amount ofdish is tested below.

METHODSThree 26x1.75 32-spoke rims were

tested, two offset and one non-offset,for comparison. The offset rims were aRitchey OCR (Off-Center Rim) andBontrager Mustang Asym (Asymmet-rical). The non-offset rim was a MatrixSingletrack. Each of these rims wasbuilt up 3X on a 32-spoke low-flangeSuntour XC Pro hub with a 45-mmflange diameter, or spoke circle (mea-sured center-to-center) using DT stain-less-steel 14g spokes, 264-mm long. TheSuntour hub measured 55 mm betweenflanges, center-to-center (see figure 1).The 55-mm distance was chosenbecause it was midway between the dis-tances measured in a previous article.(The average for a 7-sp hub was 58.4

mm and the average for an 8-sp hub was55.3 mm between the flanges, center-to-center; Forbes 199899). A 135-mm axlelength, locknut-to-locknut (see figure 1)was used at all times. Each wheel wastested at two different levels of dishapproximating the mean freewheelthicknesses of 7-sp (44.5 mm) and 8-sp(48.0 mm) freewheels established previ-ously (Ibid.). Dish was changed by mov-ing spacers from one side of the axle tothe other and redishing the wheel, e.g.,the axle was first spaced for a 7-sp spac-ing on a 135-mm axle. The wheel wasthen dished using a Wheelsmith dishinggauge. The Ritchey OCR was the first tobe built up and tested. A rim transfer forall subsequent rims used the same huband spokes.

Previously we had suggested thatwheel dish could be predicted from ahubs measurements which we expres-sed as a ratio (DS/NDS). To measuredish on wheels that are already built upwe are expressing dish as the differ-

ence in spoke tension between theDS and the NDS (DSNDS). All ten-sion measurements were taken with aWheelsmith spoke tensiometer. Ateach level of dish the wheel was mea-sured at three levels of tension corre-sponding, e.g., to tensiometer read-ings of 75, 80 and 85 for the DS. Acopper template insured that ten-siometer readings were taken 30 mmfrom the rim edge. Each reading wastaken twice. Ifthe two readings

did not agree athird reading wastaken. If there wasany doubt aboutthe reading on aspoke the proce-dure was repeateduntil a true readingwas taken. Afterone level of dishwas tested at threelevels of tensionthe axle wasrespaced and theprocess repeatedfor the remaininglevels of dish. Eachlevel of dish wasestablished using a

135-mm-long axle (locknut-to-locknut)as the overall length.

RESULTSThe chief interest for us was the

difference in tension between the DSand the NDS. The mean spoke tensionfor each side of the wheel was firstdetermined. Tension here is expressedas nominal tensiometer readings, notas Newtons or poundals. To measuredish the tension on the NDS (whichwas presumably less tight) was sub-tracted from the tension on the DS todetermine the difference in tension.The accompanying figure (see figure 3)shows the tension differences betweenthe DS and the NDS for two levels ofdish corresponding to the mean 7-speed and 8-speed spacing. The twolevels of dish are expressed in mm andmeasure the distance from the outsideedge of the locknut on the DS to theflange center. Table 1 summarizes thedata in figure 3. For both figure 3 andtable 1, freewheel width (F/W width) ismeasured as the DS locknut-to-flangecenter in mm.

DISCUSSIONFigure 3 plots dish as differences in

spoke tension between the drive sideand the non-drive side (DS-NDS). Thegraph plots three lines; one for a Bon-trager Asym, a Ritchey OCR, and astandard non-offset rim. A front wheel,

Table 1. Tension differences (DS-NDS)# F/W % reductionspeeds width Reg OCR Asym OCR Asym7-sp 44.5 12.9 3.3 5.6 74% 57%8-sp 48.5 22.6 12.0 14.8 47% 35%

Figure 2. Offset rim: Bontrager Mustang (reproduced here with permission).

Figure 3. Tension differences (dish) for regular and offset rims.

ABSTRACTOffset rims reduce the amount a

rear wheel is dished. Two offset rimsare tested and the results compared toa standard rim. Possible implicationsare discussed.

INTRODUCTIONDish in a bicycle wheel is a mea-

sure of its lack of symmetry. Usuallythis is given as a ratio of two lengths(defined later). Sometimes dish is alsoexpressed as the ratio of, and as thedifference of, the average spoke ten-sions on the drive side and the non-drive side of the hub. An undishedwheel is one with the rim centeredover the midpoint of the axle, not ofthe hub. In a front wheel, the rim iscentered over both the axle and thehub. When viewed straight on the frontwheels rim can be seen to fall in themiddle of the front hub, to rest equallybetween the flanges. A front wheel thatis not centered on the axle cannot becentered in the frame or between thebrake blocks.

In the rear wheel the rim is centeredover the axle; it is not centered overthe hub. This is the awkward solutionto the problems posed by the develop-ment of the derailleur. Before thedevelopment of derailleurs both thefront and rear wheels were centeredover the hubs. With the development ofderailleurs came multiple-cog free-wheels which presented the problem ofhow to accommodate the additionalcogs. Bicycle designers could do one ofthree things. For one, they couldspread the stays and widen the rearaxle to make room for the freewheelblock. If they did this the bottombracket would have to be widened alsoto keep the chain in line with the free-wheel. Many consider wider bottombrackets harder to pedal. Their otherchoice was to center the rim over avery narrow hub. They could move thehub flange on the left side in by thesame amount the freewheel blockmoved the right side hub flange in.However, wheels built with narrow

hubs are laterally weaker than wheelsbuilt with wide hubs. The idea they hitupon was a compromise; they spreadthe rear dropouts a little and narrowedthe rear hub a little so they could movethe whole hub over between thedropouts to make room for the free-wheel.

One effect a freewheel has is toincrease spoke tension on the right, ordrive side (DS) relative to the left, ornon-drive side (NDS). The ratio ofDS/NDS measures what is commonlyreferred to as dish. In this ratio the two

distances are those from the plane ofthe rim centerline to the outside sur-faces of the hub flanges. Increased free-wheel width increases the severity ofdish. The newer eight-speed freewheelsrequire more dish than did older fivespeeds. Increased dish results in DSspokes being tighter. Cyclists are longfamiliar with the increased tendency forspokes to break on the freewheel side(Forbes 199899). One spoke manufac-turer recommends 785-1079 N (176243lbf) spoke tension for the DS.1 This iswell below the threshold for failure,established by Brandt as 2649 N (595lbf) for lighter spokes and 3l39 N (706lbf) for heavier spokes (Brandt 1983).Another spoke manufacturer specifieswhich hub to use and recommends theDS be tightened to 1079 N (243 lbf) andthe NDS be tightened to 883 N (199 lbf).(This has the DS 22% tighter than theNDS.2) While this is a moderate amountof dish perfectly adequate for mostapplications it does not allow for differ-ences in the amount of dish requiredresulting from hubs with different free-wheel widths, axle lengths and distancebetween a hubs flanges. These areproperties of the hubs and since it israre for two hubs to have the same mea-surements no one can specify the ten-sions on each side of the wheel unlesss/he also specifies which hub to use.Shraner (1999) gives the following ten-sion recommendations for wheels withnormal rims. He recommends9001000 N (202225 lbf) of tension fornormal rims in the front wheel and inthe rear wheel he recommends600700 N (135157 lbf) for the NDSand between 10001100 N (225247 lbf)for the DS (this has the DS between5766% tighter than the NDS; Schraner1999). However, he does not specifywhich hub must be used to achieve thisrange of ratios.

Unequal spoke tension caused byrear-wheel dish has caused some manu-facturers to experiment with previouslyrejected solutions. To make room forthe wider freewheels some manufactur-ers have used longer rear axles. How-


Figure 1. Wheel cross-section for symmetricrims (after Brandt) with modifications forasymmetric rims.

Offset rims reduce the amount of dishby Vernon Forbes

the Ritchey front OCR is 24 mm wide,the same width as the Rock OCR wetested which is no longer made. Unlikethe Rock OCR, it does not appear tohave any internal reinforcing ribs and iseyeletted. Phil Wood is listed as offeringa front hub threaded to accept a discbrake in both a dished and undishedversions (Sutherland 1995). Looking attheir dimensions it appears that theundished hub has a narrower hub shaft(flange-to-flange) than the dished hub. Ifit is for a dished front wheel then usingan offset rim would be an ideal solution.The Ritchey literature used to claim a 3-mm reduction in dish for their rearwheel. Dished models of Phil Woodfront-brake hubs threaded for a diskbrake are dished between 213 mm,depending on the front axle length(locknut-to-locknut). Only two hubs had2 mm dish and the other eight were3 mm or more. The Sturmey-ArcherBFC drum brake is dished 4 mm. Wecan think of no more appropriate a usefor an offset rim than for a front wheelwith a disc or drum brake. We haveexamined the benefits of offset rims inreducing rear-wheel dish only.

BENDING-MOMENT ASYMMETRYIt is natural, however, to assume that

if form follows function we wouldexpect to be able to see the symmetryand balance reflected in force-balancedstructures. In offset rims the spokeholes are drilled closer to one side. Onecannot help but suspect for such a glar-ing asymmetry to somehow reflect anunderlying unequal distribution offorce, or lack of balance.

Offset rims have what can be calledbending-moment asymmetry. N.B.: wemake the distinction between vertical,or up-and-down bending moment andlateral, or side-to-side bending moment.The longer DS half of the rim the morebending-moment it has. The shorter theNDS half of the rim the less bending-moment it has so that a vertical load,from, e.g., sitting on a bicycle, exertsmore vertical bending-moment to theDS than the NDS side of the rim.

One possible effect of this is thatevery bump in the road would deformthe longer DS more than it did theshorter NDS, relative to the centerline.

That said, any vertical loading willresult in the rim having increased DSbending movement. At the very leastthis might result in increased denting(flat spots) of the DS half of the rimduring cornering.

Vertical loads are thought to loosenthe bottom most spokes making themlikely to become unscrewed. Anotherpossible effect of bending-momentasymmetry is that any vertical load willbend the rim on the DS and the spokesthe DS might loosen more and theirnipples be more likeley to unscrew.The wheel might be more likely to getout of true. Cornering, on the otherhand, can subject the wheel to lateralloads. Right-hand bicycle turnsincrease the tension on the DS spokesin tension peaks as the wheel rotateswhile it leans into a turn. Now if therim on the DS were also to experiencesome additional vertical bending inresponse to cornering then that wouldtend to loosen the spokes. So thetension peaks caused by lateralloading might be offset by any tensionlosses as a result of vertical loading.Brandt (1983) has suggested thatfatigue is the result of the interactionbetween peak and baseline tension in atension cycle. If this were so then wemight expect that an offset rim mightreduce the frequency of DS spokefailure in two ways. First, it wouldequalize spoke tension thus decreasingthe baseline tension in DS spokes.Second, it would reduce the tensionpeaks experienced by the DS spokesduring right-hand turns due to lateralmovement because of the rimsincreased complementary verticalbending movement during cornering.

However, this is all highly specula-tive. The possible effects of bending-moment asymmetry in offset rims arenot known. Possible effects includethe increased likelihood of rim dentson the DS as well as spokesunscrewing on the DS due to verticalmovement and a decreased incidenceof fatigue failure due to vertical move-ment attenuating stress peaks causedby lateral movement during cornering.

Despite our attempts to limit or con-trol for tension differences, measure-ment error cannot be ruled out. We

found that even differences as small as0.5 mm in axle spacing would affecttensiometer readings.

CONCLUSIONS AND RECOMMENDATIONS

Offset rims were found to significant-ly reduce rear-wheel dish for both 7-spand 8-sp spacing. The rims have addi-tional application in reducing front-wheel dish induced by hub brakes.

NOTES1. Wheelsmith tensiometer: a profes-

sional wheelbuilding device for exactspoke-tension measurements [pam-phlet; 1989]. Menlo Park, CA:Wheelsmith Fabrications, Inc. Thepamphlet comes with the tensiome-ter, although it does not give a NDStension recommendation. For moreinformation, Wheelsmith Fabrica-tions, Inc., 355l Haven Ave., Ste. RMenlo Park, CA 94025-l009Telephone: 4l5-364-4930

2. Mastering the art of wheelbuilding.l996. DT Swiss Bike Technology USAand Campagnolo. Certificationseminar brochure. Extreme SkillsSeminars and Extreme ExposurePromotions. Grand Junction, CO:LLC, p. 11.

3. Bontrager components nineteenninety nine [promotional pamphlet],p. 11. See also www.bontrager.com.

4. Ritchey web site: http://www.ritchey-logic.com/products/components/n_rims/home_rims.htm.

REFERENCESBrandt, Jobst. 1983. The bicycle wheel,

rev. ed. Menlo Park, CA: Avocet,p. 131. A book no wheelbuilderslibrary is complete without.

Forbes, V. 199899. Predicting wheelstrength from hubs. Human Power.46:810.

Schraner, G. 1999. The art of wheel-building. Denver: Buopane Publi-cations, p. 44. Recent publicationfrom DT with many insider tips fromthe European professional racingcircuit.

Sutherland, H. 1995. Sutherlandshandbook for bicycle mechanics, 6thed. Berkeley: SutherlandPublications, pp. 1125 ff.


or any wheel with no dish would plot avalue at zero. The higher the numberthe more severely a wheel is dished.Less dish is desirable. What is obviousis that the non-offset rim has the great-est tension differences, for all levels ofdish. Both the offset rims show a signif-icant reduction in dish. While both off-set traces are below the standard rimtrace, the Ritchey rim trace is belowthe Bontrager rim trace.

There exist a number of differencesbetween these two rims which mayexplain our findings. Bontrager adver-tises his rims as having 2.5 mm ofoffset,3 while Ritchey ads used toclaim a 3-mm reduction in dish; theycurrently advertise a 50% reduction indish.4 One possible explanation is rimwidth. Our measurements showed theBontrager Mustang was 21.8 mm wideand the Ritchey Rock OCR was 24 mmwide. With a wider rim you can movethe spokes further over to the NDS.While the Bontrager rim is 2.2 mmnarrower it has only 0.5 mm more dishthan a Ritchey. There is a weightpenalty for a wider rim. We measuredthe Bontrager at 415 g (he advertises430 g) and the Ritchey at 484 g. Widerrims are laterally stronger. In terms ofheight the Ritchey advertises 12 mmheight and the Bontrager advertises13 mm height. Deeper rims are radiallystronger. Both rims are made from6061-T6 aluminum alloy.

Offset rims have been criticized bysome as being weaker because theylack ferrules, or spoke sockets thatjoin the upper and lower parts of a box-section rim so the spoke pulls on bothsections of the box-section rim. Inanswer to this both rims come withinternal reinforcements. Figure 2depicts a rib which joins the top andbottom as did Wilderness Trail Bikes(WTB) in its PowerBeam rim. Bontragerrims use one rib (dual cavity or dou-ble box) while Ritchey rims currentlyuse two (triple box). Theability of internal reinforc-ing ribs to act like a fer-ruled rim is unclear. Whilewe cannot be sure if ourRitchey OCR is triple boxor not it would helpexplain why the Ritchey is

nearly 70 g heavier. This is in light of thefact that while the Bontrager is eyelet-ted the Ritchey is not.

The graph illustrates that for all free-wheel thicknesses, offset rims give adramatic reduction in dish, as mea-sured as tension differences. Becausethe Ritchey yields lower values pre-sumably the spoke holes are more off-set. Although both offset rims reduceddish compared to the standard rim theRitchey had slightly lower tensiometerreadings. Compared to the Bontragerrim, the Ritchey readings were 2.3lower for 7-sp spacing and 2.8 lower for8-sp spacing rim. This, however, maybe due to the Ritcheys being a widerand heavier rim.

DISH AS HUB MEASUREMENTSSeveral claims are made for Ritchey

OCR rims. One of them is that theRitchey OCR rim will reduce dish from6 mm to 3 mm using a Ritchey hub; a50% reduction. We previously foundthat the dish on most hubs is consider-ably more than 6 mm. We surveyed thesame 74 hubs we did in a previousstudy (Forbes 199899).

Table 2 summarizes the actualaverage amount of dish expressed asdistance measurements for 74 hubswith a 55-mm-wide hub on a 135-mmaxle we previously examined. We see from the table that actually theRitchey OCR would reduce dish from9 mm to 6 mm on a typical 7-speed andfrom 17 mm to 14 mm on a typical 8-speed. These were reflected in lowertension differences. Inspection oftable 1 reveals that when compared toa conventional rim, the Ritchey OCRrim yielded a 9.6 smaller difference intensiometer readings for 7-sp spacing,(a 74% reduction) and a 10.6 differencein tensiometer readings for 8-spspacing, (a 47% reduction).

CAUSES OF DISHThe utility of these rims may be

especially suited to wide rear hubs.Previously we noted how dish is theresult of several variables (Ibid.). Forany given freewheel both freewheelthickness and hub width contribute todish in different ways.

Consider the effects of both free-wheel thickness and hub width on dish.Increasing the freewheel thicknessmoves the entire hub over to makeroom for it. This pushes the DS flangein closer to the rim center as the NDSflange is pushed further from the rimcenter. By comparison, increasing thehub width affects dish by pushing theNDS flange further away from the rim,leaving he DS flange alone. Becausefreewheel thickness affects bothflanges and hub width affects only oneflange we view freewheel thickness toaffect hub dish at twice the rate of hubwidth. It is for this reason that we havesuggested that increasing hub widthwas not half as bad as increasing free-wheel width.

The ability of an offset rim to attenu-ate dish depends on the source of thedish. Because offset rims affect spokeson both flanges an offset rim wouldreduce freewheel-induced tension dif-ferences at the same rate as the free-wheel causes them. By comparison,hub-width-induced tension differencesaffect only one flange and offset rimsattenuate dish by affecting bothflanges. We would expect for offsetrims to reduce hub-induced dish attwice the rate caused by hub width.Offset rims would be twice as effectivein attenuating hub-induced dish as theyare in attenuating freewheel-induceddish. That said, it is reasonable for off-set rims to make for an increased wide-spread application of wider hubs, withall the benefits of increased lateralstrength.

Offset rims may find an additionalapplication for offsettingfront-wheel dish inducedby disk brakes. During thepreparation of this articleboth Ritchey andBontrager each introducedrims for use with a frontdisk brake. Interestingly,


Table 2. Dish measured as distance difference (DS-NDS)

Difference (DS-NDS)# F/W Center Center Standard OCR Asymspeeds width to DS to NDS (DS-NDS) (DS-NDS) (DS-NDS)7-sp 44.5 23 mm 32 mm 9 mm 6 mm 6.5 mm8-sp 48.5 19 mm 36 mm 17 mm 14 mm 14.5 mm


ACKNOWLEDGMENTSThe author thanks David Gordon

Wilson for his invaluable commentsduring the preparation of this article,Helios Studios in Columbia, MO, JohnW. Stephens of Garden Grove, CA, andJean Seay of San Luis Obispo, CA, fortheir assistance in the preparation ofthis article.

Figure 1 is after The Bicycle Wheelby Jobst Brandt and appears by hiscourtesy and with his permission. Theauthor thanks him for his comments inreading an advance copy of this article.

Figure 2 is after the BontragerComponents homepage,http://www.bontrager.com, andappears courtesy of Keith Bontragerand with his permission.

The author thanks Tryathletics inColumbia, Missouri, without whom thisarticle would not be possible.

Vernon is a bike mechanic inColumbia, Missouri. Requests forreprints should be sent with a with aself-addressed envelope and sufficientpostage (two international postalreply coupons for outside the USA) tohim at:

Vernon Forbes1007 Grand Ave

Columbia, MO 65203-4025 USATelephone: 573-442-0687

[email protected]

UPDATEFrom Anil Rajvanshi, author of CycleRickshaws, HP 49 (Winter 19992000)

I liked your comment on poor qualityof present cycles and am trying tomake rickshaws keeping this point ofview very much in mind. The consumermovement is catching up in India and acouple of two-wheeler manufacturershave been taken to court for poor man-ufacturing. I hope the same could bedone for cycles and rickshaws.

We are now putting twenty MAPRsin Lucknow and will be very interestedin sharing our experiences with yourreaders. I plan to visit the US this sum-mer and would like to meet interestedpeople.

With warm regards,Anil Rajvanshi

[email protected]

INTRODUCTIONI have been a research and develop-

ment engineer for many years, andwhen I started recumbent racing aboutfourteen years ago, it was only naturalfor me to want to obtain reliable dataon cycling performance. The mostimportant factor is aerodynamics, and Iaddressed the measurement of aerody-namic drag in the real world by doingcoast-down tests. The procedure forthis is described in So you want tobuild an HPV (p. 40 ff) a publicationof the British Human Power Club. Foran accurate drag result you also needto know the rolling-resistance valuesfor the tyres. As you go faster, therolling resistance becomes more impor-tant and it is therefore vital to haveaccurate data on which to base a tyrechoice. It was this requirement that ledto study and analysis to derive an accu-rate and repeatable test procedure formeasuring rolling resistance.

The testing has all been done withracing in mind. For touring or commut-ing other factors such as wear resis-tance, puncture resistance, grip in thedry and wet, and cost, come into con-sideration for tyre choice.

TESTING PROCEDUREThe tyre-testing procedure involves

rolling the tyre/wheel combinationalong a flat surface and so representsthe real case of using the tyre on theroad. The tyre is also loaded with a rep-resentative weight and starts rolling ata controlled initial speed. The distancethat the tyre rolls is inversely propor-tional to the rolling resistance. Therolling-resistance coefficient is derivedfrom knowing the initial speed and thedistance that the tyre rolls.

The speed of rolling in the tests isslow so that aerodynamic forces arenegligible. The flat surface used is fair-ly smooth concrete in my local aircraft-factory workshop, and is reasonablyrepresentative of a smooth tarmac roadsurface. In any event, as all the testsare performed in exactly the sameplace, they all relate to one another.

The power to propel tyres along theroad (Prr), is directly proportional tothe rolling-resistance coefficient (Crr),the weight of the vehicle plus rider(W), and also the speed of the vehicle(V). Prr = Crr x W V (times a constant forusers of ancient units ed.)

The power absorbed is the samewhether the vehicle has two, three orfour wheels (so long as they are per-fectly aligned, as the author confirmsbelow ed.). In the table, the power iscomputed in watts for the cases of(1) vehicle plus rider weighing 185 lb(84 kg) at road speeds of 20 mph,25 mph and 30 mph (32 kph, 40 kphand 48 kph, respectively); and (2) vehicle plus rider weighing 200 lb(91kg) at road speeds of 30 mph,40 mph and 50 mph (48 kph, 64 kphand 80 kph, respectively) which is rele-vant to faired vehicles.

TIME LOSTThe time-lost column gives a practi-

cal appreciation of the importance ofthe rolling resistance of the tyre byshowing the time lost by each of thetyres against the best tyre listed (thelast tyre in the list), over a distance of10 miles (16 km). The base time for10 miles at 25 mph is 24.00 minutes.

The time lost is derived from aerody-namic-drag values obtained in coast-down test results (see reference below)using my own racing recumbent. Datafrom the test will predict the powerrequired to ride along a level road at25 mph and 24 mph. The difference inthese two values was 28 watts for myrecumbent with the average tyres thatwere fitted at that time. The time takento ride 10 miles at 24 mph is 25.00 min-utes. The time-lost column is calculatedby proportion of the power absorbedby each of the tyres compared to theVredestein Fortezza Piste:

Time lost for tyre a = [Prr(tyre a)Prr(Vredestein)] x 60/28

It can be seen that using the wrongtyres can easily cause one to lose overa minute over the 10 miles.

Rolling resistance of bicycle tyresby John Lafford


diameter tires. My questions relate primarily to accura-cy and meaningful precision of his data.

How repeatable is his test? The factthat an increasing series of inflationpressures leads to a decreasing seriesof rolling resistance coefficients sug-gests that his final digit is meaningful(+0.0001). However it would be good tohave a statement from John about howwell his tests repeat, what averaging heemploys, etc. How accurate is his test?Here my questions spring from a cou-ple of disparate perspectives.

1. How do his numbers comparewith others? He gives good 700Cnumbers of 0.00430.0046; howeversome other sources give numbers0.00190.0033.

His best Moulton number is 0.0079whereas Kyle has given 0.0030 andBurke gave 0.0038. I would feel betterif Lafford had been able to duplicatesome other accepted result.

2. Has he taken care to eliminatesome of the obvious errors oneexpects in this kind of low-speed,coasting to rest test? Low-speedrolling is strongly affected by minor(invisible) slopes. (In the hallway atCornell, for example, there was aninvisible dip that would clearly acceler-ate a rider.) His results lose force ifeither (a) the paths differ from time totime or (b) in going down and up, somewheels stall while others just manageto crest a rise and travel much fur-ther. Also, I wonder how the wheel isbalanced and guided as it comes torest. The normal way is to make a tricy-cle, but then there is an issue of dragfrom the support wheels (particularly iftheir alignment is faulty). That supportdrag could perhaps be subtracted, butonly if it was known with high accura-cy. In my own researches I had hopedto try castering one of the two lightlyloaded support wheels, but never gotaround to it. Finally some commentsabout conditions: Because the measurement was takenat low speed, then the high-speedcalculations should have a disclaimer.Kyle believes there is a speed effect,for example.

COMMENTARY ON THE TABLE1. Some of the tyres are tested at pres-

sures above the manufacturers rec-ommended pressure. This was donefor scientific interest. This does notimply approval of operating tyresabove the manufacturers recom-mended pressure.

2. Most of the tyres are tested atseveral pressures to show the effectof pressure on rolling performance.

3. The list includes the effect of grind-ing the tread down on some tyretypes. This simulates the effect oftyre wear. This generally gives animprovement in rolling performance.In some cases it is not beneficial asthe tyre sidewall flexibility may be amore important factor in absorbingenergy as the tyre rolls.

4. The list includes some examples ofthe effect of using latex inner tubesinstead of butyl inner tubes.Generally, the latex tube will give animprovement. However, if the tyrehas a thick tread, this will dominatethe energy absorption, and latex willshow no benefit. Latex gives a goodimprovement where the tyre tread isthin and flexible so that the reduc-tion in energy caused by substitutingthe butyl tube can be seen.

5. The 700c tyres shown are among thevery best on the market. Most 700ctyres are not nearly as good as these.Some 700c tyres are very poor. Donot be misled into thinking all 700ctyres are good just because the threeshown are good.

6. General rules for good rolling perfor-mance: a. thin-tread-thickness tyres roll better; b. fat-section tyres roll better; c. knobbly tyres roll badly; d. Kevlar often gives poor rollingperformance (except Vittoria); ande. used tyres roll better than newtyres as they are thinner, and there-fore more flexible.

7. One cannot assume that all tyresfrom a particular manufacturer arefast or slow. Generally they have arange of rolling performance thatdoes not necessarily have any rela-tionship with the companys advertis-ing claims.

8. For additional rolling-resistancedata, see reports in the followingBritish magazines:

Cycling Plus, issue 62 (Feb. 97)Winter tyres; Cycling Plus, issue 68(Mid-summer 97) Road tyres;Cycling Plus, issue 81 (Aug 98)Time-trial tyres; Total Bike, issue 6(Oct 97) MTB tyres; and BHPCNewsletter, issue 58, MTB tyres.

9. Thanks are due to the following forthe loan of tyres for testing: HilaryStone, Richard Grigsby, JohnKingsbury, Michelin Tyres, CambrianTyres, Dillglove (Nokian tyres).

John Lafford

John Lafford is an engineer who hasbeen building and racing recumbentsfor 14 years. He is interested in all thetechnical aspects of cycling withemphasis on efficiency of operation.He has built two- and three-wheeledrecumbents, both faired and unfaired,and also works on power-assisted bikesand trikes. He also takes part in time-trial events using a cross-shaped-frame design of bicycle produced byhis own Arrow Bicycle Company. (Editors note: discussion of contribu-tions is always welcome in letters toHuman Power. John Laffords contri-bution included values that varied fromthose of others, and I asked JimPapadopoulos to comment. Then I senthis comments to John for a response. Iwould like to thank both for their cour-tesy in discussing the results and inallowing us to publish their remarks.

Dave Wilson)Note on Laffords paper and spreadsheet by Jim Papadopoulos

It is always heartening to see evi-dence of a great deal of careful testing.I appreciate that Lafford actually didsomething, rather than just talk about it(as I am prone to do). Of course hisnumbers raise a host of questions.None of these are criticisms per se, butthe answers might help establish howreliable his results really are.

I did not grasp immediately that hisfocus was primarily on small wheels.Spreadsheet and article should perhapsbe called Rolling resistance of small- Turn to page 18


Rolling resistance of tyres - test data John Lafford, Nov 1999Generally available recumbent tyres(Butyl inner tubes unless stated) Rolling resistance power absorbed

Unfaired wgt = 185 lb/84 kg / Faired wgt = 200 Lb/91 kg

Time lost @Test Prr Prr Prr Prr Prr Prr 25mph

pres- Rolling 20mph 25mph 30mph 30mph 40mph 50mph oversure res coef. 32kmh 40kph 48kph 48kph 64kph 80kph 10 mi.

Tyre name Size psi* Crr test watts watts watts watts watts watts sec.IRC Road Lite (new) 20" x 1 1/8" 100 0.0090 66 82 99 107 143 178 92IRC Road Lite (new) 20" x 1 1/8" 115 0.0089 65 82 98 106 141 176 90Conti Top Touring (new) 37-406 70 0.0092 68 84 101 110 146 183 96Conti Top Touring (new) 37-406 90 0.0079 58 73 87 94 126 157 71IRC Road Lite (old) 20" x 1 1/8" 100 0.0068 50 63 75 81 108 136 49IRC Road Lite (old) 20" x 1 1/8" 115 0.0064 47 59 71 77 102 128 41Michelin 28-440 70 0.0078 57 71 86 93 123 154 68Michelin 28-440 90 0.0071 52 65 78 84 112 141 54Tioga Comp Ramp (new) 20 x 1 7/8 85 0.0080 59 73 88 95 127 159 72Tioga Comp Ramp (new) 20 x 1 7/8 100 0.0079 58 73 87 95 126 158 71Hutchinson HP 25 25-451 115 0.0080 59 74 88 95 127 159 73Hutchinson HP 25 25-451 90 0.0089 65 81 98 106 141 176 89Hutchinson HP 25 25-451 100 0.0086 63 79 95 103 137 171 84Conti Top Touring (new) 37-406 70 0.0090 66 83 99 108 143 179 93Conti Top Touring (new) 37-406 90 0.0081 60 74 89 97 129 161 74Conti Top Touring (new) 37-406 100 0.0080 59 74 89 96 128 160 73Conti Top Touring (new) 37-406 115 0.0084 62 77 93 100 133 167 80Michelin (450 x 28A) 28-390 100 0.0065 48 60 72 78 104 130 43Michelin (450 x 28A) 28-390 115 0.0064 47 59 71 77 102 128 42Conti Grand Prix (new) 28-406 100 0.0072 53 67 80 86 115 144 57Conti Grand Prix (new) 28-406 120 0.0067 49 61 74 80 106 133 47Conti Grand Prix (new) 28-406 140 0.0066 49 61 73 79 105 132 45Vee Rubber (new) 20 x 2.125 40 0.0114 84 105 126 136 181 226 139Vee Rubber (new) 20 x 2.125 60 0.0105 77 96 116 125 167 209 122Vee Rubber (new) 20 x 2.125 80 0.0097 72 89 107 116 155 193 107Primo 16 x 1 3/8 (new) 37-349 100 0.0078 57 72 86 93 124 155 69Primo 16 x 1 3/8 (new) 37-349 110 0.0071 52 65 78 85 113 141 55Primo 16 x 1 3/8 (new) 37-349 120 0.0070 52 65 78 84 112 140 54Tioga Comp Pool (new) 20 x 1.75 90 0.0074 54 68 81 88 117 146 60Tioga Comp Pool (new) 20 x 1.75 100 0.0071 52 65 78 84 113 141 54Tioga Comp Pool (new) 20 x 1.75 110 0.0069 51 63 76 82 110 137 51Tioga Comp Pool (new) 20 x 1.75 120 0.0065 48 60 72 78 103 129 43Kenda w. tread ground off 16 x 1.75 80 0.0068 50 63 76 82 109 136 50Kenda w. tread ground off 16 x 1.75 90 0.0064 47 59 70 76 101 127 41Kenda w. tread ground off 16 x 1.75 100 0.0066 48 60 72 78 104 130 44Michelin Hilite S'compHD 650 x 20c 100 0.0062 45 57 68 74 98 123 36Michelin Hilite S'compHD 650 x 20c 110 0.0058 43 53 64 69 92 115 29Michelin Hilite S'compHD 650 x 20c 120 0.0055 40 50 60 65 87 109 22Hutchinson HP 25 "600A x 24""" 100 0.0070 52 65 77 84 112 140 53Hutchinson HP 25 "600A x 24""" 120 0.0068 50 63 76 82 109 136 50Hutchinson HP 25 "600A x 24""" 140 0.0068 50 63 75 81 109 136 50Primo V Monster (new) 20 x 1.75 65 0.0074 55 68 82 89 118 148 61Primo V Monster (new) 20 x 1.75 80 0.0078 57 72 86 93 124 155 68Michelin 600 x 28A 80 0.0075 55 69 83 89 119 149 62Michelin 600 x 28A 100 0.0072 53 66 79 86 115 143 57Primo w/ground off tread 37-349 85 0.0066 49 61 73 79 106 132 46Primo w/ground off tread 37-349 100 0.0063 47 58 70 76 101 126 40Primo w/ground off tread 37-349 110 0.0064 47 59 70 76 102 127 41Primo w/ground off tread 37-349 120 0.0060 44 55 66 71 95 119 33Primo w/ground off tread 37-349 140 0.0060 44 55 66 71 95 119 33Moulton Wolber line tread (new) 17 x 1 1/8 70 0.0092 68 85 102 110 147 184 97Moulton Wolber line tread (new) 17 x 1 1/8 100 0.0084 62 78 93 101 134 168 81Moulton Wolber line tread (new) 17 x 1 1/8 120 0.0079 58 73 87 94 126 157 71Primo w/ground off tread, latex tube 37-349 100 0.0066 49 61 73 79 106 132 46* 1 bar = 14.5 psi; 1 m/s = 3.6 kmh; compared with the time using the tyre (at the same power input) with lowest Crr, the last entry in the table


Primo w/ground off tread, latex tube 37-349 120 0.0061 45 56 67 73 97 121 35Primo w/ground off tread, latex tube 37-349 140 0.0058 42 53 64 69 92 115 29Vredestein Monte Carlo (new) 37-406 90 0.0069 51 63 76 82 109 137 50Vredestein Monte Carlo (new) 37-406 100 0.0067 49 62 74 80 107 134 47Vredestein Monte Carlo (new) 37-406 120 0.0064 47 58 70 76 101 126 40Hutchinson 600 x 28A 100 0.0059 43 54 65 70 94 117 31Hutchinson 600 x 28A 120 0.0052 38 48 58 62 83 104 18Conti Grand Prix w/latex tube 28-406 100 0.0077 57 71 85 92 123 153 67Conti Grand Prix w/latex tube 28-406 125 0.0069 51 64 77 83 110 138 52Conti Grand Prix w/latex tube 28-406 140 0.0067 49 61 74 80 106 133 47Schwalbe Spezial City Jet (used) 32-406 100 0.0065 48 60 72 78 104 130 44Schwalbe Spezial City Jet (used) 32-406 120 0.0063 46 58 70 75 100 126 39Nokian City Runner (new) 40-406 72 0.0083 61 76 91 99 131 164 78Nokian City Runner (new) 40-406 100 0.0078 58 72 86 93 124 156 69Nokian City Runner (new) 40-406 120 0.0071 52 65 78 85 113 141 55Nokian Mount & City (new) 47-406 50 0.0083 61 76 91 99 132 165 78Nokian Mount & City (new) 47-406 80 0.0072 53 66 79 86 114 143 57Nokian Mount & City (new) 47-406 100 0.0068 50 63 75 81 109 136 49Nokian Mount & City (new) 47-406 120 0.0063 47 58 70 76 101 126 40Nokian Mount & Ground (used) 47-406 45 0.0104 76 95 114 124 165 206 119Nokian Mount & Ground (used) 47-406 80 0.0100 73 92 110 119 159 198 112Nokian Mount & Ground (used) 47-406 100 0.0089 66 82 99 107 142 178 91Schwalbe City Jet (new) 32-406 100 0.0087 64 80 96 104 139 174 87Schwalbe City Jet (new) 32-406 120 0.0082 60 76 91 98 131 163 77Schwalbe Marathon (new) 32-406 100 0.0097 72 89 107 116 155 193 107Schwalbe Marathon (new) 32-406 115 0.0101 75 93 112 121 161 201 114Schwalbe Marathon (new) 32-406 130 0.0100 73 92 110 119 159 198 112Vredestein Monte Carlo (used) 37-406 90 0.0077 57 71 85 92 123 154 67Vredestein Monte Carlo (used) 37-406 100 0.0069 51 64 76 82 110 138 51Vredestein Monte Carlo (used) 37-406 120 0.0068 50 63 75 81 109 136 50Nokian Mount & City (new) 47-305 50 0.0135 100 124 149 161 215 269 182Nokian Mount & City (new) 47-305 80 0.0103 76 95 114 123 164 205 118Primo 20 x 1.5 (used) 37-451 85 0.0066 48 61 73 79 105 131 45Primo 20 x 1.5 (used) 37-451 100 0.0065 48 60 71 77 103 129 43Primo 20 x 1.5 (used) 37-451 120 0.0062 46 57 69 75 99 124 38IRC Roadlite 20 x 1 1/8 (used) 28-451 100 0.0068 50 63 76 82 109 136 50IRC Roadlite 20 x 1 1/8 (used) 28-451 120 0.0064 47 59 71 77 102 128 42Primo Comet 37-406 100 0.0074 54 68 82 88 118 147 61Primo Comet 37-406 120 0.0070 52 64 77 84 111 139 53Michelin (used) 600 x 28A 70 0.0081 59 74 89 96 128 160 74Michelin (used) 600 x 28A 90 0.0073 54 68 81 88 117 146 60Continental Grand Prix (used) 28-406 120 0.0082 60 76 91 98 131 163 77Haro (used) 20 x 1.5 65 0.0073 54 68 81 88 117 146 60Haro (used) 20 x 1.5 85 0.0068 50 63 75 81 108 136 49Haro (used) 20 x 1.5 100 0.0063 47 58 70 76 101 126 40Haro (new) 20 x 1.5 65 0.0077 56 70 84 91 122 152 66Haro (new) 20 x 1.5 85 0.0067 50 62 74 80 107 134 48Nokia Mount and City (new) 47-406 50 0.0104 77 96 115 124 165 207 120Nokia Mount and City (new) 47-406 70 0.0087 64 80 96 104 139 174 87Nokia Mount and City (new) 47-406 90 0.0082 60 75 90 98 130 163 76Nokia Mount and City (new) 47-406 100 0.0073 54 67 81 87 116 145 59Vredestein S-Lick (new) 32-406 60 0.0155 114 142 171 185 246 308 220Vredestein S-Lick (new) 32-406 90 0.0106 78 97 117 126 168 210 123Vredestein S-Lick (new) 32-406 100 0.0098 72 90 108 117 155 194 107

RECOMMENDED 700C TYRES FOR REAR WHEELS for comparison. Very good performance at reasonable price.Nokia Roadie (used) 700 x 25c 100 0.0046 34 42 51 55 73 91 5Michelin Axial Supercomp 23-622 110 0.0046 34 42 51 55 73 91 5Vredestein Fortezza Piste 700 x 23c 10 bar 0.0043 32 40 48 52 69 86 0

Rolling resistance power absorbedUnfaired wgt = 185 lb/84 kg / Faired wgt = 200 Lb/91 kg

Time lost @Test Prr Prr Prr Prr Prr Prr 25mph

pres- Rolling 20mph 25mph 30mph 30mph 40mph 50mph oversure res coef. 32kmh 40kph 48kph 48kph 64kph 80kph 10 mi.

Tyre name Size psi* Crr test watts watts watts watts watts watts sec.

* 1 bar = 14.5 psi; 1 m/s = 3.6 kmh; compared with the time using the tyre (at the same power input) with lowest Crr, the last entry in the table


TECHNICAL NOTESPower requirements for laid-back recumbentsReport and comment by Dave Wilson,with translation help from JanLimburg and Ellen Wilson.

This is an interpretation of the highpoints of an article by Bert Hoge andJeroen Schasfoort in HPV nieuws no.4, 1999, the magazine of the Nether-lands NVHPV. Its topic is the use of anSRM instrumented crank (givingtorque) on a regular racing bike andon five recumbents. All of the recum-bents were of the very-laid-backvariety, having seat-back angles withthe horizontal of down to 15 degrees(see photos). All of them had thebottom-bracket considerably above thelowest part of the seat: I believe thatthis is important because whirling legsnormally give a high drag, and havingthem in the forward shadow of thebody must reduce this drag. Theauthors write, A smaller frontalsurface gives less air resistance andhigher speed. It can be achieved byincreasing the height of the bottombracket above the lowest part of theseat to about 270 mm (10.6"), andreducing the seat height to about 250mm (9.8"). (These are approximatelythe relevant measurements of the M5Low Racer.) All six bicycles wereridden by one tester, Dries Baron,weight 90 kg (198 lb.), height 1.86 m.(6'1", almost a midget by Dutch stan-dards) wearing racing clothing, on a200-m-long velodrome track, presum-ably oval or circular. Ten circuits (2 kmtotal) were made for each test point.All bicycles used Continental Grand-Prix or IRC tires pumped to about 8-bar pressure (116 psi). Two speedswere chosen: 30 and 40 kmh (18 and25 mph), and the cadence was kept toabout 88 rpm. The temperature wasabout 15 C, 59 F. The measurementaccuracy was reckoned to be 2% (seegraph, figure 1).

The racing or road bike was riddenin the touring position, which Ibelieve meant that the hands were ontop of the handlebars, rather than therider being in a full crouch. All of the

What was his load? Representativeprobably means it was 45 kg, but itwould be nice to know for sure.

None of this is meant as direct criti-cism of Laffords careful efforts, butrather as an invitation to discuss somevitally interesting issues!

Jim Papadopoulos

Reply to note by Jim Papadopoulos,approximately in the order of his questions,Tires tested. The number of tyrestested is approaching 400 and I havetested tyres of all sizes. The article wasfocused on small-diameter tyres as theyare of particular interest to HPV riders.I included three good 700C tyres ofgood value.Repeatability

1. If I run a tyre up the track and itruns 20' 3" (say), and then I repeat itstraight away and follow the exactsame piece of the floor, then it also willrun 20' 3". If the direction is a bit offthen the distance will be slightly differ-ent due to the slight imperfections inthe floor.

2. If I were to repeat the test on thattyre on another day, then I might nothave exactly the same pressure in thetyre by 1 or 2 psi, and the temperaturewould probably be different and sothere would be a slightly differentresult. I have a simple test for this typeof repeatability, where I have a partic-ular Michelin tyre which I run fromtime to time. This has shown over aperiod of 18 months and 7 test sessionsthat the Crr value is repeatable at0.0051 to 0.0001 and the powerabsorbed at 25 mile/h to be 47 watts to one watt. I have always rounded thepower-absorbed figure off to a wholenumber as it would be unreasonable toassume better accuracy than this. Averaging

Jim Papadopoulos clearly appreci-ates some of the practical problems inrunning the tests. Yes, the floor doeshave very slight undulations in it. Tocater for this, in the area available, Iran the tyre-test rig backwards and for-wards in many directions to find a line

that gave the same rolling distance,running in both directions. Then, tocope with the very slight undulations inthe floor, the floor is marked out at 4'intervals from the start point of the testrun. A stop watch is used and the timerecorded for the test rig to pass the4', 8', 12', 16' 20' 24', 28' etc. markers.In the coast-down test, the retardationshould be completely uniform, and soseveral of the 4' zones are averaged togive a mean average retardation. Thisavoids any errors caused by cresting orfailing to crest a slight rise at the end ofa test run. Comparing my data with other sources

There are some better 700C thanthose I listed, but I did not includethese as they are more expensive andless durable. There are many 700c tyresa whole lot worse.

The Moulton data are for the linetread touring tyre, not the high-pres-sure slick.

I am not looking to repeat otherpeoples results. It would be relevantonly if I had the same tyres that theyhad used.

The test wheel/tyre is fitted to a tri-cycle. The two other wheels are per-fectly aligned, I know their rolling-resistance coefficient and they are onlylightly loaded. Even so, their rollingcoefficient and load and drag compo-nents are taken into account.

The weight on the test wheel is66 lb. This is representative for threewheelers, which many HPVs are, but islight for a two-wheeler. It is chosen forconvenience of installation and thenumber of times I have to pick it upand load it onto the trike test rig.Further, I have tested with a heavierweight and got a very similar result. Aslong as all my tests are done under thesame conditions then the results areproperly comparative. Most of theapplied weight is directly on the testwheel. It cannot be exactly on itbecause the tricycle would not then bestable. However, as the position isknown, moments are taken, and theexact weight used in the computations.

John Lafford

although only the faired M5 and theregular bikes were common to bothtests. The LWB Peer Gynt with lowbottom-bracket was found to have ahigher drag than that of a regularracing bike with the rider in a fullcrouch. Because of the difference inthe rider positions on the racing bike,the principal interest in the resultsshown here is in the differences amongthe recumbents, and in the accuracy ofactual power measurements taken ondifferent bicycles with the same rideron the same circuit with similar tires.

These are very valuable data. Thankyou, Bert Hoge, Jeroen Schasfoort andthe NVHPV!

Dave Wilson


recumbents required less power topropel them than did the regularracing bike in this configuration. Thereduction appeared to be a function ofhow low the rider was (see photos).The lowest power of the unfairedrecumbents was needed by BramMoens M5, which at 40 kmh took228 W, while the racing bicyclerequired 389 W input. The fully-fairedM5 required less than 130 W at thesame speed. (Table 1)

These results can be compared withthe aerodynamic drag measured in theTour tests of stationary bikes in thewind-tunnel and on bikes being riddenon a velodrome, reviewed in HumanPower, 12:4, spring 1997. There isgeneral qualitative agreement,

Table 1: Power required to propel bicyclesExpected

Bicycle type or name Power, watts increase30 kmh 40 kmh in speed*

Racing bike, touring position 181 389 0% Optima Dolphin 161 336 6%Flevobike 50-50 152 309 10%M5 20-20 131 265 17%Baron Low Racer 128 251 20%Moens (M5) Low Racer 114 228 24%*Relative to racing bike

Optima Dolphin

Flevobike Fifty Fifty

M5 20 20

Baron low racer

M5 low racer

Figure 1. Power (watts) require

hp50-2000

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