HUMAN POWER TECHNICAL JOURNAL OF THE IHPVA. Number 50 Spring 2000 $5.50 NUMBER 50, SPRING 2000

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1 HUMAN POWER TECHNICAL JOURNAL OF THE IHPVA NUMBER 50, SPRING 000 Number 50 Sprng 000 $5.50 Summares of artcles n ths ssue; mast Contrbutons to Human Power Artcles On the effcency of bcycle chan drves James B. Spcer and others Offset rms reduce the amount of dsh Vernon Forbes Rollng resstance of bcycle tyres John Lafford Note on John Lafford s paper and spreadsheet Jm Papadopoulos Reply to Jm Papadopoulos John Lafford Techncal notes Power requrements for lad-back recumbents Bert Hoge and Jeroen Schasfoort n HPV neuws Report and comment by Dave Wlson My propeller theory E. Eugene Larrabee Revews Feet on!: pedal-powered museum exhbt Mchael Elasohn Human power: the forgotten energy Arnfred Schmtz, revewed by Dave Wlson Edtoral Cycle Vson, Ronald van Waveren Letters Update, Anl Rajvansh Supplement to velocar varatons, Arnfred Schmtz..... Kudos, Chet Kyle

2 HUMAN POWER Number 50 Sprng 000 $5.50/IHPVA members, $4.00 HUMAN POWER s the techncal journal of the Internatonal Human Powered Vehcle Assocaton Number 50, Sprng 000 Edtor Davd Gordon Wlson 1 Wnthrop Street Wnchester, MA USA Assocate edtors Tosho Kataoka, Japan Hranomya-Mach Hrano-ku, Osaka-sh, Japan Theodor Schmdt, Europe Ortbühlweg 44 CH-361 Steffsburg, Swtzerland Phlp Thel, Watercraft 470-7th Avenue, NE Seattle, WA USA Producton JS Desgn & JW Stephens IHPVA Paul MacCready, Honorary presdent Chrs Broome, USA, Char Ben Wchers Schreuer, The Netherlands, Vce-char, Open, Secretary/treasurer Publsher IHPVA PO Box 1307 San Lus Obspo, CA USA Phone: ; Human Power (ISSN ) s publshed rregularly for the Internatonal Human Powered Vehcle Assocaton, a non-proft organzaton dedcated to promotng mprovement, nnovaton and creatvty n the use of human power generally, and especally n the desgn and development of human-powered vehcles. Materal n Human Power s copyrghted by the IHPVA. Unless copyrghted also by the author(s), complete artcles or representatve excerpts may be publshed elsewhere f full credt s gven promnently to the author(s) and the IHPVA. Indvdual subscrptons and ndvdual ssues are avalable to non-ihpva and non-hpva members. IN THIS ISSUE Bcycle chan transmssons Jm Spcer and hs assocates at Johns Hopkns have wrtten a paper that wll change mnds, and desgn drectons, on HPV transmssons. To gve just one example: the losses assocated wth small sprockets on the rear wheel make mddrves or countershaft gears suddenly attractve, and possbly hub gears too. They also fnd that chan lubrcaton doesn t seem to reduce losses: that wll be even more controversal. (Your edtor has hgh confdence n the data: he asked Chet Kyle, IHPVA founder and one of the foremost researchers n bcycle performance n the world, to look at them before publcaton. He had done a propretary study on the same topc, and has produced broadly smlar results.) Offset rms Vernon Forbes gves us another of hs careful studes of spoked-wheel constructon ncorporatng deralleur clusters or brake dsks that cause the wheel to be dshed (spoked asymmetrcally). He shows that the use of rms that have offcenter spoke holes brngs about a consderable reducton n the dfference n spoke tensons that otherwse makes hghly dshed wheels prone to spoke falure and occasonally to collapse. Rollng resstance John Lafford has tested, on equpment of hs own desgn and constructon, a prodgous number of bcycle tres, mostly of a sze partcularly suted to the front wheels of recumbent bkes. He measured rollng resstance and power loss over a range of speeds and nflaton pressures. Jm Papadopoulos wrote a commentary on the results, and John Lafford responded, all n ths ssue. Power requrements for unfared lad-back recumbents Bert Hoge and Jeroen Schasfoort wrote a short but valuable techncal note n the beautfully produced Netherlands counterpart to Human Power: HPV neuws. They showed, by testng a range of Dutch recumbent bkes, that the aerodynamc drag decreases as the angle of reclnng ncreases. My propeller theory Gene Larrabee, whom Human Power named Mr. Propeller many years ago, summarzes hs propeller theores and the developments that have resulted from them. He also pays trbute to those who nspred hm and gave hm the basc theores on whch he bult. Was Isaac Newton the frst to state that we all stand on the shoulders of gants? Feet-on! revew Mke Elasohn wrtes a delghtful revew of what sounds to have been an equally delghtful and truly nteractve museum exhbt devoted to human power. Human power: the forgotten energy Your edtor revews a small fascnatng book by Arnfred Schmtz, already wellknown n these pages, on the orgns of HPVs n France, on the characters of the protagonsts, and (very modestly) on hs own part n the revval of nterest n these wonderful vehcles. Edtoral from the Netherlands Ronald van Waveren, char of the Netherlands HPV assocaton, wrtes a guest edtoral about the astonshng numbers of recumbent bcycles and HPVs n the Netherlands, and n partcular about the annual celebraton known as Cycle Vson. Through delays n our publcaton we are too late to encourage you to vst ths exctng event ths year, but we hope that you wll do so next year. Letters nclude knd words from Chet Kyle; comments by Anl Rajvansh on the publcaton of hs artcle on rckshaws n the last ssue (Human Power 49); and comments and correctons by Arnfred Schmtz on hs artcle Velocar varatons, also n the last ssue. CONTRIBUTIONS TO HUMAN POWER The edtor and assocate edtors (you may choose wth whom to correspond) welcome contrbutons to Human Power. They should be of long-term techncal nterest. News and smlar tems should go to HPV News or to your local equvalent. Contrbutons should be understandable by any Englsh-speaker n any part of the world: unts should be n S.I. (wth local unts optonal), and the use of local expressons such as two-by-fours should be ether avoded or explaned. Ask the edtor for the contrbutor s gude (avalable n paper, e-mal and pdf formats). Many contrbutons are sent out for revew by specalsts. Alas! We cannot pay for contrbutons. Contrbutons nclude papers, artcles, techncal notes, revews and letters. We welcome all types of contrbutons from IHPVA members and from nonmembers. On the effcency of bcycle chan drves James B. Spcer,* Chrstopher J.K. Rchardson, Mchael J. Ehrlch and Johanna R. Bernsten The Johns Hopkns Unversty, Baltmore, Maryland 118 Masahko Fukuda and Masao Terada Shmano Inc., Product Engneerng Dvson, Saka Osaka ABSTRACT The effcences of bcycle drve trans have been studed to understand energy-loss mechansms n these systems. An analytcal study of frctonal energy loss along wth a seres of expermental effcency measurements of deralleur-type chan-drve systems under a range of power, speed and lubrcaton condtons are gven to dentfy loss mechansms. These measurements of mechancal effcency are compared to nfrared measurements performed durng drve operaton that show the heatng of drve components resultng from frctonal losses. The results of ths study ndcate that chan tenson and sprocket sze prmarly determne chan-drve effcency. Fg. 1. Expermental schematc of test stand showng elements of the drve assembly INTRODUCTION When ths study was performed, t was hoped that through dentfcaton of the loss mechansms prmarly responsble for lmtng the effcency of bcycle chan drves, methods for mprovng effcency could be realzed by elmnatng or decreasng the varous losses. Unfortunately, as wll be shown, defntve dentfcaton of these mechansms has not been successful. Rather, the results provde nformaton on the effcency of chan drves and, at the same tme, lead to conclusons elmnatng those mechansms that do not domnate effcency. We hope that the results here contrbute to the overall body of work on chan-drve effcency and also to the on-gong dscusson of ths topc (Cameron 1999; Wlson 1999). Even though desgn of chan drves s farly well-understood (Vogwell 1994) the factors affectng effcency have been consdered only n passng as part of the desgn process. Generally desgn factors that are consdered nclude chan length, load ratngs, roller mpact velocty, rotatonal forces, contact forces, chordal acton and chan vbraton (Tordon 1996). Snce some of these are dynamc effects, the work presented here was conducted on chan drves durng operaton. Hollngworth and Hlls (1986a) performed a detaled theoretcal and expermental study of chan contact forces durng lnk artculaton n heavyduty chan drves and used these results to calculate the theoretcal effcency of chan drves assumng that frctonal losses prmarly affected effcency (Hollngworth and Hlls, 1986b). They found that the effcency of the chan drve should ncrease wth the number of sprocket teeth on each of the drver and drven sprockets. Unfortunately, no expermental results were gven to verfy ther models. In the work by Keller (1983) measurements of effcency were made for dfferent transmsson systems (deralleur, nternally geared hub, fxed), usng chans exhbtng varous condtons of repar (new, used, non-lubrcated), under a varety of power-transfer cond- tons (Juden 1997). Wthout detaled analyss of Keller s results, t appears that they do not wholly support the dea that the effcency s governed by frcton. Work by Kdd, Loch and Reuben (1998) has attempted to quantfy drve effcency n relaton to models of drvetran performance based on chan contact forces. Whle statc measurements of these forces have agreed wth models, effcency-measurement results have not appeared n the lterature (Kdd et al. 1996). In ths work, the effcences of bcycle chan drves are nvestgated both expermentally and theoretcally to solate factors assocated wth loss n these systems. A computer-controlled drve-tran-testng system was desgned to measure the performance of the chan, chan rng and rear cassette n a deralleur-type system. Ths system was used to measure chan-drve performance under a varety of operatng condtons. Assumng that frctonal forces degrade the overall effcency of Number 50, Sprng 000 Human Power Human Power Number 50, Sprng 000 3

3 the system, smple analytcal models for the losses of chan drves have been developed to estmate and dentfy the prmary mechansms of frctonal loss. These models for drve losses have been used to nterpret expermental results. Addtonally, snce losses due to frcton ultmately are manfested as heatng of the drve components, nfrared mages of the operatng chan drve were taken. THEORY If t s assumed that frcton between contactng components performs work durng drve operaton, then power losses from the drve necessarly reduce effcency. The normal force producng frcton s related to the chan tenson n the lnk durng artculaton and engagement. An analyss for ths tenson can be found n the work by Tordon (1996) and n the work by Kdd et al. (1998). Snce the frcton depends on chan tenson, there are perhaps two major locatons for loss n the drve that should be dentfed beforehand snce the chan tenson s large and s transferred from the chan to the sprocket at these locatons. These nclude the surfaces between the nner lnk bushng and chan pn and between the sprocket tooth, lnk roller and nner lnk bushng. Rather than derve n detal the functonal form for the losses, the results of models wll be presented to gve the reader a feelng for the antcpated results of experment. The nterested reader can fnd the full dervaton elsewhere (Spcer et al. 1999). Inner-lnk bushng and chan pn Snce the chan tenson s large on only one sde of the drve, between the front chan rng and the rear sprocket, ths loss has sgnfcant contrbutons only at two ponts. One of these s at engagement on the front chan rng and the other s at departure on the rear sprocket. Addng the contrbutons from these two ponts, the total work resultng from frcton can be expressed as follows: (1) Wf1= T 1 0 1n 1 ( ) + ( ) ( ) µρ π tan α / / tan ϕ / sn ϕ = 1 1 ( α ) ( ϕ ) where µ 1 s the coeffcent of frcton at the pn/bushng nterface, ρ s the pn radus, T 0 s the free chan tenson, ϕ s the pressure angle (for new chans equal to [35 10 /N] where N s the number of teeth on the sprocket), and α s the artculaton angle (equal to 360 /N). The subscrpts on the angles refer to the front chan rng, 1, and the rear sprocket,. In dervng Eq. (1), t was assumed that the pn and bushng have a neat ft (all surfaces were assumed to be n contact) and that the coeffcent of frcton was a constant, ndependent of the chan tenson. The rate at whch ths work s performed represents the power loss resultng from frcton, P f. The average power dsspated per lnk by ths source s wrtten usng the perod of chan revoluton (expressed n terms of the drve-sprocket angular frequency) along wth Eq. (1). The resultng expresson must be multpled by the number of lnks n the chan to obtan the total power loss for ths mechansm. The followng result s obtaned: () Pf1Total = N1ω1Wf1/ π Note that the functonal dependence of P f1total on the artculaton angle and, consequently, on the number of teeth on the drve and drven sprockets s not clear owng to the form of Eq. (1). However, f the number of teeth on the sprockets s large such that the artculaton angles are small, tan(α/) α/, then the expresson can be smplfed such that the total power dsspated becomes: (3) 1 1 Pf 1Total N1ωµρ π 1 1 T 0 + N 1 N A smlar analyss can be carred out for the effects of chan offset wth the result that the power lost as a result of offset has a form nearly dentcal to that gven for frcton at the pn-bushng nterface except that a factor of the offset angle appears n the expresson for offset losses. Snce ths angle s small, the frctonal effects of offset should be small compared wth pn/bushng losses. Any effect would necessarly appear n the largest offset condtons. Sprocket tooth, lnk roller and nner lnk bushng A smlar analyss for the losses at the tooth/roller/bushng nterfaces can be performed wth the followng results: (4) N 1ω1 PfTotal = µ T0rR π = 1 π + 1 π + N N π N + ψ cosϕ sn ϕ n cos ψ sn ψ cot ϕ where µ s the coeffcent of frcton at the bushng/roller nterface, r R s the nner radus of the roller, and ψ s the roller rotaton angle (the angle through whch the roller executes no-slp moton on the tooth). Snce the pressure angle depends on tooth number, a smplfed form for the varaton of the power loss wth sprocket combnaton s dffcult to obtan from Eq. (4). Snce both of these loss mechansms nvolved frcton between elements of the chan, t can be assumed that the coeffcents of frcton are approxmately equal such that a total power loss can be wrtten for the chan drve. Ths power loss s obtaned by addng the losses gven as follows: (5) P T N ω ftotal = π ( α ) ( ϕ ) µ 0 ρ ϕ 1n 1 tan / cot / sn π ( ) ( ) + = 1 1 tan α / tan ϕ / R j j j j j j j= 1 r (( α + ψ) cosϕ sn ϕ1ncos( α + ψ)+ cot ϕ sn α + ψ ) ( ) } where µ s the common coeffcent of frcton. It s noted that the total power loss per sprocket s recprocally related to the tooth number f the roller angle vanshes. Usng ths expresson for the total power loss where N 1 = 5, three separate confguratons are examned and are gven as follows: Confguraton A: N = 11 Confguraton B: N = 15 Confguraton C: N = 1 These confguratons were chosen to reflect stuatons that were realzed expermentally n ths study. Assumng that the roller angle s ψ 5.6 and also assumng that the geometrcal pre-factors for each of the losses are approxmately equal yelds the followng results: (6) PfTotalA and ftotalb PfTotalC PfTotalC tan / tan / P These results ndcate that confguraton A should have 63% more power loss than C and that confguraton B should have 8% more power loss. For example, f a test of effcency ndcated a 5% power loss n confguraton C, then confguraton A should suffer an 8.% loss and B should have a 6.4% loss. DESCRIPTION OF THE EXPERIMENTAL APPARATUS To assess drve effcency, a test stand was desgned to measure the overall or average mechancal effcency of the chan drve from the front chan rng to the rear transmsson components. To assess the effcency of the drve under varous condtons, the power nput to the front chan rng was measured and was compared to the power that was output by the rear drve sprocket. The rato of the output power to the nput power was used to quantfy the overall effcency of the system. To determne the powers n the drve and drven shafts, the torques transmtted by the shafts were measured along wth the rotaton rate of the drve shaft. Knowng the rotaton rate of the drve shaft and the gear rato, the rotaton rate of the drven shaft could be calculated. The effcency of the system was calculated usng the followng formula: (7) τω % Effcency = 100% τω 1 1 where τ 1, ω 1 are the torque and the angular frequency, respectvely, of the drve shaft, and τ, ω are the torque and the angular frequency of the drven shaft. To gather the data requred for the effcency calculatons, the test stand was automated usng computer control. The essental elements of the test stand are shown schematcally n fgure 1 (see page 3). The drve shaft was drven by a varable-speed electrc motor system connected to the drve shaft. The drveshaft rotaton rate from ths system could be vared contnuously under manual control. However, once the desred rotaton rate was set, the rate was not actvely controlled and the actual rotaton of the drve shaft was measured usng a speed sensor. The drve-shaft torque was measured usng a rotary transformer torque sensor. The chan drve was confgured to the geometry found on bcycles wth the dstance between the front chan rng and rear cassette beng adjusted by mountng the entre output-shaft assembly on a translatonal platform. Mountng the output drve components on ths platform allowed for accurate adjustment of the cassette for dstance and offset from the front chan rng. Addtonally, the deralleur unt (Shmano Dura Ace ) could be adjusted ndependently to satsfy recommended mountng condtons. The output shaft torque was measured usng a second rotary torque sensor. The entre drve system was loaded usng an electromagnetc brake mounted to the output shaft. There are three sgnals that are recorded under computer control n a LabVew programmng envronment: nput and output torques and nput rotaton rate. The torque-sensor dfferental outputs were amplfed usng low-nose nstrumentaton amplfers. Snce the torque-sensor outputs were harmoncally varyng sgnals wth ampltudes proportonal to the torque, the sgnals were measured usng lockn technques to mprove the sgnal-tonose of recorded sgnal ampltudes. To relate these sgnals to actual torque values, each of the torque sensors was calbrated usng known statc loads. By measurng the torque-sensor sgnals as a functon of appled torque, a calbraton curve was obtaned that related sgnal level to the appled torque. Fnally, an nfrared-camera system was used to acqure thermal mages of drve components whle the drve was n operaton. Snce frctonal losses result n heatng of the drve components, the nfrared camera was useful n dentfyng those components that had the hghest temperature rses. The prmary component of ths system s the nfrared camera that operated wth an InSb planar array senstve n the 3 5 µm range. Agan, usng LabVew software to control the camera and the mage-acqustonboard operatons, thermal mages of the drve were acqured and stored for analyss and dsplay. For these operatons t was mportant to acqure mages of the drve so that the drve component of nterest occuped the same poston n the nfrared mage from frame to frame. By acqurng mages n ths manner, the heatng of an ndvdual component, such as a sngle chan lnk, could be tracked accurately as a functon of tme. EXPERIMENTAL PROCEDURE Four major areas for nvestgaton were dentfed and were pursued. Tme varaton. Measurements of effcency were made over extended run perods ( hours) to determne whether or not effcency vared as a functon of tme durng drve operaton. Confguraton. Effcency was mea- Fgure. Measured chan-drve effcency as a functon of tme for three dfferent drve confguratons (5 11, 5 15 and 5 1) n the no-offset condton. Tests were run for two hours, but only the frst 100 mnutes are shown here. Note that effcency s farly constant durng the entre tme perod. 4 Number 50, Sprng 000 Human Power Human Power Number 50, Sprng 000 5

4 sured as a functon of gear rato (5 11 etc.) and the effects of offset were nvestgated to assess the effects of drve confguraton. Power/rate. Effcency varatons wth nput power and rotaton rate were measured to determne f load or rate-dependent effects were present. Lubrcaton. The effects of lubrcaton and de-lubrcaton on effcency were quantfed. EXPERIMENTAL RESULTS AND ANALYSIS Tme varaton of effcency A new chan used for these tests was cleaned usng Smple Green Bke Cleaner/Degreaser and was lubrcated usng Generaton 4: Whte Lghtnng self-cleanng lubrcant. These tests lasted 10 mnutes at 60 RPM 100W for each of the followng chan-drve confguratons: 5 11 no-offset, 5 15 no-offset and 5 1 no offset. As s shown n fgure, the effcency for all long-duraton tests showed lttle-to-no long-term effcency varatons durng the tests. The measured effcences for the three confguratons are as follows: 5 11 no-offset: 91.4% 5 15 no-offset: 93.% 5 1 no-offset: 95.0% These values represent an average over the duraton of the test. As a result of these long-duraton tests, subsequent tests were run for no more than 30 mnutes to assess effcency or effcency varatons. Confguraton The next seres of tests nvestgated the effect of chan confguraton on effcency. These tests lasted 30 mnutes each and were conducted wth the 5 15 combnaton n the no-offset condton. Consequently, the 5 11 and 5 1 combnatons were tested n an offset condton as would occur for a properly confgured bcycle. The results of these tests are summarzed Table 1. Drve effcences for dfferent chan confguratons 50 RPM 60 RPM 70 RPM 60 RPM 60 RPM 100 W 100 W 100W 150 W 175W n Table 1. Frst, comparng the results here wth those n the long-duraton tests, the effect of chan offset can be estmated. These data were obtaned wth the 5 11 and 5 1 confguratons n the offset condton whle those n the long-duraton tests were taken wth no offset. Comparng the data for 60 RPM 100 W tests shows that the offset lowers the effcency by, at most, 0.5% when measurement precson s consdered. Addtonally, f the effcences are normalzed by effcences measured n the 5 15 confguraton (both sets of data were obtaned wth no offset), then t appears that the offset has a neglgble effect on effcency. More mportantly, n these md-duraton tests, the effcences show a consstent dependence on rear sprocket sze where the larger the sprocket, the hgher the measured effcency regardless of the selected power or rotaton rate. If the effcency for 5 1 s 95.% (as s found for 50 RPM 100 W), then the prevous modelng results predct a dfference n effcency of.6% between the 5 1 and 5 11 combnatons. From the data n the table, the measured dfference between the 5 1 and 5 11 combnaton s.7%. These results ndcate that the prmary mechansm for chan-drve loss could be frcton at the pn/bushng nterface and frcton at the bushng/roller nterface. Power and rotaton rate To nvestgate the effects of power and rotaton rate on drvetran effcency, more extensve measurements of effcency under varyng powers and rotaton rates were completed. The chan was the same as that used n the other tests and the lubrcaton was not changed wth measurements of effcency beng made sequentally at 5 8 mnute ntervals. All recorded values for effcency have a precson (due to short-term nose) of ±0.% and a long-term precson of ±0.3% under normal operatng condtons. Agan, the effcency results showed that hgher effcences are obtaned for those confguratons that have larger sprockets n combnaton. It was also found that the effcency decreases wth ncreasng rotaton rate for constant power nput and that effcency ncreases wth ncreasng power for constant rotaton rate. Both of these data trends can be related to the torque appled to the drve and ultmately to the chan tenson. Analyzng the effcency as a functon of tenson shows that the effcency ncreases wth chan tenson regardless of nput power or rotaton rate. Addtonally, for a gven chan tenson, the effcency was found to be ndependent of drve rotaton rate (between 40 and 80 RPM). The dependence of effcency on chan tenson s shown n fgure 3 where the drve effcency s shown as a functon of the recprocal chan tenson. Ths graph shows that for the tensons nvestgated n ths study (76. to 305 N) that the recprocal of the tenson s lnearly related to the drve effcency. For each of the lnear fts to the expermental data, the correlaton coeffcent exceeds The extrapolated Fgure 3: Varaton of chan-drve effcency wth the recprocal of the chan tenson. For ths graph, chan tenson has been calculated usng the measured torque values and the radus of the front chan rng. effcences at hgh chan tensons exceed 100% by a small amount (a few percent n the worst case). Clearly, these data ndcate that the fundamental operaton of the drve must be related to the chan tenson such that the effcency ncreases wth ncreasng tenson even though the frctonal losses should ncrease. Ths expermentally measured dependence of effcency on chan tenson can be explaned only n a lmted sense usng the models for loss developed prevously. For example, f the pressure angle changes wth tenson, then the calculated losses wll vary wth tenson n a manner not consdered prevously. Measurements of lnk tenson durng artculaton are currently beng pursued usng noncontactng optcal measurement technques to nvestgate these effects. Lubrcaton In ths phase of the study, the chan was thoroughly degreased/cleaned usng commercally avalable degreasng agents (Castrol Wrench Force Degreaser and/or Smple Green Bke Cleaner/Degreaser) and was relubrcated usng one of three commercally avalable lubrcants (Castrol Wrench Force Dry Lube, Pedro s Syn Lube or Generaton 4 Whte Lghtnng ). The results n table ndcate that Table. Effcences for dfferent drve rotaton rates and sprocket confguratons (nput power 100W).1 Castrol Dry Lube 40 RPM 60 RPM 80 RPM Pedro s Syn Lube 40 RPM 60 RPM 80 RPM Generaton 4 Whte Lghtnng 40 RPM 60 RPM 80 RPM the prevous trends for effcency as a functon of confguraton and as a functon of chan tenson are stll followed. However, these results also ndcate that the actual lubrcant used has lttle effect on the overall performance of the drve under laboratory condtons gven the precson of the measurement. In addton, the chan used for the lubrcaton study was fully degreased and was re-tested for effcency. Ths degreasng operaton conssted of a fve-mnute scrub wth kerosene followed by a cleanng wth Castrol Degreaser. The measured effcency of the de-lubrcated chan for the 5 15 combnaton at 60 RPM and 100 W was 90.3% and at 00 W was 96.5%. These effcences are essentally the same as those measured for the chan n the re-lubrcated condton. Infrared measurements durng chan-drve operaton Infrared mages of the chan drve durng operaton ad the nterpretaton of the effcency measurements that have been presented and also support aspects of the modelng of chan-drve loss snce frctonal losses should heat the drve components. Smply put, the chan components responsble for mechancal loss should heat the chan and cause ts temperature to rse. Snce the average heat deposton rate equals the average mechancal power loss, the heatng should have a functonal dependence smlar to that found for frctonal losses. To acqure nfrared mages, the chan drve was set ntally to a low rotaton rate and the components were allowed to reach a steady state n ths mode of operaton. The rotaton rate and brake resstance were then ncreased rapdly to acheve the desred rate and power settngs (100 W 60 RPM, etc.). Infrared mage acquston began pror to (or durng) the tme of power and rotaton ncrease. Images were acqured at set tme ntervals (e.g., approxmately 30 seconds) for the duraton of the test such that actual mage acquston occurred synchronously to a partcular lnk n the chan. Snce pxel ntensty s proportonal to the nfrared energy reachng the detector and the amount of nfrared emsson s proportonal to the temperature of the component, the pxel ntensty s drectly proportonal to temperature. Ths method for data acquston allows the temperature 4:00 mnutes 7:30 mnutes 11:00 mnutes 15:00 mnutes 5 1: 60 RPM, 150W Fgure 4: Infrared mages of chan drve durng operaton showng effects of frctonal heatng. 6 Number 50, Sprng 000 Human Power Human Power Number 50, Sprng 000 7

5 ncreases n varous components to be mapped as a functon of tme after mposton of the heat load. Representatve results are shown n fgure 4 where a seres of four nfrared mages from effcency tests for the 5 1 confguraton are shown. At the begnnng of the test, the nfrared mages showed only varatons of emssvty snce all components were n thermal equlbrum. From these mages (taken at the tmes ndcated) varous qualtatve observatons are gven as follows. 1. The chan pns rapdly heat on the radal surfaces and reach near steady-state temperatures wthn 4 5 mnutes.. At hgh chan tensons and low rotaton rates, both the gude and the tenson pulleys heat prmarly from the chan. 3. Steady-state temperature condtons for the chan drve are establshed wthn approxmately 15 mnutes after the begnnng of a test. These observatons are n general agreement wth the proposed frctonal-loss mechansms. The rapd heatng at the radal pn surfaces s consstent wth heatng at the pn-bushng nterface. At low chan tensons, the frctonal losses should be relatvely low and the temperature rse n the chan should be low. At hgh chan tensons and low rotaton rates, the frctonal losses n the chan should be relatvely hgh producng large temperature rses n the chan. The pulley-bearng losses should be relatvely low. Even though the nfrared mages provde a wealth of qualtatve nformaton, quanttatve analyss of chan-drve heatng must be performed usng the temporal evoluton of pxel ntensty. In Fg. 5 the nfrared pxel ntensty for postons on a chan pn, on a pulley tooth and on the body of the pulley (mdway between the bearng and the pulley teeth) are shown as a functon of tme for dfferent nput powers. These data were taken at 60 RPM n the 5 1 confguraton. These results clearly show that the chan pn rses n temperature more rapdly than the other locatons regardless of the nput power and ndcate that heatng results from frctonal losses near the pn. The data for the chan and the pulley tooth ndcate that the component temperature rses wth the nput power. For the pulley tooth, at 50 W nput power, the maxmum pxel value s approxmately 3 unts; at 100 W, 35 unts and at 150 W, 65 unts. These results are n rough agreement wth the loss models presented prevously where the frctonal losses are drectly proportonal to the nput power. Unfortunately, the power loss n each of these cases s not proportonal to the nput power owng to the dependence of effcency on chan tenson. Usng measured values for effcency under the condtons for the data n Fgure 5: Varaton of nfrared emsson wth tme durng chan operaton for dfferent drve components. At tme equal to 0 s, the chan drve was placed under full power loadng. Fg. 5 (97.% for 150 W, 94.4% for 100 W and 85.5% for 50 W) ndcates that 4. W of power were lost at 150 W nput; 5.6 W at 100 W nput and 7.3 W at 50 W nput. Obvously, for a lower power loss, the temperature rse should be lower f the lost power s converted entrely to heat by frctonal loss. It would be expected that the temperature rse would be lowest for the 150 W nput test snce the measured power loss s lowest for ths case. DISCUSSION AND CONCLUSIONS Tests of effcency for the deralleurtype chan drve ndcate that the overall effcences for the transfer of power from the front drve sprocket to the rear sprocket range from 80.9% to 98.6% dependng on the condtons of drve operaton. Prmary factors affectng the effcency nclude the szes of the sprockets n the drve and the tenson n the chan. It was found that larger sprockets provde more effcent transfer of power whle smaller sprockets proved to be less effcent. Smple, frctonal loss models were developed that gave sprocket-sze loss varatons that agreed wth those varatons measured expermentally. Typcally, a 5% loss dfference was measured between the 5 11 and the 5 1 sprocket combnatons dependng on the drve operatng condtons. Expermental results ndcated that the effcency of the chan drve vared as a functon of chan tenson. It was found that the effcency vared lnearly wth the recprocal of the average chan tenson wth the hghest effcences occurrng at hgh chan tensons and lowest at low chan tensons. For example, the hghest effcency measured n the study, 98.6%, was measured at a chan tenson of 305 N and the lowest, 80.9%, at 76. N. It was found that chan-lne offset and chan lubrcaton have a neglgble effect on effcency under laboratory condtons. Calculatons of frctonal loss resultng from offset ndcate that ths loss should be small compared to those produced by other mechansms. Ths was verfed expermentally. Lubrcaton effects on chan effcency were tested usng three dfferent chan lubrcants under a varety of test confguratons. No sgnfcant quantfable effect of lubrcaton could be nferred from these tests. Infrared measurements of drve components ndcate that frctonal losses n the chan cause the chan temperature to rse durng operaton. Ths ncrease n temperature dd not correlate wth measured effcences under varous condtons of operaton. Infrared measurements on lubrcated and delubrcated chan lnks showed that the frctonal heatng dd not depend on lubrcaton. From the results of ths study, t appears that the effcency of the bcycle chan drve depends ntmately on the chan operaton as t engages and departs from the sprockets on the hghtenson part of the drve. Owng to the hgh effcences measured under hgh chan tensons, frcton can account for only a few percent of the overall losses. Most probably, mechancal losses that are not converted to thermal energy n the drve account for the remander of the measured loss. NOTES LabVIEW, Natonal Instruments Corporaton s a computer software program useful for runnng scentfc SUMMARY OF EQUATIONS Wf1= µρ π 1 T 0 1n 1 tan α / / tan ϕ / sn ϕ = 1 1 tan α/ tan ϕ/ Pf1Total = N1ω1Wf1/ π ( ) + ( ) ( ) ( ) ( ) 1 1 Pf 1Total N1ωµρ π 1 1 T 0 + N 1 N Pf Total nstruments by computer. Natonal Instruments Corp. See for vendor nformaton. REFERENCES Cameron, A Measurng drvetran effcency, Human Power 46:5 7. Hollngworth, N.E., and D.A. Hlls. 1986a. Forces n heavy-duty drve chan durng artculaton. Instn Mech. Engrs, 00:C5, Hollngworth, N.E., and D.A. Hlls. 1986b. Theoretcal effcency of cranked lnk chan drve. Instn Mech. Engrs, 00:C5, Juden, C Measurements of effcency of chan and shaft drves. (1997). Keller, J Der Wrkungsgrad m Fahrradantreb. Radmarkt, 1: Kdd, M., N. Loch, and R. Reuben Bcycle chan effcency. The Engneerng of Sport, S. Haake, ed. Rotterdam: Balkema, Kdd, M., N. Loch, and R. Reuben Expermental nvestgaton of bcycle chan forces. Submtted to Expermental Mechancs. Spcer, J., M. Ehrlch, J. Bernsten, C. Rchardson, M. Fukuda, and M. Terada. June Effcency and energy loss locaton n bcycle chan drves. Submtted to the Journal of Mechancal Desgn. Tordon, G.V Chans. Mechancal desgn handbook. H.A. Rothbart, ed. McGraw Hll, Vogwell, J Chan drves. Rotary power transmsson desgn. K. Hurst, ed. McGraw-Hll Europe, Wlson, D.G Transmsson effcency, Human Power 48:0. *Correspondng author: James B. Spcer, Assocate Professor Dept. of Materals Scence & Engneerng The Johns Hopkns Unversty, 3400 N. Charles St., Room 10 Maryland Hall, Baltmore, MD 118, USA The Hopkns group pursues work n pulsed and ultrafast (femtosecond) laser-based materals processng and characterzaton. In contrast, the expertse of the Shmano partcpants leans towards the desgn and manufacture of cyclng components. All of the authors express ther grattude to the Baltmore Oroles for the use of Camden Yards where many frutful techncal dscussons about ths work were held. Pf Pf and Pf Pf N 1ω1 = T0rR π + 1 π + 1 N N π N + µ ψ cosϕ sn ϕ n cos ψ sn ψ cot ϕ π = P T N ω ftotal = π 1 1 α ϕ µ 0 ρ ϕ 1n 1 tan / cot / sn π = 1 1 tan α/ tan ϕ/ r + ( ) ( ) ( ) ( ) + (( α + ψ) ϕ ϕ1n ( α + ψ)+ ϕ α + ψ R j j j j j j j= 1 ( ) } cos sn cos cot sn ) 6 7 TotalA TotalC TotalB TotalC τω % Effcency = 100% τω Number 50, Sprng 000 Human Power Human Power Number 50, Sprng 000 9

6 Offset rms reduce the amount of dsh by Vernon Forbes ABSTRACT Offset rms reduce the amount a rear wheel s dshed. Two offset rms are tested and the results compared to a standard rm. Possble mplcatons are dscussed. INTRODUCTION Dsh n a bcycle wheel s a measure of ts lack of symmetry. Usually ths s gven as a rato of two lengths (defned later). Sometmes dsh s also expressed as the rato of, and as the dfference of, the average spoke tensons on the drve sde and the nondrve sde of the hub. An undshed wheel s one wth the rm centered over the mdpont of the axle, not of the hub. In a front wheel, the rm s centered over both the axle and the hub. When vewed straght on the front wheel s rm can be seen to fall n the mddle of the front hub, to rest equally between the flanges. A front wheel that s not centered on the axle cannot be centered n the frame or between the brake blocks. In the rear wheel the rm s centered over the axle; t s not centered over the hub. Ths s the awkward soluton to the problems posed by the development of the deralleur. Before the development of deralleurs both the front and rear wheels were centered over the hubs. Wth the development of deralleurs came multple-cog freewheels whch presented the problem of how to accommodate the addtonal cogs. Bcycle desgners could do one of three thngs. For one, they could spread the stays and wden the rear axle to make room for the freewheel block. If they dd ths the bottom bracket would have to be wdened also to keep the chan n lne wth the freewheel. Many consder wder bottom brackets harder to pedal. Ther other choce was to center the rm over a very narrow hub. They could move the hub flange on the left sde n by the same amount the freewheel block moved the rght sde hub flange n. However, wheels bult wth narrow hubs are laterally weaker than wheels bult wth wde hubs. The dea they ht upon was a compromse; they spread the rear dropouts a lttle and narrowed the rear hub a lttle so they could move the whole hub over between the dropouts to make room for the freewheel. Fgure 1. Wheel cross-secton for symmetrc rms (after Brandt) wth modfcatons for asymmetrc rms. One effect a freewheel has s to ncrease spoke tenson on the rght, or drve sde (DS) relatve to the left, or non-drve sde (NDS). The rato of DS/NDS measures what s commonly referred to as dsh. In ths rato the two dstances are those from the plane of the rm centerlne to the outsde surfaces of the hub flanges. Increased freewheel wdth ncreases the severty of dsh. The newer eght-speed freewheels requre more dsh than dd older fve speeds. Increased dsh results n DS spokes beng tghter. Cyclsts are long famlar wth the ncreased tendency for spokes to break on the freewheel sde (Forbes ). One spoke manufacturer recommends N ( lbf) spoke tenson for the DS. 1 Ths s well below the threshold for falure, establshed by Brandt as 649 N (595 lbf) for lghter spokes and 3l39 N (706 lbf) for heaver spokes (Brandt 1983). Another spoke manufacturer specfes whch hub to use and recommends the DS be tghtened to 1079 N (43 lbf) and the NDS be tghtened to 883 N (199 lbf). (Ths has the DS % tghter than the NDS. ) Whle ths s a moderate amount of dsh perfectly adequate for most applcatons t does not allow for dfferences n the amount of dsh requred resultng from hubs wth dfferent freewheel wdths, axle lengths and dstance between a hub s flanges. These are propertes of the hubs and snce t s rare for two hubs to have the same measurements no one can specfy the tensons on each sde of the wheel unless s/he also specfes whch hub to use. Shraner (1999) gves the followng tenson recommendatons for wheels wth normal rms. He recommends N (0 5 lbf) of tenson for normal rms n the front wheel and n the rear wheel he recommends N ( lbf) for the NDS and between N (5 47 lbf) for the DS (ths has the DS between 57 66% tghter than the NDS; Schraner 1999). However, he does not specfy whch hub must be used to acheve ths range of ratos. Unequal spoke tenson caused by rear-wheel dsh has caused some manufacturers to experment wth prevously rejected solutons. To make room for the wder freewheels some manufacturers have used longer rear axles. How- ever, ths changes the chanlne and unless the bottom bracket s also wdened t can result n dffcult shftng and premature chan wear. Another soluton to the problem of the DS beng at a hgher tenson than the NDS s to use a dshless hub. A dshless hub must be a narrower hub. It has the NDS flange moved n closer so that t s the same dstance from the rm center as the DS flange. However dshless hubs that are wder are known to be laterally stronger than narrow, dshless hubs. Recently, offset rms (Rtchey, Bontrager) have been developed that have the spoke holes offset closer to the NDS (see fgure ). Both sdes of the wheel are affected equally: the DS spokes are put at a steeper angle as the NDS spokes are put at a shallower one (see fgure 1). Ths equalzes tenson, reducng the falure rate of spokes on the DS due to fatgue. The ablty of these rms to reduce the amount of dsh s tested below. Fgure. Offset rm: Bontrager Mustang (reproduced here wth permsson). METHODS Three 6x spoke rms were tested, two offset and one non-offset, for comparson. The offset rms were a Rtchey OCR (Off-Center Rm) and Bontrager Mustang Asym (Asymmetrcal). The non-offset rm was a Matrx Sngletrack. Each of these rms was bult up 3X on a 3-spoke low-flange Suntour XC Pro hub wth a 45-mm flange dameter, or spoke crcle (measured center-to-center) usng DT stanless-steel 14g spokes, 64-mm long. The Suntour hub measured 55 mm between flanges, center-to-center (see fgure 1). The 55-mm dstance was chosen because t was mdway between the dstances measured n a prevous artcle. (The average for a 7-sp hub was 58.4 mm and the average for an 8-sp hub was 55.3 mm between the flanges, center-tocenter; Forbes ). A 135-mm axle length, locknut-to-locknut (see fgure 1) was used at all tmes. Each wheel was tested at two dfferent levels of dsh approxmatng the mean freewheel thcknesses of 7-sp (44.5 mm) and 8-sp (48.0 mm) freewheels establshed prevously (Ibd.). Dsh was changed by movng spacers from one sde of the axle to the other and redshng the wheel, e.g., the axle was frst spaced for a 7-sp spacng on a 135-mm axle. The wheel was then dshed usng a Wheelsmth dshng gauge. The Rtchey OCR was the frst to be bult up and tested. A rm transfer for all subsequent rms used the same hub and spokes. Prevously we had suggested that wheel dsh could be predcted from a hub s measurements whch we expressed as a rato (DS/NDS). To measure dsh on wheels that are already bult up we are expressng dsh as the dfference n spoke tenson between the DS and the NDS (DS NDS). All tenson measurements were taken wth a Wheelsmth spoke tensometer. At each level of dsh the wheel was measured at three levels of tenson correspondng, e.g., to tensometer readngs of 75, 80 and 85 for the DS. A copper template nsured that tensometer readngs were taken 30 mm from the rm edge. Each readng was taken twce. If the two readngs dd not agree a thrd readng was taken. If there was any doubt about the readng on a spoke the procedure was repeated untl a true readng was taken. After one level of dsh was tested at three levels of tenson the axle was respaced and the process repeated for the remanng levels of dsh. Each level of dsh was establshed usng a 135-mm-long axle (locknut-to-locknut) as the overall length. RESULTS The chef nterest for us was the dfference n tenson between the DS and the NDS. The mean spoke tenson for each sde of the wheel was frst determned. Tenson here s expressed as nomnal tensometer readngs, not as Newtons or poundals. To measure dsh the tenson on the NDS (whch was presumably less tght) was subtracted from the tenson on the DS to determne the dfference n tenson. The accompanyng fgure (see fgure 3) shows the tenson dfferences between the DS and the NDS for two levels of dsh correspondng to the mean 7-speed and 8-speed spacng. The two levels of dsh are expressed n mm and measure the dstance from the outsde edge of the locknut on the DS to the flange center. Table 1 summarzes the data n fgure 3. For both fgure 3 and table 1, freewheel wdth (F/W wdth) s measured as the DS locknut-to-flange center n mm. DISCUSSION Fgure 3 plots dsh as dfferences n spoke tenson between the drve sde and the non-drve sde (DS-NDS). The graph plots three lnes; one for a Bontrager Asym, a Rtchey OCR, and a standard non-offset rm. A front wheel, Fgure 3. Tenson dfferences (dsh) for regular and offset rms. Table 1. Tenson dfferences (DS-NDS) # F/W % reducton speeds wdth Reg OCR Asym OCR Asym 7-sp % 57% 8-sp % 35% 10 Number 50, Sprng 000 Human Power Human Power Number 50, Sprng

7 or any wheel wth no dsh would plot a value at zero. The hgher the number the more severely a wheel s dshed. Less dsh s desrable. What s obvous s that the non-offset rm has the greatest tenson dfferences, for all levels of dsh. Both the offset rms show a sgnfcant reducton n dsh. Whle both offset traces are below the standard rm trace, the Rtchey rm trace s below the Bontrager rm trace. There exst a number of dfferences between these two rms whch may explan our fndngs. Bontrager advertses hs rms as havng.5 mm of offset, 3 whle Rtchey ads used to clam a 3-mm reducton n dsh; they currently advertse a 50% reducton n dsh. 4 One possble explanaton s rm wdth. Our measurements showed the Bontrager Mustang was 1.8 mm wde and the Rtchey Rock OCR was 4 mm wde. Wth a wder rm you can move the spokes further over to the NDS. Whle the Bontrager rm s. mm narrower t has only 0.5 mm more dsh than a Rtchey. There s a weght penalty for a wder rm. We measured the Bontrager at 415 g (he advertses 430 g) and the Rtchey at 484 g. Wder rms are laterally stronger. In terms of heght the Rtchey advertses 1 mm heght and the Bontrager advertses 13 mm heght. Deeper rms are radally stronger. Both rms are made from 6061-T6 alumnum alloy. Offset rms have been crtczed by some as beng weaker because they lack ferrules, or spoke sockets that jon the upper and lower parts of a boxsecton rm so the spoke pulls on both sectons of the box-secton rm. In answer to ths both rms come wth nternal renforcements. Fgure depcts a rb whch jons the top and bottom as dd Wlderness Tral Bkes (WTB) n ts PowerBeam rm. Bontrager rms use one rb ( dual cavty or double box) whle Rtchey rms currently use two ( trple box ). The ablty of nternal renforcng rbs to act lke a ferruled rm s unclear. Whle we cannot be sure f our Rtchey OCR s trple box or not t would help explan why the Rtchey s nearly 70 g heaver. Ths s n lght of the fact that whle the Bontrager s eyeletted the Rtchey s not. The graph llustrates that for all freewheel thcknesses, offset rms gve a dramatc reducton n dsh, as measured as tenson dfferences. Because the Rtchey yelds lower values presumably the spoke holes are more offset. Although both offset rms reduced dsh compared to the standard rm the Rtchey had slghtly lower tensometer readngs. Compared to the Bontrager rm, the Rtchey readngs were.3 lower for 7-sp spacng and.8 lower for 8-sp spacng rm. Ths, however, may be due to the Rtchey s beng a wder and heaver rm. DISH AS HUB MEASUREMENTS Several clams are made for Rtchey OCR rms. One of them s that the Rtchey OCR rm wll reduce dsh from 6 mm to 3 mm usng a Rtchey hub; a 50% reducton. We prevously found that the dsh on most hubs s consderably more than 6 mm. We surveyed the same 74 hubs we dd n a prevous study (Forbes ). Table summarzes the actual average amount of dsh expressed as dstance measurements for 74 hubs wth a 55-mm-wde hub on a 135-mm axle we prevously examned. We see from the table that actually the Rtchey OCR would reduce dsh from 9 mm to 6 mm on a typcal 7-speed and from 17 mm to 14 mm on a typcal 8- speed. These were reflected n lower tenson dfferences. Inspecton of table 1 reveals that when compared to a conventonal rm, the Rtchey OCR rm yelded a 9.6 smaller dfference n tensometer readngs for 7-sp spacng, (a 74% reducton) and a 10.6 dfference n tensometer readngs for 8-sp spacng, (a 47% reducton). Table. Dsh measured as dstance dfference (DS-NDS) Dfference (DS-NDS) # F/W Center Center Standard OCR Asym speeds wdth to DS to NDS (DS-NDS) (DS-NDS) (DS-NDS) 7-sp mm 3 mm 9 mm 6 mm 6.5 mm 8-sp mm 36 mm 17 mm 14 mm 14.5 mm CAUSES OF DISH The utlty of these rms may be especally suted to wde rear hubs. Prevously we noted how dsh s the result of several varables (Ibd.). For any gven freewheel both freewheel thckness and hub wdth contrbute to dsh n dfferent ways. Consder the effects of both freewheel thckness and hub wdth on dsh. Increasng the freewheel thckness moves the entre hub over to make room for t. Ths pushes the DS flange n closer to the rm center as the NDS flange s pushed further from the rm center. By comparson, ncreasng the hub wdth affects dsh by pushng the NDS flange further away from the rm, leavng he DS flange alone. Because freewheel thckness affects both flanges and hub wdth affects only one flange we vew freewheel thckness to affect hub dsh at twce the rate of hub wdth. It s for ths reason that we have suggested that ncreasng hub wdth was not half as bad as ncreasng freewheel wdth. The ablty of an offset rm to attenuate dsh depends on the source of the dsh. Because offset rms affect spokes on both flanges an offset rm would reduce freewheel-nduced tenson dfferences at the same rate as the freewheel causes them. By comparson, hub-wdth-nduced tenson dfferences affect only one flange and offset rms attenuate dsh by affectng both flanges. We would expect for offset rms to reduce hub-nduced dsh at twce the rate caused by hub wdth. Offset rms would be twce as effectve n attenuatng hub-nduced dsh as they are n attenuatng freewheel-nduced dsh. That sad, t s reasonable for offset rms to make for an ncreased wdespread applcaton of wder hubs, wth all the benefts of ncreased lateral strength. Offset rms may fnd an addtonal applcaton for offsettng front-wheel dsh nduced by dsk brakes. Durng the preparaton of ths artcle both Rtchey and Bontrager each ntroduced rms for use wth a front dsk brake. Interestngly, the Rtchey front OCR s 4 mm wde, the same wdth as the Rock OCR we tested whch s no longer made. Unlke the Rock OCR, t does not appear to have any nternal renforcng rbs and s eyeletted. Phl Wood s lsted as offerng a front hub threaded to accept a dsc brake n both a dshed and undshed versons (Sutherland 1995). Lookng at ther dmensons t appears that the undshed hub has a narrower hub shaft (flange-to-flange) than the dshed hub. If t s for a dshed front wheel then usng an offset rm would be an deal soluton. The Rtchey lterature used to clam a 3- mm reducton n dsh for ther rear wheel. Dshed models of Phl Wood front-brake hubs threaded for a dsk brake are dshed between 13 mm, dependng on the front axle length (locknut-to-locknut). Only two hubs had mm dsh and the other eght were 3 mm or more. The Sturmey-Archer BFC drum brake s dshed 4 mm. We can thnk of no more approprate a use for an offset rm than for a front wheel wth a dsc or drum brake. We have examned the benefts of offset rms n reducng rear-wheel dsh only. BENDING-MOMENT ASYMMETRY It s natural, however, to assume that f form follows functon we would expect to be able to see the symmetry and balance reflected n force-balanced structures. In offset rms the spoke holes are drlled closer to one sde. One cannot help but suspect for such a glarng asymmetry to somehow reflect an underlyng unequal dstrbuton of force, or lack of balance. Offset rms have what can be called bendng-moment asymmetry. N.B.: we make the dstncton between vertcal, or up-and-down bendng moment and lateral, or sde-to-sde bendng moment. The longer DS half of the rm the more bendng-moment t has. The shorter the NDS half of the rm the less bendngmoment t has so that a vertcal load, from, e.g., sttng on a bcycle, exerts more vertcal bendng-moment to the DS than the NDS sde of the rm. One possble effect of ths s that every bump n the road would deform the longer DS more than t dd the shorter NDS, relatve to the centerlne. That sad, any vertcal loadng wll result n the rm havng ncreased DS bendng movement. At the very least ths mght result n ncreased dentng ( flat spots ) of the DS half of the rm durng cornerng. Vertcal loads are thought to loosen the bottom most spokes makng them lkely to become unscrewed. Another possble effect of bendng-moment asymmetry s that any vertcal load wll bend the rm on the DS and the spokes the DS mght loosen more and ther npples be more lkeley to unscrew. The wheel mght be more lkely to get out of true. Cornerng, on the other hand, can subject the wheel to lateral loads. Rght-hand bcycle turns ncrease the tenson on the DS spokes n tenson peaks as the wheel rotates whle t leans nto a turn. Now f the rm on the DS were also to experence some addtonal vertcal bendng n response to cornerng then that would tend to loosen the spokes. So the tenson peaks caused by lateral loadng mght be offset by any tenson losses as a result of vertcal loadng. Brandt (1983) has suggested that fatgue s the result of the nteracton between peak and baselne tenson n a tenson cycle. If ths were so then we mght expect that an offset rm mght reduce the frequency of DS spoke falure n two ways. Frst, t would equalze spoke tenson thus decreasng the baselne tenson n DS spokes. Second, t would reduce the tenson peaks experenced by the DS spokes durng rght-hand turns due to lateral movement because of the rm s ncreased complementary vertcal bendng movement durng cornerng. However, ths s all hghly speculatve. The possble effects of bendngmoment asymmetry n offset rms are not known. Possble effects nclude the ncreased lkelhood of rm dents on the DS as well as spokes unscrewng on the DS due to vertcal movement and a decreased ncdence of fatgue falure due to vertcal movement attenuatng stress peaks caused by lateral movement durng cornerng. Despte our attempts to lmt or control for tenson dfferences, measurement error cannot be ruled out. We found that even dfferences as small as 0.5 mm n axle spacng would affect tensometer readngs. CONCLUSIONS AND RECOMMENDATIONS Offset rms were found to sgnfcantly reduce rear-wheel dsh for both 7-sp and 8-sp spacng. The rms have addtonal applcaton n reducng frontwheel dsh nduced by hub brakes. NOTES 1. Wheelsmth tensometer: a professonal wheelbuldng devce for exact spoke-tenson measurements [pamphlet; 1989]. Menlo Park, CA: Wheelsmth Fabrcatons, Inc. The pamphlet comes wth the tensometer, although t does not gve a NDS tenson recommendaton. For more nformaton, Wheelsmth Fabrcatons, Inc., 355l Haven Ave., Ste. R Menlo Park, CA 9405-l009 Telephone: 4l Masterng the art of wheelbuldng. l996. DT Swss Bke Technology USA and Campagnolo. Certfcaton semnar brochure. Extreme Sklls Semnars and Extreme Exposure Promotons. Grand Juncton, CO: LLC, p Bontrager components nneteen nnety nne [promotonal pamphlet], p. 11. See also 4. Rtchey web ste: ms/home_rms.htm. REFERENCES Brandt, Jobst The bcycle wheel, rev. ed. Menlo Park, CA: Avocet, p A book no wheelbulder s lbrary s complete wthout. Forbes, V Predctng wheel strength from hubs. Human Power. 46:8 10. Schraner, G The art of wheelbuldng. Denver: Buopane Publcatons, p. 44. Recent publcaton from DT wth many nsder tps from the European professonal racng crcut. Sutherland, H Sutherland s handbook for bcycle mechancs, 6th ed. Berkeley: Sutherland Publcatons, pp ff. 1 Number 50, Sprng 000 Human Power Human Power Number 50, Sprng

8 ACKNOWLEDGMENTS The author thanks Davd Gordon Wlson for hs nvaluable comments durng the preparaton of ths artcle, Helos Studos n Columba, MO, John W. Stephens of Garden Grove, CA, and Jean Seay of San Lus Obspo, CA, for ther assstance n the preparaton of ths artcle. Fgure 1 s after The Bcycle Wheel by Jobst Brandt and appears by hs courtesy and wth hs permsson. The author thanks hm for hs comments n readng an advance copy of ths artcle. Fgure s after the Bontrager Components homepage, and appears courtesy of Keth Bontrager and wth hs permsson. The author thanks Tryathletcs n Columba, Mssour, wthout whom ths artcle would not be possble. Vernon s a bke mechanc n Columba, Mssour. Requests for reprnts should be sent wth a wth a self-addressed envelope and suffcent postage (two nternatonal postal reply coupons for outsde the USA) to hm at: Vernon Forbes 1007 Grand Ave Columba, MO USA Telephone: UPDATE From Anl Rajvansh, author of Cycle Rckshaws, HP 49 (Wnter ) I lked your comment on poor qualty of present cycles and am tryng to make rckshaws keepng ths pont of vew very much n mnd. The consumer movement s catchng up n Inda and a couple of two-wheeler manufacturers have been taken to court for poor manufacturng. I hope the same could be done for cycles and rckshaws. We are now puttng twenty MAPRs n Lucknow and wll be very nterested n sharng our experences wth your readers. I plan to vst the US ths summer and would lke to meet nterested people. Wth warm regards, Anl Rajvansh Rollng resstance of bcycle tyres by John Lafford INTRODUCTION I have been a research and development engneer for many years, and when I started recumbent racng about fourteen years ago, t was only natural for me to want to obtan relable data on cyclng performance. The most mportant factor s aerodynamcs, and I addressed the measurement of aerodynamc drag n the real world by dong coast-down tests. The procedure for ths s descrbed n So you want to buld an HPV (p. 40 ff) a publcaton of the Brtsh Human Power Club. For an accurate drag result you also need to know the rollng-resstance values for the tyres. As you go faster, the rollng resstance becomes more mportant and t s therefore vtal to have accurate data on whch to base a tyre choce. It was ths requrement that led to study and analyss to derve an accurate and repeatable test procedure for measurng rollng resstance. The testng has all been done wth racng n mnd. For tourng or commutng other factors such as wear resstance, puncture resstance, grp n the dry and wet, and cost, come nto consderaton for tyre choce. TESTING PROCEDURE The tyre-testng procedure nvolves rollng the tyre/wheel combnaton along a flat surface and so represents the real case of usng the tyre on the road. The tyre s also loaded wth a representatve weght and starts rollng at a controlled ntal speed. The dstance that the tyre rolls s nversely proportonal to the rollng resstance. The rollng-resstance coeffcent s derved from knowng the ntal speed and the dstance that the tyre rolls. The speed of rollng n the tests s slow so that aerodynamc forces are neglgble. The flat surface used s farly smooth concrete n my local arcraftfactory workshop, and s reasonably representatve of a smooth tarmac road surface. In any event, as all the tests are performed n exactly the same place, they all relate to one another. The power to propel tyres along the road (Prr), s drectly proportonal to the rollng-resstance coeffcent (Crr), the weght of the vehcle plus rder (W), and also the speed of the vehcle (V). Prr = Crr x W V (tmes a constant for users of ancent unts ed.) The power absorbed s the same whether the vehcle has two, three or four wheels (so long as they are perfectly algned, as the author confrms below ed.). In the table, the power s computed n watts for the cases of (1) vehcle plus rder weghng 185 lb (84 kg) at road speeds of 0 mph, 5 mph and 30 mph (3 kph, 40 kph and 48 kph, respectvely); and () vehcle plus rder weghng 00 lb (91kg) at road speeds of 30 mph, 40 mph and 50 mph (48 kph, 64 kph and 80 kph, respectvely) whch s relevant to fared vehcles. TIME LOST The tme-lost column gves a practcal apprecaton of the mportance of the rollng resstance of the tyre by showng the tme lost by each of the tyres aganst the best tyre lsted (the last tyre n the lst), over a dstance of 10 mles (16 km). The base tme for 10 mles at 5 mph s 4.00 mnutes. The tme lost s derved from aerodynamc-drag values obtaned n coastdown test results (see reference below) usng my own racng recumbent. Data from the test wll predct the power requred to rde along a level road at 5 mph and 4 mph. The dfference n these two values was 8 watts for my recumbent wth the average tyres that were ftted at that tme. The tme taken to rde 10 mles at 4 mph s 5.00 mnutes. The tme-lost column s calculated by proporton of the power absorbed by each of the tyres compared to the Vredesten Fortezza Pste: Tme lost for tyre a = [Prr(tyre a ) Prr(Vredesten)] x 60/8 It can be seen that usng the wrong tyres can easly cause one to lose over a mnute over the 10 mles. COMMENTARY ON THE TABLE 1. Some of the tyres are tested at pressures above the manufacturer s recommended pressure. Ths was done for scentfc nterest. Ths does not mply approval of operatng tyres above the manufacturer s recommended pressure.. Most of the tyres are tested at several pressures to show the effect of pressure on rollng performance. 3. The lst ncludes the effect of grndng the tread down on some tyre types. Ths smulates the effect of tyre wear. Ths generally gves an mprovement n rollng performance. In some cases t s not benefcal as the tyre sdewall flexblty may be a more mportant factor n absorbng energy as the tyre rolls. 4. The lst ncludes some examples of the effect of usng latex nner tubes nstead of butyl nner tubes. Generally, the latex tube wll gve an mprovement. However, f the tyre has a thck tread, ths wll domnate the energy absorpton, and latex wll show no beneft. Latex gves a good mprovement where the tyre tread s thn and flexble so that the reducton n energy caused by substtutng the butyl tube can be seen. 5. The 700c tyres shown are among the very best on the market. Most 700c tyres are not nearly as good as these. Some 700c tyres are very poor. Do not be msled nto thnkng all 700c tyres are good just because the three shown are good. 6. General rules for good rollng performance: a. thn-tread-thckness tyres roll better; b. fat-secton tyres roll better; c. knobbly tyres roll badly; d. Kevlar often gves poor rollng performance (except Vttora); and e. used tyres roll better than new tyres as they are thnner, and therefore more flexble. 7. One cannot assume that all tyres from a partcular manufacturer are fast or slow. Generally they have a range of rollng performance that does not necessarly have any relatonshp wth the company s advertsng clams. 8. For addtonal rollng-resstance data, see reports n the followng Brtsh magaznes: Cyclng Plus, ssue 6 (Feb. 97) Wnter tyres ; Cyclng Plus, ssue 68 (Md-summer 97) Road tyres ; Cyclng Plus, ssue 81 (Aug 98) Tme-tral tyres ; Total Bke, ssue 6 (Oct 97) MTB tyres ; and BHPC Newsletter, ssue 58, MTB tyres. 9. Thanks are due to the followng for the loan of tyres for testng: Hlary Stone, Rchard Grgsby, John Kngsbury, Mcheln Tyres, Cambran Tyres, Dllglove (Nokan tyres). John Lafford John Lafford s an engneer who has been buldng and racng recumbents for 14 years. He s nterested n all the techncal aspects of cyclng wth emphass on effcency of operaton. He has bult two- and three-wheeled recumbents, both fared and unfared, and also works on power-asssted bkes and trkes. He also takes part n tmetral events usng a cross-shapedframe desgn of bcycle produced by hs own Arrow Bcycle Company. (Edtor s note: dscusson of contrbutons s always welcome n letters to Human Power. John Lafford s contrbuton ncluded values that vared from those of others, and I asked Jm Papadopoulos to comment. Then I sent hs comments to John for a response. I would lke to thank both for ther courtesy n dscussng the results and n allowng us to publsh ther remarks. Dave Wlson) Note on Lafford s paper and spreadsheet by Jm Papadopoulos It s always heartenng to see evdence of a great deal of careful testng. I apprecate that Lafford actually dd somethng, rather than just talk about t (as I am prone to do). Of course hs numbers rase a host of questons. None of these are crtcsms per se, but the answers mght help establsh how relable hs results really are. I dd not grasp mmedately that hs focus was prmarly on small wheels. Spreadsheet and artcle should perhaps be called Rollng resstance of small- dameter tres. My questons relate prmarly to accuracy and meanngful precson of hs data. How repeatable s hs test? The fact that an ncreasng seres of nflaton pressures leads to a decreasng seres of rollng resstance coeffcents suggests that hs fnal dgt s meanngful ( ). However t would be good to have a statement from John about how well hs tests repeat, what averagng he employs, etc. How accurate s hs test? Here my questons sprng from a couple of dsparate perspectves. 1. How do hs numbers compare wth others? He gves good 700C numbers of ; however some other sources gve numbers Hs best Moulton number s whereas Kyle has gven and Burke gave I would feel better f Lafford had been able to duplcate some other accepted result.. Has he taken care to elmnate some of the obvous errors one expects n ths knd of low-speed, coastng to rest test? Low-speed rollng s strongly affected by mnor (nvsble) slopes. (In the hallway at Cornell, for example, there was an nvsble dp that would clearly accelerate a rder.) Hs results lose force f ether (a) the paths dffer from tme to tme or (b) n gong down and up, some wheels stall whle others just manage to crest a rse and travel much further. Also, I wonder how the wheel s balanced and guded as t comes to rest. The normal way s to make a trcycle, but then there s an ssue of drag from the support wheels (partcularly f ther algnment s faulty). That support drag could perhaps be subtracted, but only f t was known wth hgh accuracy. In my own researches I had hoped to try casterng one of the two lghtly loaded support wheels, but never got around to t. Fnally some comments about condtons: Because the measurement was taken at low speed, then the hgh-speed calculatons should have a dsclamer. Kyle beleves there s a speed effect, for example. Turn to page Number 50, Sprng 000 Human Power Human Power Number 50, Sprng

9 Rollng resstance of tyres - test data John Lafford, Nov 1999 Generally avalable recumbent tyres (Butyl nner tubes unless stated) Rollng resstance power absorbed Unfared wgt = 185 lb/84 kg / Fared wgt = 00 Lb/91 kg Tme Test Prr Prr Prr Prr Prr Prr 5mph pres- Rollng 0mph 5mph 30mph 30mph 40mph 50mph over sure res coef. 3kmh 40kph 48kph 48kph 64kph 80kph 10 m. Tyre name Sze ps * Crr test watts watts watts watts watts watts sec. IRC Road Lte (new) 0" x 1 1/8" IRC Road Lte (new) 0" x 1 1/8" Cont Top Tourng (new) Cont Top Tourng (new) IRC Road Lte (old) 0" x 1 1/8" IRC Road Lte (old) 0" x 1 1/8" Mcheln Mcheln Toga Comp Ramp (new) 0 x 1 7/ Toga Comp Ramp (new) 0 x 1 7/ Hutchnson HP Hutchnson HP Hutchnson HP Cont Top Tourng (new) Cont Top Tourng (new) Cont Top Tourng (new) Cont Top Tourng (new) Mcheln (450 x 8A) Mcheln (450 x 8A) Cont Grand Prx (new) Cont Grand Prx (new) Cont Grand Prx (new) Vee Rubber (new) 0 x Vee Rubber (new) 0 x Vee Rubber (new) 0 x Prmo 16 x 1 3/8 (new) Prmo 16 x 1 3/8 (new) Prmo 16 x 1 3/8 (new) Toga Comp Pool (new) 0 x Toga Comp Pool (new) 0 x Toga Comp Pool (new) 0 x Toga Comp Pool (new) 0 x Kenda w. tread ground off 16 x Kenda w. tread ground off 16 x Kenda w. tread ground off 16 x Mcheln Hlte S'compHD 650 x 0c Mcheln Hlte S'compHD 650 x 0c Mcheln Hlte S'compHD 650 x 0c Hutchnson HP 5 "600A x 4""" Hutchnson HP 5 "600A x 4""" Hutchnson HP 5 "600A x 4""" Prmo V Monster (new) 0 x Prmo V Monster (new) 0 x Mcheln 600 x 8A Mcheln 600 x 8A Prmo w/ground off tread Prmo w/ground off tread Prmo w/ground off tread Prmo w/ground off tread Prmo w/ground off tread Moulton Wolber lne tread (new) 17 x 1 1/ Moulton Wolber lne tread (new) 17 x 1 1/ Moulton Wolber lne tread (new) 17 x 1 1/ Prmo w/ground off tread, latex tube * 1 bar = 14.5 ps; 1 m/s = 3.6 kmh; compared wth the tme usng the tyre (at the same power nput) wth lowest Crr, the last entry n the table 16 Number 50, Sprng 000 Human Power Rollng resstance power absorbed Unfared wgt = 185 lb/84 kg / Fared wgt = 00 Lb/91 kg Tme Test Prr Prr Prr Prr Prr Prr 5mph pres- Rollng 0mph 5mph 30mph 30mph 40mph 50mph over sure res coef. 3kmh 40kph 48kph 48kph 64kph 80kph 10 m. Tyre name Sze ps * Crr test watts watts watts watts watts watts sec. Prmo w/ground off tread, latex tube Prmo w/ground off tread, latex tube Vredesten Monte Carlo (new) Vredesten Monte Carlo (new) Vredesten Monte Carlo (new) Hutchnson 600 x 8A Hutchnson 600 x 8A Cont Grand Prx w/latex tube Cont Grand Prx w/latex tube Cont Grand Prx w/latex tube Schwalbe Spezal Cty Jet (used) Schwalbe Spezal Cty Jet (used) Nokan Cty Runner (new) Nokan Cty Runner (new) Nokan Cty Runner (new) Nokan Mount & Cty (new) Nokan Mount & Cty (new) Nokan Mount & Cty (new) Nokan Mount & Cty (new) Nokan Mount & Ground (used) Nokan Mount & Ground (used) Nokan Mount & Ground (used) Schwalbe Cty Jet (new) Schwalbe Cty Jet (new) Schwalbe Marathon (new) Schwalbe Marathon (new) Schwalbe Marathon (new) Vredesten Monte Carlo (used) Vredesten Monte Carlo (used) Vredesten Monte Carlo (used) Nokan Mount & Cty (new) Nokan Mount & Cty (new) Prmo 0 x 1.5 (used) Prmo 0 x 1.5 (used) Prmo 0 x 1.5 (used) IRC Roadlte 0 x 1 1/8 (used) IRC Roadlte 0 x 1 1/8 (used) Prmo Comet Prmo Comet Mcheln (used) 600 x 8A Mcheln (used) 600 x 8A Contnental Grand Prx (used) Haro (used) 0 x Haro (used) 0 x Haro (used) 0 x Haro (new) 0 x Haro (new) 0 x Noka Mount and Cty (new) Noka Mount and Cty (new) Noka Mount and Cty (new) Noka Mount and Cty (new) Vredesten S-Lck (new) Vredesten S-Lck (new) Vredesten S-Lck (new) RECOMMENDED 700C TYRES FOR REAR WHEELS for comparson. Very good performance at reasonable prce. Noka Roade (used) 700 x 5c Mcheln Axal Supercomp Vredesten Fortezza Pste 700 x 3c 10 bar * 1 bar = 14.5 ps; 1 m/s = 3.6 kmh; compared wth the tme usng the tyre (at the same power nput) wth lowest Crr, the last entry n the table Human Power Number 50, Sprng

10 What was hs load? Representatve probably means t was 45 kg, but t would be nce to know for sure. None of ths s meant as drect crtcsm of Lafford s careful efforts, but rather as an nvtaton to dscuss some vtally nterestng ssues! Jm Papadopoulos Reply to note by Jm Papadopoulos, approxmately n the order of hs questons, Tres tested. The number of tyres tested s approachng 400 and I have tested tyres of all szes. The artcle was focused on small-dameter tyres as they are of partcular nterest to HPV rders. I ncluded three good 700C tyres of good value. Repeatablty 1. If I run a tyre up the track and t runs 0' 3" (say), and then I repeat t straght away and follow the exact same pece of the floor, then t also wll run 0' 3". If the drecton s a bt off then the dstance wll be slghtly dfferent due to the slght mperfectons n the floor.. If I were to repeat the test on that tyre on another day, then I mght not have exactly the same pressure n the tyre by 1 or ps, and the temperature would probably be dfferent and so there would be a slghtly dfferent result. I have a smple test for ths type of repeatablty, where I have a partcular Mcheln tyre whch I run from tme to tme. Ths has shown over a perod of 18 months and 7 test sessons that the Crr value s repeatable at to ± and the power absorbed at 5 mle/h to be 47 watts to ± one watt. I have always rounded the power-absorbed fgure off to a whole number as t would be unreasonable to assume better accuracy than ths. Averagng Jm Papadopoulos clearly apprecates some of the practcal problems n runnng the tests. Yes, the floor does have very slght undulatons n t. To cater for ths, n the area avalable, I ran the tyre-test rg backwards and forwards n many drectons to fnd a lne that gave the same rollng dstance, runnng n both drectons. Then, to cope wth the very slght undulatons n the floor, the floor s marked out at 4' ntervals from the start pont of the test run. A stop watch s used and the tme recorded for the test rg to pass the 4', 8', 1', 16' 0' 4', 8' etc. markers. In the coast-down test, the retardaton should be completely unform, and so several of the 4' zones are averaged to gve a mean average retardaton. Ths avods any errors caused by crestng or falng to crest a slght rse at the end of a test run. Comparng my data wth other sources There are some better 700C than those I lsted, but I dd not nclude these as they are more expensve and less durable. There are many 700c tyres a whole lot worse. The Moulton data are for the lne tread tourng tyre, not the hgh-pressure slck. I am not lookng to repeat other people s results. It would be relevant only f I had the same tyres that they had used. The test wheel/tyre s ftted to a trcycle. The two other wheels are perfectly algned, I know ther rollngresstance coeffcent and they are only lghtly loaded. Even so, ther rollng coeffcent and load and drag components are taken nto account. The weght on the test wheel s 66 lb. Ths s representatve for three wheelers, whch many HPVs are, but s lght for a two-wheeler. It s chosen for convenence of nstallaton and the number of tmes I have to pck t up and load t onto the trke test rg. Further, I have tested wth a heaver weght and got a very smlar result. As long as all my tests are done under the same condtons then the results are properly comparatve. Most of the appled weght s drectly on the test wheel. It cannot be exactly on t because the trcycle would not then be stable. However, as the poston s known, moments are taken, and the exact weght used n the computatons. John Lafford TECHNICAL NOTES Power requrements for lad-back recumbents Report and comment by Dave Wlson, wth translaton help from Jan Lmburg and Ellen Wlson. Ths s an nterpretaton of the hgh ponts of an artcle by Bert Hoge and Jeroen Schasfoort n HPV neuws no. 4, 1999, the magazne of the Netherlands NVHPV. Its topc s the use of an SRM nstrumented crank (gvng torque) on a regular racng bke and on fve recumbents. All of the recumbents were of the very-lad-back varety, havng seat-back angles wth the horzontal of down to 15 degrees (see photos). All of them had the bottom-bracket consderably above the lowest part of the seat: I beleve that ths s mportant because whrlng legs normally gve a hgh drag, and havng them n the forward shadow of the body must reduce ths drag. The authors wrte, A smaller frontal surface gves less ar resstance and hgher speed. It can be acheved by ncreasng the heght of the bottom bracket above the lowest part of the seat to about 70 mm (10.6"), and reducng the seat heght to about 50 mm (9.8"). (These are approxmately the relevant measurements of the M5 Low Racer.) All sx bcycles were rdden by one tester, Dres Baron, weght 90 kg (198 lb.), heght 1.86 m. (6'1", almost a mdget by Dutch standards) wearng racng clothng, on a 00-m-long velodrome track, presumably oval or crcular. Ten crcuts ( km total) were made for each test pont. All bcycles used Contnental Grand- Prx or IRC tres pumped to about 8- bar pressure (116 ps). Two speeds were chosen: 30 and 40 kmh (18 and 5 mph), and the cadence was kept to about 88 rpm. The temperature was about 15 C, 59 F. The measurement accuracy was reckoned to be ±% (see graph, fgure 1). The racng or road bke was rdden n the tourng poston, whch I beleve meant that the hands were on top of the handlebars, rather than the rder beng n a full crouch. All of the recumbents requred less power to propel them than dd the regular racng bke n ths confguraton. The reducton appeared to be a functon of how low the rder was (see photos). The lowest power of the unfared recumbents was needed by Bram Moens M5, whch at 40 kmh took 8 W, whle the racng bcycle requred 389 W nput. The fully-fared M5 requred less than 130 W at the same speed. (Table 1) These results can be compared wth the aerodynamc drag measured n the Tour tests of statonary bkes n the wnd-tunnel and on bkes beng rdden on a velodrome, revewed n Human Power, 1:4, sprng There s general qualtatve agreement, although only the fared M5 and the regular bkes were common to both tests. The LWB Peer Gynt wth low bottom-bracket was found to have a hgher drag than that of a regular racng bke wth the rder n a full crouch. Because of the dfference n the rder postons on the racng bke, the prncpal nterest n the results shown here s n the dfferences among the recumbents, and n the accuracy of actual power measurements taken on dfferent bcycles wth the same rder on the same crcut wth smlar tres. These are very valuable data. Thank you, Bert Hoge, Jeroen Schasfoort and the NVHPV! Dave Wlson Table 1: Power requred to propel bcycles Expected Bcycle type or name Power, watts ncrease 30 kmh 40 kmh n speed* Racng bke, tourng poston % Optma Dolphn % Flevobke % M % Baron Low Racer % Moens (M5) Low Racer % *Relatve to racng bke Fgure. Bcycles tested. Optma Dolphn Flevobke Ffty Ffty M5 0 0 Baron low racer M5 low racer Fgure 1. Power (watts) requred vs. speed (kph). Photos and chart courtesy HPV neuws; prepared for Human Power by JW Stephens 18 Number 50, Sprng 000 Human Power Human Power Number 50, Sprng

11 Fgure 1. Blade-element veloctes My propeller theory by E. Eugene Larrabee In 1978 I developed a useful form of propeller theory based on the work of Hermann Glauert (196 and 1938) and Sdney Goldsten (199). It was successfully appled to the propellers of the Chrysals and Gossamer Albatross human-powered arplanes n 1979, and (n reverse) to wndmlls for US Wndpower, Inc. n It s related to lftng-lne theory as developed by Ludwg Prandtl and hs assocates at Göttngen durng World War I. In t an nduced velocty s developed parallel to the blade lft drecton and perpendcular to the relatve velocty of the blade secton wth respect to the ar mass as shown n fgure 1. The flght (or axal) velocty, the rotatonal velocty, and the nduced velocty combne to produce the resultant velocty. The nduced velocty s caused by lft on each blade secton due to bound crculaton accordng to the Kutta- Joukowsk Law. Strangely enough, f the nduced velocty s small enough compared to the axal velocty t can be shown that the nduced loss of the propeller s mnmzed f the vrtual slp velocty s radally constant, correspondng to a certan radal varaton of the bound crculaton. As Albert Betz, Prandtl s assocate,wrote n 193 (NACA TR 116), The flow behnd a propeller havng the least loss of energy s as f the screw surfaces passed over by the propeller were soldfed nto a sold fgure and ths were dsplaced backward n the non-vscous flud wth a gven small velocty. The small dsplacement velocty s exactly twce Fgure. Blade radal-lft dstrbutons the vrtual slp velocty. I calculated the radal bound crculaton dstrbutons for mnmum nduced loss by a process suggested by Glauert n The dstrbutons are functons of the advance rato and the number of blades as shown n fgure. They correspond to ellptc span loadng for a wng. Apparently these crculaton dstrbutons are slghtly n error, as suggested by Goldsten n 199 and by my former student, Mark Drela, n 198. In any event they were good enough to form the bass of a Fortran code wrtten by Hyong Bang n 1978 to defne the blade chord and ptch angles for the Chrysals and Gossamer Albatross arplanes so that they had not only mnmum nduced loss but also mnmum profle drag by choce of blade secton and lft coeffcent at the desgn pont. They were propellers of hghest effcency n Glauert s words. At the relatvely low advance ratos of these propellers they are characterzed by narrow outer blade chords and wde nboard ones wth strong twst, havng almost true geometrc ptch, as shown n fgure 3. The same s true of the US Wndpower wndmlls generated by a later Fgure 3. Shape of wndmll blades produced by these methods. Fortran code HELICE, wrtten by Susan Elso French at MIT. In the case of wndmlls the dsplacement velocty s aganst the wnd drecton and the more curved portons of the blades are downwnd. They were ntended to leave a mnmum hole n the ar for a gven power output for the average wnd speed of a wndfarm of many wndmlls. Snce then Prof. Mark Drela has developed hs own XROTOR code whch s a fnte-element adaptaton of Goldsten s 199 paper. XROTOR was used to desgn propellers for the Monarch and Daedalus arplanes. French s HELICE code was rewrtten n Pascal as ELICA by Robert S. Grmes n a form sutable for IBM PCs n 198. Both Prof. Ernst Schoberl and I have used ELICA for many years personally. I publshed my algorthms n I am told that AeroVronment uses a form of them to desgn propellers for ther arplanes ncludng the Pathfnder, whch holds the alttude record for propeller-drven arplanes. E. Eugene Larrabee, professor emertus, MIT 1800 Knoxvlle Avenue Long Beach, CA USA November 1999 REVIEWS Feet On! a pedal-powered museum exhbt By Mchael Elasohn A bcycle s a relatvely smple mechansm. A frame holds two wheels. A chan runs from the chan-rng to the sprocket attached to the rear wheel. Turn the pedals and the bke moves. But how do you get those pedals to power a televson or an organ, to lght up lght bulbs or create a vacuum, to blow 300 png-pong balls around nsde a chamber, or a movng sculpture, whch conssts of twelve bcycle wheels mounted on the wall? That was the challenge facng Tom Caskey, scence exhbt desgner at the Southwestern Mchgan (communty) College Museum near Dowagac, MI. Caskey desgned and, wth some assstance, made the exhbts for the museum s Feet On! The Power of Pedalng exhbt, whch ran from March 9 to June 1, He sad he and other museum staff members came up wth the dea for the exhbt. Among the challenges n creatng t was a budget of less than $1,000. So many of the peces, such as bcycles and exercse bkes, were purchased at a Goodwll store (whch sells secondhand goods) and at rummage sales. Some tems were donated. A lot of creatvty was used. For nstance, the organ parts were purchased at Goodwll, but the exhbt also used a metal trash can, garden hoses, a bellows from a prevous museum exhbt and a bcycle pedal mechansm. The squrrel-cage blower that moves Mchael Elasohn 3) Marta Englsh of Edwardsburg, MI, pedals the lottery exhbt. A squrrel-cage blower blows ar nto the chamber, to put 300 pngpong balls nto moton. Wnnng requred puttng the sx red balls nto the egg-carton pockets. the png-pong balls around came from a furnace. I had a blower..., Caskey sad n explanng how he came up wth the dea. What are you gong to do wth a blast of ar? I wanted somethng so that as people walked n the door, they could see a lot of acton. But the 300 png-pong balls blown around n the clear plastc-walled chamber dd more than move around. There were 94 whte balls and sx red ones. What were the odds of gettng all the red ones to land n the sx pockets, whch was half of an egg carton?...about the same as wnnng the lottery, the accompanyng sgn stated. Caskey sad he ddn t expect anyone would beat the odds durng the lfe of the exhbt, whch taught vstors probablty and that t was unlkely they wll ever wn a lottery. The devce that shot a spark across a gap, to show that ar s an nsulator and the absence of ar sn t, presented the opposte problem. Caskey adapted an old refrgerator compressor to act as a vacuum pump, to remove the ar from nsde a clear-plastc dome. The televson could be powered by one or two people sttng on a couch. The pedal mechansms were two former exercse cycles, wth the chans runnng to flywheels, and V-belts runnng from there to a generator. To prevent one or two strong pedalers from overpowerng the televson, Caskey hooked up an electromagnetc brake desgned for tralers, whch acted on a dsk on the generator shaft, makng t mpossble to blow up the televson. The other two pedal-powered exhbts were four lght bulbs the harder one pedaled, the more bulbs lt up and a sculpture consstng of twelve bcycles wheels mounted on a wall, lnked by ropes and chans, so that pedalng made the wheels rotate. Caskey sad a challenge n creatng the pedal-powered exhbts was that they had to accommodate, n terms of muscles, everyone from lttle kds to football-player-szed men. It s got to be responsve for both. To accommodate varous-szed rders, Caskey made super-long banana seats for some of the exhbts. ) Lesle Gerschoffer (rear) and Marta Englsh pedal what were exercse bkes, whch power a generator whch powers the televson set they are watchng. The TV could be powered by one or two people. The mechansms of the pedalpowered exhbts for the most part were exposed, so vstors could see how everythng worked. These are purposely made kd-understandable, sad Caskey, whose museum job s part-tme. The Feet On! exhbt was located n the part of the SMC Museum, to paraphrase from ts fler, devoted to hands-on scence and technologcal exhbts that nvestgate scentfc prncples and the technologcal world that surrounds us. The sgn at the entrance read: Ths exhbton s an exploraton of energy transformaton. The exhbts demonstrate how your energy s converted nto other forms wth nterestng outcomes. You use chemcal energy (namely food and drnk) to feed your muscles they are energy transformers. Your muscles allow you to move and gve you the ablty to move dfferent thngs. Makng the exhbts pedal-powered was a means to make them hands-on, or more correctly, feet-on. You re really nvolved, Caskey sad. The 59-year-old Caskey, whose background ncludes product and graphc desgn, makng dulcmers and buldng a house, recently earned a master s degree n scence educaton at Western Mchgan Unversty and wants to get a doctorate n the same topc. The Feet On! exhbts llustrates Caskey s goal of makng scence learnable by beng fun, not just by learnng facts. You can learn physcs and subtlety and have fun..., he suggested, or you can thnk scence s dumb stuff. Mchael Elasohn 0 Number 50, Sprng 000 Human Power Human Power Number 50, Sprng 000 1

12 Mchael Elasohn 4) Tom Caskey, desgner/bulder of the Feet On! exhbt, pedals the exhbt that shot a spark across a gap nsde a vacuum. The long banana seat enabled the exhbt to accommodate varous-szed rders. Tom Caskey can be contacted by e- mal at or by mal to Southwestern Mchgan College Museum, Cherry Grove Road, Dowagac MI USA Mchael Elasohn s a reporter for The Herald-Palladum newspaper n St. Joseph, MI. Portons of ths artcle and some of the photographs, all taken by the author, orgnally appeared n that newspaper. Human Power: the forgotten energy (ISBN: ) by Arnfred Schmtz, wth Tony Hadland The last ssue of Human Power, no. 49, led wth an ntrgung artcle by Arnfred Schmtz: Velocar varatons, n whch he brefly descrbed around ten recumbents he had bult. Hs bographcal note states that he worked n shpbuldng and as a mechanc as a West German student, and later he settled n France and became enthusastcally nvolved n the HPV movement and ts gurus across Europe. He descrbed hmself as beng known as the goatherd from Provence. Arnfred Schmtz had earler become known to readers of Human Power through hs hstorcal authentc (almost an nsder s) account Why your bcycle hasn't changed for 106 years (vol. 11 no ). All ths made hm somethng of a mystery man. Ths small book 18 pages whch he was knd enough to send me, explans a great deal, n a delghtfully casual, modest, yet deeply felt way. We learn ncdentally that he s a farmer and rases goats, so that explans the goat-herd reference. However, almost nothng about hm s revealed n the frst nne chapters. These are devoted to a fuller re-tellng of the hstory of the early efforts to streamlne bcycles and to produce recumbents than I have prevously read anywhere. Here are some examples of detals of whch I wasn t fully aware. In Berln the frst nternatonal race for streamlned bkes takes place. (I beleve that was n 1913.) Charles Mochet sponsors a cup for the absolute hour record for human-powered vehcles regardless of type. (I beleve n late 1933 or early 1934). The Mochets were then professonally buldng cars and bkes, what we would today call Human-Powered Vehcles [The] Mochets bult mn-cars from 190 to They constructed some 6,000 pedal-cars between 195 and They bult about 800 [recumbent bkes] between 193 and In 193 the VV [Velocar] was awarded frst prze n the nventors Grand Prx Lepne for ts ndrect steerng for recumbent cycles [usng a unversal jont ]. There are also detals of how Georges Mochet heard about the Aspo Speed Challenge at Brghton UK n 1980 (stmulated by the annual IHPVA speed champonshps) and traveled there wth a verson of the Faure recordbreakng Velocar of 1933, but, states Schmtz, no one knew anythng about t or the Mochets. But Schmtz read about the races and about those n the U.S.A. n the French bcyclng magazne Le Cycle, and became excted by the potental. From then on the book becomes partly autobographcal, as he descrbes how he tred buldng recumbents, partly for others and partly for hmself and hs son Jurgen. (He had some dffculty persuadng hm to rde the machnes.) But the detals of hs and hs famly s HPV actvtes often takes a mnor role because Arnfred Schmtz gves nsghtful detals of many others. For nstance, the complex character of the late Wolfgang Gronen comes alve: he s gven a great deal of credt for promotng bcycle and HPV racng n Europe, as well as havng a few warts exposed. Tony Hadland, who has wrtten very fne books on Brtsh portable bcycles, on space-frame Moultons and Sturmey- Archer gears, has desgned and publshed ths book. It s obtanable from Amazon.com or by drect mal from Arnfred Schmtz, Quarter Gallas, 840 Loux Gordes, France: 140 francs, or from Rosemary Hadland, 39 Malvern Road, Balsall Common, Coventry CV7 7DU, UK. In Brtsh pounds t s UK 1.95; Europe (armal); rest of the world (armal). The book sn t a dry hstory book but rather s a lvng document (wrtten a lttle strangely n the hstorc present tense), and t sn t precse about everythng about whch we d lke to know more, but I m sure that we ll hear agan from the author. Every enthusast for HPVs should read ths book. Revewed by Dave Wlson LETTERS Supplement to Velocar varatons by Arnfred Schmtz A key pcture for ths artcle n HP 49 (wnter ) was unfortunately lost between France and the USA. Here t s, wth our apologes. It was publshed n the French sports press to llustrate the Velodrome d Hver event on February 0, 1934 n Pars. Ths was the very moment that a recumbent was recognsed as legal by the Unon Cyclste Internatonale. The rder of the Velocar, Francs Faure, was a young well-known track cyclst of the tme, but he was certanly far from beng a champon. Here he s photographed passng a champon, Henry Lemone, n the pursut race. I want to make another comment on an aspect of bcyclng that became more obvous durng my rdng varous bcycles as I was workng on the artcle: rdng n a dead straght lne s mpossble whle pedallng, whether on an uprght or a recumbent. We rde n a wavy lne, as we can see when we have wet tres on a dry road or when we rde n snow. What s wrong wth our supposedly perfect machnes f they don t want to go straght? Is t because we use our legs alone and don t balance wth our arms as we do when walkng or runnng? What do you thnk? Arnfred Schmtz, Quarter Gallas, Loux, Gordes, F840 France, 4 March 000 EDITORIAL Ronald van Waveren (translated by Ellen Wlson) I d lke to ntroduce myself to you. I am Ronald van Waveren, 48 years old, father of two grown chldren and, for four years, charman of the NVHPV (the Dutch HPV assocaton). In comparson wth many other HPV assocatons n the world, the NVHPV has grown consderably n the last few years. Perhaps ths s thanks to our recumbent-frendly nfrastructure our country s flat, wndy and has a lot of bke-paths and to the ncreasng use of recumbents n the Netherlands. It s estmated that there are more than 5,000 recumbents here at ths tme. The NVHPV has almost 1600 members, and recumbent owners and rders represent the largest percentage of members. Orgnally ths was an organzaton made up of recumbent desgners and bulders, followng the Amercan example. But snce the recumbent has now been made avalable as a serous commercal product through dverse factores, the number of recumbent owners has ncreased proportonately wthn the membershp. The NVHPV wants to be n the lmelght, but ts objectve should be to stmulate the development and promoton of the use of HPVs n general. And ths s constraned by our allegance to the recumbent. We organze actvtes such as presentatons at fars; compettons n the summer and warm-up days n the wnter; NVHPV annual meetngs n assocaton wth a number of smaller state-run events; and a large nternatonal recumbent-promotonal event called Cycle Vson. It s on the topc of Courtesy Arnfred Schmtz ths last event that I d lke to ask for your attenton. Cycle Vson, for the fourth successve tme, wll be held early n June, on the weekend of June 3rd and 4th, 000. It wll agan be located n Lelystad, on the government s testng grounds for hghway vehcles. There wll be many actvtes on ths area. A sngle tent of 1000 m can hold all the dsplays of new products of Dutch and foregn recumbent companes. Under the same roof there wll be presentatons and demonstratons, and a smultaneous secondhand market. If one s nterested n a certan vehcle, new or used, one can take test rdes on a specal adjonng parkng lot. Announcements of all events, together wth cool musc, are broadcast over loudspeakers. Internatonal compettons wll be held on the 700-m test-track wth adjacent accommodatons. One can enjoy crterums, 00-m sprnts, devl-takethe-hndmost drag races, one-hour tme trals and a sx-hour race. Cash przes totallng NLG10,000 (over 4500 n US dollars or n Euros) wll be gven out for all dstance races. On ths preemnently sutable road and n ths nternatonal framework a real effort was made n an earler Cycle Vson to break the world hour record (over 80 km/h). For ths attempt, foregn teams, among them those from Germany, Brtan, Belgum, France and Holland, partcpated when weather condtons allowed. New ths year are the sngleclass crterums such as Thys Row- Bke, Flevo s All-Weather (Alleweder) and Challenge s Hurrcane. Cycle Vson s easly accessble by tran from Schphol Amsterdam arport to Lelystad. A bus for Harderwjk wll Francs Faure passng Henry Lemone n a UCI-sanctoned pursut race at the Velodrome d Hver n Pars, February take you to Lelystad arport, and a Cycle Vson shuttle bus wll take you the last 3 km. There s also adequate parkng. For those who want to vst the event for both days there are overnght campng stes at The Oppertje. Lelystad also has hotels, B&Bs etc. The prce of admsson s only NLG7.50 per day. In 1998, Cycle Vson, an organzaton wth more than one-hundred volunteers, attracted 3000 vstors and more than 100 compettors. In 1999 t had 1000 m of exposton space, a recumbent-clothng style show; a toddlers actvty area; a chldren s recumbent tral/obstacle course; 000 m of adult recumbent tral/obstacle course wth all of the Netherlands avalable recumbents; and the awards for a large desgn competton, the Bke 000 Constructon Contest (lkewse an NVHPV ntatve). See for more nformaton. We Europeans, realzng that a trp to the European contnent s not wthn the reach of every non-european, nevertheless nvte all HPV enthusasts from every part of the globe to take part as compettors or spectators n Cycle Vson 000, a sensatonal feast that s a true bke revval. Cycle Vson s an ntatve by the Dutch HPV assocaton that has become an annual happenng, whch you as an enthusast cannot afford to mss. Edtor s note: Delays to the publcaton of ths ssue means that Ronald van Waveren s descrpton of Cycle Vson has come too late to persuade readers to travel there ths year, but we hope that a record number wll vst ths wonderful event next year. Dave Wlson Prase from IHPVA s founder, Chester R. Kyle I just got my copy of Human Power, and t s one of the best ever content, photos, graphcs, edtng, etc. Congratulatons. Keep up the good work. Best Wshes, Chet Number 50, Sprng 000 Human Power Human Power Number 50, Sprng 000 3

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