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Home , Derailleur, Hub gear

Efficiency Measurements of Transmissions - a neverending Story? by Bernhard and Peter Greb (translated by Thomas Siemann)

In Human Power 52 (Summer 2001) order to level off friction losses from the always one more gearset active than in the there was a report of an efficiency test of seals. Rohloff has determined this to be higher seven . Therefore, the losses bicycle transmissions “The Mechanical extremely important for tests under in the higher seven gears must be smaller Efficiency of Bicycle and Hub- 200W; this will be discussed later in this than the losses in the lower seven gears. Transmissions” by Chester. Kyle document. PhD, and Frank Berto. The test included Table 3: Active gear sets in the Roh- 2. Precision of measurement – loff SPEEDHUB 500/14 for each gear. three derailleur systems with from 4 to 27 The results are shown as absolute values gears as well as eight gear hub trans- with no information about the tolerances Gear 1 2 3 4 5 6 7 8 9 10 11 12 13 14 missions with from 3 to 14 gears. The of the measurements. Only the precision No. of results of the test are summarized in the active 2 2 3 1 3 2 2 1 1 2 0 2 1 1 of the dynamometer and the tachometer gearsets table below: were given without any information about Table 1: Derailleur and gearhub the width of the measuring range and the There are three planetary gear sets efficiencies measured related tolerance variations. The linked in series in the SPEEDHUB by Kyle and Berto. ergometer wheel produced variable losses 500/14. The single gears are the result of different combinations of gears within Transmission Efficiency of over 2% with different loads. The Type: (%) ergometer wheel losses at different speeds those three gearsets. 87-97 were not measured. However this is The efficiency variations of the Gear Hubs 86-95 important when evaluating transmissions four speed, Shimano seven Note: Test performed with 80W, with a large range of gears such as the 27 speed, and Sturmey-Archer 7 speed 150W, 200W input. speed derailleur system or the Rohloff transmissions do reflect the construction of the transmission. The motivated reader of the report will SPEEDHUB 500/14, because the speed find contradictions behind their measure- differences between the smallest and largest gear are more than 500%. 4. Validity – The validity of the testing ments. Our specific interest in giving a method. The measurements made by critique of the publication is based on 3. Plausibility - The report regarding Kyle and Berto were performed while differences of the results compared to our the gearhubs states correctly that the applying constant with power input efficiency measurements. These can be efficiency of planetary gear systems drops at 80W, 150W, and 200W. Those loads summarized as follows: as the number of active gears increases. were meant to reflect a typical bicycling This fact should reflect itself in the Table 2: Derailleur and SPEEDHUB situation. Rohloff does not believe that the 500/14 efficiencies as measured by measurements of the efficiency of the loads or the power applied sufficiently Rohloff. gearhubs. model a typical cyclist. The power The speed-ratio of the Sachs three produced by the cyclist consists of a Transmission Efficiency speed hub is reducing in gear one, relatively constant speed and widely Type: (%) increasing in gear three, and direct drive variable torque due to the crank kine- Derailleurs 95-98.5 in gear two. Unlike gears one and three, matics. Measurements show that while there shouldn’t be any gearing losses in speed variations of about 5% are typical, SPEEDHUB 500/14 95-98.5 gear two. At 80W the measured effi- the torque variations can be over 90% Note: Test performed with 400W ciency of gear two is much lower than throughout a single crank revolution. input. those of gear one and gear three, which is Table 4 shows the results at different not evidently plausible. At 200W the The lower range of Kyle and Berto’s power inputs. results are very similar in all three gears measurements are up to eight percent with efficiency values of 94.1%, 94.9%, Table 4: Maximum and minimum lower than those made by Rohloff. The and 94.1% for gears one, two, and three torque measurements during a reasons for this are presented in this respectively. pedal stroke. document. The trend shown that the efficiency of 1. Verifiability - The text does not say the SPEEDHUB 500/14 drops in higher Power input (W), 100 W, 300 W, 575 W, if only single measurements were per- gears is also in contrast to the design of Speed (rev/min) 75 rpm 75 rpm 50 rpm formed or if the measurements were con- the transmission as well as the fact that Max. Torque 21.6 68 200 firmed by repeated measurements. Fur- gear four and gear nine are more efficient (N·m) thermore, there is no information about than the direct drive gear eleven. In gear Min. Torque 3.8 8 20 the duration of break-in time the testing eleven there cannot be any gearing losses (N·m) samples underwent. This is especially since no planetary gears are rotating, important for hubs with dragging seals unlike in all other gears. As can be seen The power characteristics are largely which need a minimum run-in time in in Table 3, in the first seven gears there is governed by the torque component.

Human Power Number 55 11 test bench power of 160W at the Table 6: System 'B' power loss same speed. components. 5. Interpretation of the Input Power 50 100 200 300 400 500 measurements – In order to (W) give a correct interpretation of the Power results it is important to establish depen- dent 1.5 3 6 9 12 15 what the losses are composed of. losses Losses are created by friction. (3%) (W) Power The value is determined by the indepen- type of friction (rolling or dent 3 3 3 3 3 3 sliding), the size of surfaces in losses (W) contact, type of surface finish, Total 4.5 6 9 12 15 18 material hardness, lubrication, loss (W) combination of the rubbing parts. Total efficieny 91 94 96 96 96.3 96.4 Figure 1: Torque vs. crank angle for Two separate types of losses exist (%) one crank revolution. in bicycle transmissions: In system B, only three percent of the Power is area under curve. A) Power dependent losses. These are input power is lost due to power The cyclical torque of a cyclist pro- created by friction of parts that are dependent friction that exists in the chain, duces an alternating load situation on all moving under a driving load, i.e. gears, etc. An additional 3 W of power is power transmitting parts, chainlinks, chainlinks, gears, bearings, etc. The lost due to power independent friction that chainrings, bearings, gears, etc, which is quantity of the loss grows propor- exists due to tight seals. very important to keep in mind when tionally to the transmitted power. At 50 W power input the efficiency of evaluating the mechanical losses which B) Power independent losses. These system ‘B’ is at 91%, the same as system effect the efficiency. losses are created by friction of ‘A.’ At higher power inputs, the overall A precise simulation of the cyclical moving parts and are not changed by efficiency increases until it reaches 96.4% torque is not easy to produce in the the driving load, in other words these the efficiency is significantly higher than laboratory and from a measuring point of losses are constant regardless of the the efficiency of system ‘A.’ This is due view, excessively costly. For this reason load applied, e.g. Gaskets and shims. to the fact that the power dependent losses electric motors with a constant power With lubricants, the quantity of loss become dominant over the power input are used. This brings up the depends on speed, temperature, and independent losses at higher power inputs. question of how to choose the appropriate lubricant viscosity. Figure 2: Total efficiency of system power input when using a constant torque In the following example, two bicycle A through D. so that the efficiency measurement transmission systems are compared. correlates to the efficiency that would be Both have a 91% efficiency at 50W measured with the cyclical load actually input. They have two different power applied in the real world. dependent and power independent We encountered a similar problem losses. when designing our chain and chainring wear test, which is operated at constant In system A, seven percent of the in- put power is lost due to power depen- torque. Extensive comparisons between components used in real world and dent friction plus one Watt of power independent friction for each value of components worn out on the test bench showed the following: If the field-tested input power. The values shown in Table 5 are input powers from 50 W to components were used at an average of 150 W with an average cyclic torque 500 W with their respective efficiency ranging from 91%-92.8%. between 5 Nm and 30 Nm, this correlated In addition to curves for systems A to a chain tested at a constant torque of 30 Table 5: System 'A' power loss and B, Figure 2 also shows curves for Nm in our laboratory. components. systems C and D. The curve for system C It can be assumed that the reasons that describes how the power independent Input 50 100 200 300 400 500 cause the wear of components are the Power (W) losses increase from one to two Watts due same ones that are responsible for the effi- Power de- to temperature or lubricating film changes pendent 3.5 7 14 21 28 35 at the seal of system A. The curve for ciency. Therefore you can deduce from losses the comparisons that a in a lab test, a con- (7%) (W) system D describes the efficiency changes stant power input using the maximum val- Power in- of system B with a reduction from three to dependet 1 1 1 1 1 1 two Watts of the power independent loss ue of the cyclic load produces results that losses (W) are closer to reality than choosing a con- Total loss for the same reason. The examples show 4.5 8 15 22 29 36 stant power input using the average load. (W) that for power input of less than 200 W Total For example, an average power efficiency, 91 92 92.5 92.7 92.75 92.8 that even small changes of +/- 1W of 80W in real life should be simulated by a (%) power independent losses play a large role

12 Number 55 Human Power in the overall efficiency. Since power efficiency of 93%. Rider B is using an to Kyle and Berto’s results, our results in independent losses are the result of a unfavorable gear with a high efficiency Figure 3 and Figure 4 show our efficiency complex relationship between speed of 97%., however, because of the un- measurements of a 24-speed derailleur changes, temperature changes (created by favorable speed, his muscles work at system with 46-36-26 toothed chainrings own friction heating), and lubrication. 22% efficiency. The overall efficiency and Shimano XT 11-28 toothed cassette, These variations can occur in the test shows taking into consideration muscle and the 500/14 with situation. If power input is less than 200 and transmission losses that rider A is a primary gearing of 46 tooth chainring W, it must be confirmed that the influence riding more efficiently even though his and 16 tooth hub cog. Both systems had of those variations are verified by repeated transmission efficiency is lower than been run in for 100 km. tests. Over 200 W the influence of power rider B’s. The measurements include the losses of independent losses can be neglected. In order to use the rider as a “bicycle the complete transmission, , Knowing that, all measurement values engine” most effectively, the ratio incre- chain, hubs, etc. In order to simulate a shouldn’t be absolute values, but rather ments between the gears are as important strong rider who applies about 160 W and represented as a range of values showing as a good mechanical efficiency. The produces a maximum torque of 50 Nm the corresponding upper and lower most efficient energy conversion is very (285 N @ pedal), the measurements were boundaries. limited using transmissions with only a taken at a power of 314 W with constant few gears. A larger selection of gears torque. 6. Reason for efficiency with smaller increments make a favorable measurements – The reason for effi- Table 8 energy conversion possible in a wider ciency measurements is to find out which range of riding situations, but only if the crank speed (rev/min) 60 one of the different bicycle transmissions correct gear is used. Sport medical re- converts the most of the bicyclist’s power brake power, constant (W) 314 search shows that the increments between into forward motion. To propel the rider gears must be smaller than 15% to bene- torque (Nm) 50 forward in the most efficient manner, it is fit the rider’s efficiency. important that the rider be able to choose Under this point of view it does not an appropriate gear for the given load or make sense to compare transmissions Figure 3: Efficiency of a 24-speed riding situation, a gear that is suitable to with only a few gears, large gaps, and drivetrain. the rider’s fitness level. small overall range, with The development of power in the transmissions with many muscles is subject to a grade of efficiency. gears, small increments, This efficiency is the ratio of metabolic and a large range of capacity and the delivered mechanical gears. A comparison of power, i.e. the power at the crank. The different transmission efficiency depends on the muscle power systems should always combined with the speed of movement, if take the application into both variables reach their optimum, the consideration. muscle efficiency can increase by 25%. [See also article by Too and Landwer in 7. Conclusions this issue. Ed.] A) All measurements The differences in muscle efficiency below 200 W need between positive and negative fatigue to be evaluated ratios (bodily stress/developed power) can cautiously because easily vary by 10%. This is of much larger the influences of the variations of the The reproducibility of the results and value than the variation of mechanical power independent losses are high. their precision was verified by repeated efficiencies of various bicycle trans- B) From a practical point of view chan- test runs. Figure 3 shows the efficiency of missions systems. ges of efficiency play a major role the derailleur system plotted vs. distance Table 7: Comparison of muscle and only when riding above the recre- per crank revolution. Note the gear ratios mechanical efficiency of the bicycle- ational level i.e. greater than 100W. are not consistently spaced as can be seen rider system. C) When comparing transmission on the plot. systems, gear range and number of The derailleur system was tested first in Rider A Rider B gears should be taken into consi- clean and well-lubricated conditions. In Muscle Efficiency (%) 24 22 deration in addition to the efficiency. order to achieve results closer to real-life use, the chain and the were re- Transmission Efficiency (%) 93 97 Rohloff measurement results – placed with components which had been Overall Efficiency (%) 22 21 We would like to point out that the points subjected to 1000 km of field use and had represented here should be a stimulus for not been cleaned. The average efficiency Rider A is using a perfect gear ratio for the a discussion since there are so many open was measured to be 1% lower than the situation and his muscle efficiency is 24%. questions in the field of practical clean drivetrain. The plot in Figure 3. His bicycle transmission is moving in a efficiency measurements of bicycle includes the data for a new and used gear with relatively poor mechanical transmission systems. As a comparison drivetrain and a +/- 0.5% uncertainty.

Human Power Number 55 13 Figure 5 shows the ef- Conclusion – The explanations show ficiency ranges of that efficiency of bicycle transmissions Figures 3 and 4 on the depends on many factors of which exact same plot for compari- measurements may involve prohibitive son. costs. In order to measure real-life values, The efficiency of inter- factors such as contamination, lubrication, nally geared hubs wear, and production tolerances should be drops when the num- included as well as sports medical re- ber of working plane- search. We think that there is still a lot of tary sets increases. room for tests and discussions. This fact must be shown in the efficiency About the Authors results of the gear hubs Bernhard Rohloff and Peter Greb can be Figure 4: SPEEDHUB 500/14 efficiency tested. In the SPEEDHUB 500/14 there reached at: are three planetary gear sets that can be Rohloff, Moenchebergstrasse 30, Figure 4 shows the efficiency range of the used in series. The unique gear ratios are D-34125 Kassel, Germany. Rohloff SPEEDHUB 500/14 plotted vs. created by engaging different combina- Translator Thomas Siemann is at: distance traveled per crank revolution. tions gears within these planetary sets. Rohloff USA in Berkeley, CA 94707 The increase between all gear ratios on the Table 3 shows the number of the active SPEEDHUB 500/14 is always the same (working) planetary gear sets per gear. Reply from Chester Kyle percentage. and chain were re- Figure 6 shows the range of efficiency of Dear Editor, placed by components ridden 1000 km. the SPEEDHUB 500/14 plotted vs. gear I have read Rohloff's remarks on our Efficiency differences were not measure- number. The efficiency plots confirms transmission efficiency tests and have able. The range of efficiency represents the number of the active planetary sets as several comments on their discussion. the used and unused drivetrain plus the +/- represented in Table 3. Gear 11 has the Our tests were run over a two day 0.5% uncertainty. highest efficiency because it is the direct period. It would have been better to test drive gear, no plane- repeatedly over longer periods, but this tary gearsets are acti- was not possible due to limited time and vated. The curve be- funds. However, we feel that the results tween gear 1 and 7 are valid under the conditions we tested. corresponds with the We understand the position of Rohloff, curve between gear 8 whose transmission did well in our tests and 14. This is due to when compared to other hub gears, but the fact that the first whose efficiency was about 2% lower than two planetary gear sets the derailleur transmissions. It's natural for are shifted between researchers to question the test methods of gears 1 and 7 in the others when results don't agree with their same way as they are own. However, the principle reason for the between gears 8-14, Rohloff's disagreement is the difference in however gears 1-7 applied power input between the two test Figure 5: Efficiency of both derailleur drivetrain have an extra planetary methods. We will comment more on this and Rohloff SPEEDHUB 500/14 gearset activated pro- later. Rohloff's laboratory efficiencies viding a compound were about 2% higher than ours, but this is low gear. The effi- understandable given their methods. ciency between gear 1- All of our transmissions were tested 7 is about 2% lower and compared under the same conditions. due to the use of the Our test efficiencies were repeatable to third planetary gear within less than one percent over two set. In order to show separate test sessions several months apart. this fact more clearly For the conditions we tested under, our the curve between gear methods were sufficiently accurate to dis- 8-14 has been copied criminate between transmissions and gears and shifted to the left and to rank order the efficiency of the so that it can be transmissions. All of the trans- compared with the missions were tested using light oil as a curve representing the efficiencies of lubricant. However, the Rohloff was new Figure 6: SPEEDHUB 500/14 gears 1-7. The results correspond to the and not worn in before testing. This could efficiency comparison. gear combination or respectively to the have affected the efficiency under low Gears 8-14 shifted to the left to number of active planetary gears inside loads, but probably not under loads of 200 compare with gears 1-7. the hub. watts or more.

14 Number 55 Human Power We chose to compare all of our trans- To summarize, we are reasonably ANNOUNCEMENT missions at 200 watts average load or less confident that the rank order between A new association, tentatively known and at a constant cadence of 75 RPM. transmission efficiencies that we found as the Human Power Institute (HuPI), has Ordinary hub gears are never used in would not change appreciably as load is been formed in order to promote the de- bicycle racing and are seldom even in varied within a normal range. In other velopment and use of human power for an recreational cycling. They are, however, words, transmissions should rank about environmentally sustainable and socially commonly used on European city com- the same at either low or high loads. We just society. Launched in January, 2004, muter bikes where speeds are almost al- feel that the loads we tested under are HuPI seeks to establish a website infor- ways below 25 km/h. Power requirements typical of the actual conditions under mation database and foster the inter- for low speed commuting are normally which hub gears are used and represent a national exchange of information amoung less than 150 watts. 200 watts average reasonable average efficiency. In our ar- all parties interested in the technologies power is sufficient to propel a bicycle at ticle we therefore concluded that hub and benefits of human power. HuPI has over 32 km/h on level ground with no gears are about 2% less efficient that de- primarily a virtual presence on the internet wind. Therefore except in laboratory ex- railleur transmissions under typical field as the most economic means of making periments, hub gears are almost never sub- conditions. We see no reason to change information and resources available world- jected to the high loads that derailleur that conclusion. wide. transmissions are. Rohloff is correct in The Rohloff is an excellent transmis- HuPI is to be a locus for research and saying that efficiency improves as the load sion - in fact it is quite elegant in its func- development in all areas of human power increases. They tested at 400 watts, double tion - it shifts sequentially from gear 1 in a scientific and engineering context. what we did and found efficiencies ap- through gear 14 easily and logically - un- Much of this work is technological in proaching 98%. We tested only one trans- like triple chainring derailleur transmis- nature and has to do with specific tasks, mission at more than 200 watts and found sions. The Rohloff would probably serve such as the design of machines for trans- the Shimano derailleur transmission in well for HPV racing since it would much port. As well, HuPI is devoted to explor- 25th gear, under loads from 307 to 370 simplify the chain line. ing and understanding how human power watts input, was about 98% efficient (our _ Chester Kyle technology benefits society across a wide Figure 14). range of areas, including economics, agri- Because of the high inertia of the bicy- [Ed. Comment, also applying to the culture, social rubric, psychology, and cle rider system, the speed variation due to article by Vernon Forbes on the next general well being. variable torque (pedal force) at the crank page: I never cease to be amazed at the is very small. At racing speeds a computer extremely high standard hub HuPI´s first project is initiated and simulation shows speed variation is less gears will stand without failing even sponsored by Dave Wilson, editor of than plus or minus 0.13% due to the vari- when used in very heavy and sometimes Human Power for 18 years. He wishes to able torque of the crank. We therefore felt powered vehicles, such as the 550- make the wealth of information in pre- that testing at a constant speed of 75 RPM 1400kg Thuner Trampelwurm (described vious issues of Human Power more easily was realistic. Racers pedal at a higher ca- in HP54), or my Velocity Dolphin accessible, and to this end commissioned dence, but the purpose of our tests was to with a normal hub gear a compilation of all issues in the PDF approximate more normal riding conditions. taking up both the torque from a 250 W format, complete with searchable index. Simulating variable crank torque is not electric motor and from a 24 speed This archive is to be made available on the practical with an electric motor dynamo- derailleur drive, or various other electric IHPVA website and on a CD-ROM, which meter and as far as I know, no current or vehicles.] will be available for sale at nominal prices past transmission test apparatus has suc- from some IHPVA member associations, cessfully used this technique. Rolhoff ap- ERRATA FOR HUMAN POWER in particular the HPVA. plied a much higher constant torque than NUMBER 54, SPRING 2003 In mid-2004, HuPI plans to start the our average to simulate maximum chain Human Power International Journal, a tension and gear and chain wear, but this Page 6, Eq. 11: web-based open electronic journal. ρ also is not realistic. Transmission effi- „ “ should be „p“ Initially editted by Theo Schmidt, HPIJ will be available for free via the HuPI ciency varies continuously around the Page 6, Fig. 3: crank cycle - it is high under high torque website: http://www.hupi.org Re = pV/(R m T) should be: and lower under low torque. The average which is also the primary contact to HuPI. Re = LpV/(R m T) efficiency is somewhere in between. Test- Why was HuPI formed? The IHPVA ing only at high torque as Rohloff did, Page 23: first column, lines 16-17: and its members are concentrating on HPV does not give an accurate comparison. Un- ...seen in figure 5 (not 7), the com- racing, records and events. HuPI wishes to less transmissions are tested on the road or bination I=1.06 and G=2.0 (not 3.8) complement that worthy endeavor with in the laboratory using a precision research is optimal. readily available internet-based infor- crank dynamometer with an actual cyclist, mation to help foster a greater application there is really no certainty which of the Page 23: second column, lines 27-29: of human power in daily life. laboratory test methods is more valid. Un- ..G at 2.0 (not 3.8) and I at 1.06 kgm2, Founders of HuPI are: Richard fortunately highly accurate laboratory however lowering G to 1.5 (not 2.85) Ballantine, Theo Schmidt, John Snyder, crank dynamometer tests have not yet been or even 1.14 (not 2.17) may result in a Elrey John Stephens, Brian Wilson, David developed. reasonable compromise... Gordon Wilson.

Human Power Number 55 15