Efficiency Measurements of Bicycle Transmissions - a neverending Story? by Bernhard Rohloff 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 gears. Therefore, the losses bicycle transmissions “The Mechanical extremely important for tests under in the higher seven gears must be smaller Efficiency of Bicycle Derailleur and Hub- 200W; this will be discussed later in this than the losses in the lower seven gears. Gear 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 transmission 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. Derailleurs 87-97 were not measured. However this is The efficiency variations of the Gear Hubs 86-95 important when evaluating transmissions Shimano 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 torque 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.