Human Power 2001.52.PDF

POWER

TECHNICAL JOURNAL OF THE IHPVA

N UMBER 52 S UMMER 2001

Number 52

Summer 2001 $5.50

Summaries of articles in this issue; mast . . . . . . . . . . . . . . . . . 2

Contributions to Human Power . . . . . . . . . . . . . . . . . . . . . . . . 2

Articles

The mechanical efficiency of bicycle derailleur and

hub-gear transmissions

Chester Kyle and Frank Berto . . . . . . . . . . . . . . . . . . . . . . . . 3

Technical notes

Bicycle stability after front-tire deflation

Dave Wilson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

There is a better way than rolling

Detlev Tschentscher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Tire-rim compatability, John Stegmann . . . . . . . . . . . . . . . . . 13

Control of hydrofoils using dynamic water pressure

Alastair Taig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Project review

CHicK-2000 Project Team “Active Gals”

Reviewed by Mark Drela . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Book review

Richard’s 21st Century Bicycle book(s) , by Richard

Ballantine, reviewed by Dave Wilson . . . . . . . . . . . . . . . . . . 19

Letters

Battle Mountain crank arms, Matt Weaver . . . . . . . . . . . . . . . 19

Response to Matt Weaver, Danny Too . . . . . . . . . . . . . . . . . . . 20

Crank-arm length and leg length/proportions?

John Stegmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Response to John Stegmann, Danny Too . . . . . . . . . . . . . 21

Editorials

A bit of history viewed from Eastern Europe

Marek Utkin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

The future of Human Power, Dave Wilson . . . . . . . . . . . . . . . 23

HUMAN

HUMAN POWER

Number 52 Summer 2001 $5.50/IHPVA members, $4.50

The mechanical efficiency of

bicycle derailleur and hub-gear transmissions

Chester R. Kyle, Ph.D.

Frank Berto

H U M A N P O W E R

is the technical journal of the

International Human Powered Vehicle

Association

Number 52 Summer 2001

Editor

David Gordon Wilson

21 Winthrop Street

Winchester, MA 01890-2851 USA

<dgwilson@mediaone.net>

Associate editors

Toshio Kataoka, Japan

1-7-2-818 Hiranomiya-Machi

Hirano-ku, Osaka-shi, Japan 547-0046

<HQI04553@nifty.ne.jp>

Theodor Schmidt, Europe

Ortbühlweg 44

CH-3612 Steffisburg, Switzerland

<tschmidt@mus.ch>

Jean Anderson

P.O. Box 12858

San Luis Obispo, CA 93406-2858

<jean.anderson@ihpva.org>

Philip Thiel, Watercraft

4720 - 7th Avenue, NE

Seattle, WA 98105 USA

Production

JS Design & JW Stephens

IHPVA

Paul MacCready, Honorary president

Ben Wichers Schreuer, Chair

Open, Vice-chair

Open, Secretary/treasurer

Publisher

IHPVA

PO Box 1307

San Luis Obispo, CA 93406-1307 USA

Phone: +805-545-9003

E-mail: <hp@ihpva.org>

Human Power (ISSN 0898-6908) is

published irregularly for the International

Human Powered Vehicle Association,

a non-profit organization dedicated to

promoting improvement, innovation and

creativity in the use of human power

generally, and especially in the design

and development of human-powered

vehicles.

Material in Human Power is copyrighted

by the IHPVA. Unless copyrighted also

by the author(s), complete articles

or representative excerpts may be

published elsewhere if full credit is

given prominently to the author(s) and

the IHPVA. Individual subscriptions and

individual issues are available to non-

IHPVA and non-HPVA members.

I N THIS ISSUE

The mechanical efficiency of bicycle

derailleur and hub-gear transmissions

Chet Kyle and Frank Berto have given us

a long-awaited and very valuable report

on a precise study of the efficiencies of a

wide range of bicycle transmissions. It is

both quantitative and well discussed. One

intriguing conclusion is that, in general,

hub gears have efficiencies about a couple

of points lower than do derailleurs.

However, hub gears that were “run in”

and lubricated with light oil rather than

grease showed efficiencies almost up to

the derailleur level. As the authors state,

one arrives at more (interesting) questions.

T ECHNICAL NOTES

There is a better way than rolling

Detlev Tschentscher is following the

pioneering work of John Dick, who

made “Springwalker”, in studying and

building human-powered “exoskeletons”

that promise to make walking faster and

possibly capable of surmounting higher

obstacles and rougher ground.

Further experiments on run-flat stability

after front-tire deflation

Dave Wilson reports further experiments

that seem to confirm (though on the basis

of only two tests) that a good tight fit of

tire to rim is also vital to provide run-flat

stability and control.

Tire-rim compatability

John Stegmann relates, humorously at

times, his adventures in manufacturing

rims and in coping with the tendency of

tires to creep and to allow the tubes to pop

out and explode. He found that a good tight

fit is important.

Control of hydrofoils using dynamic

water pressure

Most (all?) HP hydrofoils have had

their angle of attack controlled through

a surface skimmer attached to a linkage.

Al Taig has developed a lower-drag and

cleaner alternative: using the impact (pitot)

pressure picked up on the leading edge of

the strut supporting the foil from the hull

and controlling the attack angle from, e.g.,

a bellows.

P ROJECT REVIEW

CHicK-2000 project team “Active Gals”

Mark Drela reviews the report and

videotape of a remarkable Japanese team

that has achieved record performances

with a talented woman pilot and an

innovative plane. The wing uses a stressed-

skin construction, allowing the main spar

to be an I-beam and producing a “. . . wing-

tip deflection [that is] amazingly small

considering its low empty weight of 31 kg

and its immense wing aspect ratio of 44.”

B OOK REVIEW

Richard’s 21st century bicycle book(s),

by Richard Ballantine.

Your editor reviews two versions of

the same book by Richard Ballantine:

one in British English for the UK-European

market, and one in American English for

the North Americans. He gives two thumbs

up.

L ETTERS

Comments by Matt Weaver and John

Stegmann on a paper in Human Power 51

on crank-arm length on recumbents, and

responses by author Danny Too.

E DITORIALS

Marek Utkin writes a guest editorial

from Poland on aspects of the HPV scene

there.

Your editor reviews some discussions on

the future of HUMAN POWER.

I NTRODUCTION

Since human power provides the

propulsion for a bicycle, losses in

mechanical energy are far more impor-

tant than if purely mechanical or elec-

trical power is used.

The mechanical efficiency of a drive

system is defined as the ratio of the

power output to the power input in per-

cent. Typically, automotive drive sys-

tems are from 80% to 99% efficient [1],

meaning that from 1% to 20% of the

energy input is lost in friction. A well-

oiled straight chain-and-sprocket bicy-

cle drive can be as high as 99% efficient

[2]. With other types of bicycle trans-

missions, however, the range in effi-

ciency can be similar to an automobile,

that is from 80% to 99% [5–11]. In a

bicycle, small losses can mean large

performance differences—especially in

competition [3, 4].

For example, suppose Christopher

Boardman, the present holder of the

bicycle world hour record (56.375 km;

Manchester, England, 1996), were to

use a bicycle with a drive that lost 2%

more energy than his record machine.

Boardman would travel almost 0.5 km

less in one hour [3]. The hour record

has been broken several times in the

past 30 years by less than 0.5 km. If an

Olympic 4000-meter pursuit team were

to use bicycles that were 2% less effi-

cient, they would be about 2 seconds

slower in the 4000-meter team-pursuit

race, which would have moved them

from first place to fourth place in the

1996 Atlanta Olympics (4 min 8 sec vs .

4 min 6 sec) [4]. By using the wrong

fixed gearing, differences of 2% are eas-

ily possible.

Previous published reports

There have been many published

reports on the mechanical efficiency of

bicycle transmissions during the past

century; however, only a few have

measured the efficiency using accurate

mechanical means [1, 2, 5, 6, 7, 8, 9,

10, 11]. These studies found that bicy-

cle drive efficiency depends upon many

conditions such as load, chain tension,

rpm, gear sizes, and the transmission

type. As mentioned, the efficiencies

varied from about 80% to 99%. The fac-

tors causing energy loss will be dis-

cussed in more detail later.

Mechanical methods of testing nor-

mally employ dynamometers that mea-

sure torque and rotational speed at the

input and output of the drive system

(with mechanical or electronic trans-

ducers). The combined energy losses in

C ONTRIBUTIONS TO H UMAN P OWER

The editor and associate editors (you may choose with whom to correspond) welcome

contributions to Human Power . They should be of long-term technical interest. News

and similar items should go to HPV News or to your local equivalent. Contributions

should be understandable by any English-speaker in any part of the world: units should

be in S.I. (with local units optional), and the use of local expressions such as “two-by-

fours” should either be avoided or explained. Ask the editor for the contributor’s guide

(available in paper, e-mail and PDF formats). Many contributions are sent out for review

by specialists. Alas! We cannot pay for contributions. Contributions include papers,

articles, technical notes, reviews and letters. We welcome all types of contributions

from IHPVA members and from nonmembers.

Bicycle crank

dynamometer,

furnished by

the USOC

Sports

Sciences

Division

2 Number 52 Summer 2001 Human Power

Human Power Number 52 Summer 2001 3

all drive-train components such as

the bearings, chains, sprockets, gears,

and derailleurs are usually included in

the efficiencies. However, some studies

report the efficiency only of isolated

components [6, 7, 9]. Thom [6] mea-

sured the efficiency of three-speed hub

gears and bearings without including

sprocket losses. Dell’Oro [7] isolated

derailleur losses from the rest of the

drive system. Cameron [9] measured

the required static force to lift a known

weight with a bicycle chain draped

over a single sprocket. He assumed

losses were constant with rpm, and

estimated fixed-gear efficiencies under

various loads. The remaining studies

measured the overall efficiency of the

bicycle drive system [1, 2, 5, 8, 10, 11].

Indirect methods such as repetitive

field time trials, field or laboratory oxy-

gen-consumption studies, crank-power-

meter field trials, or crank-power-meter

studies on stationary trainers, lack the

necessary precision to give reliable

results. Usually such methods have an

error band of several percent.

N EW TESTS

During 9–13 October 2000, in the

Laboratory of the Browning Research

Facility on Bainbridge Island, Wash-

ington, the authors and Peter Kauff-

man, technical consultant to Browning

Research, used a specially-devised

dynamometer system to measure the

mechanical efficiency of eleven bicycle

transmissions. The transmissions were

two Browning automatic bicycle trans-

missions (a 4-speed, and a 12-speed),

a Shimano 27-speed mountain-bike

derailleur transmission and eight inter-

nal hub-gear transmissions (Shimano

3-, 4- and 7-speed, Sachs 3- and 7-speed,

Sturmey Archer 3- and 7-speed, and a

Rohloff 14-speed.

Most of the previous bicycle-trans-

mission tests were done on derailleur-

type chain drives [1, 7, 8, 9] and these

efficiency tests were limited to only

a few gears. As far as the authors

know, the wide-ranging 27-speed trans-

missions available today have not been

tested, or at least the tests have not

been published. No doubt manufactur-

ers have tested their transmissions for

efficiency, but if so, the results of their

tests are unpublished.

Prior to the 1970s, before derailleur-

equipped bikes became really popular,

there were some efficiency tests per-

formed on planetary hub gears [5,

6]. Hub gears are still quite popular

today in Europe where they are used

mainly on city commuter bikes. Hub-

gear transmissions have the advantage

of being nearly weatherproof, with low

maintenance—and they permit a chain

guard that completely shields the chain,

and allow bicycle commuting without

worrying about soiling good clothes on

a greasy chain. However, they have

never been popular with serious rec-

reational cyclists or racers since the

range of gears has been limited. Also,

they are heavier than a derailleur-type

transmission and they have had the

reputation of being mechanically inef-

ficient. Recently, however, there has

been a revival of interest in the hub

gear for several reasons. They are now

available with an increasing number of

gears (as many as 14), they lend them-

selves to fully automatic operation, and

they can easily be adapted to bikes

with an electric-motor boost. Regarding

the hub gear’s reputation for mechani-

cally inefficiency, this paper will pres-

ent information that shows this is not

necessarily so.

Purpose of current tests

The purpose of the current tests was

to compare the mechanical efficiency

of the most common types of bicycle

drives under identical conditions. Since

limited time was available, the test

apparatus had to handle all of the

most common types of bicycle trans-

missions and to rapidly measure effi-

ciency. Since power input to a bicycle

crank is typically between 50 and 400

watts [4], and since losses can be as

low as one to two percent, the trans-

mission test system had be sensitive

enough to determine power differences

of just a few watts (less than 5).

T EST EQUIPMENT

The test system consisted of four main

elements (see photo on page 3).

1. Bicycle crank dynamometer

To measure input power, a dyna-

mometer fed power to a bicycle crank

by means of a 2-horsepower variable-

speed DC motor, mounted on gimbals

so that the motor case could rotate

freely. The motor case was restrained

by a torque arm attached to an elec-

tronic load cell that measured the

torque force. Oscillations in the load

were smoothed by connecting the

torque arm to the load cell through a

thin nylon cord that transmitted force

through a flywheel-type inertial damp-

er. The rpm of the motor shaft was

measured by timing each revolution

torque and ω is the angular velocity of

the crank.

2. Bicycle-drive-train fixture

A special test fixture was built to

mount a bicycle bottom bracket, crank

and chainrings, plus a rear hub without

spokes or wheel. On the non-drive side

of the hub, a sprocket was attached to

the hub which drove a Monarch bicycle

ergometer wheel. The adjustable fix-

ture was built by Jim Merz for Brown-

ing Research, and it allowed rapid

changing of front sprockets, chains and

rear hubs.

3. Monarch ergometer wheel

To measure power output, a Mon-

arch aluminum ergometer wheel was

driven by a chain from the drive-train

fixture through two 36-tooth sprockets,

one on the ergometer wheel, and one

on the non-drive side of the bicycle

hub. A nylon cord, approximately 3 mm

in diameter, was wrapped twice around

the ergometer wheel with one end

attached to a transducer and the other

hanging downward with a suspended

weight. The direction of rotation of

the wheel was away from the hanging

weight so the tension in the load-cell

cord (slack side) was a small fraction

of the applied hanging weight (load

side). The ergometer load and thus

the power output could be adjusted by

hanging various weights on the nylon

cord. Knowing the difference in tension

between the two cords and the rpm,

the output power from the bicycle

hub could be calculated. The rpm of

the ergometer wheel was measured

electronically.

The power output of the system was:

P o = k ω o ( Τ 1 − T2), where P o is the out-

put power, k is a proportionality con-

stant, ω o is the ergometer wheel angu-

lar velocity, T1 is the weight, and T2 is

the slack-side tension.

A disadvantage of this method was

that the friction losses in the ergometer

wheel drive were unknown. In order

to find the corrected transmission

efficiency, the ergometer drive losses

would have to be determined, and this

was done only at 75 rpm. However,

for determining the rank order between

transmissions, since they were all test-

ed under identical conditions, no cor-

rection is necessary. The efficiencies

reported in this article include ergom-

eter-wheel drive losses, so the actual

transmission efficiencies would be

higher by 2 to 2.5%.

4. Data-acquisition system

A portable computer was adapted by

Peter Kauffman of Browning to receive

signals from the load cells and revolu-

tion counters. The computer sampled

the transducers and averaged the read-

ings over a selected time interval.

The software automatically calculated

ergometer power along with the

mechanical efficiency of the bicycle

drive including the ergometer drive. All

of the data and calculations were dis-

played in tabular form on the computer

screen, and the data were stored for

later analysis.

T EST PROCEDURE

• The load cells were calibrated

using weights. The load cells agreed

with the weights within ± 0.2%. The

accuracy of the angular-velocity trans-

ducers of both the crank and the

ergometer wheels were checked by two

methods. The crank rpm was verified

with a stop watch. The rpms of both

the crank and the ergometer wheel, as

indicated by the transducers, were then

used to compute the gear ratio which

was compared with the known ratio.

The calculated gear ratio agreed with

the known ratio normally within three

significant figures (one part in 1000).

• The first test series was with the

crank dynamometer directly connected

to the ergometer wheel through two

36-tooth gears. The purpose was to

estimate the power losses of the ergom-

eter wheel drive. Since chain tension

is probably the most important factor

in gear friction [8] the ergometer wheel

weights were the same as those used

in normal testing—from 1.8 kilos to 16

kilos. The speed of the crank and wheel

were constant at 75 rpm. This test did

not directly measure ergometer-wheel

drive losses since the wheel rpm did

not vary (as when testing transmis-

sions). Also, the bottom-bracket bear-

ings were in the loop, making an extra

set of bearings. The friction losses were

small (from 1 to 6 watts; see fig. 13*),

but as previously mentioned, account-

ing for the losses would raise the

reported efficiencies by 2 to 2.5%.

• The test fixture was then used to

test the efficiency of eleven transmis-

sions. Weights were chosen to produce

80 watts, 150 watts and 200 watts out-

put power at 75 crank rpm. All chains

were well oiled with light machine oil.

Hub gears were usually left with their

original grease lubricant, but this was

replaced in two hubs with light oil.

The transmissions that were tested

had the following gears.

Derailleur-type transmissions

4-speed automatic: Browning

This transmission has a gear layout

similar to a standard derailleur system

except electronically actuated hinged

gear segments in the rear cluster shift

the chain up or down either automati-

cally or manually. The Browning chain

guide and tensioner, with its two jock-

ey pulleys, has a similar appearance to

a derailleur, and probably has nearly

identical friction characteristics. It is

however a passive follower. In this

paper, the two Browning transmissions

and the 27-speed derailleur transmis-

sion will often be referred to as “derail-

leur-type” transmissions. The Browning

4-speed was tested with a 42-tooth

front chainring and a 12-, 17-, 23-, and

32-tooth rear cluster.

12-speed automatic: Browning

An automatic transmission similar

to the Browning 4-speed, except with

three front chainrings 48/38/30, and the

same 4-speed rear cluster 12/17/23/32.

The gears are (1) 30/32; (2) 38/32;

(3) 30/23; (4) 48/32; (5) 38/23; (6) 30/17;

(7) 48/23; (8) 38/17), (9) 30/12);

(10) 48/17; (11) 38/12; and (12) 48/12.

27-speed: Shimano

A Shimano Ultegra 27-speed moun-

tain-bike transmission with three front

chainrings (44/32/22 teeth) and a

9-speed rear cluster (12, 14, 16, 18,

20, 23, 26, 30, and 34 teeth). Because

of time constraints, only 15 of the

27 gears were tested: (1) 22/34;

(3) 22/26; (4) 32/34; (7) 22/20; (9) 32/26;

(10) 44/34; (11) 22/16; (15) 32/20;

(16) 44/26; (18) 22/12; (20) 32/16;

(21) 44/20; (24) 32/12; (25) 44/16; and

(27) 44/12.

Planetary-geared rear hubs

3-speed: Sachs

An internal planetary-geared rear

hub with a 40-tooth front chainring

and a 19-tooth rear cog. The three hub

gears are: (1) Ratio = 0.75); (2) 1.00;

and (3) 1.33.

3-speed: Shimano

A rear hub with a 40-tooth front

chainring and a 19-tooth rear cog. The

three hub gears are: (1) 0.74; (2) 1.00;

and (3) 1.36.

3-speed: Sturmey Archer

A rear hub with a 40-tooth front

chainring and a 19-tooth rear cog. The

three hub gears are: (1) 0.75; (2) 1.00;

and (3) 1.33.

4-speed: Shimano Auto D

A rear hub with a 31-tooth front

chainring and a 23-tooth rear cog. The

four hub gears are: (1) 1.00); (2) 1.24;

(3) 1.5; and (4) 1.84.

7-speed: Sachs

A rear hub with a 40-tooth front

chainring and a 19-tooth rear cog. The

transmission shifter was damaged and

could be shifted to only two gears:

(1) 0.59 and (4) 1.00.

7-speed: Shimano Nexus

A rear hub with a 40-tooth front

chainring and a 19-tooth rear cog. The

seven hub gears are: (1) 0.63); (2) 0.74;

(3) 0.84; (4) 0.99; (5) 1.15; (6) 1.34; and

(7) 1.55.

7-speed: Sturmey Archer

A rear hub with a 40-tooth front

chainring and a 19-tooth rear cog. The

seven hub gears are: (1) 0.60; (2) 0.69;

(3) 0.80; (4) 1.00; (5) 1.24); (6) 1.45; and

(7) 1.68.

14-speed: Rohloff

A rear hub with a 40-tooth front

chainring and a 16-tooth rear cog.

The fourteen hub gears are: (1) 0.279;

(2) 0.316; (3) 0.360; (4) 0.409; (5) 0.464;

(6) 0.528; (7) 0.600; (8) 0.682; (9) 0.774;

(10) 0.881; (11) 1.000; (12) 1.135;

(13) 1.292; and (14) 1.467.

R ESULTS AND DISCUSSION

We tested each transmission at

three loads: 80 watts, 150 watts, and

200 watts (power output at the ergom-

eter wheel)—all at 75 rpm. The crank

speed of 75 rpm was chosen as being

typical of recreational cyclists. There

was insufficient time available to test

each transmission at both variable load

and variable rpm. The power outputs

of 80, 150 and 200 watts, represent

the typical energy requirements of com-

muting or recreational cyclists in good

physical condition, traveling at speeds

from 24–35 kph (15–22 mph), on a

level, smooth road with no wind [1, 3].

Bicycle racers can produce steady

*See pages 8–11 for figures and tables.

4 Number 52 Summer 2001 Human Power

Human Power Number 52 Spring 2001 5

electronically. The output shaft of the

motor was connected to a bicycle

crank through a flexible coupling.

Knowing the torque and the rpm, the

input power to the crank could be

calculated. The dynamometer was fur-

nished by the U.S. Olympic Committee

(USOC) Sports Sciences Division.

The power input to the bicycle crank

was given by:

P i = k τω where P i is the power, k

is a proportionality constant, τ is the

power outputs that are much higher

than this for periods of more than

one hour—from 300 to 450 watts [3].

Although the occasional recreational

cyclist may produce over 200 watts,

it is doubtful that cyclists using hub

gears would frequently put out more

than 150 watts unless being chased by

rabid dogs. The results of the tests are

shown in figures 1–14.

P LOTTING EFFICIENCY

In figures 1–12 the efficiency is plot-

ted in three ways.

1. Efficiency vs . power output

Here all of the individual power

and efficiency data points were plotted

for each gear. These curves give the

detailed performance of each transmis-

sion under varying load. As examples,

see figures 1, 4 or 5. All transmissions

were not plotted but they could be,

using the data in tables 1 and 2.

2. Average efficiency vs . gear number

Here, efficiencies for all test loads

were averaged for each gear and the

averages were plotted against the gear

number. This curve shows the effect of

gear ratio on efficiency under varying

load conditions. For examples see fig-

ures 2, 6, 8, 10, or 11.

3. Average efficiency vs . load

Here, transmission efficiencies for

each load were averaged for all gears.

This curve is a measure of the per-

formance of each transmission under

varying conditions. For example, see

figures 3, 7, 9, or 12. These curves pro-

vide probably the simplest way to com-

pare transmissions.

C ONCLUSIONS

By viewing the curves, several general

observations and conclusions can be

made.

1. Efficiency generally increases with

the load—for all transmissions.

Figures 1, 3, 4, 5, 7, 9, 12, or 14

all show this trend. Although friction

increases with chain load, rpm, and

other factors [8], obviously the residual

friction in a gear train becomes less

important as the input power increases,

while the friction factors that increase

with load go up less rapidly than the

load.

The clearest example of this is

shown in figure 14. This was the only

case where we tested a transmission

at over 200 watts and under 80 watts.

More tests were planned, but a shear

pin parted in the drive train and this

experiment was aborted. The uncor-

rected efficiency increased from about

91% to over 97% as the output power

increased from 50 watts to 370 watts at

75 rpm.

By assuming that ergometer-wheel

rpm has no effect on the drive losses

(fig. 13), a rough estimate of the abso-

lute system efficiency can be made.

Spicer shows that drive-train losses

are a function of the crank rpm [8];

however, as previously explained, this

effect was not measured. When correct-

ed for ergometer-drive losses, the trans-

mission efficiency increases from 1% to

3% (see fig. 14). Efficiency is over 98%

at the highest load. The corrected effi-

ciencies are in good agreement with

Spicer [8] who found that efficiency

was over 98% with 52/15-tooth sprock-

ets at 200 watts.

2. Hub gears are generally about 2%

lower in efficiency than derailleur-type

gears. But there are exceptions.

This is illustrated by figures 3, 6, 7,

and 12. Figure 12 shows that the effi-

ciencies of the Shimano 4, Sachs 7,

Shimano 7, Sturmey 7 and the Rohloff

14 all cluster about two percent lower

than the Browning 4, Browning 12, or

the Shimano 27.

However, two of the 3-speed hub

gears did not follow this trend.

The grease in the Sachs 3 and the

Sturmey Archer 3-speeds was replaced

with light oil, and unlike the other hub

gear transmissions, the efficiencies of

the Sachs 3 and Sturmey 3, compare

well with the best of the derailleur

transmissions (figs. 7, 9, and 12).

Also, these transmissions were worn

in, whereas many of the others were

new. Manufacturers would do well to

replace heavy grease in their hub gears

with light oil. Although oil wouldn’t

last as long as grease, the energy

savings would be significant. Unfor-

tunately commuters have a tendency

to ignore maintenance until something

breaks, so light oil probably wouldn’t

be a popular choice.

Also, with the Shimano 4, the first

gear (a 1.0 ratio) had a higher efficien-

cy than the derailleur transmissions,

even though gears 2, 3, and 4 had a

lower efficiency (see fig. 6). In a plan-

etary transmission (also called epicy-

clic), even when the hub ratio is 1.0,

the planet gears are still in motion [12];

however, all of the planetary transmis-

sions we tested had high efficiency at

1.0 gear ratios.

3. As the gear ratio increases, the

efficiency tends to decrease for all

transmission types.

This is illustrated by the trend lines

in figures 6, 8, 10, and 11. Even though

the greatest efficiencies are sometimes

near the highest gear ratios, the aver-

age efficiency decreases with higher

ratios, (the high efficiencies were:

Shimano 4 = gear 1, Rohloff = gear 9,

Browning = gear 2, and Shimano 27 =

gear 21).

4. With modern transmissions, where

multiple gears are available, there is

often a difference of 1% to 3% in effi-

ciency between adjacent gears.

This applies to both hub gears and to

derailleur gears. See figs. 2, 6, 8, 10, and

11 (especially figures 8, 10 and 11).

In figure 11, in the Shimano 27-speed,

there is a 4% difference in efficiency

between gears 21 and 24 and between

gears 24 and 25. In figure 8, for the

Rohloff 14, there is a 3% difference

between gears 7 and 8.

An average 2% difference in efficien-

cy is thus easily possible if the wrong

gears are chosen.

If racers, or even commuting or tour-

ing cyclists, could choose optimum

gears they would be hundreds of

meters ahead at the end of 60 km

(37 mi). For example, if Lance Arm-

strong, in the Tour de France 58.5-km

time trial (36.4 mi) were to choose

the wrong gear, a drop of 2% in efficien-

cy would cause him to be 410 meters

behind (27 seconds) at the end of the

time trial, easily enough to lose the

stage [3]. Incidentally, Armstrong aver-

aged about 54 kph (33.6 mph) for the

time trial (58.5 km long = 36.4 mi).

With commuting riders who travel

24 kph (15 mph), instead of 54 kph

(33.6 mph), it only gets worse. A 2%

drop in efficiency would lead to an

800-meter gap (about 2 minutes). The

reason for the increasing gap is that the

slower cyclist spends much more time

on the course [3]. The point is, why

waste energy when it is unnecessary.

5. The tests show that some gears

are inefficient.

Hub gears

In hub gears, such as the Rohloff

14, the efficiency no doubt depends on

how many elements of the gear train

are in motion as each gear is selected

(see fig. 15). In the Rohloff, gears 3, 5,

7, 12, and 14 have the lowest efficiency.

This superb but complex transmission

has roller bearings and uses light oil as

a lubricant. Shifting is quite simple: suc-

cessive gears are reached by pulling on

the single shift cable in one direction

or the other. No attempt will be made

to explain this mechanism. It is obvious

from the diagrammatic illustration (fig.

15) that it cannot easily be explained.

Derailleur gears

On the other hand, factors affecting

the efficiency of derailleur gears

become clear by examining the curves

in figures 10 and 11. For example, a

12-tooth sprocket seems to cause ineffi-

ciency. In the Shimano 27-speed, gears

4, 9, 15, 18, and 24 have the lowest

efficiency. The two gears with the low-

est efficiency of the 15 tested, both

use a 12-tooth sprocket. The gears with

12-tooth sprockets (18, 24 and 27) have

an average efficiency of 91.2%, while

those involving 16-tooth sprockets (11,

20 and 25) have an average efficiency

of 93.5%.

Other gears

In the Browning, the 12-tooth sprock-

ets averaged 92.1% efficiency, while

the gears involving a 17-tooth sprocket

averaged 92.9%. The two lowest effi-

ciencies of the 12 gears tested had

12-tooth sprockets (gears 9 and 12).

Apparently the sharp angle of chain

link bend in the 12 causes increased

friction compared to larger sprockets.

So it appears that larger gears than 12

are necessary for efficient operation.

When there is a choice of gear ratios

that are close, cyclists should choose

the gearing combination with larger

diameters [8].

Cross-chain gears make little differ-

ence. In the Shimano 27, the cross

chain between the two big gears on the

Shimano has a higher-than-average effi-

ciency (gear 10, 44/34), while the cross

chain between the two small sprockets

involves a 12-tooth sprocket (gear 18,

22/12; see fig. 11). In the Browning,

the large cross-chain gears (gear 4,

48/32), have a higher-than-average effi-

ciency, while the small-gear cross

chain involves a 12-tooth sprocket (see

fig. 10).

For some reason that is not appar-

ent, the mid-chainrings on both the

Browning 12 and the Shimano 27 did

not have high efficiencies. On the

Browning 12, gears using the 30-tooth

chainring (1, 3, 6, and 9) had a lower-

than-average efficiency. On the Shima-

no 27, gears using the 32-tooth chain-

ring (4, 9, 15, 20 and 24), all had a low-

er-than-average efficiency. This does

not appear to be a coincidence, but the

reason is not clear.

Had more time been available, it

would have been interesting to mea-

sure the effect of such things as rpm,

all gears in the 27-speed, a wider range

of power inputs, and various chain and

hub-gear lubricants. As usual, there are

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