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HUMAN
POWER

T E C H N I C A L J O U R N A L O F T H E I H P VA
NUMBER 52 SUMMER 2001
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
There is a better way than rolling
Detlev Tschentscher. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tire-rim compatability, John Stegmann . . . . . . . . . . . . . . . . .
Control of hydrofoils using dynamic water pressure
Alastair Taig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11
12
13
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 . . . . . . . . . . . . . . .
Response to Matt Weaver, Danny Too. . . . . . . . . . . . . . . . . . .
Crank-arm length and leg length/proportions?
John Stegmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Response to John Stegmann, Danny Too . . . . . . . . . . . . .

Number 52
Summer 2001

Editorials

$5.50

19
20
21
21

A bit of history viewed from Eastern Europe
Marek Utkin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
The future of Human Power, Dave Wilson . . . . . . . . . . . . . . . 23

HUMAN POWER

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 nonIHPVA and non-HPVA members.

2

Summer 2001

IN

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.

TECHNICAL

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.

CONTRIBUTIONS

TO

$5.50/IHPVA members, $4.50

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.

PROJECT

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 stressedskin construction, allowing the main spar
to be an I-beam and producing a “. . . wingtip deflection [that is] amazingly small
considering its low empty weight of 31 kg
and its immense wing aspect ratio of 44.”

BOOK

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.

Chester R. Kyle, Ph.D.
Frank Berto

INTRODUCTION

Since human power provides the
propulsion for a bicycle, losses in
mechanical energy are far more important than if purely mechanical or electrical power is used.
The mechanical efficiency of a drive
system is defined as the ratio of the
power output to the power input in percent. Typically, automotive drive systems are from 80% to 99% efficient [1],
meaning that from 1% to 20% of the
energy input is lost in friction. A welloiled straight chain-and-sprocket bicycle drive can be as high as 99% efficient
[2]. With other types of bicycle transmissions, however, the range in efficiency 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 efficient, 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 easily 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 bicycle 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 factors causing energy loss will be discussed in more detail later.
Mechanical methods of testing normally employ dynamometers that measure torque and rotational speed at the
input and output of the drive system
(with mechanical or electronic transducers). The combined energy losses in

Photo, courtesy of Chet Kyle

Number 52

HUMAN POWER

The mechanical efficiency of
bicycle derailleur and hub-gear transmissions

LETTERS

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.

EDITORIALS

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.

HUMAN POWER

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-byfours” 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.

Number 52 Summer 2001

Human Power

Bicycle crank
dynamometer,
furnished by
the USOC
Sports
Sciences
Division

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] measured 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 oxygen-consumption studies, crank-powermeter 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.

today in Europe where they are used
mainly on city commuter bikes. Hubgear 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 recreational 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 inefficient. 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 themselves to fully automatic operation, and
they can easily be adapted to bikes
with an electric-motor boost. Regarding
the hub gear’s reputation for mechanically inefficiency, this paper will present information that shows this is not
necessarily so.

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 furnished by the U.S. Olympic Committee
(USOC) Sports Sciences Division.
The power input to the bicycle crank
was given by:
Pi = kτω where Pi is the power, k
is a proportionality constant, Ï„ is the
torque and ω is the angular velocity of
the crank.

NEW

Purpose of current tests

To measure power output, a Monarch 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:
Po = kωo(Τ1−T2), where Po is the output power, k is a proportionality constant, ωo is the ergometer wheel angular 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

TESTS

During 9–13 October 2000, in the
Laboratory of the Browning Research
Facility on Bainbridge Island, Washington, the authors and Peter Kauffman, 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 transmissions (a 4-speed, and a 12-speed),
a Shimano 27-speed mountain-bike
derailleur transmission and eight internal 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-transmission tests were done on derailleurtype 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 transmissions available today have not been
tested, or at least the tests have not
been published. No doubt manufacturers have tested their transmissions for
efficiency, but if so, the results of their
tests are unpublished.
Prior to the 1970s, before derailleurequipped bikes became really popular,
there were some efficiency tests performed on planetary hub gears [5,
6]. Hub gears are still quite popular
4

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 transmissions and to rapidly measure efficiency. 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 transmission test system had be sensitive
enough to determine power differences
of just a few watts (less than 5).

TEST

EQUIPMENT

The test system consisted of four main
elements (see photo on page 3).
1. Bicycle crank dynamometer

To measure input power, a dynamometer fed power to a bicycle crank
by means of a 2-horsepower variablespeed 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 electronic 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 damper. The rpm of the motor shaft was
measured by timing each revolution
Number 52 Summer 2001

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 fixture was built by Jim Merz for Browning Research, and it allowed rapid
changing of front sprockets, chains and
rear hubs.
3. Monarch ergometer wheel

Human Power

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 tested under identical conditions, no correction is necessary. The efficiencies
reported in this article include ergometer-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 revolution counters. The computer sampled
the transducers and averaged the readings 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 displayed in tabular form on the computer
screen, and the data were stored for
later analysis.

TEST

PROCEDURE

• The load cells were calibrated
using weights. The load cells agreed
with the weights within ±0.2%. The
accuracy of the angular-velocity transducers 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 ergometer 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 transmissions). Also, the bottom-bracket bearings 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, accountHuman Power

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 transmissions. Weights were chosen to produce
80 watts, 150 watts and 200 watts output 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 automatically or manually. The Browning chain
guide and tensioner, with its two jockey 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 transmission will often be referred to as “derailleur-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 mountain-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
*See pages 8–11 for figures and tables.

Number 52 Spring 2001

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.

RESULTS

AND DISCUSSION

We tested each transmission at
three loads: 80 watts, 150 watts, and
200 watts (power output at the ergometer 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 commuting 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
5

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.

PLOTTING

EFFICIENCY

In figures 1–12 the efficiency is plotted 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 transmission 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 figures 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 performance of each transmission under
varying conditions. For example, see
figures 3, 7, 9, or 12. These curves provide probably the simplest way to compare transmissions.

CONCLUSIONS

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 uncor6

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 absolute 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 corrected for ergometer-drive losses, the transmission efficiency increases from 1% to
3% (see fig. 14). Efficiency is over 98%
at the highest load. The corrected efficiencies are in good agreement with
Spicer [8] who found that efficiency
was over 98% with 52/15-tooth sprockets 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 efficiencies 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. Unfortunately 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 efficiency than the derailleur transmissions,
even though gears 2, 3, and 4 had a
lower efficiency (see fig. 6). In a planetary transmission (also called epicyclic), even when the hub ratio is 1.0,
the planet gears are still in motion [12];
however, all of the planetary transmissions we tested had high efficiency at
1.0 gear ratios.
3. As the gear ratio increases, the
Number 52 Summer 2001

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 average 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 efficiency 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 efficiency is thus easily possible if the wrong
gears are chosen.
If racers, or even commuting or touring cyclists, could choose optimum
gears they would be hundreds of
meters ahead at the end of 60 km
(37 mi). For example, if Lance Armstrong, in the Tour de France 58.5-km
time trial (36.4 mi) were to choose
the wrong gear, a drop of 2% in efficiency 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 averaged 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: sucHuman Power

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 inefficiency. In the Shimano 27-speed, gears
4, 9, 15, 18, and 24 have the lowest
efficiency. The two gears with the lowest 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 sprockets averaged 92.1% efficiency, while
the gears involving a 17-tooth sprocket
averaged 92.9%. The two lowest efficiencies 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 difference. In the Shimano 27, the cross
chain between the two big gears on the
Shimano has a higher-than-average efficiency (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 efficiency, while the small-gear cross
chain involves a 12-tooth sprocket (see
fig. 10).
For some reason that is not apparent, 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 lowerthan-average efficiency. On the Shimano 27, gears using the 32-tooth chainring (4, 9, 15, 20 and 24), all had a lower-than-average efficiency. This does
not appear to be a coincidence, but the
Human Power

reason is not clear.
Had more time been available, it
would have been interesting to measure 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
more questions than answers.

CREDITS

The authors wish to thank Browning
Research for making available the facilities of their laboratory for this project
and for supporting this study.
Thanks also to the Sports Sciences
Division of the United States Olympic
Committee for loaning us the bicyclecrank dynamometer.

REFERENCES

1. Kyle, C.R. and V.J. Caiozzo. 1986
(May). Experiments in human
ergometry as applied to the design of
human-powered vehicles. Int. Jl.
Sport Biomech. 2:6–19.
2. Marks, L.P. 1979. Mark’s standard
handbook for mechanical engineers,
8th ed. NY: McGraw Hill. p3–29, 11–7.
3. Bassett, D.R., C.R. Kyle, L. Passfield,
J.P. Broker and E.R. Burke. 1999.
Comparing the world hour record in
cycling, 1967–1996: Modeling with
empirical data. Medicine and Science
in Sports and Exercise, 31:11,
1665–1676.
4. Broker, J.P., C.R. Kyle, and E.R.
Burke. 1999. Racing cyclist power
requirements in the 4000-m individual
and team pursuits. Medicine and
Science in Sports and Exercise,
31:11, 1677–1685.
5. Whitt, F.R. and D.G. Wilson. 1982.
Bicycling science. Cambridge: MIT
Press. Figure 11.16, p. 296.
6. Thom, A.P., G. Lund and J.D. Todd.
1956 (July 1). Efficiency of threespeed bicycle gears. Engineering,
180:78–79.
7. Dell’Oro and M. Malone. 1995. Bicycle
derailleur losses. Melbourne:
University of Melbourne, Department
of Mechanical and Manufacturing
Engineering.
8. Spicer, J.B., M.J. Ehrlich, J.R.
Bernstein and C.J.K. Richardson
(Johns Hopkins University); M.
Masahiko Fukuda and M. Terada
(Shimano Inc.) 1999 (June) .
Efficiency and energy-loss location in
bicycle chain drives. Journal of
Mechanical Design.
9. Cameron, A. Measuring drive-train
efficiency. 1998–99. Human Power,
Number 52 Summer 2001

46:5–7.
10. Wilson, D.G. Transmission efficiencies. 1999. Human Power, 48:20.
11. Kyle, C.R. 1998 (September 15).
The mechanical efficiency of bicycle
transmissions. Report to Browning
Research.
12. Berto, F., R. Shepherd and R. Henry.
2000. The dancing chain. San
Francisco: Van der Plas Publications,
pp 23, 48–52.

THE

AUTHORS

Chester Kyle, adjunct professor of
mechanical engineering at California
State University at Long Beach, is a
consultant on the science of sports
equipment and has worked with several
teams and organizations: US Postal Service 2001 Tour de France team, design
teams for USA 1984 and 1996 Olympics
cycling teams’ bicycles and clothing,
and Nike, as well as others, for aerodynamic sports clothing.
Co-organizer of the first International
Human Powered Speed Championships
at Irwindale, California, in 1975, Kyle
and eleven others founded the International Human Powered Vehicle Association (IHPVA) the following year. Kyle
is past president and secretary of the
IHPVA, as well as the de facto historian
of the organization. Editor and publisher of Cycling Science (1989–1991) and
science editor of Bicycling Magazine
(1984–1989), Kyle is a frequent contributor to scientific and popular publications.
Chet Kyle and his wife, Joyce, live on
ten acres of rural pasture and forest in
a home they and their four, now-grown
children built near Weed, California.
Frank Berto, author of more than 150
articles and several books on cycling
technology, was engineering and West
Coast editor of Bicycling Magazine
(1986–1990). Berto is a consultant
on oil field gauging and instrumentation, cycling equipment and technology
(especially gearing), as well as a frequent expert witness on cycling litigation. He is also a historic aircraft and
machinery enthusiast.
Frank and Connie Berto live in San
Anselmo, California, on a large plot of
land affectionately called “Sleepy Hollow”.
Berto’s latest book, The Dancing
Chain, was reviewed in Human Power
51, Fall 2000.

7

96

96

96

93

95

92
91
90

88

Sachs
Shimano
Sturmey

89

Gear 1 = 0.75
Gear 2 = 1.0
Gear 3 = 1.36

84
50

100

150

200

2

50

150

200

3

4

5

6

7

8

9

10

11

12

13

14

250

Figure 8. Rohloff 14 (average efficiency vs. gear)

96

90
88
Sachs 3
Shimano 3
Sturmey 3

92
Gear 1
Gear 2
Gear 3
Gear 4

90

92
Shimano 7
Sturmey 7
Sachs 7
Rohloff 14
Shimano 4
Sachs 3
Shimano 3
Sturmey 3

90

100

150

200

50

250

100

150

Output (watts)

Figure 4. Browning 4-speed (efficiency vs. load)

92
Browning 12
Trend

91

90
1

2

3

4

250

5

6

7

8

9

10

11

12

Gear number

Figure 10. Browning 12 (average efficiency vs. gear)

Figure 9. Hub gear bicycle transmissions (average efficiency vs. load)

95
96

200

Output (watts)

Output (watts)

Figure 3. Sachs 3, Shimano 3, Sturmey 3 (average efficiency vs.
load)

93

86
50

250

94

88

88

200

95

94
Efficiency (percent)

Efficiency (percent)

96

96

94

94

95

93

94

94

Efficiency

90

Efficiency

92

92

91
90
89

88
Gear
Gear
Gear
Gear

86

1
2
3
4

84
50

100

150
Output (watts)

200

250

Efficiency (percent)

Efficiency (percent)

92

84

Efficiency (percent)

2

Figure 7. Browning 4-speed, Shimano 4-speed (average efficiency vs.
load)

94

93
92

92

Shimano 4
Sachs 7
Shimano 7
Sturmey 7
Rohloff 14
Browning 4
Browning 12
Shimano 27

90

91

88
87

88

Shimano 27
Trend

90

Shimano 4
Browning 4

89

86
1

2

3

4

1

3

Figure 6. Browning 4, Shimano 4 (average efficiency vs. gear)

Number 52 Summer 2001

5

7

9

11

13

15

17

19

21

Gear number

Gear number

Figure 5. Shimano 4-speed (efficiency vs. load)

8

100

Output (watts)

94

150

88
Gear number

Figure 2. Sachs 3, Shimano 3, Sturmey 3 (average efficiency vs. gear)

96

100

Rohloff 14
Trend

86

250

96

50

Browning 4
Shimano 4

1

Figure 1. Shimano 3-speed (efficiency vs. load)

86

90

89

3

Gear number

Output (watts)

91

90

88

88
1

92

Efficiency

86

Efficiency

90

93

Efficiency (percent)

92

92

94

94
Efficiency

Efficiency (percent}

94

Human Power

Figure 11. Shimano 27 (average efficiency vs. gear)

Human Power

23

25

27

86
50

100

150

200

250

Output (watts)

Figure 12. Derailleur-type transmissions compared with hub gears
(average efficiency vs. load)

Number 52 Summer 2001

9

R2 = 9.97064E-01

8

98

Efficiency (percent)

Power loss (watts)

6
5
4
3

95

2

3

4

93.0
95.3
95.3

93.3
95.0
95.0

93.3
94.8
94.9

90.3
93.8
93.3

Browning 12
Automatic

80
150
200

91.1
93.8
92.7

92.5
93.9
95.2

91.3
92.5
92.8

91.6
94.5
94.2

92.5
93.3
94.3

91.2
92.9
92.7

Shimano 27
Ultegra Mtn. Grupo

80
150
200

93.1
94.6
95.0

—
—
—

92.8
94.6
94.5

89.4
92.9
93.6

—
—
—

—
—
—

18
—
90.7
91.8
91.9
—
—

20
—
90.9
93.0
93.8
—
—

21
—
94.3
95.0
95.9
—
—

24
—
86.9
91.0
91.4
—
—

25
90.6
93.8
94.8
95.5
97.1
97.2

27

54
80
150
200
307
370

94
Uncorrected Eff.
Corrected Eff.
Uncorr. Eff.
Corrected Eff.

93

Shimano 27
(continued)

91

1

1

96

92

2

Gear =
Power
80
150
200

Maker/Speeds
Browning 4
Automatic

97

7

0

Table 2. Derailleur-type transmisions: mechanical efficiency vs. load

99

y = -3.60886E-12x3 + 8.73374E-08x2 - 1.98405E-04x + 1.88475E+00

90
0

2000

4000

6000

8000

10000

12000

14000

16000

50

18000

100

150

200

250

300

350

400

Output (watts)

Net ergometer load (grams)

Figure 13. Power loss vs. net ergometer load

5

6
7
Efficiency Percent

8

9

10

11

12

91.9
93.8
94.0

90.7
93.5
94.4

90.9
92.2
93.4

91.1
93.7
94.1

89.8
93.4
93.2

89.8
91.8
93.5

92.6
94.5
94.2

—
—
—

90.0
92.5
93.1

92.1
93.9
94.2

91.7
93.8
93.9

—
—
—

Figure 14. Shimano 27-speed, gear 25 (44/16) uncorrected and
corrected (efficiency vs. load; 75 crank rpm; correction is
estimated)

1

2

3

95.0
94.2
94.1

92.9
95.6
94.9

93.6
94.8
94.1

4

5

6
7
8
Efficiency Percent**

Shimano 3

80
150
200

90.5
93.0
93.2

93.5
93.9
95.0

87.2
88.6
87.2

Sturmey 3

80
150
200

92.3
93.3
93.0

95.4
95.3
95.6

91.8
91.8
91.8

Shimano 4
Automatic

80
150
200

93.6
95.6
95.3

90.1
90.9
92.8

87.1
88.9
90.0

85.8
87.0
88.0

Sachs 7

80
150
200*

88.7 —
89.9 —
91.0* —

—
—
—

89.2
92.3
93.0*

Shimano 7

80
150
200

90.8
91.8
92.8

90.7
92.9
94.5

87.4
89.9
90.3

89.0
89.0
91.8

83.6
85.6
86.4

90.9
92.8
93.7

88.2
90.4
91.4

Sturmey 7

80
150
200

87.3
89.1
89.7

88.7
89.0
90.3

88.4
91.1
91.3

93.0
93.3
94.7

89.3
90.4
91.0

86.0
88.5
88.6

83.0
85.4
85.3

Rohloff 14

80
150
200

89.1
90.6
91.3

90.3
92.5
92.5

87.8
89.9
90.9

90.3
92.2
93.4

87.5
89.6
90.5

87.8
91.0
90.9

86.1
89.9
90.2

9

10

11

12

13

14

Figure 15. Diagrammatic view of the Rohloff hub

TECHNICAL

Bicycle stability after
front-tire deflation
Dave Wilson (reporting partly for
Soohyun Park)
89.7
92.6
92.8

90.8
92.7
92.7

87.7
90.4
91.1

89.7
92.3
93.5

87.1
90.4
90.0

87.8
89.7
91.1

86.1
89.1
90.4

*The shift mechanism was broken, and would shift to only two gears.
** All efficiencies are uncorrected for the power consumed by the ergometer wheel drive. Although this is not large,
it would increase the indicated efficiencies by 2 to 2.5% in most cases.

10

NOTES

Number 52 Summer 2001

Human Power

We reported in Human Power, 51
(pp. 16–18) on experiments to provide
steering stability after a front tire
has deflated, there having been many
reports of “flopping” instability that
caused riders to be thrown off virtually
instantaneously. We reported the tentative findings of Andy Oury, who
increased the bead-seat diameter of
so-called “drop-center” rims1 and thereby greatly decreased the tendency of
Human Power

89.5
93.0
93.6

16

91.0
93.6
93.9

91.1
93.3
93.7

Table 1. Hub gear transmisions: mechanical efficiency vs. load
Gear =
Maker/Speeds Power
Sachs 3
80
150
200

15

deflated tires to “flop” from side to side.
This past academic year another MIT
undergraduate student, Soohyun Park,
chose to do her BSME thesis2 on a
continuation of this study. She first
researched an improved bicycle model,
resulting in the use of a BMX bicycle
with a weight mounted on it representing approximately a rider’s weight and
center of mass. She found that over a
wide range of weight values and positions the tire behavior when this bicycle was pushed across the laboratory
floor was better represented than in the
previous program.
Park then built up the bead-seats of a
wheel that had caused me serious trouble when the tire had deflated as I
was in front of a very large truck. She
Number 52 Summer 2001

used fiberglass tape and polyester resin
(Oury had used layers of masking
tape, which gave a soft seat of low
strength). She found, as did Oury, a
steady improvement in behavior as
the bead-seat diameter was increased.
Subsequently I continued the build-up
(the fit between the tire and rim was
exceedingly loose) until the diameter
was too large for the tire, and then
machined it down (using a profiled
router) until a smoothly shaped rounded-edge bead seat was produced that
allowed the tire bead to snap into position only after the tube was inflated to
about half final pressure.
When this final step was taken the
difference in performance changed dramatically. Flopping disappeared entirely, and the tire could provide safe
and stable bicycle direction during the
deceleration after deflation.
These results therefore add to the
previous somewhat tentative recommendation: that wheel and tire manufacturers and standards organizations
should arrive at standards for the sizes
and profiles of rims and of tire beads so
that a fit tight enough to produce stable
steering under deflated conditions is
achieved. There seems little doubt that
many deaths and injuries would thereby
be prevented.
—Dave Wilson
<dgwilson@mediaone.net>
1. Cycle and motorcycle tires and wheel-rim
standards. ETRTO, supplied by the Taiwan
Bicycle Industry R&D Center, Taichung,
Taiwan, 2001.
2. Park, Soohyun (2001). Run-flat performance of bicycle tires and modified rims.
BSME thesis, Cambridge, MA: MIT.

11

There is a better way
than rolling
by Detlev Tschentscher

Human-powered vehicles on land
usually have wheels. But there are
attractive alternatives.

WALKING

AND RUNNING AIDS

Humans are just ordinary mammals
except for two differences:
• we walk on two legs; and
• we consider ourselves to be intelligent.
This should mean that we have the
ability to improve our lives. It is surprising therefore that we do not use this
intelligence to improve our natural way
of movement: walking on two legs.
John Dick (one of the designers of the
Springwalker, member of the DARPA*
team) describes the situation as follows:
“We have had 150 years of engineering
now, and still there is no powered exoskeleton.”
When we refer to human-powered
vehicles on land, we usually mean
wheeled vehicles. And, as we all know,
there has been enormous progress as
these types of bicycles and other HPVs
have evolved. They seem to be given
attention only when breaking a record.
Nearly every college in the U.S. has a
project group devoted to human-powered vehicles. The technology and
parts to build an advanced bicycle
are available for reasonable prices all
over the world. But what makes us
believe that rolling is the only way
of moving such that it is worth so
much attention? Of course, if we had
to choose between walking or riding
a bike for traveling a distance of a
few kilometers on a gravel road we
would definitely choose the bike. The
reason for this is obvious: riding a
bike takes less effort than walking.
But what does this prove? Simply
that a mechanically supported method of movement is easier than a nonsupported movement.
To be able to compare walking to
rolling, as in the situation described
above, we should establish equal
opportunities between the two methods. Both the cyclist and the runner
should be mechanically supported.
But what does a device for the support of human running look like? To
give an answer we first need to ana*US Defense Advanced Research Projects Agency, Department of Defense

12

lyze where and how the human way of
running needs to be supported. One of
the main weak points in human running
is, that (because of our leg design) we
use only little energy for the forward
movement. If we would divide a normal
step into separate actions, only the part
where we jump up to move forward is
useful in gaining ground. The rest of
the movement is wasted for our fight
against gravity.1 Another approach for
support is to focus on increasing the
distance covered with just one step.
Research in bionics shows that kangaroos for example can run long distances at very high speed with very low
energy consumption. They can jump up
to a length of six meters and store the
energy that would normally be wasted
by a kind of spring-mechanism, using
their tail as a kind of spring. Several
approaches have been made to make
this simple phenomenon available for
humans.
In the early 1920s a number of patents came up which basically used the
idea of a pogo-stick attached to the
lower leg. But these patents did not
result in much improvement to running.
Until 1990 nothing really significant
occurred. Then a group of people
around the technician John Dick built a
prototype of an improved exoskeleton
which he called the “Springwalker”. The
device was a huge step towards a

Figure 1. One of the illustrations from the
Springwalker U.S. patent document

Number 52 Summer 2001

usable walking device. It combined the
use of artificial legs with a spring pack
on the back of the runner (see fig. 1).
Although the Springwalker was reported in all news media it was never
improved to become a functioning
device for the market. Today inventors
focus on servo-powered versions of the
Springwalker for military use. But a
few other attempts have gone into production. Several kangaroo-boots have
appeared on the market recently.2
Most of these are aimed at fitness
enthusiasts and are based on several
spring-systems attached to ski-boot-like
boots. With these boots it is possible
to jump up to four meters at two
meters high. Two technicians, Atanow
and Gordejew, of the Lufthansa-university of Ufa, even created a boot powered by a fuel engine. With this device
it is possible to take a one-hour walk
using only a matchbox full of petrol
(gasoline). But these efforts cover only
a small section of the latest research on
walking machines.
Most of the current research is in
robotics. To create a servo-powered
device that is able to walk requires
sophisticated development combining
biomechanics with information technology. This challenge has stimulated most
advanced research institutes and companies to work on walking robots in
some form or another. The number of
projects is immense. Even big overviews such as the “walking machine catalog” of the German institute of the FZI
Research Center for Information Technologies at the University of Karlsruhe3
are not able to show the full range of
historic and current projects. Most of
the projects are focused on multi-legged
vehicles or humanoid-legged robots.
The key issue of these projects is to
control the complex process of moving
servo-powered legs without losing the
balance. But all these devices have one
thing in common: they rely on artificial
power sources.
Only very few studies follow the
former Springwalker in using human
power as the only power source. One
of them is the network-initiative Kenguru4 that I started. We plan to build
an empowered running device such as
the Springwalker, except that a different kind of technology will be used: the
power of the runner’s arms. First contacts to industrial and other organizations have been made. All actual information about all current projects and
the Kenguru initiative can be viewed on
Human Power

the internet on my homepage (see reference 4).

REFERENCES

1. Homepage of the DARPA: http://
www.darpa.mil/dso/thrust/md/
exoskeletons/index.html
2. A good example of “kangaroo” boots
are made by Powerskip. See
http://www.powerskip.com
3. Link to walking machine catalog:
http://www.fzi.de/ids/WMC/
walking_machines_katalog/
walking_machines_katalog.html
4. Homepage: http://www.kenguru.de
Detlev Tschentscher is a production
engineer who has been working on
designs for human-powered legged
vehicles for four years.
—Detlev Tschentscher
Neusser Landstrasse 352
Germany 50769 Cologne
Tel: +49 (0) 221-978622
Fax: +49 (0) 40 360 306 4005
E-mail: <Detlev@springwalker.de>

money?” (Bike Tech 2:5), I talked to
a South African aluminium producer/
extruder and decided that their 6063
aluminium alloy would be soft enough
to roll easily, would be strong enough
after heat treatment, and would then be
suitable for anodizing if required.
Chris Juden’s article, “The aluminium
rim: Design and function,” (Bike Tech
3:2), was the great inspiration. It provided a wealth of information on rims,
tires and wheels. I chose to make a rim
with an inside width of 16 mm which
would suit tires from the then-popular
22-mm high-pressure tires to the more
practical 38 mm. My new IZIZI profile
should result in a mass of 280 gms/
meter and suit the stock 4-mm aluminium rod that would be used to pin the
joint. I based it on the successful Rigida
1622 which is similar to the Moulton.
(IZIZI was the name I chose because
it reads the same when viewed from
either side of the wheel.)

Tire-rim compatability
John Stegmann

Dave Wilson’s thoughts on the subject of front-tire blowouts (Human
Power 51, Fall 2000) reminded me of
the difficulties we encountered making
rims a decade ago. When I commented
to Dave that we had not considered
that tire manufacturers too might have
difficulty in maintaining size standards,
or that the wheel size might diminish
during wheel building, he asked to
reproduce the account which I wrote
for Cycling Science, with adjustments
if desired (Cycling Science, June 1990).
I had been inspired in 1987, by articles
that had appeared some years previously in Rodale’s technical journal, Bike
Tech, to make my own bicycle rims in
order to overcome two difficulties. One
was the high cost of imported aluminium-alloy rims, and the other was the
difficulty in purchasing rims of unusual
sizes and drillings that were needed for
the recumbents we were making. Suppose I could make the rims I wanted
and cover the cost by making and
selling popular rims? I discussed the
idea with friend and factory-owner Bill
Rosenberg, and came to an arrangement whereby he would assist me to
make the tools and would manufacture
the rims in his factory, and I would
provide the capital, the design, and
marketing.
After reading Mario Emiliani’s, “Heat
treated rims: Are they worth the
Human Power

Illustration from Cycling Science, June 1990

By the end of January 1988 we had
sample extrusions from the new die.
We made two rollers—stage 1 and
stage 2—and we marked out the hole
centers by hand. It all looked good
and we placed our first order for
50kg. The first rims we made were for
my new experimental FWD recumbent
with crank axle attached to the front
fork, based on information and encouragement from Californian Tom Traylor.
The bicycle was designed for 25-520
7.9-bar (115 psi) wired-on tires and was
to be ridden in the Argus Tour on 5th
March 1988. All it needed was wheels.
There was no time for heat treatment
as the bike was completed six days
before the event and I still had to
Number 52 Summer 2001

learn to ride it! To our surprise, the
rims proved to be quite satisfactory
and were never heat treated. Although
heat treating after rolling is definitely
the preferred procedure, a certain
amount of hardening does take place
during rolling, as well as during use and
with age.
The next rim was made to suit a popular 25-622 fold-up high-pressure tire.
We had it heat treated and anodized
in dark bronze, and built a beautiful
wheel with stainless-steel spokes and
a red powder-coated hub. I had made
an appointment in the morning with my
bank manager to apply for a loan to
start manufacture. I pumped the tire to
6.9 bar (100 psi) and set it aside. We
were excited at the success and by the
prospects. Little did we know that our
problems were about to begin.
I was still busy in my workshop five
hours later when the tube exploded!
Why? Was the tire defective? Had the
tire or tube been badly fitted? Was the
rim under size? I checked as much as I
could, yet found no obvious reason for
the failure. I therefore fitted a new tube
using talcum power to ensure that the
tire moved onto the rim properly, and
took the beautiful wheel with me to
the bedroom to show my wife in the
morning. Two hours later, at 3 A.M., we
almost died from shock when we were
woken by a very loud bang! Another
tube had burst!
At that time Karl Wright, an electronic-engineering student, was boarding with us. He was an excellent student (graduated top of a class of
over 800) but was equally puzzled.
Together we measured and calculated,
and destroyed several tubes under reasonably controlled conditions. We saw
how, slowly, the tire would bulge and
the tube creep out from below and
then rapidly balloon. If we were quick
enough we could deflate the tube
before it burst. We made a series of
rims, ever larger, until we could no
longer mount the tire. It took more
than a month to develop a theory to
explain the phenomenon, and another
six weeks to prove it. This is what we
established.
1. We had assumed that because the
flanges are almost 6 mm high, a variation of, say, 2 mm in bead-seat circumference would have an insignificant
effect since this would make a difference of only 0.63 mm in the diameter
of 622 mm. Wrong! The smallest difference in circumference can be disas13

trous. Tie a string around a beer
can and you will easily slip a matchstick between them. Similarly, if the
bead-seat circumference was 1952 mm
instead of 1954 mm, there would be sufficient slack for the tire to blow off the
rim. This also is the reason why rims
work fine with quite a shallow well.
2. Given that the air pressure is
equal, the stress in the casing of a narrow tire will be less than that of a fat
tire since the force is a function of the
cross-sectional diameter. Therefore, if
there is a little slack in the rim/tire fit,
at some point around the wheel the tire
will lift a little. That lifting increases
the cross-sectional diameter and consequently also raises the stress in the
tire fabric slightly more than elsewhere.
This increased tension slowly draws to
that region whatever other slack there
might be. This may take time, but can
be speeded up by dusting the tire/rim
interface with talcum.
3. The 25-520 tires for the first
wheels had wire beads. The 25-622 foldup tires that blew off used synthetic
beads. We had only one other 622 tire.
It had steel beads and worked fine.
We found that the tires with synthetic
beads could be mounted on a larger rim
than the wire-beaded tire. However,
we reasoned that that was not where
our problem lay. Our problem had to
do with the fact that synthetic beads
squash. Our rim had a bead-seat ledge
that was too narrow for the flattened
synthetic bead, so the tire tended to
slide off into the well. This action
reduces the cross-sectional diameter
which allows the tire to be pulled
around, usually to the opposite side of
the wheel, where a bulge would form
and the failure occur.

REMEDY

and mountain bikes arrived. IZIZI rims
were fitted to the recumbents used by
Lloyd Wright for two of his winning
rides in the 105 km Argus Cycle Tour,
and to Wimpie van der Merwe’s recumbent when he set the course record
(which still stands) and three IHPVA
world records, one of which still
stands. Despite these achievements and
the fact that we exported rims (Kingcycle), local dealers avoided us saying
that buyers wanted a big-name rim. The
expected (hoped-for!) swing to recumbents never happened. None of these
factors was good for business. We did
not make enough money to afford to
re-tool to make aero or mountain-bike
rims. In retrospect, that is probably
what we ought to have done to save
the business.
—John Stegmann
<recumbent@cybertrade.co.za>

Control of hydrofoils
using dynamic water
pressure
By Alastair (“Al”) Taig

Hydrofoils are used on watercraft to
provide lift, and/or stability. Generally,
foils may be fixed or capable of varying
their angle of incidence. Fixed foils
may be angled to be part submerged,
and part above the water surface, so
that as they rise, the submerged area
of foil decreases, and an equilibrium
will be achieved. But foils which break
the surface cause wave drag and suffer
from “ventilation” (pulling air down to
the upper surface of the foil due to
decreased pressure). Thus, fully submerged foils, with some means to prevent them reaching the surface, are
potentially more efficient.

The remedy was twofold. First, we
had the extrusion die altered very
slightly, to broaden the bead-seat ledges
to 2.5 mm. Five weeks passed before
the new material arrived. Second, we
had to ensure that the circumference
of the bead seat was between being
exact and no more than 0.5 mm smaller,
(1953.5–1954 mm).

POST

SCRIPT

We had other difficulties, so the time
delay between needing to beat the cost
of imported rims and being ready to
manufacture was almost two years.
During that time the price of imported
rims dropped significantly, aero rims
14

the foils, mounted on the tip floats,
have a variable angle of incidence, they
may be adjusted to provide variable lift,
independently.
This could be by manual control,
requiring a skilled “pilot”, or by an automatic system which maintains each foil
at a constant depth below the water
surface.
Existing, state-of-the-art foil boats
(such as the sailboats, Rave and Hobie
Trifoiler) use devices that follow the
surface (a kind of water ski on the Trifoiler) connected by a mechanical linkage to the adjacent foil. These surface
followers provide increased water drag,
and are vulnerable to damage.
The following diagram illustrates the
proposed pressure-controlled system,
in which dynamic water pressure is utilized to adjust the angles of the lifting
foils.

Figure 1. Angled and horizontal foils

FOIL

ACTUATION

A foil boat generally requires some
means to keep the boat from pitching
and heeling excessively when lifting. If
Number 52 Summer 2001

Figure 2. General arrangement of foil strut and
pitot-tube location

In this design, a short tube, called a
“pitot tube”, in the leading edge of the
“fin”, about 200 mm above the foil, is
pressurized by a combination of depth
below the surface, and the dynamic
pressure due to speed through the
water. This pressure compresses the air
trapped inside the fin, and is picked
up by a bellows (or other sealed type)
actuator. This has a piston that pushes
on a lever fixed to the hinged foil, as
shown. Positive pressure produces a
positive angle on the foil, increasing its
lift. When the hole reaches the surface
of the water, pressure will be lost and
the foil angle will decrease. As there
will be a time delay as some water
enters or leaves the tube, the pressure
in the fin and actuator will tend to settle to just maintain the pitot at a “mean”
water level. The diameter of the hole
in the pitot tube controls the rate of
Human Power

Figure 3. Diagram showing dimensions used in
the equations

change of the foil angle, hence the sensitivity to waves. Static water pressure,
at the pitot, also acts on the actuator,
but the effect is relatively small as the
craft rises on the foils.
The position of the foil pivot in relation to the center of lift of the foil determines the force required on the control
lever, to increase the foil angle. It is
advantageous to pivot the foil a small
distance ahead of the lift center, so that
the lift will act to reduce the foil angle.
This is a stable condition and avoids
any tendency for the angle (and hence
lift) to increase uncontrollably. If the
pivot is close to the lift center, the force
required at the actuator will be relatively low and the size of the actuator
can be minimized. This is important in
order to reduce the volume of the air
space in the fin (as shown in the diagram of the system).
The reason a space is sealed in the
fin (rather than connecting the pitot
tube to the actuator with tubing), is to
provide a reservoir of trapped air in
the fin to prevent water from entering
the actuator. If the system filled with
water, the reaction rate of the mechanism would be slow, and the static
water pressure at the pitot tube would
not assist in pressurizing the actuator.

BALANCE

OF FOIL FORCES

Foil lift (L) acts at a distance ‘b’
behind the pivot center
Actuator force (F) acts on a lever of
length ‘h’.
The moments of these forces must
balance for equilibrium.
L.b = F.h
But, L = 0.5ρV2 SCl
That is L = 500V 2 S Cl
(1)
where L is lift, Newtons ρ = water
Human Power

density, = 1000 k g / m 3
S is area of foil (sq. m)
V is speed (m/sec)
Cl is lift coefficient of the foil
And p = 500 V 2
(2)
p is dynamic pressure, N/sq. m
Also F = pA
(3)
A is actuator piston area, sq. m.;
But L.b = pSC l b and F.h = p.Ah
Hence SClb = Ah (p cancels on both
sides of the equation)
Or Cl = Ah/Sb = constant depending
on the dimensions.
This implies that the foil lift
coefficient will remain constant until
the pitot tube reaches the surface
(when p decreases).
The system performance can be modified by a return spring, which holds
the foil at its minimum angle until the
speed is sufficient to pressurize the
actuator to overcome the spring. This
arrangement is preferred, as the craft
has less drag with the foils at minimum
angle, and will reach “foil speed” more
easily.
In this case:
L.b = (F – P).h
(4)
where P is the spring force acting at
the actuator.
The factor, 500V 2 does not cancel in
this case
P.h = F.h − L.b
P.h = pA.h − p S C l . b
(5)
And p = 500V 2
eq. (2)
Equations (1) (2) (3) and (5) can be
used to find the proportions of the
specific foilcraft.
Step 1.
Knowing the design weight (W) of the
craft, assume that L is 0.5W
A practical maximum value for Cl is
assumed as 0.8.
The design lift-off speed can be used
to determine the foil area, S, from
eq. (1)
Pressure, p, for this speed is found
from eq. (2).
Step 2.
Assume a speed at which the foils
should begin to provide lift. This
must be within the fully immersed
speed capability of the craft. At this
speed, F = P, and Cl = 0. Calculate the
pressure, p0, at this speed, from
eq. (2).
Then P = p0 A. (The piston area, A, is
not known at this stage.)
Step 3.
Using eq. (5) at lift-off speed, the area
A can be found by substituting p0A
for P.
Number 52 Summer 2001

SAMPLE

CALCULATION

AUTHOR

NOTES

Step 1.
Craft weight, W = 118 kg (260 lbf)
Foil lift, L = 59 kg = 579N (130 lbf)
Lift-off speed,Vl = 4.9m/sec (16 ft/sec)
L = 500V 2 SCl (0.97V 2 SCl)
eq. (1)
S = 0.0603 sq m (0.654 sq ft) at
Cl = 0.8
p = 12005 N/sq m (248 lbf/sq ft)
Step 2.
Assume speed when foils start lifting,
V0 = 3 m/sec (10 ft/sec)
p0 = 4500 N/sq m (97 lbf/sq ft)
P = 4500A N (97A lbf)
Step 3.
Using dimensions
h = 0.61 m (24 in); b = 0.0127 m
(0.5 in)
P.h = pA.h−pSCl.b
4500A × 0.61 = 12005A×0.61−12005 ×
0.0603 × 0.8x0.0127
Giving, A = 0.001607 sq m (2.49 sq in)
Return spring preload,
P = 4500 × 0.001607 = 7.23 N (1.63 lbf)
(The above numbers apply to a sailboat being developed by the author.)
This example shows that a practical
design can be achieved, using dynamic
pressure to operate the hydrofoils.
For the design of a human-powered
boat, the lift-off speed will probably
be less than the 4.9 m/sec used in the
above (sailboat) example. A speed of
around 3 m/sec would be more reasonable, and when applied to the above
analysis would result in larger-area
foils. But the utilization of dynamic
pressure for actuation is still feasible.
I built my first sailboat about nine
years ago, and the angled foils were
intended for stability rather than fulllift capability. They enable a sailboat to
carry more sail-power than otherwise.
The three later craft have lifting capabilities, but rarely get fully foilborne on
my home lake, due to fickle winds and
weeds. However, the latest, pressurecontrolled foil system has been proven
to work on the current (#4) boat. Even
in the no-lift configurations the boats
are fast and meet my goal of being the
fastest sailboat on the lake. The name
“Alf” comes from that crazy TV extraterrestial who liked to EAT CATS.
By the way, I am a retired engineer,
with a career devoted mainly to automotive steering and brake development.
—Alistair Taig
<alistair.taig@gte.net>

15

PROJECT

Review by Mark Drela

REVIEW

CHicK-2000 Project Team “Active Gals”

The CHicK-2000 human-powered aircraft by the ActiveGals group has a
number of notable features.
The wing structure employs a
stressed skin which provides the necessary torsional stiffness in addition to
its usual duties of forming the airfoil
contour. The most common approach
has been to rely on a tubular spar to
provide all the bending and torsional
stiffness, with secondary foam sheeting
and a thin Mylar wing skin providing
the airfoil shape.
Using the stressed skin for torsion
instead allows the use of a full-depth
I-beam spar to provide the bending
stiffness. The I-beam spar is a far more

Remarkable achievement of ActiveGals HPA team in Japan
This note gives some details
of the human-powered aircraft
“HYPER-Chick KoToNo Limited”
built by the team “ActiveGals” in
Japan, and sent by the team’s
leader Toshiaki Yoshikawa (letter,
26 March 2001). Mark Drela’s review
of the remarkable achievements of
the team follow this note.
The technical data are shown in
the drawing. The photographs show
the plane itself and some of the
team members, including the pilot
Kotono Hori, who successfully
made the first FAI I-C class humanpowered flight in Japan in 1992.
On 4 and 5 November 2000, the

team made the first flight of an HPA
with stressed-skin construction.
Both the I-beam spars and the styrene paper mentioned in Mark Drela’s review were reinforced with
carbon fiber. The result was an aircraft that could fly (at a height of
2 meters) needing only 160 watts of
power input to the pedals, a world
minimum for an HPA.
Yoshikawa wrote, “It has a composite structure, CFRP on spar and
GFRPed styrene paper on skin.” He
wrote also that the team is “working
to realize a new circling method,”
described thusly: “The new circling
method is by twisting the flexible
wings during banking by
applied aeroelasticity.
“The twist of the right wing
is applied in the opposite
direction of that of the left
wing. This has been found to

In flight, above, with pilot
Kotono Hori (left).
Right: Project leader Toshiaki
Yoshikawa
Opposite: Working on one of
the wings of the craft—and
the technical chart.

16

Number 52 Summer 2001

The ActiveGals group appears to have
solved this problem with their fiberglass-reinforced styrene paper.
The stressed skin is also very
demanding of design details and construction quality to preclude local
buckling or failure. Again, these problems appear to have been surmounted
as the aircraft is clearly structurally
sound. Construction photos reveal
meticulous craftsmanship.
Other reported innovations include
the use of aeroelastic effects to twist
the wings for roll control. Judging from
the type of control yoke, the pilot
appears to have full three-axis control
of the aircraft, although it is not clear
how the wings are twisted in practice.
—Mark Drela, MIT
professor of aeronautics
and astronautics,
Massachusetts Institute of Technology
(principal designer and constructor of
several MIT HPAs).

reduce power loss during the HPA’s
turn.”
Circling flight is difficult because
of the greatly increased power losses and the control difficulty in the
turns. (The “inside” wing goes much
slower than the outer wing and
tends to lose lift.) Stressed-skin construction allows the use of wingwarping (in opposite directions)
during the turn. It also greatly
reduces wing deflection and permits
the use of a very high aspect ratio,
43.7, further reducing the aerodynamic losses.
The aircraft is on display at the
Kakamigahara Aerospace Museum.
—Dave Wilson

Photos and chart, CHicK-2000 team

(from a communication from Toshiaki Yoshikawa)

efficient bending member than the tube
spar, and hence provides a stiffer and
stronger wing for a given weight.
Not surprisingly, the wing-tip deflection of the CHicK-2000 under load is
amazingly small considering its low
empty weight of 31 kg and its immense
wing aspect ratio of 44. The high aspect
ratio obviously contributes to the modest specific flight power of 3.6 W/kg
pilot mass, despite a fairly high wing
loading of 46 Pa which gives a rather
fast cruising speed of about 8 m/s. Low
power coupled with high speed gives
the potential for large range, and also
gives the ability to handle windier conditions than more lightly-loaded HPAs.
One practical disadvantage of a
stressed-skin HPA structure is that
common construction materials such as polystyrene foam do
not have a sufficient shear modulus for the task.

Human Power

CHicK-2000 Project Team “Active Gals”
6-36-11 Suzuhara-cho
Itami city, Hyogo 664-0882, Japan
{no e-mail address provided]

Human Power

Number 52 Summer 2001

17

BOOK

Richard has been more dedicated and
more successful.
RICHARD’S 21st CENTURY BICYCLE
The books differ mainly in the use,
BOOK(S) by Richard Ballantine.
respectively, of American English and
reviewed by Dave Wilson
British English, including some translaThis book is two books, or one book
tions of slang. Some examples slipped
in two versions. One is for non-Norththrough. For instance, how many AmerAmerican readers; and was published
ican readers would know what to
by Pan Books (Macmillan) in Britain at
expect if an HPV were classed as
the end of 2000. Earlier editions came
“dodgy”? (Roughly it means that it
out in 1972, 1975 and 1989. It is a very
wouldn’t be a good bet.)
successful book: one of the messages
The British version of the book has,
on the cover states “…the best-selling
as the sole representative of cycling on
bike book of all time, with over onethe front cover, Richard’s daughter in a
million copies sold!” As I wrote this I
carbon Windcheetah tricycle HPV with
was about to leave for Norwalk, CT, for
a lot of advanced components. We must
the June first launching of the Northgive Richard some of the credit for the
American version with the author himpublisher’s belief that a bike book with
self.
an HPV on the cover was not going
Before I wax too enthusiastic about
to put people off buying it. The U.S.
the book(s) I should
publisher, The Overlook
confess my biases.
Press (Woodstock and
I first met Richard
New York), apparently
Ballantine in 1980 in
felt that doing this in
Bremen, Germany, at
North America would
a bicycling conferbe too risky, and I think
ence called “Velothat many of us would
City”. I had brought
agree, with some sadalong one of the first
ness.
Avatar 2000s, which
Inside the books have
received a great deal
many similarities: there
of favorable publiciare 22 chapters having
ty. (We hadn’t patentthe same titles, starting
ed it in Europe, and
with “Get a bike!” to
several rather faith“Done!” All the chapters
ful copies were subare written with a
sequently manufacbreezy enthusiasm coutured by some new
pled with a deep knowlU.S. version of Richard Ballantine’s
enterprises that did
book.
edge of the field and
well with them.)
an instinct for telling
Richard had already
people, from raw beginbought an Avatar, and put it (with a
ners to seasoned enthusiasts, what they
rather wild British female model) on
want to know.
the cover of “BICYCLE”, the British
Of particular interest to HPVA memmagazine he published and edited, as
bers is chapter 5: “Zzzwwaaaammo!”,
“the bicycle of the future.” He felt that
27 pages devoted entirely to extolling
it could also be fast, formed the Nosey
HPVs, and, on a quick scan, having
Ferrett Racing Team, recruited Derek
more illustrations than any other chapHenden, who made several full fairings
ter. That alone sets Richard’s book well
for it, and named it the “Bluebell”. This
apart, (i.e., well ahead) of all competiwent on to win the IHPVA World Speed
tors.
Championship in the US and many
You will enjoy this book. The British
races in Europe over several years.
version has the ISBN number 0 330
Therefore I start by being biased in
37717 5; it costs UK£16.99. The North
favor of Richard Ballantine. He did a
American version has ISBN 1 58567 112
great deal for the Fomac-made Avatars,
6; I bought my copy from the Overlook
and for recumbents and HPVs in Britain Press, Lewis Hollow Road, Woodstock,
and Europe.
NY 12498, for US$28.50 including P&P;
We are an “odd couple”. Richard is
the bookstore price should be about
an American who has lived in Britain
US$18.00.
for decades; I am an ex-Brit who has
—David Gordon (Dave) Wilson
lived in the US for decades. We both
<dgwilson@mit.edu>
do what we can for bicycling and HPVs.

Above: A closer view of the cockpit and propeller of the
CHicK-2000 aircraft. Right, Takashi Hattori, right-wing runner; below, Kouta Sata, left-wing runner.

18

Number 52, Summer 2001

Human Power

REVIEW

Human Power

Number 52 Summer 2001

LETTERS
Danny Too responds to two letters
about his article (with Chris Williams),
“Determination of the crank-arm length to
maximize power production in recumbent
cycle ergometry” (Human Power 51, Fall
2000).

Battle Mountain crank arms
Matt Weaver

In light of crank-arm length, I have a
few observations on the recent article
on bicycle cranks [by Danny Too and
Chris Williams]. It took me a moment
to deduce what was actually tested, but
if cranks are of any interest to you, I
find it important to note and relay the
following.
1. The test was a variable-rpm,
“fixed-torque” test: relatively light pedal
force, proportionately lighter for longer
cranks; riders “gave their all” (maximum exertion) for 30 seconds. Cadences reached high rates (>170 rpm)
for the shortest cranks, and modest
rates (135 rpm) for the longest cranks;
cadences dropped to the low 80 rpm
range for short cranks, and low 90 rpm
for longest cranks in the final five
seconds. Calculated power output was
proportional to cadence: the faster
you can spin, the more power you
get (fixed torque, and flywheel inertia
ignored).
2. The torque decided upon was
referred to as the “appropriate load” or
“85 g/kg of subject body mass” (apparently total mass, not lean or leg-muscle
mass).
3. I’m not sure what “appropriate
load” is, but it can be deduced. The
apparatus was as follows: a 52/14 single-chain drive to a flywheel with a
1.615-meter circumference, with a friction belt of known net tension wrapped
about it. That’s roughly a 0.5-meter
diameter (20-inch) flywheel, (mass/
inertia not given)—comparable to moving the belt tension force a distance of
6.0 meters for every revolution of the
cranks: effectively a fixed-mean crank
torque = 0.8 N.m per kg total rider body
mass. (0.27 ft.lbf per pound total rider
weight) (ignoring flywheel inertia).
For example, for me (“85g/kg” belt
tension mass, and 80kg rider body
mass, 175 mm cranks): belt tension =
6.8 Kg×9.81m.s−2 = 67 N (15 lbf); pedal
tangential force = 364 N (82 lbf); or
roughly 1/2 to 1/3 my mean pedal force
normally developed during a sprint (30,
and 5 sec, respectively).
19

4. Test starting rpm (at t=0) is not
given, except that it said the ergometer
flywheel was accelerated until “inertial
resistance had been overcome.”
5. Inertia still exists, and cadence
varied between start rpm, 174 rpm and
82 rpm during 30-second test. Power
sink/source from flywheel during rpm
changes may or may not have been significant depending on flywheel inertia
(not given, except for the ergometer
model number).
Some observations about the experiment.

1. The “appropriate” fixed torque
chosen was relatively low for a “healthy
male” 30-second cycling sprint bout
2. Pedal cadence given maximum
effort shot into the uncharacteristically
high 170 rpm range (for short cranks)
and swung through a nearly 2:1
cadence range.
3. Longer cranks, in spite of lower
pedal force, yielded substantially lower
peak pedal cadences (135 rpm) and
consequently lower peak power.
4. Interestingly, longer cranks were
turning faster at the end of the 30-second bout.
5. Unlike the experiment, real
cycling consists of relatively steady
cadence with mean pedal force varying
with fatigue state of muscles.
6. It seems to me the following
occurred: light pedal force reduces to
a “spinning” contest, the fixed crank
torque specified in the experiment was
“light” for a sprint; peak power goes to
the fastest spin in this experiment (with
relatively light load, it is typically easier
to spin rapidly unusually short cranks
(110 mm) than unusually long cranks
(265 mm)).
This is can be considered from experience, from neuromuscular adaptation/
control given untrained subjects, and
muscle group force/velocity curves.
The final (slowest) cadence was likely
lowest for the short cranks due to
greater utilization/exhaustion of rider
muscles using short cranks, and lessexhausted state of rider legs given long
cranks and inability to generate as
much work during the 30-second bout
(i.e., short cranks wind out and then
fatigue; long cranks lumber along awkwardly with less cadence variation for
the brief 30 seconds).
7. Conclusions from the experiment
as it relates to cycling:
I would not conclude in any way
that short cranks are preferred for peak
20

power; I would not conclude in any
way long cranks are better for longer
events (especially based on a brief
30-second maximal and large cadence
variation anaerobic bout). I would
suspect that if a sufficiently high
“appropriate-load” torque were chosen,
the experiment observations would
reverse, with the longer cranks superior for peak power. My primary conclusion, honestly, is simply that a group
of maximally-exerting healthy guys can
spin the relatively light, arbitrarily-specified mean crank torque (0.8 N.m per
kg total rider body mass) to higher
cadences with unusually short cranks
(174 rpm, 110 mm) than they can
with unusually long cranks (265 mm,
135 rpm), and they are likely more
fatigued after 30 seconds with the
shorter cranks).
8. “Optimal” crank length and
cadence is indeed important for serious
cyclists, and critical for racers, as noted
in the study.
9. To come to some useful conclusions about power/crank lengths. I
would perform tests specific to the
nature/duration of interest (e.g., for a
kilo sprint, a simulated-inertia ergometer or real bike with different cranks/
gearing and a stopwatch—perhaps
already done); (e.g., for hour/long rides,
various fixed cadences, and rider-chosen cadence, and measure total work
and ideally O2 uptake/CO2, HR, etc.).
10. Given such fixed cadence data, a
2D cadence/power (aerobic and anaerobic bouts) “map” for different crankarm lengths and cadence could be generated and would be greatly valued by
many cyclists. Such maps of course are
dependent also on muscle type, limb
lengths, etc.
11. Some crank experiments:
In my garage in 1995 I prepared
some tools to discover such basic
information. I built a computer-controlled cadence ergometer to explore
my 152-mm cranks. Cadence was regulated precisely by digital feedback control to an electromagnetic brake, and
instantaneous torque/crank angle via a
load-cell rig was logged as well. No
matter how hard or easily I pedaled,
the cadence remained fixed at its set
point. I had great fun for several days
stomping on the pedals and listening to
the controller magnetics hum and surge
with each leg stroke.
I had validated the velocity uniformity. But, during my enjoyable pedaling,
Number 52 Summer 2001

a loose wire shorted and destroyed the
power-electronics circuit. Other than
logging a few torque profiles and discovering that my left (dominant, but
knee-operated) leg is hopelessly weaker than my right, I ended up resuming
crank-power testing by utilizing hillclimb tests, because of limited time.
More recently, I found something
interesting about cadence. I was invited
to test my output on an ergometer at
the home of John Howard. I had time
for only a 30-minute ride, but discovered quite dramatically how, beyond
a certain increase in cadence, my
“perceived exertion” rose significantly
while my power output dropped simultaneously. I averaged 420 watts for the
test, for which I was delighted, yet
I would drop below 350 watts with
a mere 10-rpm cadence increase over
what appeared most productive. Such
observations make the use of recently
available tools like the “Tune” hub/
downloader or the SRM meter (though
crank-length changes may be a problem
there) critical for racing cyclists.
If I had my wish, I’d have access to
a Tune hub and get to know myself
better! I hope enthusiastic and endeavoring researchers like Danny Too continue their quest in providing all the
detailed studies necessary to fully
and truly map out the relation of
crank length and rider position to
real cycling-performance characteristics. Good cranking!
—Matt Weaver <weaver@e2000.net>

Response to Matt Weaver
I wish to thank Matt Weaver for his
comments and observations regarding
my article in the last issue of Human
Power 51 (Fall 2000) on crank-arm
length. Matt Weaver’s comments (#1–5)
and observations (#1–11) above regarding my article on crank-arm length are
correct and well summarized. However,
I would like to comment and expand
upon his observations.
This particular study was used
to determine how power output/
production (as measured/determined
by pedal cadence or flywheel revolutions) changes (or the trend of power
production) with changes in crank-arm
length for a fixed load. The load
selected (85 g/kg of each subject’s
body mass), although relatively low for
“healthy male” 30-second cycling sprint
bout (as stated by Mr. Weaver), was
based on the load limitation of the
ergometer (that would still ensure
Human Power

accuracy) with the heaviest subject
tested. Based on the literature available
with upright ergometers, there is an
interaction between pedaling cadence,
load, and power output. With the addition of another variable (crank-arm
length), one would expect that there
will be an interaction between crankarm length, pedaling rate, load, and
power output. Therefore, Mr. Weaver
is correct in stating “that if a sufficiently high appropriate load torque were
chosen, the experimental observations
would reverse, with the longer cranks
superior for peak power.” In fact, this
is what has been observed, based on
the trends from data I had collected
on females, examining the interaction
between crank-arm length, load and
power output in the same recumbent
position. Females were selected
because they are not as heavy (nor
as powerful) as males, and the highest
load used and tested (165 gm/kg BM),
were within the maximum load capacity of the ergometer. The data and
results from this study will be submitted for publication in some future issue
of Human Power. Based on this one
study and the delimitations and limitations of it, Mr. Weaver is correct
in stating that “Unlike the experiment,
real cycling consists of relatively steady
cadence with mean pedal force varying
with fatigue state of muscles” and that
he “would not conclude in any way
long cranks are better for longer events
(especially based on a brief 30-second
maximal and large cadence variation
anaerobic bout).” To address these
issues, I have data collected on power
output and time to exhaustion, when
different crank-arm lengths are used
with different pedaling cadences, and
incrementing workload until exhaustion (or when the selected cadence can
no longer be maintained). I have not yet
analyzed the data or the trends associated with it. That data will also eventually be submitted for publication in a
future issue of Human Power.
In conclusion, there are clear limitations as to the information that can be
obtained from a single study, as well
as how the data are interpreted or can
be interpreted. It is obvious that the
data obtained in the laboratory are not
always “specific to the nature/durations
of interest” as noted by Mr. Weaver.
Unfortunately, that happens to be
the nature of the beast (research).
Research to be undertaken properly
and correctly is slow and tedious,
Human Power

needs to be done under an environment
where all conditions and variables are
very carefully controlled and accounted
for (while the experimental variable is
manipulated and tested), and is not
always going to be “specific to the
nature/durations of interest”. However,
research does produce empirical data
that provide information and direction
regarding how performance may be
enhanced in the real world.
—Danny Too <too@brockport.edu>

Crank-arm length and
leg length/proportions?
John Stegmann

Over the years Danny Too and coresearchers have taken the trouble to
measure and explain things that most
of us interested in recumbency would
like to know but tend to rely on intuitive guesses. Their research into the
effects of crank-arm length on power
production has left me wishing to know
why there was no discussion on the
relationship between crank-arm length
and leg length/proportions?
Cyclists have (always?) imagined
that people with short legs (short
femurs?) will be happier with short
cranks, and long-legged cyclists with
long cranks. The cyclists used for the
test varied in height from 1.72 m to
1.88 m, and there must surely be the
possibility of greater variation in their
leg configurations? I now wonder if
there is evidence to support this old
notion. A century ago Archibald Sharp
(Bicycles and tricycles, p. 266) considered the speed and motion of the
cyclist’s knee-joint and wrote: “The
shorter the crank, in comparison with
the rider’s leg, the more closely does
the motion of the knee approximate to
simple harmonic motion; with simple
harmonic motion the polar curve is
two circles.” From this it would appear
that the near-circular motion produced
by shorter cranks would favour higher
pedaling speeds. Plotting the Too and
Williams maxped and minped figures
from Table 1 on the graph in figure 2
(p. 4), using a scale of 1000 W=145 rpm,
the power and rpm curves are an
almost perfect match. The crank-arm
lengths in the study varied exceptionally; far more so than the cyclist’s legs.
Yet the results show that shorter cranks
allowed higher rpm, and higher rpm
produced greater power.
—John Stegmann
<recumbent@cybertrade.co.za>
Number 52 Summer 2001

Response to John Stegmann
Stegmann: “Their research into the
effects of crank-arm length on power
production has left me wishing to know
why there was no discussion on the
relationship between crank-arm length
and leg-length/proportions?”

First, we do have the data on leg
lengths and leg-length/proportions (as
well as other anthropometric data) on
all subjects tested. Second, we did not
discuss it because: (1) we did not examine the leg-length/proportion data in the
study (since that was not the focus of
the study), and even if we did, that
would be a different topic and study
altogether; (2) discussion of leg length
and proportions would have detracted
the reader from the “meat” and trends
found in the study; (3) leg-length/
proportions would have been expected
to randomly vary (as would height and
weight) for the subjects tested, and
without having selected (or matched)
equal number of subjects for different
leg-length/proportion, the discussion
based on the results could be biased
and provide inaccurate or misleading
information; and (4) discussion of leg
length and proportions may result in
more equivocation and confusion than
clarity. Regarding this last point, we
do not believe it is the leg length or
leg-length proportions that is important, but rather, it is the hip, knee and
ankle angles that results from an interaction between crank-arm length and
leg length (or leg-length proportions) to
maximize power production and minimize fatigue that is important. The reason for this statement? There is no theory or theoretical basis to explain or
justify why differences in leg lengths or
leg-length proportions should result in
greater or lesser power production with
different crank-arm lengths. However,
there is a theoretical basis for why
some joint angles (hip, knee, ankle)
will result in greater force/power output, and how these joint angles may be
produced with different combinations
of leg length and leg-length proportions
interacting with different crank-arm
lengths. Based on the tension-length
and force-velocity-power relationships
of contracting muscles, there is/are
some hip, knee and ankle angle(s) (or
joint range of motion) that will maximize power production and performance, and that there is an interaction
between crank-arm length, pedaling
rate, and load. What is/are this/these
21

optimal joint angles to maximize
cycling performance? This has not been
determined yet because of the difficulty
in manipulating, reproducing and then
testing various combinations of joint
angles with subjects of different leg
lengths and leg-lengths proportions.
Even if the optimum joint angles were
determined, to obtain these optimum
joint angles may result in crank-arm
lengths that are similar (or different)
for subjects of the same leg length with
different leg-length proportions, or of
different leg lengths with the same leglength proportions. This would imply
(and possibly conclude) that the optimal crank-arm length is very individualized, and dependent on, both the
leg length and leg length-proportions of
the cyclist (in addition to other factors
such as pedaling rate and load). This
would not be a very satisfying answer
to those looking for a quick and simple
solution to a very complex problem. In
some of my previous investigations, I
was able to manipulate hip angles (and
observe the changes in cycling performance), while maintaining the same
knee angles, by adjusting the seat-tube
angle in conjunction with the seat-topedal distance. This provided information regarding the optimum hip angle to
produce power when interacting with a
certain knee angle (and helped explain
why power output in some recumbent
positions is greater than in upright
cycling positions). We have also examined the effects of changes in seatto-pedal distance on joint angles and
on power production (which we will
be submitting to Human Power for
publication). However, this interaction
between hip and knee angle to maximize power production is much more
complex when crank-arm length is
systematically manipulated because a
change in crank-arm length affects both
the hip and knee angle simultaneously.
This makes it very difficult to determine whether the changes in cycling
performance when manipulating crankarm length is primarily attributed to
changes in hip angle, knee angle, or
both (the net effect of this interaction)
especially since this involves multi-joint
muscles acting on multiple joint segments simultaneously.
Stegmann: “Cyclists have (always?)
imagined that people with short legs
(short femurs?) will be happier with
short cranks, and long-legged cyclists
with long cranks. The cyclists used for
the test varied in height from 1,72 m to

22

1,88 m, and there must surely be the
possibility of greater variation in their
leg configurations?”

It is very possible that there is greater variation in their leg configurations.
But again, it is probably not the actual
leg configurations that is as important
as the leg configurations that will result
in the hip, knee, and ankle angle that
will maximize power production when
interacting with some given crank-arm
length. And there are probably as many
different leg configurations with crankarm-length combinations that would
result in the optimal joint angles to
maximize power production as there
are cyclists. Hypothetically, if a study
was conducted with very tall people
(long-legged cyclists) versus very short
people (short-legged cyclists), I would
suspect that similar curvilinear trends
for both groups would be found for
power output with incrementing crankarm length. However, the crank-arm
length that would maximize power output would probably be different for
the two groups (depending on the load
used, pedaling rate, and fatigue level)
because the same crank-arm length
would result in different joint angles
(that may or may not be optimum) for
the two groups.
Stegmann: I now wonder if there is
evidence to support this old notion. A
century ago Archibald Sharp (Bicycles &
Tricycles, p. 266) considered the speed
and motion of the cyclist’s knee-joint
and wrote: “The shorter the crank, in
comparison with the rider’s leg, the
more closely does the motion of the
knee approximate to simple harmonic
motion; with simple harmonic motion
the polar curve is two circles.” From
this it would appear that the near-circular motion produced by shorter cranks
would favour higher pedaling speeds.

I don’t know if there is evidence to
support the notion mentioned above,
but I would agree that shorter cranks
would favour higher pedaling speeds (if
minimal loads are used). However, as
the load increases (and continues to
increase), the pedaling speed (at some
point) will start to decrease. At this
point, longer cranks would be favoured
to minimize fatigue and to maximize
power output. If you are interested,
there is a paper we had published (with
data involving upright-cycle ergometry)
that included a discussion of the interaction between crank-arm length and
pedaling rate, and its effect on the kinematic and quasi-static moment contriNumber 52 Summer 2001

bution to the total joint moments to
affect the joint-moment cost-function
minimum. The reference for the paper
is: Too, D. & Landwer, G.E. (2000).
The effect of pedal crank-arm length
on joint angle and power production
in upright-cycle ergometry (Journal of
Sports Sciences 18:153-161).
Stegmann: Plotting the Too &
Williams MAXPED and MINPED figures
from Table 1 on the graph in Figure 2 (p.
4), using a scale of 1000 W=145 rpm,
the Power and rpm curves are an
almost perfect match. There should be
a very close match between MAXPED
and MINPED from Table 1 with Peak
and Minimum Power from the graph in
Figure 2, since MAXPED and MINPED
were determined from the flywheel revolutions for a 5-sec interval, as was Peak
and Minimum Power (which was then
used to generate a regression equation
for Peak and Minimum Power).

Yes, the crank-arm lengths in the
study varied exceptionally; far more so
than the cyclist’s legs. Yes. The crankarm length was deliberately selected so
it would vary exceptionally far more
than the cyclist’s legs. The reason? We
wanted to examine the extreme ranges
of crank-arm lengths that could possibly be used (and a few in between),
in order to determine the trend in
power production/output with incrementing crank-arm lengths.
Stegmann: Yet, the results show that
shorter cranks allowed higher rpm, and
higher rpm produced greater power.

Yes, that statement is correct, but
only for the load used in that study
(85 g/kg of each subject’s body mass),
since there is an interaction between
pedaling rate, load, and crank-arm
length. If the load is increased and continually increased, at some point, pedaling rate will decrease resulting in a decrement in power. At this point, a longer
crank-arm length will be more effective
in producing power. We have data to
support this, and will be submitting a
paper for publication in a future issue
of Human Power.
—Danny Too <dtoo@brockport.edu>
State University New York Brockport
Dept. of Physical Education & Sport
350 New Campus Drive
Brockport, NY 14420-2989
Tel:716-395-2403 Fax: 716-395-2771

Human Power

EDITORIALS
A bit of history viewed from
Eastern Europe
by Marek Utkin M.A., Poland

In what must now be considered
historical, a bicycle-design contest was
organized by Dave Wilson in the magazine Engineering over 33 years ago.
Two successful Polish entries became
known through publicity in the technical HPV and cycle literature (e.g., in
Bicycling Science).
One of the entrants, Kazimierz
Borkowski, creator of the sliding-seat
rowing-action bicycle, claimed that “it’s
just for sports and recreation”. He was
an engineer in the biggest Polish bicycle plant, Romet, and never developed
his concept further. Nowadays Rowingbikes, very sophisticated (and practical) machines, are made by Derk Thijs
in The Netherlands.
Another entrant, Stanislaw Garbien,
developed a modern SWB recumbent
with front and rear suspension, drum
brakes, optional fairing and variablegear constant-ratio swinging cranks.
Now, after the collapse of the Iron Cur-

The future of HUMAN POWER
This heading is deliberately ambiguous. It refers to the movement as well
as to the journal. There are discussions
underway on a new basis for the international association, and therefore for
the journal. Here is a concise summary
of the present position just written by
Richard Ballantine, who is taking an
active part in trying to ensure a healthy
continuation of both.
“The IHPVA was founded as a USbased organization in 1975. HPV clubs
from other countries joined the IHPVA
as chapters, of equal status with chapters based on US states or regions.
Over time, the non-US clubs grew in
size, and eventually came to want independent status and an international
organization that was truly democratic
rather than US-dominated.
“Following the Lelystad Declaration
in 1995/96, the IHPVA was reorganized
in January, 1998. The original IHPVA
became the North American HPVA.
HPV clubs from other countries
became autonomous, and a new IHPVA
was formed, comprised of representatives of clubs and groups from various
countries. Yet the work of the IHPVA,
Human Power

tain, I can reveal that the designer of
this bike was working as an aircraft
armament engineer, a really top-secret
occupation. I got in touch with him
when he retired in 1987, and he was
still trying to develop a new kind of
bike drive-train. The prototype of Stanislaw Garbien’s bike was in use for a
long time, but in about 1980 it was converted into an upright bicycle with conventional drive and with the front beam
serving as a luggage carrier. This conversion from recumbent to upright is in
some way significant. Eastern Europe
(including Poland) is very fashion-sensitive. It’s not easy to be a trendsetter
there: if the item is not of Western origin, it is usually ignored or laughed at.
A young engineer, Jacek Ziolkowski,
who made his three-wheeled HPV
from a MiG-17 auxiliary fuel tank
(HPV News, Sept. 1987), died after
being hit by a car while riding his conventional bike. It’s a great irony: if he
had ridden a recumbent, he would have
probably survived, maybe with a broken leg. His vehicles are now in Warsaw’s Museum of Technology.
At the end of the 1980s and the

beginning of the 1990s in Poland it
seemed that HPVs would find their
niche, but after the “opening to the
West,” cars became much more affordable, and the mountain bike appears to
be the only bike on the market. The
popularity of practical HPVs is inversely related to the availability of cars.
This can be confirmed by looking at
France and Britain in the 1920s, Sweden during and shortly after WW II, or
Poland and Russia in the 1980s, when
all sorts of pedal cars and HPVs were
made by amateurs and also by small
manufacturers.
It is difficult to fight the car, but
there is another medium that helps HPV
enthusiasts to communicate and not to
feel alone: the world wide web. May
human power be with you!
—Marek Utkin
<utkinmrk@free.polbox.pl>
Marek Utkin, a graduate of industrial design in Warsaw’s Fine Arts
Academy is a correspondent for the
international trade magazine, Bike
Europe, and writes for some Polish
popular scientific and technical magazines.

which is the responsibility of the member clubs, continued and continues to
be performed almost exclusively by
North American HPVA members, who
do the record-keeping, maintain the
web site, and produce Human Power,
all on a volunteer basis. At the Brighton
meeting, HPVA representatives politely
said that this cannot go on -- other
IHPVA member countries need to do
their fair share of the work.
“The US IHPVA representative, Paul
Gracey, raised this matter in a recent
post to the IHPVA Board:
‘The one aspect of the IHPVA that
is ongoing day-to-day and seems to me
to be under-appreciated is/are the Web
and Internet services. Our visibility to
the world is embodied in those services
located in cyberspace and the publication Human Power. Like everything
else that is related to the Internet, the
bloom of newness may be fading and
this may at some time need to be put
on a compensated basis. This, and the
caring for records reports and other
archival materials is the major reason it
may yet be desirable to try to establish
a physical location and some sort of
endowment to see to its care.’”
Voluntary submissions to Human

Power have fallen, and most of my
many letters to people in many countries asking for contributions are
unproductive, so that our publication
frequency has dropped to semi-annual
from quarterly. Another long-term editor of HPV-related magazines told me
recently that he realized soon after he
started that in this field the editor has
to write most of the material. (I’ve tried
to avoid that, except for the reviews.)
Another view recently expressed is
that, with the internet giving instant
information on anything, we don’t need
paper publications any more. I hope
that that is not a general belief. With
each new revolution in electronic storage I find that my records of another
part of my life are lost forever (I’ve
recently thrown away reels of unreadable computer tapes, and large-format
diskettes, likewise inaccessible) and I
value paper for archival material more
and more.
The message I want to pass along
here is simply “prepare for more
change, and take part if you wish to
influence the direction!”
—Dave Wilson
Editor, Human Power

Number 52 Summer 2001

23

International Human
Powered Vehicle
Association
IHPVA
PO Box 1307
San Luis Obispo, CA 93406 USA
http://www.ihpva.org


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