human power no. 54

8/12/2019 HUMAN POWER No. 54.

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N UMBER 54 S PRING 2003

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

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

Editorials

Commentary

Theo Schmidt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

The politics of human powered vehicles

Richard Ballantine . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Articles

HPV Science

David Gordon (Dave) Wilson . . . . . . . . . . . . . . . . . . 4

Factors affecting performance in human--powered

vehicles: a biomechanical model

Danny Too and Gerald E. Landwer . . . . . . . . . . . . . 14

E. Eugene Larrabee: a remembrance

Mark Drela, Theo Schmidt, Dave Wilson

Paul MacCready and Sarah Wright. . . . . . . . . . . . . 16

Minimum induced loss wings and propellers

for human-powered vehicles (May 1985)

E. Eugene Larrabee . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Various efficiencies of a human-powered

flywheel motor

J.P. Modak and A. R. Bapat . . . . . . . . . . . . . . . . . . . 21

Number 54

Sping 2003 $5.50

HUMANPOWERTECHNICAL JOURNAL OF THE IHPVA



2 Number 54 Human Power Human Power Number 54

H U M A N P O W E Ris the technical journal of the

International Human Powered Vehicle

Association

Human Power 54, Spring 2003

Editor

Theodor Schmidt

Ortbühlweg 44

CH-3612 Steffisburg, Switzerland

[email protected]

Associate editors

David Gordon Wilson

21 Winthrop Street

Winchester, MA 01890-2851 USA

[email protected]

IHPVA

Richard Ballantine, UK, Chair

Paul Gracey, HPVA representative

Published by

HPVA

PO Box 1307San Luis Obispo, CA 93406-1307 USA

[email protected]

Production

JS Design, JW Stephens

Human Power (ISSN 0898-6908) is

published irregularly by the Human

Powered Vehicle Association, a non-

profit organization dedicated to pro-

moting 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 copy-

righted by the HPVA. Unless copy-

righted 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 HPVA. Individual subscriptions and

individual issues are available to non-

HPVA and non-IHPVA members.

Contributions to Human Power

The editors welcome contributions

to Human Power . Contributions can

include papers, articles, technical

notes, reviews and letters, and shouldbe of long-term technical interest.

Contributions should be understand-

able by any English-speaker in any

part of the world: units should be in

S.I. (with local units optional). Ask

the editor for the contributor’s guide

(paper, e-mail or pdf formats). Some

contributions are sent out for review by

specialists. We are not able to pay for

contributions.

FROM THE EDITOR

FarewellsThis issue of Human Power is long

overdue. We have problems and transi-

tions in Human Power , the HPVA, the

IHPVA, and in the world. I must note a

number of farewells:

The German HPV chairman Ralf

Wellmann died of his own will amid the

preparations for the next HPV World

Championships in Friedrichshafen, and

deeply shocked those of us who knew

him. Steve Donaldson, secretary of the

British Human Power Club, was in col-

lision with a car while cycling through

Bucksburn, Scotland. He died in hospital.

Steve was a familiar competitor at inter-

national championships, and active in the

IHPVA. We all miss these two young men

greatly.

We also sadly note the passing of

Gene Larrabee, who was one of the firstto show how to design really efficient

propellers suitable for record-breaking,

human-powered airplanes and hydrofoils.

Known as “Professor Propeller”, Gene

furnished his courses with attractive and

clear illustrations. In this issue we publish

a series of these, with captions, as a com-

memorative article on minimum induced

loss wings and propellers, preceded by an

obituary.

Also in this issue Human Power is lucky to be able to

include extracts from Bicycling Science

III which is being published in early 2004,

written by our own Dave Wilson (with

contributions by Jim Papadopoulos else-

where in the book). We include a chapter

on aerodynamics which presents an easy

way of incorporating Reynolds-number

effects, and part of a chapter on unusual

and future HPVs.

Danny Too’s article on the biomechan-

ics of HPVs systematically lists the factors

affecting human-powered propulsion with

emphasis of the biomechanical aspects.

Finally, we have an article by

J.P. Modak and A.R. Bapat which has

been in the pipeline for some years and

appears here at last in a condensed ver-

sion. It describes an investigation of a

human-powered flywheel motor and

attempts to create mathematical models

for this.

Transitions Human Power itself is in transi-

tion. This is the last issue John “Elrey”

Stephens helped produce, as he is mov-

ing on to a new venture soon, and also

because Human Power and HPV News

do not yet conform to a sustainable busi-

ness model for which we have lobbied.

As a print professional E lrey helped to

improve the quality of Human Power

in the last few years, for which we are

very grateful. Human Power readers

can expect one or two more issues in the

present style, but in 2004 there will have

to be some changes.

The IHPVA has a new chairman,

Richard Ballantine, who is striving to

change the present status of an “inter-

national agreement” into a more formal

and professional legal form. One of the

benefits of this would be that the respon-

sibility for the physical production of

Human Power could be transferred from

the HPVA to the IHPVA and also allow

increasing our readership.

Richard, besides being a successful

author and publisher of bicycle media,

is like many of us a “political cyclist”and writes briefly about the connection

between HPVs and the war on Iraq.

COMMENTARY

The editorial views expressed in Human

Power are those of the authors and do not

neccessarily coincide with those of the

board and officers of the HPVA.

In this war on Iraq, we have a num-

ber of casualties (as of May/June 2003):

5500 to 7200 Iraqi civilians, 5000 to

50,000 Iraqi soldiers, about 200 US/UK

soldiers, and about ten journalists (http://

www.iraqbodycount.net/). When I started

writing this editorial, bombs and missiles

were raining down upon Mesopotamia,

this ancient land between the Tigris and

Euphrates rivers, the cradle of human

civilisation. The present population,

trapped between the plans of a barbaric

dictatorship and a group of ruthless busi-

nessmen, paid a heavy price for living

on top of large deposits of oil. That the

war has much to do with oil is evident,

as after replacing the dictator, the busi-

nessmen ordered the oil wells and the oil

ministry to be well-guarded while allow-

ing the world-famous national museumand library to be looted and the hospitals

and food stores ransacked. Some of

humanity’s oldest written records, clay

tablets from the age-old monuments of

the area, describe how rulers went to war

in order to gain strategic positions and

natural resources, justifying their rapes

in the names of gods. Thousands of years

later this is still so; it appears we have

progressed no further than th en.

The relatively modern accomplishment

called democracy seems to have failed.

Something is fundamentally wrong when

a few men are able to launch wars against

the wishes of the overwhelming majority

of the world’s population, governments

and churches. This war has divided

friends, united foes, and accomplishedthe opposite of what its proponents claim.

The businessmen have weakened the

only legal world government, the United

Nations, and are attempting to erect a

kind of military-economic empire, to be

defended by new technology — including

a new generation of nuclear weapons. All

this generates hateful anti-western feel-

ings and terrorism is increasing daily.

What has this to do with “Human

Power”? The main reason is the strong

connection with oil. Oil is cheap in terms

of money, but commands a heavy price

in terms of human life. This is not new,

there have been other oil wars with far

more deaths and misery. What is new is

the audacity with which our fragile hard-

earned progress of human civilisation

and achievements such as human rights,

democracy, freedom and justice are being

eroded by our sinister characteristics such

as fear, greed, and fundamentalism. The

Charter of the United Nations and asso-

ciated works of International Law have

been transgressed. Lies and deceptions

abound. The land of the free is becoming

the land of the fearful. Never before have

the dystopias predicted by Orwell andHuxley gotten so close to reality.

The human principle of “right” has

yet again succumbed to the animal prin-

ciple of “might”. Is all then lost? Are we

doomed to remain prisoners of our archa-

ic instincts, to be animals forever? I do

not think so. Never before has the whole

world been able to debate a war before

it happened. Never before has there been

such universal worldwide democratic par-

ticipation with so many millions of people

demonstrating in the streets or with their

voices, pens and keyboards. Never b efore

have the United Nations denounced a

war of aggression so clearly. The action

of the present U.S. government and its

vassals is a large setback, but not the

end. Thanks to modern communications

and independent media, disinformationand propaganda can be unveiled more

quickly and anybody capable of logical

thought can separate truths and untruths.

The new information society is fighting

back. The key to future peace is literacy.

For example, people who read the classic

Animal Farm by George Orwell may find

out why our rulers employ soldiers and

fire teachers, and how they subtly control

us with methods more effective than cen-

sorship. As global awareness increases

we may be heading for a new Renaissance

and be able to escape the presently rather

dark ages together. At some point we will

become true humans.

—Theo Schmidt

T HE POLITICS OF

HUMAN POWERED VEHICLES

Richard Ballantine

Richard Ballantine, chair of the IHPVA

and of the British Human Power Club,

writes on the connection between HPVs

and the Iraqi War.

Citizens in developed countries enjoy

high living standards: plenty of food and

water, advanced health care, and abun-

dant availability of consumer services and

goods. Citizens in “developing” countries

do not — and cannot. As Edmund Wilson

notes in his marvellous and utterly engag-

ing new book, The Future of Life,¹

raising living standards in developing

countries to the same level as developed

countries would require the resources of a

planet five times the size of Earth.

Withdrawals from nature’s bank

already running deeply in the red.

fuels, water, fish, timber, land, and

vital resources are being depleted

than they can be renewed. Crucial

a minority of the world’s populati

something over one thousand mill

people, account for about 80 per c

consumption. The majority, about

thousand million people, get by on

is left, and of this group, about on

sand million do not have enough f

water to sustain life.

The problem in want is not scar

There is enough to go around. The

lem is that too few people have to

Perpetuating this status quo is the

cause of wars, internal conflicts w

countries, destabilized societies agovernments, and support for rep

regimes.

The war in Iraq is about black

gold — the last significant reserve

oil. Once Iraq is conquered, the co

forces intend to take the oil to pay

the costs of the war, establishing a

regime, and rebuilding the countr

oil will go to developed countries

used to fuel motor vehicles.

As every reader of Human Po

knows, the majority of journeys a

and local, and can be accomplishe

efficiently by cycling. Standard up

bikes are great, but HPVs are bett

er, safer, and more comfortable. T

also practical for transporting frei

The politics of HPVs are simple

developed countries, HPVs can m

large proportion of transport requ

ments, and in so doing, reduce co

tion of petroleum. The decrease in

of environmental footprint in term

resource depletion means less inc

for taking oil through economic a

tary force. As well, there is less da

the environment and human healt

pollution.Finally, and not least, HPVs sui

ern demographic trends. The popu

of the world is increasing, and at

time, more and more people are l

in cities. In high density urban env

ments, where space is limited, bik

HPVs are not just hugely more ene

cient than motor vehicles, they ar

faster.

Bombs and cars go together —

the end, HPVs will beat both.¹Wilson, Edward O. 2002. The future of life.NY: Alfred A. Knopf. ISBN: 0-679-45078-5

Eccles



Drag= CD ⋅ (frontal area ) ⋅ (dynamic pressure)

CD SA , ≡( ) ⋅ ( )

drag

surface area dynamic pressure

W = (drag force) ⋅ (relative vehicle velocity) (

Power, watts= drag force, newtons vehicle velocity, m/ s( ) ⋅ ( )

˙ /

/ /

/

/ / W hp

d rag l bf v elo ci ty ft s

ft lbf s hp

d ra g l bf ve lo ci ty m il e h

mile lbf h hp( ) =

( ) ⋅ ( )−( )( )

= ( ) ⋅ ( )

−( )( )550 375

Figure 2. CD and CD, SA for a circular cylinder

Flow direction →

D r a g c o e f f i c i e n t

(Sphere) (L/D)

CD

CD, SA

Velocity V

D y n a m i c p r e s s u r e o f a i r ,

P a ( N / m 2 )

Effect of density, ρ1

(½), ρV² S e a l e

v e l ,

2 3 ° C

, 7 5 ° F

3 0 5 0 m

, 1 0

, 0 0 0 f t ;

6 ° C

, 4 3 ° F

mile/h

m/s

Fig. 1. Dynamic pressure of air vs .

velocity and altitude


Editor’s note: Human Power is ableo include extracts from Bicycling

Science III , which will be published inarly 2004, written by our own Dave

Wilson (with contributions by JimPapadopoulos elsewhere in the book).

We include a chapter on aerodynam-cs which presents an easy way ofncorporating Reynolds-number effects,

and part of a chapter on unusual anduture HPVs.

SummaryThe following is a collection of

xtracts relevant to HPVs fromhree chapters of the third edition

of Bicycling Science: from those onaerodynamics, on unusual pedaledmachines, and on HPVs in the future.

Readers of, and contributors to, HumanPower have been loyal users of the sec-ond edition of Bicycling Science, andwe have chosen some topics that havebeen substantially updated in the hopehat they will be useful. (The MIT Press

plans to publish the third edition some-ime in 2003.)

Two of the new topics in the aero-dynamics chapter are a clarification ofhe two principal alternative definitions

of the drag coefficient, and a simplifiedmethod of calculating the Reynoldsnumber, which influences the drag,ometimes dramatically.

Drag coefficientsOne aim of aerodynamic experimentson an object is to measure its drag coef-ficient, CD, defined as the non-dimen-ional quantity

CD ≡ drag ⁄ [area ⋅ (dynamic pressure)] ( Eq. 1)

The drag is the force in the directionof the relative flow (or of the dynamic

pressure). The area A and its relateddrag coefficient CD are defined later.The product CD ⋅ A (in the same units as

A) is a very useful number in studies ofthe drag of bodies. The drag is simplythe product CD ⋅ A times the dynamic

pressure. We list this product later (intable 1) for some types of HPVs.

The dynamic pressure is the maxi-mum pressure that can be exerted bya flowing stream on a body that forcesit to come to rest. At speeds that arelow relative to the speed of sound (say,below 45 m/s or 100 mile/h), the dynam-ic pressure is closely approximated by:

in which (for SI units) ρ is the air den-sity in kg/m3, and V is the velocity ofthe air in m/s. The constant gc = 1.0 forSI unit systems. It is found in Newton’slaw of motion F= m a /gc

where F is in newtons, N, m is in kg,and a in m/s2 In U.S. units, gc has the

value 32.174 lbm-ft/lbf-s2 when theequation relates m in pounds mass, Fin pounds force, and acceleration a inft/s2. The dynamic pressure vs. velocityand altitude is given in figure 1. At thetime of writing, the HPV speed recordwas about 35 m/s and was set at an alti-tude of between 2500 and 3000 m, and itcan be seen that the dynamic pressurewould have been over 600 N/m2 (0.087lbf/sq.in.).

Different definitions of areaand of drag coefficient

The area can be defined in severalways, each one leading to a differentdefinition and a different value of thedrag coefficient CD. The usual definitionis the frontal area, and unless otherwisestated, this is the form of drag coeffi-cient we will use.Thus, the drag force is given by

(Equation 3)

Another form of drag coefficient isdefined in terms of the surface area ofthe body, and is used only for slenderand/or streamlined bodies, where thedrag is primarily from skin or surfacefriction, rather than from the eddiescoming from bluff bodies. Here wegive this form the subscript “SA ”, and isdefined as:

(Equation 4)

For a given body at a given condition,the surface-area coefficient of drag issmaller than the frontal-area coeffi-cient because the surface area is largerthan the frontal area. For a sphere thearea ratio is 4.0. For a long cylinder ofdiameter D and with spherical endsthe ratio is 4 ⋅ (1 + L/D), where L is thelength of the straight portion of the cyl-inder. The measured value of CD for arounded-end cylinder aligned with theflow increases with L/D, whereas the

value of CD, SA decreases with L/D tocompensate for the increasing surfacearea (fig. 2).

The significance of not confusingthese two definitions can be illustratedby the following anecdote. In the earlydays of the quest for the Du Pont SpeedPrize for the first human-powered

vehicle to reach 29 m/s, 65 mile/h, anMIT student decided that he could winthe prize by assembling many pedalersin a line within the same frontal area asone pedaler. He had found that the dragcoefficient for a reasonably streamlinedsingle-rider recumbent vehicle was 0.15and that the frontal area could be below0.5 m2. He calculated the drag at 29 m/s

to be about 38 N, leading to a power required to overcomeair drag alone at over 1100 W.He decided to build a vehiclecarrying ten to fifteen ridersin a line, because the frontalarea would be the same, there-fore (he thought) the dragwould be the same, and theair-drag power required fromeach of ten riders would be aneasily-manageable 110 W. Heconfidently forecast reaching

80 mi/h, 36 m/s.For various reasons that

plagued development the vehicle was quite slow. But thefallacy behind the designer’sreasoning was that the dragcoefficient based on frontalarea would not increase asthe vehicle was made longer.It would and did, probablyquadrupling the drag of aone-person faired body of the

same frontal area. It is often preable when calculating the drag ostreamlined body, therefore, to udrag coefficient based on surfacHowever, either form may be usconfidence so long as the value experimentally for one configurais not applied to the analysis of

pletely different shape.The propulsion power, W , nec

to overcome drag is

(Equation 5)

(We use W as a symbol for quwork, such as joules or ft-lbf, anthe rate of doing work, which isin watts or ft-lbf/s or horsepowe

Since the drag force is approx proportional to the square of thity, the power to overcome dragapproximately proportional to tof the velocity.

Only in still air is the vehicle vthe same as the relative velocityto calculate the drag force. Wheis a headwind or a tailwind, the

velocity is different from the ve velocity.

In SI units the relationship is(Equation 6)

If the drag is m easured in pouforce and the velocity is given in

per second, the power is in ft-lbThis may be converted to horsepby dividing by 550 (1 hp= 550 ft-lbor miles per hour (1 hp = 375 milmay be used:

(Equation 7)

Dynamic pressure ≈⋅

⋅

ρ V

gc

2

2

(Eq. 2)

HPV scienceby David Gordon (Dave) Wilson



Reynolds number, Reair density relative air velocity a length

air viscosity≡

( ) ⋅ ( ) ⋅ ( ) (Eq. 8)

Re = ( ) ⋅ ( ) ⋅2

3105sphere diameter, m relative velocity, m / s (Eq. 9)

ρ =⋅

pressure in pascals

286.96 temperature in kelvin (Eq. 10)

Re =⋅ ⋅⋅ ⋅

ρµ

V L

R T (Eq. 11)

Figure 3. Reynolds-number

parameter for air

Figure 5. Drag coefficient vs . Reynolds num-

ber for useful shapes (plotted from data

from Hoerner [2], and other sources)

Re≡p V/(RµT)

p≡ pressure in kPa

V≡ flow velocity in m/s

L≡ specified length in mm

P a r a m e t e r ( R µ T ) , W / m

Air temperature

(R≡ gas constant for

air = 286.96 J/kg deg K

µ≡ absolute viscosity of air in

kg/m.sT≡ absolute temperature in K

These are all incorported in the

parameter at left.)

Reynolds number

D

r a g c o e f f i c i e n t , C D

A t m o s p

h e r i c p r e s s u r e a t a l t i t u d e ,

k P a

Height above mean sea level

T e m

p e r a t u r e a t a l t i t u d e

P r e s s

u r e

T e m p e r a t u r e

U.S. standard

atmosphere

Figure 4. U.S. standard atmosphere (plot

from U.S. Government data)


DragFor any one shape of body, the vari-

able that controls the drag coefficient ishe (dimensionless) Reynolds number,

defined in general as

(Equation 8)

where the length has to be specified forach configuration. For a sphere andor a circular cylinder in flow trans-

verse to the cylinder axis the specifiedength is the diameter. (One states “the

Reynolds number based on diameter”.)For streamlined bodies the length in theflow direction is more usually specified.

This length for an aircraft wing is calledhe “chord”. The specified length in

bodies like streamlined fairings is moreusually the actual length.

For a sphere moving in air at sea-evel pressure and 65 °F (19 °C), this

becomes approximately

(Equation 9)

A more general method of determin-ing the Reynolds number for any pres-sure and temperature is shown in figure

3. Air density is a function of pressureand temperature:

(Equation 10)

where the factor in the denominator isR, the “gas constant” for air, 286.96 J/kg-deg.K. The air pressure can be obtainedfrom the local weather office — but itis always given for mean sea level, andmay need converting for the altituderequired by using, for instance, the stan-dard-atmosphere curve of figure 4. (The

pressure variation with altitude in fig. 4would be useful everywhere on earth;the temperature would vary consider-

ably.) The pressure will probably notbe given in pascals (N/m2), and may beconverted using an appropriate part ofthe following:1 bar=105 Pa=0.9869 atm=14.5038 lbf/ sq.in.=750.062 mm Hg=29.530 in. Hg.

The temperature in kelvin is the temperature in celsius + 273.15. Sea-levelair density is about 1.2 kg/m3 at 16 °Cor 60 °F and about 1.14 kg/m3. at 38 °C,100 °F for dry conditions. If the humid-

ity is 100%, the density at thecooler of these temperaturesdrops by about 1%, and byabout 2.5% at the hotter tem-

perature.However, it is not strictly

necessary to calculate the airdensity purely to determinethe Reynolds number. Sinceboth the density and the air

viscosity are functions oftemperature, the parameterR ⋅ µ ⋅T is just a function oftemperature, where µ is the“absolute” viscosity of air inkg/m.s., and T is the “abso-lute” temperature in degrees

kelvin. The Reynolds numbercan then be found from the

pressure, temperature, veloc-ity and length alone:

(Equation 11)

where the denominator is the parameter plotted as a func-tion of temperature only infigure 3. An example of theuse of these charts follows.

Coefficient of drag vs. Reynoldsnumber for various bodies

The drag coefficients of various bod-ies versus Reynolds number have been

plotted in figure 5.It can be seen that at Reynolds

numbers over 3 × 105, even smoothspheres do not need trip wires or roughsurfaces because a laminar boundary

layer will spontaneously becomturbulent under these conditionWhen the boundary layer becomturbulent at increased velocity aReynolds number, the drag coeffalls sharply from 0.47 to 0.10. (Tdrop in drag coefficient with incof velocity or Reynolds numberusually rapid enough to counterthe need for greater propulsionincreasing as it does with the cuof velocity. However, hypotheticcertain bodies in certain conditiwhere a very rapid reduction incoefficient is experienced as therelative velocity V is increased ctheoretically, achieve an increasspeed of 20 – 30% without any inin power.) A golf ball about 40 mdiameter driven at an initial veloof 75 m/s has a Reynolds numbe2 × 105 at the start, and would bthe high-drag-coefficient region were smooth. The dimpling shif“transition” point to lower Reynnumbers and gives a low CD. Th

paradoxically, a rough surface cto low drag.

ExampleFind the Reynolds number for air

at 20 °C, sea-level pressure

(110 kPa), flowing past a

cylinder 200-mm diameter at

10 m/s.

At 20 °C the parameter R⋅ µ ⋅T is

1.64 (fig. 3). Therefore

Re= 110,000× 10× 200/(1000×

1.64) = 1.34× 105



Fig. 6. Optimum (L/t) of wing an

sections and of one 3-D stream

body (plotted from data from H

[2] and other sources)Length/thickness ratio (L/t) (Length/diameter ratio, (L/D) for the 3-D body)

D r a g c o e f f i c i e n t

P r e s s u r e l o s s e s

Three-dimensional axisymmetric

streamlined boy at Re = 106

Increasing roughness

F r i c t i

o n l o s

s e s


Compared with a golf ball, abicyclist travels much slower but hasa larger equivalent diameter, so theReynolds number may be similar. Abicyclist using an upright posturemay be considered for simplicity as a

ircular cylinder normal to the flow,a curve for which is shown in figure

. If we take a cylinder diameter of00 mm to represent an average person,

and if we use a speed of 5 m/s, theReynolds number is 2 × 105 — belowhe “transition” region of about × 105. Therefore there may be some

advantage to wearing rough clothing forpeeds in this region. Most bicyclists

have become aware of the penalty ofonverting themselves into smooth but

highly unstreamlined bodies by donninga wet-weather cape or poncho, which

usually, and somewhat paradoxically,reatly increases the wind resistance

without increasing the cross-sectionalarea. Perhaps some “trips” woven intohe cape material would be beneficial.

Even better would be some type oframe that would convert the capento a low-drag shape. Sharp (1899)

proposed this scheme in 1899, andapes with inflatable rims were for sale

around that time.

Most everyday bicycling occurs in theReynolds-number range of 1 – 4 × 105,and the reduction in air drag throughthe use of some form of practical low-drag shape as an enclosure or “fairing”can approach 90%. An even greaterreduction in drag can be produced withspecial-purpose fairings for racing orsetting speed records.

Low-drag shapes do not generallyexhibit the sharp transition from highdrag (separated flow) to low drag(attached flow) as the Reynolds numberis increased. Rather, the point of transi-tion of the boundary layer from laminarto turbulent tends to move upstreamtoward the leading edge of the bodyas the Reynolds number is increased.Thus, the drag coefficients for stream-lined shapes (represented by an airship)

given in figure 5 show a continuous fallas the Reynolds number is increased inthe laminar-flow region, followed by amoderate rise to the fully turbulent con-ditions and then a continued fall.

The Reynolds numbers of stream-lined fairings for human-powered

vehicles lie in the interesting transitionregion between 1.5 × 105 and 1.5 × 106.The curves in figure 6, taken fromHoerner (1965), show that for a drag

coefficient based on maximum cross-sectional (or frontal) area, the minimumdrag coefficient is given by streamlinedshapes with a length/(maximum thick-ness or diameter) ratio of about 4.

Reducing theaerodynamic drag of bicycles

To reduce the wind-induced drag ofa bicycle and rider, two alternatives areto reduce the frontal area of rider plusmachine and/or to reduce the drag coef-ficient that the combined body presentsto the air-stream. For years, bicyclistshave adopted one or other of these

possibilities, but only recently havethere been concerted attempts at reduc-ing frontal area and drag coefficientsimultaneously. The results have beenremarkable. A selection of interesting

and typical data has been assembled intable 1 [3, 4]. The drag coefficients andthe frontal areas are given in the firsttwo columns, and the product of thetwo, CD· A , in the fourth column. Typical

values for these three for an “uprightcommuting bike” are 1.15, 0.55 m2, and0.632 m2. This bicycle, sometimes called“the British policeman’s bicycle”, andrider and this set of values are usuallyregarded as the “base case”, to whichimprovements can be made.

An obvious improvement is for therider to change position. A so-called“touring position” is used when rid-ing a “road bike” (one with “dropped”handlebars) but with the hands on thetop of the bars. This reduces the dragcoefficient from 1.15 to 1.0 and thefrontal area from 0.55 to 0.4 m2, giv-ing a reduction in CD·A from 0.632 to0.40 m2. The fifth column of the tableshows the power required at the drivingwheel to overcome the aerodynamicdrag at 10 m/s (22 mi/h). This is a speedat which aerodynamic drag is becom-ing dominant on unfaired bicycles.This fifth column shows immediatelywhy ordinary people do not commuteon upright bikes at 10 m/s: it requires345 watts, approaching half a horse-

power, just to overcome aerodynamicdrag. The power into the pedals alsohas to supply losses in the transmission,

normally small, and the rolling frictionof the tires on the roadway, for whichsome typical data are given in the lastthree columns. The total would be over400 watts, a level that NASA, testing“healthy men”, found could be main-tained for only one minute. Just makingthe switch to a road bike and using thetouring position would lower the total

power required (on level ground in calm

wind conditions) to around 275 watts,and a nominally healthy male couldkeep this up for about 30 minutes, atypical commuting duration. (It wouldbe very atypical to be able to commutefor 30 minutes at constant speed, but ifthe typical male could do that, the dis-tance would be 18 km, 11 mi.)

A further dramatic improvementoccurs if the rider uses a racing bike(little different from the road bike, butwe have specified a lighter weight anda frontal area that includes the effectsof tight clothing and having the handson the “full-drop” part of the handle-bars; the rolling drag implies the useof light, supple, high-pressure tires).(Loose clothing can increase aerody-namic drag, at speeds of over 10 m/s, by30%.) The drag coefficient goes downto 0.88 (mainly because the head isdown in front of the rider’s rounded

back); the frontal area is 0.36 m2, andCD·A becomes 0.32. The power requiredto ride at 10 m/s is, including tire andtransmission losses, about 210 watts,which even NASA’s healthy man couldkeep up for almost an hour. Peoplewho ride such bikes are m ore likelyto be “first-class athletes”, who can becapable of riding at 10 m/s indefinitely,which might be translated as until the

need for food, sleep or other demof the body must be answered. one-hour standing-start record win 1996 for conventional racing Chris Boardman at 56.375 km, rean estimated average power outover 400 watts.)

Prone, supine and recumbepositions and bikes

The frontal area can be reducbelow that required for a convenracing bike only by adopting a c

pedaling position. Speed recordbeen won on bicycles designed head-first face-down horizontal-(prone) pedaling, and for feet-firup horizontal-body (supine) pedin the strict forms of which a peor other viewing device (includiis needed; and for a w ide varietwhat is known as “recumbent” ping. The purists would say that frecumbent pedaling is supine, anstrictly the position used by theof “recumbents” is in fact “semi-bent.” However, this form of bichas become known in the Englisspeaking world as recumbent, “’or “bent” (and in Europe as Liegor liegfiets). A well-known succrecumbent, the Tour Easy (fromRacers), is shown in table 1 as ha drag coefficient of 0.77, a frontof 0.35 m2, and a CD·A of 0.27 m2

siderably lower than that of the bike with the rider in a painful cThereby lies a principal reason frecumbent’s growing popularityturn of the millennium: it can betaneously fast and comfortable.data may not be typical: also givthe table are measurements on a“Peer Gynt” recumbent for whicsiderably higher drag values wesured.)

The drag of any HPV is greatlyreduced if it is enclosed in a strlined fairing. Paul van Valkenbudeveloped Sharp’s idea (mention

above) in the “Aeroshell”. Tabledata for the use of this inflatabl

plus a skirt to extend the shapeto the ground. A drag less than hof the racing bicycle was attaine

Table 1. Bicycle drag coefficients and other data¹

Machine and rider

Dragcoeff.

on fron-tal area,

cD Frontal area CDA

Power toovercomeair drag

at 10 m/s(22 mi/h)

watts

Power to overcome rollingresistance AT 10 m/s forspecified total mass, kg,

and CR value

CD m2 ft2 m2 watts kg. CR watts

Upright commuting bike 1.15 0.55 5.92 0.632 345 90 0.0060 53

Road bike, touring position 1.00 0.40 4.3 0.40 220 95 0.0045 38

Racing bike, rider crouched, tight clothing 0.88 0.36 3.9 0.32 176 81 0.0030 24

Road bike + Zipper fairing 0.52 0.55 5.92 0.29 157 85 0.0045 38

Road bike + pneumatic Aeroshell + bottom

skirt

0.21 0.68 7.32 0.14 78.5 90 0.0045 40

Unfaired LWB recumbent (Tour Easy) 0.77 0.35 3.8 0.27 148 90 0.0045 40

Faired LWB recumbent (Avatar Blubell) 0.12 0.48 5.0 0.056 30.8 95 0.0045 42

Vector faired recumbent tricycle, single 0.11 0.42 4.56 0.047 25.8 105 0.0045 46

Road bike in Kyle fairing 0.10 0.71 7.64 0.071 39.0 90 0.0045 40

“M5” faired low racer 0.13 0.35 3.77 0.044 24.2 90 0.003 26

“Flux” SWB, rear fairing 0.55 0.35 3.77 0.194 107 90 0.004 35

Moser bicycle 0.51 0.42 4.52 0.214 118 80 0.003 24

Radius “Peer Gynt” unfaired 0.74 0.56 6.03 0.415 228 90 0.0045 40

“Peer Gynt” + front fairing 0.75 0.58 6.24 0.436 240 93 0.0045 41

ATB (mountain bike) 0.69 0.57 6.14 0.391 215 85 0.0060 50

¹ Data from various sources, including Gross, Kyle and Malewicki (1983), and Wilson (1997).



Figure 7. Vertical-axis commercially sold

pedaled lawn mower

Figure 8. Sickle-

bar push lawn-

mower (National

Agricultural Hall of

Fame, Kansas)

Figure 10. The author’s push

snow-plough

Figure 11. The Thuner Trampelwurm


Unusual human-poweredmachines

In this chapter we aim to expandyour experience, and perhaps makeyou want to use, or even design andmake, some interesting human-pow-

red devices other than bicycles. Thisaim has an obvious relationship tobicycling, which is an activity havinga transportation component that canusually also be accomplished by theuse of a motor-vehicle. People in thedeveloped world who choose to bicycle

enerally do so for reasons connectedwith their own health and w ell-beingand that of the region in which theyive, and perhaps out of concern forhe earth as a whole. There are rather

imilar, but far more limited, choiceshat such people can make for mowingrass and clearing snow, for example,

and for recreational boating. The role ofhuman power in the modern high-tech-nology world has, alas, to be restricted.Only a very few enthusiasts bicycleacross North America, Russia, Asia orAustralia for pleasure. While we are

ngaged in some advocacy for humanpower, we are not recommending thathuman power should be used for suchprodigious feats as bicycling acrossa continent, nor to clear snow from aupermarket parking lot, nor to cut therass of a golf course. However, evenn large countries like the USA, over

half the daily “person-trips” by auto-mobile are under 8 km, 5 mi, normallyan easily-accomplished bicycling dis-ance by most people in most weatheronditions. Likewise, most lawns and

driveways are of sizes that can easilybe handled by human-powered devices.The past enthusiasm for reducing whathas been called “back-breaking” laborhrough the incorporation of gasoline-ngine- and electric-motor-powered

devices has led to an almost totalneglect of efforts to improve human-powered tools. In consequence, theres today an unfair competition between

highly developed modern electric hedgelippers, for example, and manualhears that have not been sensiblymproved for a hundred years. Perhaps

we need a new series of Kremer prizeswhich have been just for HP aircraft)or specified achievements in human-

powered tools.

Human-powered lawn-mowers andsnow-removers

In the first two editions of Bicycling Science we had illustrations of MichaelShakespear’s pedaled lawnmower. In

view of the extremely limited bud-get and time he had available, it wasbeautifully designed and executed. Hisachievement might have inspired oth-ers. A commercial riding mower cameon the market later using a vertical-axishigh-speed rotaryblade that, becauseof the powerrequired for thistype of cutter, madea slowly advancingcut of only about300-mm width(fig. 7). However, itdid cut long grassand weed stalks,often missed byreel-type mowers.

Another typethat would cut longgrass was sold inNorth America and

probably elsewherefor much of theearly part of thelast century and isshown in figure 8.

A so-called “sickle-bar” or row of clip-

pers in front of the wheels of a “push”mower was driven from a cylinder camthat would seem to have a high fric-tion. This type of cutter has no intrinsicsystem of removing and collecting theclippings.

A compact and stylistic riding mowerwith a central reel was built by ChrisToen in the Netherlands.

The author has discussed ridingmowers in Pedal Power (McCullagh1977). He believes that the energyrequired to pedal a machine across softground (a lawn) is so high that the onlyway in which pedaling would be superi-or to pushing a mower would be for the

pedaler to be either stationary or mov-ing slowly, while the cutter, presumablylight in weight, covers a considerablearea.

Snow removersThe use of snow shovels at the first

snowfall of the winter always seemsto produce reports of heart attacks.It is another example of a heavy taskinvolving the use of the muscles of thearms and back, and of having the backbent uncomfortably. It would be betterto use the big muscles of the legs andto have a more natural posture, which,combined, presumably would be lesslikely to over-strain the heart. It wouldbe delightful to have a small lightweightdevice that, from leg operation alone,

would scoop up a quantity of sn project it in a desired direction,does with considerable effort usa snow shovel. Nothing like thatbeen on the market, or even in tent literature, so far as can be lefrom searches carried out by theand his students. One favorite tois shown in figure 10. This is an “push-plough” bought by the auta “garage sale.” He made and inslarge fiberglass “blade” with a mcutting edge. He likes to demonthat, on the asphalt surface of hway (about 50 m2) he can clear sabout half the time taken by hisbors with similar driveway areatheir engine-powered snow-blow

We do, however, need better h powered snow-removal devicescient, fun to use even for older anonathletic people, and compacstowed.

A multi-human-powered lanvehicle, the Thuner Trampe

The Thuner Trampelwurm is type of human-powered “road tr(fig. 11). Although other linked tof HPVs exist, none is as radicathe Trampelwurm, a brainchild oSwiss artist Albert Levice. Ten twwheeled trailers, each for one pare hooked up behind a long-whrecumbent tricycle in such a wathey follow the leader almost pely — almost as if on rails defined

path of the leading trike. It was ficult task for a group of studenHansueli Feldmann at the EnginCollege of the Kanton of Bern into come up with a usable system



Figures 12 and 13.

“Vél’Eau 12” HP boat


designed a good compromise withalmost perfect tracking and enoughtability to drive up to about 15 km/h

without the train beginning to snakeback and forth. Even so, hydraulic yawdampers are required at the connectinginks. A similar pitch-stability problem

was solved by using the trailer units inpairs: each pair having one pinned andone sliding coupling. This also allowshe train to be shortened easily, very

handy if only a few people want to uset. Each unit has a seat and pedals or

a linear drive or a rowing mechanism,as well as a roof made of canvas on aubular frame.

Four complete vehicles were builtby unemployed persons at the city ofThun in Switzerland, and extravagantlydecorated by local school children. The

ity of Thun owns and operates three

of the vehicles. A part-time staff of six people run the project, taking bookingsand doing the frequent repairs neces-sary. Another ten people are engagedas drivers; the vehicles ply for custom-ers in the pedestrian part of Thun andare available to be booked privately.

Although as heavy as an automobile andas long as any legal road vehicle, theTrampelwurm can negotiate the mostcrowded and narrow pedestrian areasin safety and can also travel on theroads as long as they are not too steep.Parties enjoy the tricks of the drivers,like catching up with their train’s owntail, forming a temporary human-pow-ered merry-go-round, or diving into a

particular steep narrow tunnel in roller-coaster fashion. Operating from April toNovember, the number of people trans-

ported per year is on average 5,700.

Human-powered watervehicles

Recreational and utilitywatercraft

The Vél’eau 12 Vél’eau 12 is a human-powered boat

with seats for twelve persons, six oneach side facing one another, offset toallow for ten pedal drives (fig. 12, 13).These are connected to the longitudi-nal propulsion shaft under the floor.

All drives except the helmsman’s havefreewheels, so the danger associatedwith multiple fixed pedals is removed.

An arrangement of universal joints anda telescoping section allow the propul-sion shaft — exiting at the uppermost

point of the transom — to connect tothe propeller / rudder unit in such away that this can be steered almost 90

degrees to either side and also

lift 90 degrees, for example inshallow water or for clearingthe propeller. Internally, the

propeller unit contains a simple untwisted chain drive witha step-up ratio of about four.The two-bladed propeller has adiameter of 550 mm and a pitchof 700 mm.

Vél’eau 12 is 12 m long and1.3 m wide. The hull is hard-chine and made from 6-mmmarine plywood glued andsealed with epoxy. Plastichoops support a removablecanvas roof with clear sides.There is also a leeboard to pre-

vent excessive sideways drift in windyconditions. The complete craft weighsabout 250 kg.

Vél’eau 12 is easily driven by as fewas two persons. The all-day cruisingspeed is about 5 knots, with crews offour to ten average persons. Vél’eau 12is owned by the French companySolartis (formerly Ecoinventions),which rents it out to groups that oftentake camping equipment for w eek-longtrips, mainly on the river Saône.

Human-powered vehiclesin the future

To write about the future is, ofcourse, risky. It is easy to review recenttrends and to extrapolate. However, wewill give some relevant data on bicycleusage and manufacture, with appropri-ate cautions on extrapolating them. Weshall point out that, although we like

to think of ourselves as free creatures,what we do is largely controlled bygovernmental actions, and that theseactions are highly uncertain, even indemocracies.

Government regulations andincentives

A major component of nationalbehavior comes from laws and regula-tions and on the degree to which theseare enforced. While it could be statedthat these laws and regulations in turncome from the people of their respec-tive countries, the “law of unintendedconsequences” applies to laws them-selves in addition to regulations andcustoms, and thereby shape communi-ties in ways that they might not origi-nally have foreseen.

Some examples are the following.In the nineteenth century in the U.S.the federal government saw an over-whelming need to connect the various

parts of the country and to “open upthe West” and it gave generous induce-ments to railroad companies to buildlines. For this and many other reasons

was born an era of “railroad barons”such as Cornelius Vanderbilt: peoplewith great wealth and power. Oil wasdiscovered, and “oil barons” such as

John D. Rockefeller joined the ranksof America’s multi-millionaires. TheSherman Anti-Trust Act became lawin 1890 and the Interstate CommerceCommission (ICC) was given, to quotethe Handlins (1975), “extensive rate-fixing authority [by 1910]. The courtsbecame battlegrounds across which

lawyers sallied to establish the bound-aries between licit combinations andconspiracies in restraint of trade…litigation was a wholesome alternativeto the overt violence and chicanery thathad enlivened entrepreneurial contestsin the 1870s…. While sometimes, as inthe case of railroads and urban transitsystems, those constraints [e.g. rate-fix-ing and rule-making] were so narrowas to stifle growth, in most industriesentrepreneurs bore the burden lightlyand even profited from it…”. The com-ing of automobiles and the empiresassociated with them created conflicts.The ICC and other regulatory bodiesseemed to have opposite effects onrailroads and highways: railroads beganlosing money and merging or going outof business while truckers began tak-ing over freight hauling, even over longdistances along the same routes cov-ered apparently more efficiently by therailroads. Similarly, differential taxationand regulation made it far less expen-sive for a family and even an individualto drive an automobile or to take a busbetween two cities than to take a train,and passenger railroads have died outin the USA except when highly subsi-dized.

This may seem to be a topic thatis unrelated to bicycling, but have

patience! Economists show that trucksand automobiles are also subsidized, infact subsidized to a far greater extentthan are the few persisting passengerrailroads. However, the subsidies are ofa totally different character. Subsidiesfor passenger railroads and subwaysystems are tax monies that are handedover to the railroad managements.Subsidies for highway users are costsimposed on general taxpayers and onmany others (for instance, the costs ofhighway maintenance, snow clearing,bridge repair, accident services, police,

pollution costs, delay costs, urban-sprawl costs, and so on) that are notcharged directly to highway users. It is

politically very difficult to correct theseanomalies, because lobbyists connectedwith all the powerful groups that w ouldbe affected are very active in advancinglegislation favorable to the industriesthey represent, and vice versa. Thereare virtually no powerful lobbyists look-ing out for the interests of the weakergroups, including poor people, pedestri-ans, and bicyclists, who would benefitfrom the correction of anomalies andthe promotion of fairness.

In summary, users of automobin particular are highly subsidizethe U.S., by an average for the qtifiable costs alone assessed by seconomists as 67 cents per milemoney (or between $4,000 and $

per automobile per year). Thereusers of other forms of transporincluding urban bicyclists, are cing with this enormous motor-vsubsidy. In other countries withfuel and other taxes, the subsidilower than those in the USA, buare still significant. And a fuel ta

very crude method of recoverinof the “external costs” of using m

vehicles. To produce greater fairroad use, three complementary of taxation are needed: electroncollected per-km road-use taxes

parking taxes, both varying withand time of day, in addition to futaxes. (Preferably, proposers of should also stipulate the destinathe monies collected. It is the auopinion that these taxes should deposited in a trust fund that is to near zero each month by a undistribution to all (at least to all local) citizens through a “negatiincome tax, i.e., a refund or rebthis way, poor people would recguaranteed small income. Rich pwould receive the same rebate ibut their additional expenditurebe likely to be higher than this rif they used automobiles.) The ahas been advocating this policy stridently since the early 1970s tfriends have called it “WilsonomIt is gradually coming to be acceeven by economists. It has beenup by Greenpeace Germany, andbe incorporated into legislation and possibly elsewhere. [It has bsuggested many times in Switzebut not yet implemented, Ed.] Aent approach with similar consehas been proposed recently by B(2001).

The vital relevance to our arghere is that most bicycling occuin urban and suburban areas. Thare also the locations where theincreasing traffic accompanied block and “road rage”, apparentlyover the world. If there were a gintroduction or increase of all thforms of taxation, to an extent a

priate for each urban area, therbe a gradual reduction of motoruse, starting with those people w



Cycling performance

Resistiveforces Propulsive forces

Environmentalfactors

Internalmechanical

factors

Internalbiomechanical

factors

Externalmechanical

factors

Environmental factors

Air resistance Gravity Rolling resistance

Surfacearea

Relative vehicle velocity

Crosssectional

area

Fluid viscosity

Air density

Dragcoefficient

Windspeed/direction

Uphill Downhill

Level

Vehicleweight

Wheeldiameter/ deformation

Wheel/terrain

Vehicle velocity

Altitude Humidity

Temperature

Orientation

Shape

Streamlinedness

Smoothness

NowindHeadwind

Tailwind

Crosswind

Hardness Smoothness

Material Tire pressure

Internal biomechanical factors

Power production Torque production

Internal musclefriction/viscosity

Speedof contraction

Muscleforce

Resistancearm

length

Forcearm

length

Musclemoment

armlength

Rcom

Fiber arrangement Fiber

type LoadSeries/parallel

elasticcomponent

Level/pulleyclassification

Angle pull

Recruitment pattern

Typeof contraction

Musclelength

Number/sizemotorunits

Synchronization

Firingfrequency

Isometric Dynamic

Concentric Eccentric

Sitesof attachment

Number of joints crossed

Jointangle(s

Figure 1. Cycling performance

Figure 2. Environmental factors

Figure 3. Internal biomechanical factors


use of motor-vehicles is a daily choicebetween two level-value alternatives,and who would happily decide not todrive if it were made a little less attrac-ive.

There have been many movements inmany countries to introduce road-useaxes, sometimes called “congestionaxes”, and there are now places whereolls on high-speed roads parallel to

heavily used roads are collected elec-ronically. However, the complexity ofegion-wide introduction of road-useaxes for a large nation or group of

associated nations is so great that iteems likely that they will be first intro-

duced comprehensively in an islandnation and, if successful, spread rapidlyo others.

Governments can also regulate. Cityenters, parks, and other recreational

areas can be prohibited for motorvehicles. Highways can be declared off

imits for bicyclists. There have beeneveral campaigns in Asian countries to

banish rickshaws and to restrict bicy-les. In democracies, motor-vehicle and

oil-producer lobbies are very powerful,and it is necessary that bicyclists haveobbyists to counteract what would

otherwise be absolute power. “Powerorrupts, and absolute power corrupts

absolutely.”The comments of Andrew Oswald

(2000) on the alleged ruination ofBritain’s universities are relevant tothe bicycle situation. “These measureswere the work of outwardly rationaland plausible politicians. As with mostmistakes in life, they did not happenbecause of outright malice. They weremade by honest men and women withthe best of muddled intentions. The

problem was sheer mental sloth, plusan eye on short-term exchequer advan-tage, rather than on any appraisal oflong-term costs and benefits….”

A reduction in the large subsidiesto motor vehicles is the key to greatlyincreased use, coupled with fairerregulations for all classes of vehicles.However, forecasting the future useof bicycles and other human-powered

vehicles is an impossible task, depen-dent on government actions that might

be directed at one set of problemsunrelated to bicycles, and might yetcreate unintended effects on bicycleusage. “The price of liberty is eternal

vigilance.”

ReferencesBarnes, Peter. 2001. Who owns the sky?

Covelo, CA: Island Press.

Gross, Albert C., Chester R. Kyle, andDouglas J. Malewicki. 1983. “Theaerodynamics of land vehicles.”

Scientific American, 249:9 (Dec.).Handlin, Oscar and Mary F. 1975. The

wealth of the American people. NewYork: McGraw-Hill.

Hoerner, S. F. 1965. “Fluid dynamicdrag.” Bricktown, NJ: Hoerner.

McCullagh, James. C. (ed.). 1977. “Pedal power.” Emmaus, PA: Rodale Press.

Oswald, Andrew. 2000. “A sorry state.”The Economist (July 1).Sharp, A.1899. CTC Gazette, January, no. 11.London: CTC.

Wilson, David Gordon. 1997. “Wind-tunnel tests.” review of Tour , das

Radmagazin, article. Human Power

12:4 (Spring), San Luis Obispo, CA:IHPVA.

AcknowledgementPictures and information on the

Thuner Trampelwurm and the Vél’eau 12supplied by Theo Schmidt

The authorDave Wilson is the former editor of

Human Power , co-author with Allan Abbott of the book Human-powered

vehicles, and professor of mechanicalengineering, emeritus, at MIT.

Factors affectingperformance inhuman poweredvehicles: abiomechanicalmodelDanny Too and Gerald E. Landwer

AbstractThere are a large number of bio-

mechanical factors that affect cyclingperformance. These factors can oftenbe grouped into one of three categories:1) environmental factors, (2) internal

biomechanical factors, and (3) externalmechanical factors. The interactionof different factors within a category

an be complex, but need to be exam-ned and understood if more effective

human-powered vehicles are to bedeveloped. The purpose of this papers two-fold: (1) to examine the factorsn each category, their interactions, and

how they affect performance in human-powered vehicles, and (2) to provide a

biomechanical performance model forthese factors.

IntroductionPerformance in land and water based

human-powered vehicles are a func-tion of the amount of propulsive forces

produced versus the amount of resis-tive forces that need to be overcome.Greater production of propulsive forceswith greater reduction of resistive force

will result in greater performance ina human powered vehicle. Propulsiveforces are often affected by internal bio-mechanical factors, external mechani-cal factors, and their resulting interac-tions, whereas resistive forces are oftena function of environmental factors andinternal mechanical forces (muscle fric-tional forces and viscosity; see fig. 1).Designers of human powered vehiclesgenerally focus on how resistive forces

can be minimized (as opposed to con-sidering how propulsive forces mightbe maximized) because environmentalfactors are universal, more predictable,less complex, and independent of theinteractions involved in maximizing andmaintaining propulsive forces.

Environmental factorsEnvironmental factors such as gravi-

ty, friction, and air resistance are gener-ally resistive forces that inhibit cycling

performance on land. The extent thatfrictional forces or rolling resistanceaffect cycling performance is dependenton the type of terrain encountered; thesmoothness/irregularities and hard-ness of the contact surfaces betweenthe wheel and road; the cyclist/vehicleweight; the type of material of thewheel/tire and road surface, road tex-ture; tire tread pattern, size, thickness,diameter and hardness (air pressure);

deformation of the rolling wheel, and vehicle velocity (2, 6; see fig. 2).

Aerodynamic drag is affected byfactors such as: air density (altitude,humidity, and temperature), vehicle

velocity, cyclist-vehicle cross-sectionalarea perpendicular to the direction of

motion, and the drag coefficient (shape,streamlinedness, orientation, andsmoothness of the rider and bicycle).Changes in air density by cycling at highaltitudes, or changes in the drag coeffi-cient (by modifying the vehicle shape orsize, or the use of aerodynamics suits,fairing, solid disc wheels, etc.) can sig-nificantly alter cycling speed, time, and

performance (5, 6, 7).

Internal biomechanical factorsInternal biomechanical variables

affecting propulsive force and cycling performance involve factors related toforce/torque development and power

production as depicted by the proceed-ing biomechanics performance model

(see fig. 3).These are factors not often under-

stood or considered by designers ofhuman powered vehicles because ofthe complexity of their interactions.Manipulation of these factors canmodify and alter the effective muscleforce/torque/power generated andtransmitted to the vehicle. These fac-tors include: position of initial and finalmuscle length, change in muscle length,muscle moment arm lengths, force arm

length, load imposed on muscletance arm length, direction/line/of force (resultant, stabilizing, rdislocating), point of applicationangles, muscle angle of pull, sinmulti-joint muscles, muscle fibeand arrangement, type and numof lever/pulley systems involvedof muscular contraction (concenisometric, eccentric), speed of ction, muscle recruitment patternfrequency, synchronization, numsequence of motor units involvetribution of series and parallel ecomponents, internal frictional fand viscosity within the muscledifferences in segmental limb leand limb ratios (2, 4, 8). Changeinteractions occurring in the intbiomechanical variables resultin

propulsive force are often the remanipulations of external mechfactors.

External mechanical factorExternal mechanical factors i

constraints imposed upon a cycthe structure of the vehicle and

power is transmitted to the vehiThese factors include: the seat-tdistance; seat tube angle; seat h

pedal crank arm length; handlebheight, length, and position; cycbody position, orientation, and jconfiguration; foot-pedal positiochainwheel size and shape (circ

versus elliptical); use of cams; gratios; the wheel size, mass, diamand inertial properties; and loss

power transmission due to frict




Figure 1.The vortex theory of airfoils

s due to Nicolai Yegerovitchoukowsky (sometimes translit-rated Zhukovskii) and Wilhelm

Kutta, and dates from 1911.oukowsky devised the confor-

mal transformation which mapshe flow about a circular cylinder

with bound vorticity into the cor-esponding flow about a lifting

airfoil. Kutta showed that if thebound vorticity is adjusted toplace the aft stagnation point in

the flow about the cylinder at thesingular point (where x = -a, y = 0),the transformed flow about theairfoil will leave the trailing edgesmoothly, and this determinesairfoil lift. The lifting “circulation”,or vorticity, in physical airfoilflow is due to the difference in

vorticity between the upper andlower surface boundary layers.

All modern airfoil theory containsthe Kutta-Joukowsky results as aspecial case.

Figure 2Since the lift, and hence the

bound vorticity, must go to zeroat the tips of a monoplane wing,here must be a certain spanwiseradient of lift which minimizeshe kinetic energy of trailing

vorticity comprising the vortexwake. Max Munk showed (in 1916) that an elliptic lift distribution

does this by creating a spanwiseuniform downwash velocity ofhe nascent trailing vortex sheet.

Albert Betz later showed that

such a trailing vortex sheet wouldwind itself up into two “tip vor-tices” with no change of energylevel. The spanwise constantinduced angle of attack for ellipticloading (which is optimum) maybe written

αi =w/V=(lift) / π ⋅ (ρ ⋅ V 2 /2) ⋅b2

or = CL / π ⋅ ( AR) where CL is the wing lift coef-

ficient, (lift/S) (ρ ⋅ V 2 /2), AR is theaspect ratio equal to b2 / S, and Sis the wing area.

Figure 3The large span of a human-pow-

red airplane wing, 29 m (95.14t), is made necessary by thelow flight speed, 7 m /s, and theow density of air, 1.225 kg/ cubic

meter at 760 mm Hg and 15degrees Celsius. If the wing pro-

file drag coefficient is taken tobe twice the turbulent skin fric-tion coefficient as given by vonKarman,

0.242/ √ CF =log10 (CF ⋅ Re), the power to fly the loaded wing isabout 155 W.

Figure 4The much smaller 1.5 m (59 in)

pan of a human powered hydro-oil wing is made possible by the

much higher density of water,000 kg per cubic meter. Sincehe hydrofoil operates close tohe surface, the amount of fluid

it can influence is halved and theinduced angle is doubled. The

power to fly such a loaded hydro-foil wing is about 195 W at a speedof 6 m/s under the same assump-tions as the human-powered air-

plane wing.

Figure 5.The concept of propeller “slip”

is as old as the steamboat screw propeller. The difference betweengeometric pitch and effective

pitch was first accounted for byProf. J. M. W. Rankine (the proto-

typical Scotch engineering profes-sor) and W. Froude, who showedthat the propeller thrust must

produce an increase in slipstream velocity, half of which is realisedat the propeller disc.

Figure 6 Albert Betz showed in 1919 that

the slipstream velocity behind athrusting propeller should giverise to a radially constant “dis-

placement” velocity of its trailing vortex sheets, analogous to thespanwise constant downwash

velocity behind an ellipticallyloaded wing. He wrote (trans-lated): “The flow behind a screw

with minimum energy loss is as ifthe path traversed by each blade(a helicoidal surface) becamerigid, and displaced itself rear-ward with a certain velocity, orturned itself about the screw axiswith a certain angular velocity.”The misleading idea here is thestatement that the helicoidal vor-tex sheets should move as rigidbodies. The correct interpretationis given in the figure.

Figure 7 Just as an elliptic bound vortic-

ity distribution gives rise to a con-stant downwash velocity behinda wing, so certain radial bound

vorticity distributions give rise toslipstream vortex sheet motionwhich satisfies the Betz conditionbehind propellers. The bound vor-ticity distributions are functionsof the advance ratio (or inversetip speed ratio) and the number ofblades. The dimensionless bound

circulation G (for Goldstein) isalso approximately the ratio ofaverage axial slipstream velocityat a given radius to the displace-ment velocity. To minimize theslipstream kinetic energy (orinduced loss) for a given thrust,airspeed, and diameter, the tipspeed ratio and the number ofblades should be increased, there-by making the slipstream moreuniform.

Figure 8 Just as a wing has profile

drag, so propellers have profilelosses. The profile efficiency of a

propeller blade element is η profile = tanφ ⁄tan(φ + ε) whereφ is the helix angle of the bladeelement relative velocity W,accounting for the induced

velocity w. In order to minimize profile losses of a propeller, themost heavily loaded portions

near 80% radius should operateat φ = π / 4 − ε /2, and the bladenumber should be reducedto increase the blade chordReynolds number, therebyreducing ε, the “glide angle”,equal to the arctangent of airfoilsection Cd / CI . The conditionsfor reducing profile losses are inconflict with reducing inducedlosses.



Flywheel

Hopper

Channel

Chain

Pedals

Clutch

Gear Pinions (torque rise)

Gear Pinions (speed rise)

Cone

Die

Flywheel

PinionsChain

Thigh

Leg

Chainwheel

Knee

Foot / Pedal

Saddle

Bicycle Frame

Hip Joint

Figure 1. Schematic of a

human-powered brick-

making machine devel-

oped for MHADA, Bombay.

Figure 2. Schematic of human-powered flywheel motor.


Variousefficiencies of ahuman-poweredflywheel motorJ. P. Modak and A. R. Bapat

[ Editor’s note: This article is based ona lengthy scientific paper “Formulationof generalised experimental models andtheir optimisation for transverse forceexerted on the pedal and various effi-ciencies of a human-powered flywheelmotor” received by Human Power . Forreasons of space some sections havebeen replaced by editor’s summaries.]

AbstractIn the recent past a human-powered

process machine has been developedfor brick making, wood turning, clothes

washing and drying and earthen- pot making (Modak 1982 and 1998, Askhedkar 1994). The machine consistsof a human-powered flywheel motorusing a bicycle-drive mechanism withspeed-increasing gearing and a flywheel,which drive the process unit thougha clutch and torque-increasing gear-ing (Gupta 1997). The operator putsenergy into the flywheel at a convenient

power level for about one minute. Afterenough energy is stored, pedaling isstopped and the energy in the flywheelis made available to the process unit.Suitable duties are those requiring upto 2 kW and up to 10 kJ in total energyat each application. In a previousinvestigation by the authors (Modak

and Bapat 1994), a generalised experi-mental model for the human-poweredflywheel motor was established forsome responses of the system. The

present investigation focuses on someadditional responses. The generalisedexperimental models established in this

research are amply validated by experi-mental findings. [ Editor’s note: the pro-cess unit has been previously describedin Human Power (Modak & Moghe1998) including drawings and pictures.This article covers the human-poweredflywheel motor.]

Background of present workDuring 1979–99, Modak (1982, 1994,

1997, 1998, and n.d.) developed ahuman-powered brick-making machinefor manufacturing bricks out of a mixconsisting of lime, fly-ash and sand. Inthis machine human power is the mainenergy source. The machine describedin figure 1 consists of a pedaled fly-wheel with a speed-increasing transmis-

sion (abbreviatedas Human-PoweredFlywheel Motor, orHPFM), a transmis-sion unit (spiral-jawclutch and torque-increasing transmis-sion), and the pro-cess unit consistingof an auger, a cone

and a die. Althoughthe system wasdeveloped essen-tially on the basis ofintuition and pastgeneral experience,it proved to be func-tionally feasible andeconomically viable.This concept wasalso tried on a win-nower (for remov-

ing food grain shells), a wood stting machine, and a blacksmith as developed by the Center of Sfor villages in Wardha, India. Ththe outcome of one project sponby the Department of Science anTechnology of the Government

during 1995–1998.Scope of present research

As an extension of earlier maematical models (Modak & Bapasome more models are formulatthe response variables of the enunit, such as the transverse forced on the pedal, the crank, pedafoot positions with respect to ththe pedal and flywheel energies

paper essentially reports on expmentation which involves descrand varying independent variablmethod of measuring the responables, the procedure of experimtion, data collection, presentatioanalysis, concluding with a quallogical analysis for the optimisathe models.Experimentation

Independent variables

G is the gear-ratio between th pinions at the flywheel. This is vbetween 1.14 and 4; there are fivThere is further fixed ratio of 1.9by the chain drive. Thus the totafrom the pedals to the flywheel c

varied between 2.2 and 7.6.I is the flywheel’s inertia. This

varied between about 0.26 and 3by fitting different flywheels, alssteps.

R indicates the mechanical eninput by the rider during one mi

pedaling time. Twelve male rideage group of 20–22 years and of stature were chosen for the expments. Each rider accelerated thwheel for about one minute, sub

Figure 9The thrust and power load-

ngs of a minimum induced losspropeller may be written as qua-dratic functions of the displace-ment velocity and four loadingntegrals which can be evaluated

numerically and account for wakeeometry and radial glide number

distribution. Once the displace-ment velocity has been found,the efficiency can be predicted. Ifsatisfactory, the propeller geom-etry can then be determined. Thedimensionless bound circulationfunction G is here calculated byan approximation due to Prandtl.

Figure 10The geometry of a minimum

nduced loss propeller is com-pletely defined as soon as its dis-placement velocity, correspond-ng to a specific thrust or poweroading, has been calculated. The

associated radial variations of

blade chord Reynolds number andMach number should be calcu-lated to see if they are consistentwith the radial variation of glidenumber (section drag/lift ratio)used to calculate the loading inte-grals.

Figure 11These are results of a propeller

design calculation for a humanpowered airplane. The designpower of 400 W is more than

xpected for level flight to insurefficiency during the climb. The

Clark Y airfoils yield a lift coef-ficient of 0.5 at alpha equal zerodegrees, measured with respecto the f1at under surface. Notehat specification of a design lift

coefficient of 0.6, correspondingto an angle of attack of 1 degree,

produces a slightly non-uniform pitch/diameter ratio. The cal-culated chords inboard of 30%radius are too small because oferrors in the Prandtl approximatebound circu1ation, and should beincreased appreciably, both forthis reason, and also for structuralintegrity.

Figure 12These are resu1ts for a simi1ar

design calculation for a humanpowered hydrofoil propeller.The small diameter of 360 mm14.17 in) is made possible by the

high density of water. The highhaft speed of 900 rpm is neces-

sary to make the tip speed anappropriate multiple of vehiclespeed with this small diameter.The low design lift coefficient of0.3 is chosen to increase bladechord Reynolds number and mini-mise cavitation.



0

20

40

60

−20

0 360

For right leg For left leg

90 180 270

Crank angle in degrees

Avgerage force = 38.8 N

Pedal energy (approx. 1 minute) = 2616 Nm

0

20

40

60

80

100

E n e r g y [ % o

f i n p u t ]

Moment of inertia I [kg m2]

0 . 2

5 5

1 . 0

6 1

1 . 8

6 7

2 . 6

7 3

3 . 4

8

Pedaler input energy (measured from exhaled air)

Flywheel kinetic energy acquired

Pedaler output energy (measured from foot force

on pedal and distance traveled)

0.2 1.0 1.8 2.6 3.48

0

20

40

60

80

100

120

140

160

180

200

300

0

100

200

400

500

F t a v g . / c y c l e [ N ]

E n e r g y p e r c y c l e

[ N m ]

F l y w h e e l T o r q u e [ N m ]

Moment of inertia I [Kg m2]

4

0

2

12

8

6

10

14

R Ft G*I*a

igure 3. Instantaneous Ft vs. crank angle

Figure 4. Ft, R, and flywheel load torque vs. I, averaged over 1 min.

Figure 5. Energy efficiencies measured at the end of 1 min. pedallingduration


Figure 5 presents the variations of pedal energy and flywheel energy at theend of the one-minute pedaling dura-tion versus I, given as percentage of theinput energy (average values from the12 riders). G is given as 2.0.

[ Editor’s note: Two sections “Analysisof results” and “Corroboration of gener-alised experimental models” (not givenhere) detail the best combination of

variables to use for a specified objec-tive function, e.g., if the objective is tominimise pedal force Ft, the smallestavailable values for I and G are to beused. However in terms of efficiency, asseen in figure 7, the combination I=1.06and G =3.8 is optimal. In terms of maxi-mum power, as seen in figure 4, thesame combination very nearly gives themaximum flywheel torque, and hencemaximum flywheel power (neglect-ing flywheel losses). The generalisedmathematical model however gives dif-ferent optima for efficiency when the

variable in question is I, and the authors

conclude that for this case more experi-mental evidence is needed in order tounderstand the relationships.]

ConclusionThere exists a considerable similar-

ity in this investigation and of previ-ous investigators (Sargeant et al 1978)regarding the pattern of transverseforce Ft exerted on the pedal at everyinstant during the cycle of each leg.There has been some difference in the

pattern of Ft forboth the legs dur-ing the rise of Ftcompared with the

previous investiga-tions. This needsto be confirmed byadditional research.It is not desir-able to keep theflywheel momentof inertia I in therange of 1.4 to2.4 kg m2. This isbecause during this

variation of I all thethree parameters R,Ft and G ⋅ I ⋅ α havefairly large values.

In view of keep-ing internal human-body energy lossesand frictional

energy losses ata minimum, it isnecessary to keepG at 3.8 and I at

1.06 kg m2, however lowering G to 2.85or even 2.17 may result in a reasonablecompromise between the intensity oftaxing muscles and incurring consider-able internal physiological energy lossin the human body.

References Askhedkar, R. D. and Modak, J. P. 1994.

“Hypothesis for the extrusion of limefly-ash sand brick making machine.”Building Research and Information,UK, 22:1, 47–54.

Bapat, A. R. and Pote, G. R. 1994.“Design and Development ofSpirometer,” InternationalConference on Signals, Data, System,SDS ’94, Hyderabad (India), Dec.12–14.

Gupta, J. K. and others. 1997. “Design proposals for a new type of clutchesessential for process machines withmanually energised flywheel motoras an energy source.” Proceedings,

Mechanic Transmission andMechanisms (MTM 97) organised byUniversity of Tianjin, China. July1–4,

pp. 383–388.Modak, J. P. 1982. “Manufacture of lime

fly-ash sand bricks using a human powered machine.” Project Reporton behalf of Maharashtra Housingand Area Development Authority,Bombay, India.

Modak, J. P. 1984. “Bicycle, itskinematics and modifications.”

Proceedings of National Conon Machines and Mechanismat I.I.Sc., Banglore, India, pp.

Modak, J. P. and Bapat, A. R. 199“Formulation of the generalisexperimental model for a madriven flywheel motor and itsoptimisation.” Applied Ergon25:2, 119–122.

Modak, J. P. and Moghe, S. D. 199“Design and development of human powered machine formanufacture of lime-flyash-sabricks.” Human Power , 13:2,

Modak, J. P. and others. 1997. “M powered manufacture of keybricks.” International JournalBuilding Research and InformUK: Elsevier Pub., 25:6, 354–3

Modak, J. P. and Sohani, V. V. [n.“Formulation of generalisedexperimental model for an exunit of a manually energised

machine for extruding keyedbricks.” Accepted for publicaInternational Journal of BuildResearch and Information, U

Sargeant, A. J., Charters, A., DavC. T. M., and Reeves, E. S. 197“Measurement of forces appland work performed in pedala stationary bicycle ergomete

Ergonomics, 21:1, 49–53.

About the authorsDr. J.P. Modak is a professor

mechanical engineering departmPriyadarshani College of Engineand Architecture, Nagpur, India.has to his credit a number of res

papers published in national annational journals. He has complseveral sponsored projects on menergised process machines in l

years. He has received several nawards covering the areas approtechnology, manually energised and applied robotics.

Dr. A.R. Bapat is a professor iIndustrial engineering departmeof Shri Ramdeobaba Kamala Ne

Engineering College, Katol RoadNagpur, 440013 (India). He has tcredit a number of research pap

published in national and intern journals. He is also the author obook titled A textbook of engine

drawing. He is also the recipienMaharashtra State National Awaoutstanding research work in ening and technology, 1992. His e-maddress is [email protected]

himself to a comfortable maximum-xertion level. The load torque requiredo be overcome on the flywheel shafts I ⋅ α, where α is the average angular

acceleration during the pedaling dura-ion of one minute. The load torque to

be overcome on the pedals is thereforeG ⋅ I⋅ α. The total air exhaled during

xperimentation was recorded by apecially-designed and fabricated spi-ometer (Bapat and Pote 1994). Thepecialty of measuring the exhaled air

with respect to time is an improvementover the earlier investigation (Modakand Bapat 1994). The total (physiologi-

al) energy input by the rider is esti-mated from the exhaled air collected inhe spirometer and the corresponding

oxygen intake.[ Editor’s note: Part of the paper

omitted here) compares the kinematicproperties of the standard upright

bicycle geometry with several modi-fied geometries: One called the “quick-eturn-ratio=1" drive gives smallerhan usual knee angles and a moreven force distribution around a com-

plete pedal-crank revolution. A furthermechanism is called the double-levernversion, and the last is an ellipticalhainwheel having its length twice its

breadth. In all these, the rider’s thighand lower leg together with the pedal-rank are considered parts of a four-barinkage, with foot action not includedn the mathematical model. Tangential

or pulling forces possible by “ankling”and/or using pedal clips are thus notpart of the model. This predicts that themodified mechanisms are kinematicallybetter than the standard configurationby factors of up to 38 %. These predic-ions are, however, not validated byhe subsequent experiments, wherehe standard geometry is found best inerms of efficiency. However, the test

persons seemed to prefer the configura-tion called “double-lever inversion” foraccelerating the flywheel.]

Dependent variables

Ft, the transverse force exerted onthe crank, is measured using straingauges which are mounted midway onthe cranks. The instantaneous strain

values are stored in a computer mem-ory for further processing. The crankangle is measured digitally by usinga circular ring having equally spaceddrilled holes and a photoelectric sensorwhich measures the interruptions ofthe light beam as the ring rotates. The

pedal energy is estimated in terms ofthe pedal force Ft, the circumference

of the pedalrotation, andthe number ofrotations ofthe pedal dur-ing the periodof pedaling.The flywheelenergy isestimated interms of I (theflywheel’smoment ofinertia), and

the terminal flywheel speed which ismeasured by a tachometer. An X-T plot-ter gives the graph plot of the instanta-neous flywheel speed during the periodof pedaling.

Conduct of experimentExperiments were conducted while

varying I and G independently. Alltwelve riders operated the system forevery combination of I and G and the

values of the corresponding indepen-dent and dependent variables wererecorded.

Figure 3 describes the variation ofinstantaneous Ft vs. crank angle forboth the legs for one cycle of opera-tion of the pedal crank. (Here the resultis the average of 3 riders from the 12,chosen at random.) The total averageFt is 38.8 N and during one minute an

energy of 2616 Nm is accumulated, thusthe average power here is about 44 W.I is given as 0.225 kg m2 and G is givenas 1.5.

Figure 4 presents the measurementsof some physical quantities versus I(average values from the 12 riders).These are the energy input R, the tra-

verse pedal force Ft and the flywheelload torque, all averaged over the pedal-ing duration of one minute. G is givenas 2.0.

human power no. 54

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