Human PowerThe Technical Journal of the

International Human-PoweredVehicle Association

David Gordon Wilson, Editor15 Kennedy Road

Cambridge, MA 02138, USA617-253-5121 (office)

617-876-6326 (residence)IHPVA

P.O. Box 51255Indianapolis, IN 46251, USA

Phone: (317) 876-9478Marti Daily PresidentBlake Davis Corresponding

SecretaryBruce Rosenstiel TreasurerPaul MacCready International

PresidentAlc Brooks VP Water

Tom McDonald VP LandLynn Tobias VP Air

David Gordon Wilson Executive VPAllan Abbott Board Members

Mike BurrowsPeter Ernst

Chet KyleGardner Martin

Human Power is published quarterly by the Interna-tional Human-Powered Vehicle Association, Inc., anon-profit organization devoted to the study andapplication of human muscular potential to propelcraft through the air, in the water and on land.Membership information is available by sending aself-addressed, stamped business-sized envelope to:

IHPVAP.O. Box 51255Indianapolis, IN 46251-0255 USA

Material in Human Power is copyrighted by theI}-IPVA. Unless copyrighted by the author(s), com-plete articles or representative excerpts may be pub-lished elsewhere if full credit to the author(s) and theIHPVA is prominently given.

Special thanks to Sabina Rataj, David Wilson, MartiDaily, Kim Griesemer and The Professional Edge,without whom this issue would not have beenpossible.

In This Issue-1 Backward versus Forward Pedaling:

Comparison Tests by RamondoSpinnetti

2 Editorials by David Gordon Wilson3 Briefly News: Recent Developments4 Angular Momentum and Bicycle

Stability by Brenan J. McCarragher6 Corrections to "Dynamical Stability

of the Bicycle" by Y. Le Henaff7 Oxygen Cost of Submaximal Exer-

cise in Recumbent and Convention-al Cycling Positions by Ingrid E.Antonson

8 The Bioenergetics of Power Produc-tion in Combined Arm-Leg CrankSystems by Richard Powell andTracey Robinson

19 Oh For the Wings by Arthur C.Clarke

Editorials by David Gordon Wilson

Coming of Age?A few weeks ago there arrived

almost together two publications of greatpotential significance for the human-power movement: the June 1987 issue ofAmerican Bicyclist, and the new editionof Richard Ballantine's Richard's NewBicycle Book. The cover of the maga-zine, which is a trade journal principallyfor bicycle dealers, a group generallyrather skeptical about the prospects forrecumbents, gave the theme of thisissue: "Recumbents: The Laid-Back,Fast-Forward Alternative - The Market,the Makers, the Models." RichardBallantine's book is the first I know of onbicycles in general that is frankly enthusi-astic about HPVs in general and recum-bents in particular. He has already hadconsiderable influence on all of us:Richard bought one of the first Avatarsto be exported; he lent it to DerekHenden of London who modified it tobecome the fully faired recumbentBluebell, and with nonracer AustralianTim Gartside pedalling, came to theCarson (California) IHPSC October 3,1982 to beat the Vectors, Easy Racer andSteve Ball's Dragonfly. Subsequently theemphasis shifted from tricycles to recum-bent bicycles in the quest for speed.Richard's chapter fifteen is headed"ZZZWWAAAMMO!" and is as enthus-iastic as the title on the new vehicles.

The two publications will give theHPV movement a great deal of favorableacceptance. We appreciate therecognition!

And on public TV the second in theseries by Philip and Phylis Morrisoncalled "The Ring of Truth" featuredvarious HPVs including an aircraft andmany bicycles. Shortly afterwards, eventhat old Sixty Minutes curmudgeonAndy Rooney extolled the bicycle as thefriendliest of man's inventions. We areindeed honored.

Apologies!In the last issue I half-apologized for

publishing letters favorable to HumanPower because we had until then receiv-ed no complaints. Pride goeth before afall; we fell badly in that very issue, andwe have been justifiably taken to task.We introduced so many errors into themathematics of Y. Le H6naffs article asto reduce its usefulness greatly. We listthe corrections on page 6. We omitted

the addresses of several authors and ofmanufacturers. And in my own articleon a propeller development I did nothold myself to the international units Itry to require of authors generally. Meaculpa! The journal is put out by manyoverworked people trying to squeezetime out of many other demands, and ithas not been possible previously forissues to come back to me to be proof-read. With this issue we are trying theexperiment of paying for a professionallayout house (which is giving us a breakon its usual charges) and I will be able tosee the proofs before final printing.Study it carefully and let us have yourcomplaints or plaudits. As in so manyinnovations, President Marti Daily set upthis new experimental arrangement.

The Right to PrivacyAnd with regard to the publication of

authors' addresses, we normally get theirprior permission to do so in order thatinterested people can write to themdirectly rather than go through the non-existent bureaucracy of this journal. In away these addresses are priviliegedinformation, and can lead to an invasionof privacy. It can lead also to unreason-able demands. Most come from non-members of the IHPVA, but becauseHuman Power is, thank goodness, readfairly widely by nonmembers I would liketo make this plea. If you write forinformation, include a stampedaddressed envelope. If you call longdistance, don't leave a message expect-ing our authors to call you back at theirown expense. This month I, for one, havehad a bumper crop of people who havecalled or written from near and far withlong lists of requests, almost demands,for very specific information, requiring,often, library research, and much copy-ing and postage, as if we were some sortof free reference service. Often theystate that they have heard about theIHPVA or about, for instance, the bookBicvcling Science, but they want to getinformation without subscribing toeither. I feel used when I give themeverything they want, as I usually do, andequally I feel that I am a lousy ambassa-dor when I don't. All of the officers of theIHPVA spend a huge amount of theirtime and a great deal of their own moneyon the organization, and I would like ourvaliant authors to be spared that load.

2

Angular Momentum and Bicycle Stabilityby Brenan J. McCarragher

ABSTRACTA flywheel was mounted to the front fork

of a bicycle to investigate the effects of angularmomentum on bicycle riding and steeringcharacteristics. A range of angular-momen-tum settings were tested on a series of coursesincorporating the situations most encounteredby bicyclists. Test subjects were used andtheir lateral deviation from the test course wasevaluated. Also a Cooper-Harper ratingsystem was used to determine test riders'subjective ratings of the bicycle. The resultsshowed that large amounts of positive angularmomentum had an extreme stabilizing effectwhich made turning difficult, while negativeangular momentum proved difficult tocontrol. The learning curves generatedindicated good improvement at the positivesettings, while minimal improvement wasshown at the negative stettings. Most im-portantly, the experiment showed that theangular momentum of the front wheel of abicycle can have significant effect on thecontrol and steering of the vehicle.

INTRODUCTIONThe balancing and controlling of

bicycles is a complex subject. The bicyclelean in addition to the offset of the frontfork complicate the rigid-body geometryof the bicycle and make bicycle dynamicsdifficult to describe. Recent documenta-tion shows that despite the complications,no real controversy exists concerning howa rider steers and balances a bicycle. Onesteers into or under a fall, similar to bal-ancing an inverted pendulum on one'sfinger. However, when attempting toanswer why some bicycles are easier tosteer than others, experts are often incomplete disagreement, even aboutfundamental concepts. Some expertsassert that gyroscopic action has littleinfluence, while others insist the oppositeis true [1,2]. This uncertainty is a result ofthe complex dynamics described above.Specifically, it is this uncertainty concern-ing the effect of angular momentum andgyroscopic action that has prompted thisstudy.

David Jones [3] constructed a bicyclein which the gyroscopic action of thefront wheel was cancelled by a flywheelrotating backwards. He found that thismade little difference on the stability ofthe bicycle. His only reaction was that"the 'feel' was a bit strange." He thentried to run the vehicle without a rider

ning against the road wheels, it collapsedquickly. However, with the flywheelspinning with the road wheels it showed"a dramatic slow-speed stability, runninguncannily in a slow, sedate circle beforebowing to the inevitable collapse." Jonesconcluded that the light, riderless bicycleis stabilized by gyroscopic action, where-as the heavier ridden model is not andrequires constant rider effort to maintainstability.

The intention of this project, then,was to test and expand Jones' conclusionsin a more quantitative and systematicmanner than was previously done. Bymounting a flywheel to the steeringcolumn of a bicycle, this project tested theeffect that the angular momentum of thefront wheel has on bicycle stability. Theflywheel was able to rotate forward andbackward at high speeds allowing a widerange of angular momenta to be tested.

THEORETICAL BACKGROUNDIn this experiment, a rotating

flywheel was mounted on the front forkof a bicycle. Due to its mass and velocity,this rotating wheel generated angular mo-mentum H as defined by

H I p (1)where I is the moment of inertia of thewheel about the spin axis and p is theangular velocity, or spin velocity. By thelaws of gyroscopic motion, when a rotoris forced to precess, as occurs with abicycle wheel when a rider is executing aturn, the motion will generate a gyro-scopic couple or torque M, given by

M = I x p (2)where n is the precession velocity. M, ,and p are mutually orthogonal vectorswith their relationship defined by theright-hand rule of cross products. Thecorrect spatial relationship among thethree vectors may be remembered fromthe fact that dH, and hence p, is in thedirection of M, which establishes thecorrect sense for the precession f. Thusthe spin vector always tends toward thetorque vector.

Consider now a bicycle with forwardangular momentum making a right-handturn. The M, p, and 2 vectors are shownin Figure 1. As can be seen, if the spinvector tends toward the couple M, a set offorces representing the couple make therotor turn into the circle prescribed, re-

quiring the rider to lean into the curve. Inthe same respect, if the rider turns leftwith forward angular momentum, theopposite couple again forces the rider tolean into the turn.

p

w

FIGURE 1: Bicycle wheel with forward angularmomentum making a right-hand turn

On the other hand, if the angular mo-mentum is in the reverse direction, thespin vector p switches directions (Figure2). If the rider turns right, the torque triesto straighten the rider, requiring less lean.For the analogous situation for a left-handturn the opposite couple again requiresless lean.

P

F

W

FIGURE 2: Bicycle wheel with reverse angularmomentum making a right-hand turn

The strength of the gyroscopic couple, ofcourse, depends on the strength of both pand f. Thus the faster a bicyclist travelsand the quicker he turns the front wheel,the stronger will be the gyroscopiccouple.

A rider traveling with a linearvelocity v on a circular course with radiusof curvature r has an angular velocity fequal to

f=vr (3)

According to these dynamics, the bicycleproceeding on a curved path with a leanangle Q will have three forces working onit (Figure 3). These forces are gravity W,centripetal C, and the gyroscopic force G.

4

nnrq fniinrl thnf with t'he fuw'Poo cin-

F

C

FIGURE 3: Dynamic forces working on a bicycleIn equilibrium, the sum of the

moments of these forces about point A iszero, MA = 0. With counterclockwisemoments being defined as positive, thisequation becomes-mgdsinQ +mv2 dcosQ + HQcosQ = 0 (4)

rwhere d is the height of the center ofgravity of the bicycle and H is the amountof angular momentum. Knowing thatangular momentum is the product of themoment of inertia I and the angularvelocity w (1), and also substituting (3)for Q, the equation becomes-mgdsinQ + mv2 dcosQ + Iw v cosQ = 0(5)

r rSolving for the lean angle Q one gets

tan Q =v2 + I v wrg rmgd

(6)

orQ = tan-1 2 + I v w (7)

g r rmg d The lean angle, therefore, is dependentupon the velocity, the radius of curvature,and in the presence of angular momen-tum, the mass of the system, the height ofthe center of gravity, and, of course, theamount of angular momentum.

It has been suggested that the bicy-cle-rider system be evaluated as a two-body problem to better account for thecontrol that the rider exerts. In order todetermine and solve these equations, oneneeds to know many additional terms.First the center of mass of both the riderand the bicycle need to be found separ-ately. In order to do this, one must as-sume a mass fraction and mass distribu-tion of the two bodies to account for therider's lower body being part of the bi-cycle system. Also an upper-body anglemust be assumed in order to calculate thelean angle of the bicycle. The manyuncertainties and assumptions warrantthat this method not be used as a theo-retical comparison for the actual data.

TFST 1FSIGN THF RICYCLF

The primary goal of the test vehiclewas to design a bike that would have thecapability for additional angular momen-tum without dramatically altering theother characteristics of the bicycle. Thiswas accomplished by mounting on thebicycle a flywheel to provide the addi-tional angular momentum, and a counter-weight to provide balance. Because thefront wheel is the main device used insteering a bicycle, it was decided tomount the flywheel on the fork of thefront steering column so as to betterexamine the effects of the angularmomentum on both the stability andsteering characteristics. The flywheel waspowered by a small motor mounted justforward of the front fork of the bicycle.The motor was in turn powered by abattery mounted behind the seat. Weightwas added to the flywheel in order toobtain the necessary angular-momentumsettings. The motor was able to spin inboth directions so as to allow for forwardand reverse angular momentum.

TESTING PROCEDUREBecause the goal of the experiment

was to investigate the effect of angularmomentum on bicycle riding character-istics, a range of four additional angular-momentum settings was chosen. Thedesired test speed was 4.5 m/s (10 mph),so all angular-momentum settings weredetermined with reference to the amountof angular momentum generated by thefront wheel of the bicycle when travelingat this speed. For this report, a negativesetting means the flywheel was rotatingin a direction opposite of the front wheel,while a positive setting means the twowheels were spinning in the samedirection.

A setting of zero times angular mo-mentum was chosen as the control and asa basis for comparison to other bicyclesand other settings. This setting wouldshow the effects of the physical construc-tion only. A negative one additionalangular momentum was used to cancelthe front wheel's momentum, in order todiscover what the effect the lack of a forcecouple may have. Thus by default, onecan determine what effect the angularmomentum of a regular wheel has. Also,it was desired to look at the two extremecases, and therefore positive and negativeten times additional angular momentumsettings were chosen. Due to the virtuallyuncontrollable nature of the bicycle at thenegative ten setting, this setting wasreduced to negative five times the angular

momentum of the front wheel of thebicycle.

In order to investigate the riding andstability characteristics of the bicyclewhen traveling linearly, a straight coursewas used. The second course used was acircle so as to determine the riding char-acteristics when turning. And a serpen-tine test course was used to examine thecharacteristics of the bicycle when quicklychanging directions. On each course thelateral deviation was taken at discreteintervals. Because each test rider is dif-ferent, and because people learn andadapt, each bicyclist rode the test coursethree times, allowing for the generation oflearning curves.

In order to fully test the effect of thecoupling force created by angular mo-mentum on the steering and stabilitycharacteristics of the bicycle as previouslydescribed, the lean angle had to bemeasured. A camera was set up on atangent to the circle to take a photographas the rider turned along the circularcourse.

Because the test rider has such an in-volved role in defining the riding charac-teristics of a bicycle, a system of subjec-tive data collection was necessary. TheCooper-Harper Rating System [4] wasused to help facilitate this aspect of datacollection. Through slight modification,this system allows the riding character-istics of the bicycle to be defined in termsof the compensation required. Basically,the system entails deciding between threesets of opposites and assigning each anumerical value. For this experiment, thequality was either:

a. Satisfactory: good enough withoutimprovement [value 1-3]

b. Unsatisfactory but Acceptable: justgood enough, adequate for thepurpose, but improvement isdesirable [value 4-6]

c. Unacceptable: not suitable for thepurpose but still controllable[value 7-9]

d. Uncontrollable: unacceptable for thepurpose and of the poorest quality[value 10]

RESULTS

THE STRAIGHT COURSE

The straight course proved to be theeasiest of the three test courses rangingbetween 50 and 125 mm (2 and 5 in) root-mean-square (rms) deviations, with norider experiencing trouble maintaining

(continued on page 13)

5

I

__ _1

%

2

Corrections to "Dynamical Stability of the Bicycle"by Y. Le Hnaff

We greatly regret that several errorsoccurred in our publication of this articlein Human Pouer 6/1. Here are thecorrected versions in the order the errorsappeared, starting on page 15 of thatissue.

FIGURE 1 CAPTIONThe caption should read: Side view

and bicycle dimensions. Lengths: MM'= TT' =MP + PM' = 1 + L = a = 1.0m; 1 =0.2r; wheel radius r = 0.33 m. Trail T = TOis measured positively forwards. Thefork angle is (p = 20° .

EQUATION (1)

tanO + v2 tan Oa/ag (1)

GEOMETRY OF THE BICYCLEFor the upright bicycle in Figure 1,

the plane of the front wheel coincideswith the plane of the frame and cuts theground plane along XX'. M and M' arethe centers of the hubs, T and T theground-contact points of the wheels. Thefront-fork axis makes an angle with thevertical, intercepts the ground at O andcuts the line MM' at P, defined as thefork point. P is fixed on the fork axis andprojects at H on the ground trace OT ofthe frame plane; P is also at a fixedposition with respect to the center ofgravity of the system supposed [4] withinthe frame plane. We write MP = 1, PM'= L and, of course, 1 + L = a.

The angles X (POX) and (p = POX'are defined respectively in the front-wheel and frame planes; only when thosetwo planes coincide do we have (p + 0 = X -

(p = r/2. When the handlebar is turned,it can be seen experimentally that thefront wheel slides slightly downwards;therefore, (p increases and X decreases.

Jones computed the height h of thefork point which is related to the heightof the center of gravity and hence to itspotential energy h = HP, in the frameplane for obvious dynamical reasons.Writing OP = , we have:

h = zsinqp (2)

In the frame plane, the vector relation

-O') - -M' M'T'T'OOP + PM' + M'T' + T'O = 0

projected on M'T' yields:

zsinp + Lsin((p + 0 - n/2) = r (3)

where r is the radius of the wheel and((p + 0 - n/2) is the downward tilt of theframe in its plane.

Similarly, in the front-wheel plane,the corresponding relation

OP + PM + MT + TO =0

projected on MT gives:

(4)

PAGE 16On page 16, the last sentence in the

caption of Figure 2 should read: "Thefront-fork axis is along OZ'." The Greeksymbol in the first line of the first columnshould be X, and the second paragraphshould be:

"A second relation can be obtainedconsidering a bike running on a curvedpath (Figure 2). We take O as the originof the coordinates; OZ' as along the forkaxis;

-4-4-- ---4

i, j, k, and k' as unit vectors on axesOX, OY, OZ and OZ' respectively; and

finally n as the unit vector normal to theplane of the frame. Then we have:

sinO = n k

k x j = nsin(p-4-) -4

i x j = ksina

"DYNAMICAL EQUILIBRIUM"The last line of the paragraph under

"Dyamical Equilibrium" should read:"wheel allows it to swivel more freely."

CLOSING MATTERReference 7 should be: Th6orie

g6n&ale .... The zip code in the author'saddress should be 92160.

BRIEFLY NEWS...(continued from page 3)

seven member panel in Palm BeachCounty, Florida, in June 1989 where therewill be speed and performance trials.Write for a brochure to M. LinskeyMerrill, Director, NE Office, H.A. PerryFoundation, 147 Martin's Lane,Hingham, MA 02043, phone 617-749-9064, and state whether your interest isas a contestant, a sponsor of a vehicle, orof the race, or as a spectator.

Maggie Linskey Merrill gave theIHPVA board a presentation on thecompetition at the Washington DCIHPSC meeting. The designs will belimited to fully flooded vehicles with aminimum of two persons, and safetyconcerns are being fully addressed.

Bike Tech ArticlesThe June 1987 issue has two articles

about training: "Test Conconi at Home!"by Pat Ennis and Michael Argentieri,about anaerobic-threshold training; and"Sepcificity of Training" by Peter J. VanHandel, about the details of the intensityand quantity of daily training. The thirdarticle is by Danny Pavish, and is basedon his lecture in the Third IHPVA Scien-tific Symposium in Vancouver, 1986:"After the Gold Rush - Is HPV Mach 0.1Just One Level Straight Away?"

The cover story article in the August1987 issue is by editor Jim Redcay: 'TheBest Campy Gruppo Yet?" The secondarticle is by our own Chet Kyle: "Unsolv-ed Bicycle Design Problems," mainlyabout alternative transmissions andabout regenerative braking. JohnForester contributed the third piece:"Downhill Heat - The Thermal Effects ofSteady-State Braking."

NWHPVA NewslettersTom McDonald has good practical

articles in these newsletters. The Nov-Dec, 1986, issue, no. 11/6, has GregTrayling's "Constructing a Fairing-MoldPlug." I don't have the next issue, butvol. III/2 has a short piece on shockabsorbers made from clothes pins andrubber bands, and a tantalizingunillustrated report on Jim Schneider's"Pedaltroller" rowboat conversion. Twouseful construction articles are in vol.III/5: Paul Dunham's "Create PerfectMitered Joints;" and "Working withCoroplast" by Bob Stuart.

Interspersed among the technicalarticles are some well-done interviewswith designers and builders, and bookreviews and stories.

(continued on page 12)

6

Xsin(n - X) + Isin(X - - r/2) = r

OXYGEN COST OF SUBMAXIMAL EXERCISE INRECUMBENT AND CONVENTIONAL CYCLING POSITIONSBy Ingrid E. Antonson

[This article is from a thesis submitted tothe Academic Faculty of Colorado StateUniversity in partial fulfillment of therequirements for the degree of Master ofEducation.]

ABSTRACTIt was the intent of this study to com-

pare the physiological efficiency ofrecumbent and conventional cyclingpositions at submaximal workloads andto determine the effect of accustomed-ness to a particular position on the physi-ological efficiency of cycling in thatposition. Thirty healthy men, ten recum-bent cyclists, ten conventional cyclists,and ten physically active noncyclists, 21to 41 years of age, cycled for six minutesat 51.5 Watts (0.07hp) followed by sixminutes at 1545 Watts (0.21hp) in eachposition. Using an alpha level of p<0.05,no significant differences were foundbetween the recumbent and conven-tional cycling positions for oxygenconsumption (V02), minute ventilation(VE) or heart rate (HR). There were nosignificant differences in V02 or VEbetween the subject-groups. The non-cyclists had a significantly higher HR inboth positions than the conventionalcyclists at the lower workload and thanboth the conventional and the recum-bent cyclists at the higher workload. Theresults suggest thatfor submaximalcycling a recumbent position is no lessefficient than a conventional positionand, given a recumbent position canoffer decreased wind resistance and mayoffer increased comfort, the use of arecumbent position for cycling activitiessuch as touring and recreational riding issupported.

INTRODUCTIONHuman-powered speed records

clearly indicate an advantage of a semi-recumbent riding position; however, forsubmaximal efforts this advantage is notas clear. The effect of a semi-recumbentposture on the physiological efficiency ofthe rider must be assessed to determineif this postural change decreases thephysiological efficiency beyond any gainoffered by this body position at submaxi-mal workloads.

Many of the effects of supine versussitting positions during cycling-ergo-meter exercise have been known for

some time. It is well established that HRis lower in a supine position than in asitting position both at rest and duringcycling exercise [1,2,3,4]. Several studieshave shown no difference in V02 be-tween cycling in a supine position and anupright cycling posture for submaximalcycling [4,5,6,7] and one study [8] report-ed a lower V02 in a supine position at130.8 Watts (0.18hp). These previousstudies [1-8] used a supine body positionin which the subject was horizontal, aposition which is impractical for a recrea-tional HPV because of the cyclist'slimited visibility in the direction of travel.Kyle and Mastropaolo [9] measuredmaximal power output using a "supine"racing tricycle, a conventional HPV, anda prone position and reported that thesupine position resulted in 96% of thepower output attained in the convention-al cycling position. Physiological para-meters were not quantified and submaxi-mal efforts were not investigated in theirstudy.

The primary objective of this studywas to compare the physiological effi-ciency of recumbent and conventionalcycling positions at submaximal work-loads, where improved physiologicalefficiency would be indicated by con-sumption of less oxygen per kilogrambody weight for a given workload. Asecondary objective was to determinethe effect of accustomedness to aparticular position on V02, HR, and VE(the rate of pulmonary ventilation interms of volume expired per minute).

METHODThirty healthy male volunteers, 21 to

41 years of age, were selected as subjectsaccording to the following criteria: 10subjects were accustomed to regularcycling in a conventional cycling posi-tion, 10 were accustomed to regularcycling in a recumbent cycling position,and 10 were unaccustomed to cyclingbut were physically active. Accustomed-ness to cycling was determined by self-reported regular riding in the respectivepositions requiring an average of at least40 km (25 miles) per week for the pastthree months. One recumbent cyclistwas an exception, having ridden at leastthat amount for several months buthaving ridden a bit less than that in thethree-month period immediately

preceding the testing. Self-reportedcycling of less than 1.6 km (one mile) perweek for the past three months and noperiod of regular riding, as definedabove, for the past five years was re-quired to qualify as unaccustomed tocycling. The noncyclists participated inanother type of regular physical activityfor at least 30 minutes three days perweek. A standard Monark model 868ergometer with dropped-style handle-bars, a touring saddle, and toe clips andstraps was used for cycling in the conven-tional position. The same ergometerwith a recumbent seat attached to therear was used for cycling in the recum-bent position. The recumbent seat wasadjustable for the seat-back angle andthe height of the bottom bracket relativeto the seat bottom (the intersection of aline along the front of the seat back witha line along the top of the seat), althoughonly one setting for these variables wasused. The recumbent position used inthis study had a seat-back angle of 120degrees from horizontal with the seatbottom, a position approximately mid-way between the extremes of the recum-bent vehicles ridden by the subjects.Both the standard and recumbent seatwere adjustable to leg length. Each testconsisted of six minutes of cycling at 51.5Watts (0.07hp) followed by six minutes at154.5 Watts (0.21hp). The subjects wererandomly assigned to perform either inthe recumbent or the conventionalposition first and a rest period of 30 to 40minutes intervened between the twotests. The ergometer was equipped witha cadence meter with a gauge placed inview of the subject. Subjects cycled at acadence of 70 rpm during all exercisetests. This cadence was chosen toaccommodate both well-trained cyclistsand those untrained in cycling. HR wascontinually monitored. The average HRfor the last 10 seconds of each minutewas recorded. V02 was measured on aminute-by-minute basis using an open-circuit indirect calorimetric technique.The outputs from the ventilation meterand oxygen and carbon-dioxide ana-lyzers were digitized, reduced by a micro-computer, and minute-by-minute valueswere displayed for VE (liters min-1), V02(liters kg-1 min-1), and HR. Mean valuesfor V02, VE, and HR from the last three

(continued on page 17)

7

- -- -- ---

THE BIOENERGETICS OF POWER PRODUCTION INCOMBINED ARM-LEG CRANK SYSTEMSby Richard Powell* and Tracey Robinsont

SUMMARYTests on young adults of average

athletic ability showed that maximumpower output could be increased by overthirty percent using combined arm-and-leg cranking compared with leg crankingalone. Furthermore, the efficiency oflower-power steady-state power produc-tion was found to be higher for arm-and-leg cranking. Some differences betweenmale and female subjects in the contribu-tion from the arms was found.

INTRODUCTIONA considerable volume of research

has been generated over the years whichhas investigated the optimal speeds andexpected work outputs for leg, arm, androwing ergometry. When combined armand leg ergometry has been studied inthe past, findings suggest a greater maxi-mum work output is possible (11-20%higher) when compared to leg ergometryalong (Reybronck et al. 1975; Nagel et al.1984). However, the efficiency of per-forming submaximal work using arm,leg, or combined arm-leg productionsystems is unclear.

Because sport and recreationalcycling is predominantly a steady-stateeffort, the possibility of capturing greatermuscle power through an arm-and-leg-powered mechanical drive system at anequivalent steady-state cardiac cost(heart-rate response) could translate intoa more efficient human-powered cyclingdevice. We were interested in determin-ing if it is bioenergetically feasible to ex-pect improved work output using armsand legs at equivalent submaximal phys-iological efforts when compared to workproduction using arms or legs alone.

BACKGROUNDIt's a well-known fact that maximum

oxygen uptake (V02 max) is about 10%higher if a person is tested on a treadmillrather than on a bicycle ergometer. Thereason for this occurrence is explainedas being due to a greater total activemuscle mass involvement in runningcompared to stationary bicycling; hence,V0 2 max is higher in running even

*Associate Professor, tgraduate student,Department of Physical Education andRecreation, New Mexico State University

though maximum heart rates achieved(cardiac cost) are the same in both typesof all-out tests.

Because conventional bicycling usesonly the legs for power production itseemed that using arms and legs to-gether to produce steady-state workcould result in a higher VO2 at any givensubmaximal cardiac cost, and a largerpotential work output as well comparedto using legs alone. While it is clear thatmaximum work output is better in com-bined arm-leg systems when comparedto legs alone, such maximum efforts arelargely anaerobic and demonstrate littlewith regard to steady-state efforts.

The intention of our research was tocompare the physiological cost of produc-ing work under three types of conditions:arm ergometry, leg ergometry, and com-bined arm-and-leg ergometry. Two im-mediate questions to be answered wereas follows:1. is combined arm-leg ergometry under

various levels of steady-state workmore physiologically efficient com-pared to arm or leg ergometry alone?

2. under maximum-power productionconditions, how do the threeergometry methods compare?

APPROACHA structural housing was developed

in which subjects sat in a seat 500 mm.high with an arm-crank ergometer cen-tered in front of them. The axis of thearm crank ergometer was 1220 mm. highand positioned to allow complete armextension at the farthest point of thecranking cycle. A second leg-crank ergo-meter was centered in front of eachsubject with its axis 280 mm. high andpositioned to allow complete leg exten-sion at the farthest point of the crankingcycle. Both ergometers were electrically-braked systems.

Thirty-two subjects (17 males and 15females; mean age - 25.3 years) weretested over three separate sessions atthe same time one week apart. All threesessions were used to test progressive leg-and/or arm-cranking performance, withthe order of testing (arms only, legs only,or arms and legs) randomly split amongthe subjects.

During all three exercise tests,oxygen consumption (VO2) and carbon-

dioxide production (VCO2) were calculat-ed every 15 seconds based on minutevolume of expired air (VE), true 02 andCO2 concentrations. In addition, heartrate (HR) was recorded every 30 seconds.

The exercise protocols were in two-minute step increments. The arm crank-ing started at 25 watts output and increas-ed 25 watts following each two-minutestep. This protocol, while not adjusted tobody weight, conformed closely to simi-lar protocols followed elsewhere(Williams et al. 1983). The leg crankingstarted at 33.3 watts output and increas-ed 33.3 watts following each two-minutestep; the approach conformed to proto-cols used elsewhere (Niemela, 1980). Atwo-minute leg-crank warm-up workstage at 33.3 watts preceded the combin-ed arm-leg treatment. The combinedarm-leg cranking started at 25 and 33.3watts respectively (total watt ouput =58.3) with 25 and 33.3 watt increments,respectively, following every two minutes(total watt increments = 58.3). All crank-ing was performed at 50 RPM and con-tinued until fatigue.

Because of the expected differencesamong subjects in work-productioncapability, linear-regression equationswere computed for each individual,plotting V02, VE, and HR each againstcumulative workload in watts; groupequations were subsequently derivedfrom individual ones. Cumulative work-load was calculated by determining theworkload in watts for each successiveminute completed, plus the fraction (tothe last completed 15 seconds) of thefinal minute of work. A 7:48 maximumwork time for arms, for example, wouldyield a maximum cumulative workloadof 475 watts (25 + 25 + 50 + 50 + 75 + 75+100 + [0.75 (100)]. In this way, every 15-second measure of V02 and VE andevery 30-second measure of HR could beplotted against a cumulative work outputto that point, and individual patterns ofcontinuing physiological adaptation todiscrete workload steps could be derivedfor each of the three exercise treatments.

FINDINGSAfter calculating linear-regression

equations (the best "fit" for the data) foreach individual, we then grouped theequations by sex. We examined the

8

slopes of the equations as an index ofrelative physiological cost of the exercisetreatments in producing power output;the larger or more vertical the slope, themore taxing was the exercise treatmentrelative to the physiological variableexamined. The ventilation data whenplotted against cumulative workload(Figure 1) showed no statistically signifi-cant changes in the slopes of the equa-tions for women and a significant differ-ence in the men for arm cranking.Women, in particular, probably find armcranking more taxing than legwork dueto a relatively weaker upper body muscu-lature compared to men; they stoppedsooner than the men due to rapid localmuscle fatigue long before breathingbecame labored at the higher workloadsencountered by men. There appeared atendency for combined arm-leg work toyield slightly more work output for agiven ventilation, but it was notsignificant.

The oxygen-consumption data whenplotted against cumulative workload(Figure 2) showed no statistically signifi-cant changes in the slopes of the equa-tions for the men or women. This seemsreasonable because oxygen consump-tion should relate directly to powerproduced. The tendency again for armcranking to appear less efficient prob-ably reflects the more anaerobic natureof such work by itself.

What was most revealing was theheart-rate data plotted against poweroutputs (Figure 3). In both the men'sand women's grouped data, there wassignificantly more power output at heartrates beyond 140 beats/minute usingcombined arm-leg cranking. In short,even at a given steady-state cardiac cost,

power output is highest when using armsand legs together; further, it appears thatthis advantage increases as oneapproaches fatigue.

When we looked at the "maximum"data of all subjects combined (themaximum cumulative powerloadsreached at fatigue and the physiologicaldata corresponding to that failure point),the advantage of combined arm-legcranking over legs only was dramatic(Table 1). The maximum cumulative

power output was approximately 31%greater using arms and legs compared tolegs alone. To achieve that differencecost approximately 15% more in oxygenconsumption. One could roughlyassume that the 31% advantage in all-outpower production was partly due togreater aerobic metabolism (15/31 =48%) and partly due to anaerobicmetabolism (17/31 = 52%). Arm crankingcan clearly be seen to be an inferiormethod of power production by itself,and, at least at maximum effort, isprobably limited by local muscle fatiguerather than aerobic support systems(given that an average maximum heartrate achieved by our subjects was only160).

CONCLUSIONSBased upon the foregoing research,

we concluded the following.1. Combined arm-and-leg power produc-

tion provides a decided advantageover leg cranking alone, especially inall-out work. About half of this advant-age seems to be due to increased aero-bic metabolism and half due to anaero-bic work.

2. The efficiency of steady-state powerproduction can be enhanced by com-bined arm and leg work. We cannotsay decisively by how much at thistime, because the power advantage isapparently influenced by how intensethe steady-state work is, and by therelative contribution of arm power toleg power.

3. The advantage of any arm-leg power-ed machine is largely going to be off-set by the possibility of additionalweight/frictional resistance of a drive-train system that would enable alllimbs to generate power.

POSTCRIPTWhile we are not alone in our en-

deavors to develop an efficient and prac-tical arm-leg powered cycle, the obsta-cles we have experienced and observedin other prototypes revolve around

(continued on page 18)

TABLE 1

MAXIMUM POWER OUTPUT AND CORRESPONDING PHYSIOLOGICAL RESPONSES TO THREETYPES OF HUMAN POWER-PRODUCTION SYSTEMS

EXERCISE SYSTEM MAX. H.R.-1 V0 2 max VEmax 1 MAX CUMULATIVE(Rotary Cranking) (Beats min) (ml kg min) (L min) Power Watts

Arms 160.06a

23.73a

7 6.9 8a 499.09a

Legs 1 6 9.7 5 b 33 .7 5 b 97 .85 b 1 0 2 1.8 6b

Arms & Legs 1 70 .0 3 b 38 .7 7c 1 03 .3 3b 1 3 3 9 .5 5C

Note: Components with different letters are significantly different(p<0.05) when compared columnwise.

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100 200 300 00 500

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under the static torque vs. crank anglecurve for reverse pedaling is approxi-mately 40% greater than for forwardpedaling).

The resources available to theauthor were clearly a limiting factor.Definitive conclusions are difficult todraw from a single-subject experiment.From the information in the paper, I wasnot able to determine the scatter in themeasurements. How many repetitionsof the maximum power measurementwere made for a single pedaling fre-quency and direction? How were thestatic tests performed (there appeared tobe differences in the photographsbetween the angles reported and thosevisible in the photograph, e.g., backwardand forward 30 degrees)? The balance ofmy comments will assume that the tech-niques and measurements reported areindeed stable for a larger population.

It is well established that maximummechanical power output on a cycle-ergometer is very sensitive to the pedal-ing position. In our work, we have observ-ed differences of approximately 20% inpeak power output between upright andrecumbent positions. I feel that this isdue to changes in the mechanical rela-tionship of the muscle groups involvedas well as recruitment of different num-bers and types of muscles (particularlythose of the upper body). It is clear,upon examination of the photographs inthe paper, that there is a large differencebetween both cycle designs in the rela-tive position of the rider with respect tothe pedals. It is possible that this differ-ence may contribute much to the ob-served difference in power output,independent of pedal rotation direction.A definitive study would need to com-pare power output measured in theoptimum position for forward pedalmotion with that measured in theoptimum position for reverse pedaling.The word "optimum", of course, impliesquite a lengthy study indeed!

Many thanks again for passing thearticle to me. I am not quite yet ready toturn the gearbox in the aircraft around,but I found Mr. Spinnetti's workinteresting.

RESPONSEI thank you and Dr. Steven Bussolari

for reviewing my article and thisopportunity to respond. There are fivepoints of interest that I shall respond toin the same order in which they werementioned in his review.

(1) Scatter in the MeasurementsThe maximum power output data

for each bicycle was the average of twoalternate runs at a single cadence value.

(2) Crank AnglesThe crank angles in the photo-

graphic sequence represent the twodirectionally divergent angular displace-ments of the pedals from the T.D.C.positions of the two bicycles. Therefore,the two thirty-degree positions are quitedifferent.

(3) Pedaling PositionThe twenty-percent difference that

he observed between upright and recum-bent pedaling positions is understand-able. I would also expect to observe thissort of difference when pedaling back-wards as well. The upright positionseems to have a gravitational advantage.

(4) Bicycle Design DifferenceThere is a large difference in the

relative position of the rider's legs withrespect to the pedals throughout thepower stroke, but this is my whole point!Pedaling backwards causes this differ-ence because the four-bar linkageformed by: (1) the pedal crank, (2) therider's leg, (3) the rider's thigh, and (4)the bicycle frame (commonly called aquick-return mechanism) is not kine-matically symmetrical with respect to itsdirection of rotation. When pedalingbackwards, it has a slow, smooth powerstroke with a high average torque and aquick return stroke. Conversely, whenpedaling forward it has a quick powerstroke with a high peak torque, but lowaverage torque and a slow, smoothreturn stroke. Consequently, contrary tohis speculation, the difference is depen-dent upon the direction of rotationrather than being independent of it.

(5) The Daedalus ProjectTurning the gearbox around for

backward pedaling of the aircraft wouldbe premature at this point, but so woulda lengthy study to investigate optimumperformance. I would suggest that atleast a modest training program involv-ing at least one rider be run on theDaedalus flight simulator, pedaling inboth directions. A subsequent com-parison test could then indicate whetherfurther investigation is warranted.

Ramondo Spinnetti Li

BRIEFLY NEWS...(continued from page 6)

HPV NieuwsAs mentioned earlier, this is the

magazine of the Dutch HPV Association.It is a substantial journal, usually 20pages, well-illustrated, and demonstratesthat there is a great deal of inventivenessin Holland. In a recent issue thereseemed to be a strong emphasis onrecumbent bicycles and tricycles withfront wheels that were both pedalled andpowered, like geared "Big Wheels." TheJune 1987 issue has an article, promisingto be the first in a series, on power pro-duction in various recumbent positions.If I run into a Dutch acquaintance again,I will ask for help to produce a digest ofthis and other articles.

Daedalus Gear TransmissionHere is some information omitted

when I discussed this transmission in theeditorial of the last issue of HP. The off-the-shelf gears are made by ARROWGEAR, 2301 Curtis Street, DownersGrove, IL 60515, phone 312-969-7640.They were machined for weight reduc-tion, and the housing was designed andmade, by Bob Parkes of the Daedalusteam, phone 408-253-0246 (homenumber).

HP-Helicopter Activity inBritain and Japan

An article by A.D. Cranfield, leaderof the "Vertigo" project and formerengineer at Westland Helicopters, in theSeptember 1987 Chartered MechanicalEngineer (Inst. Mechn. Engrs., UK)"Pedalling Towards a Vertical Take-off'states that "any design would work onlywithin ground effect," which means thatthe height must be within one rotor dia-meter. The graph shows the theoreticalpower saving achieved by reducing theheight/diameter ratio (Z/D). The groupis using the AeroVironment Gossamerairfoils and twin counter-rotating two-bladed rotors beneath the pilot. "Agroup at Nihon University in Japan hasbuilt a rigid-rotor-hub machine virtuallyidentical in configuration to Vertigo. It isknown that very similar dynamic prob-lems are being encountered by thegroup." This refers to blade-to-bladeinterference during crossovers, and wakeinterference from a reflection of thedownwash from the walls of the hangar.

Toshio Kataoka wrote from Japanconfirming some of the above, after he

(continued on page 16)

12

ANGULAR MOMENTUM(continued from page 5)

speed. When tested, a normal bikeaveraged just under a 50 mm ( 2 in) rmsdeviation.

Figure 4 shows the average rms forall the trials versus the amount of angularmomentum. From this graph one can seethe slight 'bowl-shape' one might expectfrom theory, with a greater average devi-ation at angular momentum settings ofnegative five and positive ten. Also thegraph shows almost no disparity betweenthe negative one and zero settings, imply-ing little effect of small amounts of angu-lar momentum, for the straight course atleast. The difference between the normalbike and the zero-angular-momentumsetting is due to the additional weightadded to the front fork of the bicycle.

I

P

I

10

8

6I

4.

-10

I ave: overal

\•

ANGULAR MOMENTUMANGULAR MOMENTUM

10

FIGURE 4: Root-Mean-Square deviation forstraight course

The corresponding Cooper-Harperdata agree with the general trend of therms data. Interestingly, however,Cooper-Harper shows a considerablediscrepancy between the negative oneand the zero settings (ratings of 4.5 and3.5 respectively). The ratings also jumpedthe gap between satisfactory and unsatis-factory. These results seem to imply thatalthough a rider may not do that muchmore poorly in terms of lateral deviation,the bike does not 'feel' as stable at thenegative-one setting as it does at the zerosetting. As one rider wrote, "a differentfeel for some reason," and another wrote,"strange but unidentifiable effect."

A different trend is evident when oneexamines the three trials separately. Asignificant drop in rms deviation at thepositive-ten setting is clear. In fact, thethird trial at positive ten had the lowestrms of any test run. This finding is alsosupported by the corresponding Cooper-Harper data. When examining this trendin light of the theory presented, it wouldsuggest that the additional angularmomentum creates a large force couple

making it difficult to turn the front wheelof the bicycle. Consequently, because thisis a straight course, the bicycle becomesmore stable at this angular-momentumsetting.

14

12

I I6 10

I ,

-5

-1

0

10)

4 3or I

1 2TRIALNUMBER

FIGURE 5: Lateral-deviation learning

Curves for the Straight CourseThe learning curves for the straight

course are shown in Figure 5. The graphsindicate slight learning at the negative-five, negative-one and zero settings, withpossible difficulties at the negative-fiveand negative-one settings. On the otherhand the learning curves show a signifi-cant decrease in the deviation at the posi-tive-ten setting, implying that not onlydoes the large coupling force help main-tain course, but also that it is easy to learnto control this force.

THE CIRCULAR COURSE

The circular course exhibited some ofthe same trends as did the straight course.Figure 6 again shows the bowl-shape onemight expect from theory due to the in-creased force couple on the extreme ends.This difference between the normalbicycle and the zero-angular-momentumsetting is again about 25 mm (1 in). Thecorresponding Cooper-Harper data alsodemonstrate the bowl-shape thus agree-ing with the rms lateral-deviation find-ings. So once again one can say that thelateral-deviation results agree with the"feel" of the riders.

16

i 14

102

B.0 -O

I

-10 -5ANGULAR MO0

ANGULAR MOMENTUM

5 10

FIGURE 6: Root-Mean-Square deviation for thecircular course

A definite difference exists, however,between the rms deviation on the circularcourse and on the straight course at the

negative-one setting. Figure 6 shows thatthe negative-one setting has a very effectwhen riding a circle. In fact, the negative-one setting had as great a rms deviationas the positive-ten setting. The straightcourse did not demonstrate this adverseeffect. Also there was a dramatic increasein rms deviation at negative one in allthree trials, clearly implying that lack ofangular momentum is highly undesirablewhen riding a curve.

The data for the learning curves fur-ther demonstrate the apparently extremeundesirability of the negative-one setting(Figure 7). Although the curve shows apropensity for learning at negative one,the values of deviation are still high com-pared to the zero setting. In fact, all threetrials of the ten-times-angular-momentumsetting are below their correspondingnegative-one trials.

In this instance, the Cooper-Harperdata slightly disagree with the lateral-deviation findings. For example, all threetrials of the negative-one setting are ratedbetter than the positive-ten setting. Alsothe ratings for negative one are relatively

16.

I4.

2.

0

-s-1

0 1

TRIALNUMBER

3 4

FIGURE 7: Lateral-deviation learning curves forthe circular course

close to those for zero additional angularmomentum (4.1 and 3.5 respectively).Apparently the riders did not notice alarge difference in the characteristics atthe negative-one setting, despite the rmsdata showing a discrepancy.

THE SERPENTINE COURSE

In an effort to describe the character-istics of a bicycle when changing direc-tion, a serpentine test course was used.Once again the data were consistent andmaintained a bowl-shape (Figure 8). Forthis course, however, there is a dramaticincrease in rms lateral deviation at thepositive-ten times angular momentum.By comparison, the increase for both thepositive- and negative-five settings aresmall, although still significant. Again,the negative-one and zero settings exhibitsimilar rms deviation with the negative-one setting still somewhat higher.

13

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"o _ ~ ~ .

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0 3 4

10v I

v ! !

4u

300

2o5 20

:0

ANGULAR MOMENTUM

FIGURE 8: Root-Mean-Square deviation for theserpentine course

The Cooper-Harper ratings showed abowl-shape. Again, the negative-one set-ting received more than 1.5-point higherrating than the zero setting despite thefact that their rms deviations were sosimilar. Another interesting point is therating for negative five. The lateraldeviation of negative five is comparative-ly close to the positive five, and yet theriders rated the negative-five settingmuch more difficult. Apparently nega-tive angular momentum was not wellliked by the test riders.

40

30

20'

S

0

415

.10

1 2TRIAL NUMBER

3 4

FIGURE 9: Lateral-deviation learning urves forthe serpentine course

Figure 9 shows the learning curvesfor the serpentine course. These plotsshow, however, the negative-five timesangular momentum actually has a lowerrms deviation than does the positive-tensetting. This course is the only one toexhibit such a result. And again, thepositive-angular-momentum settingsshow promise in ease of learning.

THE LEAN-ANGLE STUDY

The test results of the lean-anglestudy are shown in Figure 10. The rigid-body theory consistently predicted alarger lean angle than was actually exper-ienced. The actual data, however, dosupport Sharp's [2] idea of a larger leanangle at positive angular momentum and

a smaller lean angle at negative settings.The theoretical values were calculatedusing the average speed and weight ofthe test riders involved. The actual valuesshown are the mean averages of all leanangles collected.

20-

18-

16

14.

12

I0.

-10 -5 0

ANGUIAR MOMENTUM

5 10

FIGURE 10: Lean angle versus angular momentum

DISCUSSION

TiE ZERO SETTING

Overall, the zero times additionalangular momentum showed nothingunusual or extraordinary. In all threecourses the zero setting was at the base ofthe "bowl-shape", leading one to believethat the angular momentum of the frontwheel did add a needed support forbetter control. In most cases the zerosetting produced average rms deviationsof about 25 mm (1 in) greater than anormal bike. These numbers help definethe actual effect on the riding characteris-tics due to the added weight.

The riders also found the zero settingthe easiest to control as demonstrated bythe Cooper-Harper ratings. On theaverage, the riders found the zero settingto be 0.5 to 2 points lower than the nega-tive-one setting. In all three courses, thezero setting received an average mark ofabout 3.5. This corresponds to the borderbetween satisfactory and unsatisfactory.The zero setting is the only one to consis-tently remain below the unsatisfactoryrange.

A possible explanation for theCooper-Harper rating being the lowest atthis setting may have to deal with theriders' psychological view of the experi-ment. Some riders began the experimentwith preconceived notions as to what wasexpected to happen. "This is supposed tobe the easiest, isn't it?" was a commonquestion when a test rider began a courseat the zero-angular-momentum setting.Although this reasoning may have hadsome actual effect, it is difficult to sayhow much. One instead must rely on the

consistency or the aata to araw conclu-sions.

THE NEGATIVE-ONE SETrING

Because of the negative-one setting,one begins to realize the importance ofthe angular momentum created by thefront wheel of a normal bicycle. Al-though the negative-one setting may nothave been dramatically different than thezero setting, it consistently demonstrateda greater rms deviation. These data aresupported, and even enhanced, by thesignificantly higher Cooper-Harper rat-ings. Also the negative-one setting madethe important jump from the satisfactoryto the unsatisfactory but acceptable cate-gory on the Cooper-Harper scale. Theriders felt that some improvement waswarranted for this case.

On the straight course, the differencein rms deviation between the negative-one and zero settings is a few millimeters.When one considers the theory as describ-ed previously, this result can be easilyexplained. The rider is traveling in astraight line and therefore tries to mini-mize the amount of turning of the frontwheel. Only small turning angles arenecessary to maintain this course: that is,minimal external moments are applied.Thus by the conservation of angularmomentum, no significant torque is cre-ated; therefore the rider will experienceno significant force couple to overcome.Any torque created, assuming the riderstays relatively close to the course, will bedwarfed by the gravitational forcespresent, and indeed, the rider's ownstrength. Because very little turning isneeded, there is little difference betweenthe zero and the negative-one settings,due to the small torque created.

If one examines the circular andserpentine courses, however, one noticesa considerable difference between thenegative one and zero settings. In bothinstances there is an average rms devia-tion difference of approximately 25 mm.Again, by examining the theory, this dif-ference can be explained.

Contrary to the straight course, therider is required to turn the front bicyclewheel. This turning creates a force couplein the case of the zero setting, but in thecase of the negative-one setting the forcecouple is cancelled by the flywheel.Apparently, the force couple createdhelps the rider keep the bike in place.However, the rider first needs to establishthe proper lean and turning angles. Soonce the rider gets on the course and hasthe wheel turned the proper amount, the

14

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angular momentum helps the ridermaintain that direction.

This theory also helps explain whymany riders commented about difficultybeginning the course, but once on trackfound it easy to handle. Some riders evengave two Cooper-Harper ratings, one forthe first part of the course, and another,better one for the second part of thecourse.

On the other hand, the negative onesetting has no angular momentum vector.Therefore, no torque is created to impedeany slight movements the rider maymake. Instead these unimpeded move-ments lead to lateral deviation. This isdefinitely clear on the serpentine coursewhere the rider is required to change thedirection of turn. In this instance, whenthe rider turns too far, there is no torqueto resist the sudden change.

The above explanation must also beconsidered when examining the Cooper-Harper data. In all instances, includingeven the straight course, the negative-onesetting received noticeably less favorablemarks than did the zero setting. This canbe attributed to the lack of angularmomentum and of the supportive torqueat the zero, setting, but also must beattributed to the expectations of the rider.All but one of the test riders classifiedthemselves as 'experienced' bicyclists.Because they had previous bicyclingexperience, they depended on the angularmomentum and force couple to resist anysudden changes they maymake. Nowwhen that resistance is removed, theriders found it more difficult to ride thebicycle. The unexpected lack of resistanceis probably responsible for the strange"feel" many of the riders said to haveexperienced.

THE NEGATIVE-FIVE SETTINGOriginally, the plans of this experi-

ment had called for a maximum reversesetting of negative ten times the angularmomentum of the road wheel. Thissetting was first tested on the straightcourse and proved to be uncontrollableby two riders. One rider, in fact, haddifficulty making it to the course. Assuch, it was decided to reduce the nega-tive limit to a negative five times insteadof ten.

Overall, five times the angularmomentum of the front wheel in thereverse direction proved to be the mostdifficult setting to control with sharpincreases in rms deviation on all courses.In fact, the negative-five setting proved tobe more difficult than the positive-ten

setting on all runs except the serpentine.The negative-five setting, however, didprove to be more difficult than a positive-five setting on the serpentine course.

The Cooper-Harper data show fur-ther that the negative-five setting was themost difficult to control. For the straightand the circle courses the negative-fivesetting received marks on the upperbound of unsatisfactory but acceptable.Furthermore, for the serpentine course anunacceptable rating was recorded. Theriders' comments also mentioned a greatdeal of compensation and physicalstrength required to operate the bicycle atthis setting.

Theory indicates that a large torqueis created due to the additional angularmomentum. The theory would seem toimply that the additional momentumwould lead to a stabilizing force whentravelling in a straight line, similar to butlarger than that experienced at the zero-angular-momentum setting. By the samearguments presented there, the bicycleshould experience a force helping to keepit on course. The data taken, however, donot support this claim. On the contrary,the data seem to show the exact oppo-site-that negative angular momentumleads to a destabilization of the bicycle.

From the circle and serpentine coursedata, one again sees a large increase inrms deviation at the negative-five setting.Once more a torque is created due to anychanges in the angular momentum vec-tor. Understandably then, the rider hasmore difficulty turning at this setting.Nevertheless, it is intriguing that thenegative-five setting has a greater rmsdeviation on the circle than the positive-ten setting; and that the negative five hasa greater rms deviation than the positivefive does on the serpentine course. Inaddition, the riders at this amount ofreverse angular momentum averaged 25mm more in rms deviation than thepositive ten on the straight course whereno turning is necessary. According totheory, the larger amount of angularmomentum should produce a largertorque making it more difficult to turn.

Why should a negative settingexhibit such bad results compared to apositive setting? The answer to thisquestion most likely lies within the rider.As was stated previously, all but onerider was 'experienced', and thereforeexpected certain things from a bicycle. Interms of angular momentum, the cyclisthad always experienced a positiveamount of angular momentum. There-fore, when the rider turned to a certain

direction, he expected a certain torque.At the negative setting, however, therider instead experiences the oppositetorque than he was expecting. Instead ofenhancing his lean angle, it resisted theangle; instead of helping the rider turn acorner, the move was impeded.

This explanation is also supported bythe comments of the test riders. As oneperson wrote, "I can't figure out how tocompensate for it [this setting of angularmomentum]. You just can't turn thewheel when you want to and where youwant to. It surprises you." Anotherwrote, "Unpredictable, I can't figure itout."

THE PosTIVE-TEN SE-rINGDespite the fact that the negative-ten

setting was uncontrollable, the positive-ten setting proved to be quite control-lable. According to theory, the positive-ten setting should produce a large torquerelative to a normal bike. Most instancesshowed this to be the case.

For the straight course, the averagerms deviation for positive ten was slightlygreater than the rms deviation for thenegative-one case and considerably lessthan that of the negative-five case. Atfirst glance, this is a curious result con-sidering the vast difference in the totalamount of angular momentum. One cansee a better explanation for this curiosityif one looks at the three trials separately(Figure 5). In this case, the great variancewithin the three trials at positive ten isapparent. Between the first and thirdtrials, the rms deviation decreased byalmost 100 mm (4.5 in). The course andsetting generate one of the steepest learn-ing curves in the entire experiment.Apparently, the rider learns to control thebicycle and the additional forward angu-lar momentum. In fact, the third trial atthe positive-ten setting has a lower rmsdeviation than does the zero setting, andeven reaches the level of rms deviationfor a normal bicycle.

In this case theory suggests the torqueis so large the rider is capable of movingwithout affecting the bicycle a great deal,and that any slight deviation will bequickly corrected. Apparently, however,the cyclists took some time to get used tothis strong effect. Nevertheless, once therider learned how to work the bike at thissetting, he rarely had problems. "Just letthe bike do it," wrote one rider. Anothersaid, "I could not have changed course if Iwanted to." A third felt it was extremelystable, relating it to "a helping hand thatwouldn't let you fall."

15

_ _ _ ·1· __

'' "

While the positive-ten setting may help acyclist run a linear course, the largeamount of angular momentum makesturning very difficult. The results of boththe circle and the serpentine showed thisresult, with the serpentine demonstratingan even greater difficulty in changing thedirection of turn. The rms deviation forthe circle increased 25 to 50 mm at thissetting, while the serpentine exhibited asmuch as a 200 mm (8 in) increase, beingthe only course and setting to have ahigher rms than the negative-five setting.The Cooper-Harper ratings also supportthe theory with the riders finding positiveten more difficult than both the negative-one and zero settings on all three courses.

Such dramatic increases warrantedfurther study, so an intermediate value ofpositive five times additional angularmomentum was studied for the serpen-tine course. This setting performed asexpected, and received marks betweenthe positive ten and the zero settings.Also, the positive-five setting fared betterthan the negative-five setting in both rmsdeviation and Cooper-Harper data.

Undoubtedly the additional ten timespositive angular momentum generates alarge force couple. This large torquelends an extreme stabilizing effect whichfacilitates linear travel, but makes turningthe bicycle highly difficult. This extremeeffect is brought within acceptable levelswhen the positive-ten setting is reducedto a positive five times forward angularmomentum of the front bicycle wheel.

LEARNING CURVESLearning curves are important be-

cause they show how well a rider adaptsto unfamiliar circumstances. This adapt-ing process may shed light on the stabilitycharacteristics of a bicycle. Also, insightinto the interpretation of rider evaluationsmay be gained through learning curves.

All three sets of learning curves showthat the rider adapts to the varyingamounts of angular momentum. In allinstances, the Cooper-Harper ratinggenerally agrees, showing that the testriders also realize that they are adaptingto the unfamiliar circumstances. The zeroand negative one settings have the flattestlearning curves showing the least amountof learning. Most likely this is becausethese settings are closely associated witha normal bicycle, so not much needs to belearned.

The negative-five setting does notexhibit typical learning curves (i.e. oneswith negative slopes). In two of the three

instances, the rms deviation actuallyincreases on the second or third trials. Inlight of the counter-intuitive effects dis-cussed previously, it appears as thoughthe negative-five setting is difficult tolearn because of its unexpected reactions.

The positive-ten learning curves (andthe positive five in the case of the serpen-tine course) exhibit a consistent and rela-tively steep downward slope. Examiningboth the rms-deviation learning curves,the Cooper-Harper learning curves, andthe riders' comments, it is evident that thepositive-ten setting is easiest to learn. Infact, on both the straight and the circlecourse, the third trial at this setting prov-ed to be the best test run for that course.Clearly, there is an aspect about forwardangular momentum that enhances therider's ability to adapt to the bicycle. Yet,this aspect definitely does not exist withthe reverse amounts of angularmomentum.

LEAN ANGLEAs was previously stated, the lean-

angle data varied noticeably from therigid-body analysis. The obvious reasonfor this is the bicycle-rider system is not arigid-body system. The rider has toomuch freedom and variation to be con-sidered as a rigid body. Figure 9 showsthat theory call for lean angles around 20a.Although this should be an equilibriumcondition, the rider compensated for thelarge angle with shifts of weight andorientation so as to keep the bicycle at amore comfortable lean angle. The rider,therefore, plays too involved a role in thestability and riding characteristics of abicycle for the bicycle-rider system to bemodeled solely as a rigid body.

The data do, however, follow thegeneral trend that theory suggests. Theydisplay a greater lean angle at the posi-tive-ten setting and a lesser lean angle atthe negative five. The negative-onesetting exhibited a peculiar drop in leanangle when compared to the zero setting.This difference supports earlier claims ofa noticeable effect due to the normalangular momentum of a front bicyclewheel. It is difficult to say, however,whether this drop is indicative of the testrider's expectations or actually a directeffect of the angular momentum. Mostlikely, the explanation is a combination ofboth reasons.

CONCLUSIONS AND COMMENTSUndoubtedly, the gyroscopic action

of bicycle wheel has an effect on the

riding of the bicycle. Although thecouples produced are unable to accountfor dynamic equilibrium, they do add tothe stability and ease of riding a bicycle.Forward angular momentum is anadvantage to a limited extent, whilereverse angular momentum has adverseresults. The question remains as to howmuch angular momentum is the optimalamount. Having extensively ridden thetest bicycle, I have found that an angular-momentum setting between four and fivetimes the normal amount was mostcontrollable for my general riding. Forracing, where weight is a serious factor,there is a tradeoff between the extraweight required and the extra stabilitygained.

REFERENCES

1. Frank Rowland Whitt and DavidGordon Wilson, Bicycling Science,[Cambridge, MA: The MIT Press,1985, Second Edition].

2. Archibald Sharp, Bicycles andTricycles, [Cambridge, MA: The MITPress, 1977].

3. D. E. H. Jones, "The Stability of theBicycle", Physics Today, [April 1970]:p.34 - 40.

4. George E. Cooper and Robert P.Harper, Jr., The Use of Pilot Rating inthe Evaluation of Aircraft HandlingQualities, report NASA TN D-5153,Ames Research Center, 1970.

5. J. L. Meriam, Engineering MechanicsVolume 2: Dynamics, [New York:John Wiley & Sons, 1978].

AUTHORBrenan J. McCarragher233 Massachusetts AvenueCambridge, MA 02139(617) 661-4111 '

BRIEFLY NEWS...(continued from page 12)

HP Helicopters ...

visited Professor Naito. He said that theold HPH is in the Kawaguchi LakeAutomobile Museum. Toshio Kataokawas also kind enough to send a videotapeof the Eleventh Annual Japanese Birdmanrally, held on August 2, 1987 at LakeBiwa, a delightful, funny competition. Iwill send the tape to Marti Daily for theIHPVA collection. a

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·7

OXYGEN COST(continued from page 7)

minutes of exercise were used in thedata analysis. Three-way subject-groupby workload by position ANOVA's wereemployed (p<0.05) for HR, V02, and VE.

RESULTS (Table 1)No significant differences were indi-

cated between the two cycling positionsfor HR, V02 or VE at either workload.For both positions and workloads, nogroup differences were shown for V02 orVE. For both postures, group differenceswere shown for HR between noncyclistsand the conventional cyclists at the lowerworkload and between the noncyclistsand both cyclist groups at the higherworkload. The subject group differencesin HR are summarized in Table 1.

DISCUSSIONEffect of Body Position

Cycling in the recumbent positionused in this study did not significantlyalter the physiological efficiency of thesubjects from that of cycling in a conven-tional position at submaximal workloads.Although. previous studies found a de-creased HR [1,2,3,4] and a lower V02 [8]in a supine position, the lack of anydifference in this study may be explain-

ed by the recumbent position used. Therecumbent position used in this studydiffers from a conventional cycling posi-tion in both gross body position and inthat there is no weight supported by thearms; however, it is a much more uprightposition than the supine position used inthese earlier studies [1-4,8]. The grossbody position used in recumbent cyclingin this study is closer, in degree of beingupright, to a conventional position thanto a supine position, and thus, the dif-ferences between recumbent andconventional cycling can be expected tobe less than between conventional andsupine cycling.

Effect of Accustomedness to PositionThe recumbent cyclists did not show

a greater physiological efficiency in therecumbent position than the convention-al cyclists, nor did the conventional cy-clists demonstrate a greater physiologi-cal efficiency in the conventional posi-tion than the recumbent cyclists. Thislack of difference may be at least par-tially explained by the subjects' cyclingexperience. The group of recumbentcyclists included several cyclists whospent more time cycling in a convention-al position than in a recumbent position,although both were done on a regularbasis. There was variation in the quantity

and intensity of riding done by thecyclists and there was variation in theseat-back angle and bottom bracketheight of the recumbent vehicles riddenby the subjects. All the noncyclists had,at some time, ridden a bicycle and,without exception, this experience was ina conventional cycling posture. Morestrictly controlled subject-groups andtraining regimes may demonstrate adifference in physiological efficienciesfor the different positions based on thesubjects' cycling backgrounds.

The HR for the noncyclists may behigher at the higher workload than thatof both groups of cyclists because of adifference in the types of training of thetwo groups. Endurance training, such ascycling, will decrease the HR response toa given level of submaximal exercise [10].Six of the ten noncyclists engaged inweight lifting, rather than an endurancetype of exercise, as their primary sourceof physical activity. The effect of thecyclists' endurance training was moreevident at the higher workload whereboth cyclist groups had significantlylower HRs; however, the noncyclists hadthe highest mean HRs at both workloadsand in both positions.

CONCLUSIONSSince a recumbent posture can offer

decreased wind resistance and no loss inphysiological efficiency at submaximalworkloads, this posture can offer improv-ed mechanical efficiency; i.e., less energyoutput to achieve a given velocity, overthe conventional posture. Although forsubmaximal workloads, such as touringand recreational cycling, the full advant-age of the decreased wind resistance willnot be realized, the recumbent position,with no loss in physiological efficiency,may also offer increased comfort overthe conventional bicycle.

RECOMMENDATIONS FORFURTHER STUDY1. A similar study should be conducted

using more homogeneous subject-groups. Cyclists groups should train inas similar body positions as possibleand in similar quantities. Noncyclistsshould undertake endurance trainingof an amount equivalent to that of thecyclists. All subjects should be of simi-lar height and weight to minimizevariation due to individual differencesin optimum crank-arm length.

2. A similar study should be performedusing a high-quality ergometer for

TABLE 1 OXYGEN CONSUMPTION (ml kg-I min-i)Recumbent position Conventional position

Group 51.5 Watts 154.5 Watts 51.5 Watts 154.5 Watts

R 13.39+3.26 32.45+5.11 13.23+2.93 32.27+3.73(n-10)C 14.46+1.44 32.83+4.81 15.18+1.95 33.38+4.58(n-10)N 14.08+3.56 32.17+5.06 13.53+2.83 31.44+4.91(n-10)

HEART RATE (beats min-1)Recumbent Position Conventional Position

Group 51.5 Watts 154.5 Watts 51.5 Watts 154.5 WattsR 96.3+8.2 133.1+9.5 93.3+9.1 130.0+10.1(n-10)C 88.8+8.3 124.2+11.2 88.6+5.9 122.2+10.2(n-10)N 99.8+14.1* 142.8+22.7

^100.5+15.4* 141.5+22.6

^

(n-10)

MINUTE VENTILATION (1 min-i)Recumbent Position Conventional position

Group 51.5 Watts 154.5 Watts 51.5 Watts 154.5 WattsR 27.65+6.39 67.48+3.92 27.34+6.02 64.50+3.18(n-10)C 29.12+5.13 64.83+8.78 29.25+4.95 62.88+6.58(n-10)N 31.23+10.40 74.10+16. 52 28.53+7.66 69.00+12.62(n-10)

Values are mean for the last three minutes of each workload +S.D.R- the recumbent cyclists.C- the conventional cyclists.N- the noncyclists.* significantly different from conventional cyclists.

significantly different from conventional cyclists and recumbentcyclists.

17

- -- --

which workload is independent ofpedal cadence to minimize variationdue to individual differences inoptimum cadence.

3. A study should be conducted to seekthe optimum body position for sub-maximal cycling in the recumbentposition by using different seat-backangles and bottom-bracket heights.

4. Prone body positions should bestudied in addition to conventionaland recumbent postures.

5. Similar studies using higher workloadsapplicable to racing cyclists and speedattempts should be conducted.

6. Larger subject-groups and femalesubjects should be included in similarstudies.

REFERENCES1. Manyari, D.E., Nolewajka, A., Purves,

P., & Kostuk, W.J. (1980). Right andleft ventricular function and volumechanges at rest and during exercise inthe supine and sitting position. Circu-lation, 62 (suppl.III), Abstract No. 868.

2. Poliner, L.R., Dehmer, G.J., Lewis, S.E.,Parkey, R.W., Blomquist, C.G., &Willerson, J.T. (1980). Left ventricularperformance in normal subjects: Acomparison of the response to exer-cise in the upright and supine posi-tions. Circulation, 62,528-534.

3. Thadini, U., & Parker, J.O. (1978).Hemodynamics at rest and duringsupine and sitting bicycle exercise innormal subjects. American Journal ofCardiology, 41, 52-59.

4. Stenberg, J., Astrand, P-O., Ekblom, B.,Royce, J., & Saltin, B. (1967). Hemody-namic response to work with differentmuscle groups, sitting and supine.Journal of Applied Physiology, 22, 61-71.

5. Bevegard, S., Holmgren, A., & Jonsson,B. (1960). The effect of body positionon the circulation at rest and duringexercise with special reference to theinfluence on stroke volume. ActaPhysiologica Scandinavica, 49, 279-298.

6. McGregor, M., Adam, W., & Sekelj, P.(1961). Influence of posture on cardiacoutput and minute ventilation duringexercise. Circulation Research, 9, 1089-1092.

7. Bevegard, S., Freyschuss, U., &Strandell, T. (1966). Circulatory adap-tation to arm and leg exercise insupine and sitting position. Journal ofApplied Physiology, 21, 37-46.

8. Bevegard, S., Holmgren, A., & Jonsson,B. (1963). Circulatory studies in welltrained athletes at rest and duringheavy exercise with special reference

to stroke volume and the influenceof body position. Acta PhysiologicaScandinavica, 57, 26-59.

9. Kyle, C.R., & Mastropaolo, J. (1975,October). The effect of bodyposition upon power output incycling. Presented to the 26thAnnual Fall Meeting of theAmerican Physiological Society,San Francisco, CA.

10. Brooks, G.A. & Fahey, T.D. (1984).Exercise Physiology. Humanbioenergetics and its applications(p. 334). New York: Wiley.

AUTHORIngrid E. Antonson1340 E. LewisPocatello, ID 83201 USA Li

LETTERS TO THE EDITOR

Shaft DrivesAs I read your comment on shaft

drives in Human Power 6/2 I wasreminded of a day in 1979 when I was inthe American Embassy in London withFrank Whitt looking at the GossamerAlbatross, which was on display prior tothe historic Channel flight. I do notknow much about HPAs, but I didremember reading something aboutthe shaft-drive mechanism used by oneof the early teams of experimenters.Frank was very interested in drive sys-tems and gears and we talked a littleabout the subject in relation to theAlbatross. .. I had a miniature taperecorder and decided that I would liketo have Frank on record saying some-thing. He said he was happy to talk intoit - what should he say? On the spur ofthe moment I suggested that he tell mewhy bicycles don't use shaft driveanymore.

I have just rummaged through myold tapes thinking how nice it would beif I could report his answer word-perfect.Alas! I cannot find the tape! (John goeson to report on his work with a mopedthat used a timing belt, and on the newfolding "Strida" bicycle, that apparentlyalso uses a toothed timing belt.... Wehave to report his last sentence:) Pleaseforgive me for not being able to findsomething negative to say aboutHuman Power.

John Stegmann1 Heath StreetNewlands 7700, South Africa

Eve - 1 I--_ _s . . I'l( Lerrers contrnuea on page Lz

ARM-LEG POWER(continued from page 9)

devising acceptable steering systemsthat are comfortable, compatible withmore conventional rear-wheeldrive/transmission systems, and yetelegant in simplicity.

In pedalling some of our arm-legpowered prototype cycles, I've noticed(more subjectively) that there is someunknown "equation" that would makecombined arm-and-leg powered cyclesmore efficient. I find that periodicallyresting my arms while still pedalling withlegs, "feels" the best. On the theoreticalside of this issue, the next step we arefollowing is to look at the bioenergetics ofproducing power under varying contribu-tions of arm and leg efforts; the purposehere would be to determine what kind orlength of rest periods might be optimumfor the arms under sustained arm-legpedalling.

Physiologically speaking, the armmusculature is not designed for aerobic(endurance) work. There seems to befound naturally a disproportionate num-ber of fast-twitch fiber types (anaerobic)in the arms compared to the more aero-bic slow-twitch fibers. The results wereported were based on average youngadults. My suspicion is that specificendurance training in the arms (witnesswheelchair sports) would enhance stillfurther the advantage already demon-strated in combined arm-leg powerproduction.

REFERENCESNagle, F., Richie, J., and Giese, M., 'VO2 max

Responses in Separate and Combined Armand Leg Air-Braked Ergometer Exercise",Medicine and Science in Sports and Exercise,16:563-566, 1984.

Niemela, K "Criteria for Maximum OxygenUptake in Progressive Bicycle Tests."European Journal of Applied Physiology,44:51-59, June, 1980

Reybronck, T., Heigenhauser, G., Faulkner, J.,"Limitations to Maximum Oxygen Uptakein Arms, Legs, and Combined Arm-LegErgometry." Journal of Applied Physiology,38:774-779, 1975.

Williams, J., Cottrell, E., Powers, S., andMcKnight, T., "Arm Ergometry: A review ofPublished Protocols and the Introduction ofa New Weight Adjusted Protocol," ournalof Sports Medicine, 23:107-112,1983.

AUTHORSRichard Powell and Tracey RobinsonDept of Physical Education & RecreationNew Mexico State UniversityBox 3MLas Cruces, NM 88003 USA505-646-2215 O

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-- �

Oh For the WingsArthur C. Clarke

(This short piece was given to me byArthur C. Clarke after he came to a talk Igave on the IPVA at the Sri Lanka Instituteof Engineers. He is a well-known author ofscience fiction, credited with many accuratepredictions of future inventions. The piece isfrom "The Challenge of the Spaceship "(Harper '59) and originally appeared inHoliday 1955. -DG W)

The rapid development of automa-tion now makes it virtually certain thatthere can be no escape from an age ofcompulsory leisure in the not-too-distantfuture. It is also equally certain thatmost of mankind won't be content to oc-cupy its spare time exclusively with paint-ing, ballet dancing, orchestral composi-tion, poetry recital, monumental sculpt-ing and similar aesthetic activities.Which leads us to conclude that one ofthe greatest benefactors of the humanrace in the years ahead will be the manwho can invent a new sport.

A completely new and original sportis a very rare invention indeed. We arelucky enough to have witnessed the birthof a major one - skin diving - during the

last decade.* It now seems quite possi-ble that an even more spectacular andunexpected recreation will arrive in thequite near future. That new sport maybe-flying.

Before you ask indignantly whereI've been hiding since 1903, let me makeclear exactly what I mean. The flying Irefer to is one of man's most ancientdreams, forgotten since the internal-combusion engine gave us (at a price)the freedom of the air. It is flight bymuscle power alone - the practicalachievement of the legend of Daedalus,the conversion into reality of Leonardoda Vinci's sketches.

We are so accustomed to the roar ofthousands and tens of thousands ofhorsepower in the sky that we have takenit for granted that muscle-powered flightis an aerodynamic impossibility as far ashuman beings are concerned. Ourbodies, it has been generally assumed,are far too heavy and underpowered forthe job. And anyway - who cares?

Let's deal with the last point first. Agreat many people would care, if theyhad the slightest idea that such a feat asman-powered flight was even theoreti-cally possible. There is always a sense ofachievement in doing something withoutmechanical aid, and discovering the

*This was written c. 1955. Ed.

limits of the human body's ability. Onlythe most torpid and unimaginative ofmen can fail to feel some sense of excite-ment at the idea of competing with thebirds in their own element, on their ownterms.

The development of aerodynamicsas an exact science now allows us to ana-lyze the problem of manned flight as astraight-forward engineering proposi-tion. There is a certain whimsical inter-est in the fact that the subject is nowbeing studied by a group of youngBritish aerodynamicists at the College ofAerodynamics, Cranfield - in the inter-vals between calculating what happensto vehicles re-entering the Earth's atmos-phere from outer space at twenty timesthe speed of sound.

The crux of the problem is howmuch power a man can develop. Forvery short periods (say a couple ofseconds) this may be as much as 1-1/2hp, if the legs and arms are used simul-taneously. This is equivalent to liftingone's own weight through five feet everysecond - a sort of high-jump perform-ance, in fact. It obviously has no rele-vance to sustained, steady operatingconditions, but may be of importance inconnection with take-offs.

The continuous power which a mancan produce for longer periods - up toan hour - is just under half a horsepower,and a little more if arms as well as legsare used. (.45 hp legs alone; .6 hp alllimbs working). When one looks at thedisparity in size between a horse and aman, this figure is quite surprising. How-ever, the definition of a horsepower - arate of working of 550 foot-pounds persecond - was laid down at the beginningof the steam-engine age by James Watt,and we can be quite sure that he chose asmall and skinny horse for his standardso that the performance of his engineswould appear correspondingly impres-sive. Even then, he probably cooked thefigures.

The basic problem of manned flight,therefore, is that of building an aircraftthat can fly on a half-horsepower engine.This would be a considerable feat of aero-nautical skill, and it is not certain that isis possible. What does appear to bepossible, however, is to build a two-manmachine that could be sustained in theair by muscle power alone. The point isthat an aircraft carrying two men wouldhave double the power, but much lessthan double the drag and weight, of a"single engined" one, and would becorrespondingly more efficient. It mightbe even better to have a still larger crew,

all but one of its members pedalingfuriously with hands and feet while theodd man out steered the machine andprovided power with legs alone.

To concentrate on the minimum-sized, two-man machine, calculationsmade by B.S. Shenstone indicate that itwould have to weigh about five hundredpounds (more than half that being theweight of the crew) and would have awingspan of about sixty feet. The verylarge wingspan arises from the fact thatthe aircraft must have the extremely lowwing loading - the amount of deadweight each square foot of wing area hasto support - of about two pounds persquare foot, as compared with the fifty ormore pounds per square foot of amodern airliner (not to mention thehundred pounds per square foot and upof a supersonic fighter).

Incidentally, it might be mentionedthat Mr. Shenstone is the Chief Engineerof British European Airways. His interestin this particular problem should causeno alarm to BEA passengers; it is a pure-ly private one and doesn't indicate thatthe company fears that its customers willever have to get out and push.

The airframe would have to beextremely "clean," since no power couldbe wasted overcoming unnecessarydrag, even at the low speed of 30 mph,which is about the limit to be expectedfrom such a vehicle. To obtain the requir-ed low drag, what is known as "boundary-layer control" would be needed. This in-volves sucking air from the wing throughslots placed at strategic locations, thuspreventing the build-up of turbulenteddies. One of the most difficult engin-eering problems in the design would begetting the power out of the men andinto the airscrew without too much lossthrough gears, chains or bearings. Avery efficient transmission system wouldbe required, as the crew would be at thefront or center of the aircraft, and thepropeller would probably be at the rear.

Without going into too many detailswhich still remain for the experts on sub-sonic flight to work out, we can get afairly clear idea of the two-man aerialbicycle of the near future. It would lookvery much like one of today's gliders,and would be built from similar mater-ials. The wing would be excessively longand thin - only about five feet wide at theroots, but with a total span of sixty feet.There would be no undercarriage, aspring-mounted skid serving for landinggear.

To keep frontal area to a minimum,the crew would sit - or even lie in a reclin-

19