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KJuyverwtjy i - ^o^^ nS DELFT
THE COLLEGE OF AERONAUTICS
CRANFIELD
THE AIR RESISTANCE OF RACING CYCLISTS
by
V' Ka , • . REPORT m, 106 OCTOBER. 1956, T H E C O L L E G E O F A E R O N A U T I C S C R A IT F I E L D The A i r R e s i s t a n c e of Racinp; C y c l i s t s b y -T, N o n w e i l e r , B . S c , S U H II A R Y T e s t s i n a c l o s e d - s e c t i o n v ; i n d - t u n n e l on t h r e e d i f f e r e n t c y c l i s t s mounted on a r a c i n g b i c y c l e cjre d e s c r i b e d , and f i g u r e s q u o t e d f o r t h e r e c o r d e d a i r r e s i s t a n c e . Some comments ore a l s o i n c l u d e d on t h e i m p l i c a t i o n s of t h e r e s u l t s c o n c e r n i n g t h e povrer-output of r a c i n g c y c l i s t s » MEP
COMTENTS Introduction
Escperinental Method
Subjects tested and their Pcstijr©
Accuracy of Results and Corrections Applied Discussion of Results
Applications of Data to deduce the Povrer of a Cyclist Conclusions
Aclcno\7ledgements References
Figures 1 - 4 .
Introdaction
Interest recently displayed in the problem of huraan-pOTrerod flight has revealed the dearth of information v/hich exists concerning the power attainable by a human-being, As a contribution to such limited data, wliich is of interest to physiologists, tests were undertaken to determine the air . resistance of some amateur racDjig cyclists mounted on their bicycles ±n a closed section wind-tunnel. After describing
the e:cperimental method PJid the results obtained, \fo shall examine briefly the v/ay in which such data determine the useful poYirer-output of a cyclist,
2, Experimental Method
A strijjped-dDwn racing cycle, as used by one of the subjects tested, was suspended in the vertical centre plane of the closed v/orking section of the tunnel by wires
attached to an overhead balance. In addition, tvro heavy weights were hung at the end of tdjres passing through the floor of the tunnel, and attached to the wheel axles, so as to stabilise the bicycle. This was necessary of course as no -poxt of the machine could contact the floor of the tunnel if p. tine balcjice reading of air drag v/ere to be obtained,
The subjects to be tested mounted the cycle, and the tunnel was svrf.tched on to provide air streams of various
speeds between l\0 and 55 ft,/sec. It did not prove practical to allow the subjects to pedal i/hilst the drag was recorded, as even if they remained deliberately 'at rest', their move-ment ojid tliat of the bicycle was enough to mcke it difficult
to obtain a steady reading from tlie drag balance. Nor W£LS
it pi'actical to conduct tests with the cycle yawed to the v/ind direction,
Figure 1 is a drawing of the bicycle rigged in the tionnel, v/ith a subject mounted on it, \/hose dimensions corres-pond v/ith those of 'Subject B' of this report,
Figure 2 consists of photographs further illustrating the rig,
3, Subjects Tested gnd their Posture
Three subjects were tested, loiovi-n hereafter as 'A', 'B' and 'C' who are amateur members of a local cycling club, In view of the difficulty of defining accurately the dimen-sions and posture of a human subject, only the barest detai],s relevant to this subject \ïill be given. Indeed, it seems doubtful whether any use vrould be served by trying to do more than tliis,
The approximate height cxid v/eights of the subjects are as follov/sï
'A' : height 5ft.7-iin.; vraight 1441b, 'B' : ' 5ft,10^in.J ' 1501b, 'C' : ' 6ft,0^in.j ' 1791^. Unless otherv/ise stated they v/orc siaiglets, shorts ejid
special shoes as nonncily used by racing cyclists. Subject 'B' (see figure 1) may be regarded as corresponding closely in most vital statistics with a 'standard' man as defined by the \7ell-knov«i surveys,
Two different positions were adopted in the tests by each subject, vdiich are posed raid defined in most
essentials by subject 'A' in fig, 3J these will hereafter be termed the 'racing' rnd 'touring' positions. No more upright position than the latter (figure 3b) could be
4, Accuracy of Results and Corrections Applied
Only figures for air resistance were measured; owing to the \ansteadiness of the subject already referred to it would be impossible to expect that the di'ag data could be read from the balance recorder with an accuracy of any more than about + 1 oz, (in a total varying between 6lb, and IJlb.) Calibration of the tiinnel balcmce in tliis rcjnge suggested errors due to non-linearity in response end hysterisis effects in the recording mechanism of the same magnitude, Further there was a tendency for the bicycle sometimes
suddenly to yaw a little, so that soïie of the results may suffer in this respect. Again of course it was impossible to guarontee that the subjects posture was always identicaJL as the tunnel speed was changed. Repeated tests on subject
'A' sviggested that the overall accuracy of drc^ measurement was about + 3 per cent,
Corrections v/ere applied for solid blockage using the expressions'
effective increase in speed _ 0,65 (model vol-ume)
tunnel speed (tiinnel x-section oxca) x (breadth) v/here the 'model volvime' included rn assessment of the subjects volume by assum.ing his specific gravity was unity» The vrake blockage wo.s assessed by the formula;^
effective increase in speed _ _1_ drag area
tunnel speed " tunnel x-section area Typically solid blockage accotinted for a 0,4 per cent increase in effective speed, and wcke blockage for a 2 per cent increase, The tore drag of the supporting v/ires v/as measured independently by sepcrt'.te experiment and formed about 4 per cent of the total.
It v/ill be apprjrent that these corrections provide a ncrns of converting the data into those relevant to the 'model'
in mid-r±r. No effort has been made to cJ.low for the 'ground effect' v/liich v/ould exist in practice: it is considered that it is likely to be negligible,
5, Discussion of Results
The air resistance of the subjects in the 'to\iring' and 'racing' positions is detailed in Tables I end II,
S u b j e c t 'A' S u b j e c t »B' S u b j e c t 'C' S u b j e c t 'A' S u b j e c t 'B' S u b j e c t 'C' The t e r m 'dr (üynamic heac Re£ TABLE I
sistonce i n the Touring:; Position S p e e d ; Resistrnce
If'.
Speeds 3 5 . 5 f t , / s e c . D r a g 4 6 . 6 f t , / s e c . 3 3 . 9 f t . / s e c , 41.8ft,/sec, Vf,9ft./sec, 37.2ft,/sec, 47.8ft,/sec. TABIE II area; in the Rrxjing Position 39.2ft ./sec. Drag 43.9ft,/sec. 47.4ft ./sec, 50,2ft./sec. 53.3ft,/sec. 54.1ft./sec. 39.3ft./sec. 45.8ft,/sec, 53.3ft,/sec, 38.9ft./sec. itS,1ft,/sec, area t 4,03sq.ft. 4.00sq,ft. 4.02sq.ft. 3.96sq.ft. 3.90sq.ft, 3.91 sq.ft. 3,9^q.ft» : 3.17sq»ft. 3.l6sq,ft. 3.07sq,ft. 3.17sq.ft, 3.25sq.ft. 3.05sq.ft. 3»39sq.ft, 3.33sq»ft. 3.3^q.ft. 3,50sq.ft, 3.48sq»ft,
rrea' u s e d here refers to the quotient ( d r a g / tliis ( n o e a s y r e f e r e n c e arer a v a i l a b l e , subject ' B ' so that h i s about 0 , 9 3 ) .
i'
v/ac drc A s tl'ii-s r e p o r t t e r m i n o l o g y , d e f i n e d a s±i
^x
l e v e l conditior m , p , h » Thu£ •sorioept is obviously/' to be preferred as . for the formation of coefficients is
.s a m a t t e r of interest, the J estimc
frontal area of .ted as 3.6sq,ft, in the racing position,
-g coefficient b a s e d o n this
m ? y b e used by those unacqur
; should b e p o i n t e d out that
tire a would be
-inted v.dth CwCrodynamic the c
(density o f the air) x (speed) • LS this dra equals 25,6(V/lOO)^lt g = O0OO256 V*x(drag >,/sq area 3ynaraic head is Under standard sea-,ft«, v/here V is in ) lb.
»
The results tabulated above shov/ that in the
'touring position' all subjects had (sxirprisingly) about the same drag, but that in the 'racing position' there is some positive correlation vd.th the size of the subject tested. The mean drag areas for the subjects are
At 3.15sq.ft. ; B; 3.35sq.ft.; C; 3.50sq.ft.,
A being the shortest and lightest subject, and C the tallest and heaviest of those tested. These data reveal a variation of ± 5 per cent about the figure of 3.'33-'Sq.ft,, v/hereas for example the height of the three subjects vcried _+ 32" P^^ cent about a cenird figure, The lack of similar vrxiation in the figures relating to the more upright 'touring' position
probably results from the constraint exercised by the prox-imity of the tunnel roof in teJcing up of this position. There is apparently no significant voriation of drag area with speed (i.e. the sor resistance varies directly vidth the
square of the speed) much as one might anticipate.
One ca.- tv/o other test results of interest may be quoted» The 'drag area' of the bicycle vrithcjut cyclist was measured as 1 sq.ft., which is remexkable high. Of course
it cannot be assumed that the c±r pressure on the cyclist provided only the extra 2 sq,ft, or so of drag area, because M s presence v/ould shroud part of the bike structure,
In another test the subject 'A' v/as clothed in jacket and flannel trousersi his drag area in the racing position then increased by 30 per cent to 4.09sq,ft»
Subject 'B' experimented v/ith various positions, unusual for him, and one of these (photographed in fig. 2c) yielded a drag area 0.18sq,ft. (5 per cent) lower than that of his noiT:ial racing position. The elbov/s v/ere kept closer in and
the head lower in this attitude. However similar modifica-tions by subject 'A' resulted in an increased drag. Time did not allcw variations of saddle and handlebar position to be tried, end of course it is not knov/n in what vvay these modifications in posture affect the efficiency of muscular operation,
Finally it is v/orth pointing out that side forces and yav/ing moments ^vere recorded by the balance, though no record of these v/as taken. The lift force was £>Jw^ays
negligible. So far as v/as possible the bicycle was maintained in an attitude facing the oncoming v/ind, so the^e side forces presumably arise from the asymmetric leg position, Aerodynami-cally speeking, the 'model' even with the physical constraint supplied by the rig, had poor stability characteristics in yav/, and tlois contributed sometimes to the difficulty of steadying the balance readings. This fact however v/ould not seen to have any practical significance,
6, Application of Data to deduce the Foi/er of a Cyclist Any applications of the data to estii"nate the useful power supplied by a cyclist ore fraught v/ith difficulty ov/ing
to the fact that whilst cycling a \iniform speed is not pre-served, the relative v/ind speed and direction is continually changing rnd the ground siirface is not level, Hov/ever, as most s]peed trials or distcnce races ore conducted on a closed course it is permissible to assume that, on the average, these variations are unimportrntj if anything it is not difficult to persuDwde oneself that their neglect v/ill underestimate the average pca/er output (defined as total v/ork done •; time), Tlius, figiores for an 'average' power based on that needed to maintain the average speed in still air on level ground rore not v/ithout interest or value. To calculate these a figure of 0,006 was used as a coefficient of friction (to include rolling and mechanical resistance), on the basis of informa-tion kindly supplied by Raleigh Industries Ltd,
The average powers attained for exaEple by subject 'B' can in this way readily be deduced frcci his speeds over various distances, and his 'speed versus pov/er' characteristics are shov/n in fig., 4. His best results on road races are
given helow in Table III! it is only fair to point out that he v/ould not mind being classified as a good amatc\ir middle-distance rcjc±n.g cyclist, v/ithout being perhrps an exceptional one,
TABLE III
Inferred 'average' pov/er of Subject 'B'
Distonce m i l e s 10 25 30 50 100 Time h r s . m i n s . s e e s , 23 17 59 52 1 14 15 2 7 12 4 30 53 Mean Speed ra,p,h, 25.72 25.05 2 4 . 2 4 2 3 . 4 3 22.15 Average pov/er needed t o overcome F r i c t i o n h . p , 0,062 0 . 0 6 0 0,058 0,056 0.053 Air Drag h , p , 0,389 0.351 0,318 0,294' 0,248 T o t a l R e s i s t a n c e h , p , 0.451 0.411 0.376 0 . 3 5 0 0.301
In appreciating these pov/er levels, it is interesting to note that climbing tv/o 8in<« stairs a second corresponds approxi-mately to a useful output of about 0.35 h.p. As v/ould be expected there is a steady drop in average pov/er level v/ith duration of effort.
-8-These figures should be compored v/ith the follov/ing list of tlie highest penners recorded in bicycle ergcxieter tests on trained cyclists during physiological experiments; the list has been composed by Dr. D.R. \7ilkie of the University College, London, Dept, of Physiology, of ter exomination of many references,
TABLE IV
Highest Pov/ers recorded in Ergometer Tests Duration of effort, minsa
Highest recorded figure „ p for average pov/er J . »
1
0.54
2
0,47
5
0.41
10
0.38
30
0.34
60
Oo28
270
0,19
These suggest not only lov/er pov/ers but a more rapid diraunition of pcz/er v/ith duration of effortj for a duration of ^hour the figure (from Table III) for subject 'B' is 30 per cent higher, and at the longest dirration of effort (3 hours) it v/ould be at least 75 per cent Iiigher, than the data of the ei-goneter tests. There may well be many good reasons to explain this disparity, but it is important to note that it exists; no doubt the
sviitabilityof the posture of the subject tested on the laboratory machine, and his incentive for extreme effort, affect the
answer e Moreover there would undoubtedly be a considerable difference between the performcnce of any one subject and another - even assvimlng both were trained cyclists, - and also for the same subject fraii one day to the next.
It is amusing to speculate that if subject 'B' could reach speeds corresponding to the record achievements at the distances quoted in Table III, his pov/er output ivould have to be increased by at least 25 per cent (and by 50 per cent at
the tv/o extremes of distcnce cjuoted). Becjring in mind that he is a man of average size, end that changes in the essential racing posture have been found to have only a relatively small effect on the air resistance to be overcome, it is probable that this gives 0. fair idea of the a.ctual pov/er attornments of the record breakers, A tentative assessment of these
attainments in shorter distance races is given, on this basis,
in fig, 5,
* It is undez-stood much hi.gher pov/ers have been recorded by professional cyclists working on ergometers in escperiments conducted by bicycle manufacturers. These figures are not hovTOver published,
7. Conclusions
(i) A method of evaluating the dro.g of a cyclist on a bicycle has been evolved v/hich go.ve results repeatable v/ithin + 3 per cent.
(ii) The drag is found to vary o.s (speed) , and to be only slightly influenced by the size of the subject ond his posture in the generally adopted ro^cing position,
(iii) The dro.g of the bicycle itself was recorded as about 30 ]?er cent of the toto.l recorded v/hen mounted by a cyclist,
(iv) The results imply that roo.d cyclists generate con-siderobly higher pov/ers then have been recorded by ergometer tests in physiological laboratories, ,
Acknov/ledgenents
The subjects of these tests were Messrs, M, Buck, B, Fletcher, and M, Street of the St. Neots Cycling Club, v/hose enthusiastic cooperation in this v/ork is most gratefully
acknov/ledged. The unusual task of designing the rig for
the bicycle in the tunnel v/as undertaken by Messrs, G, Hollov/ay and S, Lilley,
Reference£
1 . A.D. Young and HoB. Squire
2, A, Thctt
Blockage Connections in a. Closed Rec-tangular Tunnel. Pt. I - Simple Approx-imate Poraulae for Genercl. Application. A.R.C., R. ond M, No. 1984. (1945). Blockage Corrections ond Choking in the R,A,E, High Speed Tunnel,
F1G I.
RIGGING OF BICYCLE IN TUNNEL SHOWING MAN DIMENSIONS AND POSITION OF SUBJECT "B" WHEN MOUNTED.
c. View through tunnel window during test, illustrating a modified racing position of Subject ^'B"
't
a. Racing Poaition b. Touring Position
FIG. 4.
POWER fJEEDED BY CYCLIST "B" TO KMINTAN SPEED IN STILL AIR AND ON LEVEL SURFACE.
