Drag levels and energy requirements on a SCUBA diver

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Drag levels and energy requirements on a SCUBA diverM. A. Passmore and G. RickersDepartment of Aeronautical and Automotive Engineering, Loughborough University, Loughborough, UKAbstractThe popularity of sport diving has increased rapidly since its inception in the 1950s. Overthis period, the trend has been to increase the amount of equipment carried by the diver.There are many undoubted safety advantages associated with the additional kit, butunder some conditions, it can impose an additional burden in the form of increased drag.The purpose of this paper is to identify the drag penalties for a number of simple self-contained underwater breathing apparatus (SCUBA) configurations. This is achievedthrough scale model experiments conducted in a wind tunnel. Some comments on theassociated energy requirements are made, and from these, the effect on a divers bottomtime is briefly addressed. The configurations tested include a study of the effect of theequipment configuration and the effect of small changes to the diver incidence.The tests show that the addition of a pony cylinder gives a 10% increase in dragcompared with a conventional octopus set-up. When a dive knife, large torch and asurface marker bouy (SMB) are also added this increases to 29%. Over the range tested,the average effect of swimming at a head up incidence to the flow is to increase the dragcoefficient by 0.013 per degree. This amounts to 16% at 5 and 49% at 15. Estimates ofthe effect of the drag changes on bottom time show that the drag increases result inapproximately similar percentage reductions in bottom time. Some simple suggestionsfor drag reduction are proposed.Keywords: diver, drag, SCUBA, energy requirement, drag reductionNomenclatureA projected frontal area (m)Cd coefficient of dragD drag force (N)Et endurance time (min)l model characteristic length (m)Pin input power (W)Re Reynolds numbert time (s)U tunnel freestream speed (m s) 1)Correspondence address:Dr Martin A. Passmore,AAE, Loughborough University,Loughborough, Leics,UK LEH 3TU.E-mail: m.a.passmore@lboro.ac.uk 2002 Blackwell Science Ltd Sports Engineering (2002) 5, 173182 173a angle of incidence ()g mechanical efficiencyq fluid density (kg m)3)l absolute viscosity (Ns m)2)t kinematic viscosity (m2 s)1)subscriptsa airfs full scalem modelw waterIntroductionPrior to the 1950s the exploration and enjoymentof the underwater world was limited to a very fewprofessional divers, generally undertaking com-mercial operations. The invention in 1951 of theSelf-Contained Underwater Breathing Apparatus(SCUBA) opened up the possibility of the devel-opment of a new and exciting sport. The numbersof people participating in this activity has expandedsteadily and today more than 2 million peopleworld-wide regularly go diving. The sport hasgrown into a mature industry with voluntary andcommercial operations providing training, thearrival of diving package holidays and a plethora ofequipment manufacturers.In the early days, the SCUBA gear was essen-tially very simple. The diver strapped on a cylindercontaining compressed air which was fitted with afirst stage regulator and a second stage mouthpiece.A reserve system told the diver when air was run-ning low. Weights were added to assist the descentand the diver wore a mask and a pair of fins. Thedevelopment and expansion of the sport has led to amuch better understanding of physiological factorsassociated with the sport and also to the develop-ment of safe diving practices. Some of the latterhave focused on the equipment used; in particularrelated to the provision of some form of backup airsupply. This may be in the form of an additionalregulator (octopus) attached to the same cylinder,for use by another diver or a second completelyindependent air source. More adventurous divinghas also led to the requirement to carry otheradditional equipment items.One of the potential disadvantages of the addedequipment is the load they impose on the diverunder swimming conditions. The additional dragincurred will inevitably increase the workload andhence consumption of air. The problem is partic-ularly important when the diver must make head-way against a natural current. The degree to whichthe additional energy consumption is an importanteffect is unknown but it is a function of the increasein drag and the relative swimming speed of thediver. Any increase in oxygen consumption inevit-ably reduces the time that the diver will be able toremain submerged but also increases the risk ofdecompression sickness.The purpose of this paper is to identify the dragpenalties for a number of simple SCUBA configu-rations. This is achieved through scale modelexperiments conducted in a wind tunnel. Somecomments on the associated energy requirementsare made, and from these the effect on a diverssubmerged time (bottom time) is briefly addressed.The configurations tested include a study of theeffect of the equipment configuration and the effectof small changes to the diver incidence.The diving environmentThe conditions under which diving takes place canvary considerably; it includes fresh or seawater and aDrag levels and energy requirements M. A. Passmore and G. Rickers174 Sports Engineering (2002) 5, 173182 2002 Blackwell Science Ltdwide range of temperatures from around 4 C totemperatures in excess of 30 C. Consequently thefluid properties also vary considerably, but for thepurposes of this study, it is clearly convenient toadopt some reference conditions. This is taken to beseawater at 15 C. The average salinity of the oceansis around 3.5% making the density approximately1026 kg m)3. The kinematic viscosity at this tem-perature is 1.246 10)3 Ns m)2, Hoerner (1958).The range of water speeds encountered by a divercan also vary considerably. In still water, it is simplya question of the swimming speed of the diver,which can be controlled to prevent fatigue. But,when there is a naturally occurring current the divermay be forced to work at a particular rate, and it is inthese circumstances that the drag on the diverbecomes potentially important. In commercial sit-uations, it is generally agreed that the effective workof a diver ceases at a current of 1.8 to 2.0 knots(approx. 1 m s)1) IAUECA (1987). A similar valuecan be associated with a swimming diver, anecdotalevidence would suggest that a current of 2 knotswould quickly bring about fatigue. This wouldsuggest that for the purposes of this work the upperspeed limit should be 2.0 knots or 1.0 m s)1.Experimental designThe primary non-dimensional parameter of con-cern in low speed flows of the type under consid-eration here is the Reynolds number (Re). Thisparameter represents the ratio of inertial to viscousforces in the flow. If the Reynolds number of thewind tunnel experiment matches that seen for adiver in water then the results will be directlyapplicable, as the flow fields will be similar. Rey-nolds number is defined asRe qUll UltWhere U is the free-stream speed, and t is the ki-nematic viscosity. The characteristic length (l) canbe selected as convenient but in this case, the lengthof the diver including fins is employed. This avoidsthe complication of changing the reference lengthas the frontal area is modified with the changes inconfiguration. Therefore to match the real worldand wind tunnel Reynolds numbers:Re Uwlfstw UalmtaWhere the subscript w refers to water, a to air, m tomodel and fs to full scale.In many cases, particularly when consideringbodies with large scale flow separations the dragcoefficient Cd is reasonably independent of Reynoldsnumber once a critical value is exceeded. In the caseof a complex shape, such as a SCUBA diver, wherethere are many external protuberances there is lesschance of this overall independence, as differentparts of the equipment will have different criticalReynolds numbers. As the diver may be exposed to arange of flow speeds, it may be necessary to simulatea range of Reynolds Numbers to get a more completepicture of the loads that the diver will encounter.The wind tunnel used for the measurements is asimple closed circuit design with an open workingsection. The working section dimensions areapproximately 1.0 m by 0.75 m with a length of2.0 m. To avoid distortions to the flow-field theblockage must be limited to typically less than 5%,although smaller ratios are desirable. Blockageratio is defined as:Blockage ratio model frontal areatunnel cross sectional area100The model dimensions can be determined bycombining the factors above, along with therequirement that the scale must be sufficiently largefor the details to be accurately manufactured. Inthis work, a one-third scale 50th percentile malefigure is used. The main dimensions of the modeland diving equipment are listed in Appendix 1. TheTable 1 Reynolds number comparisonsSea waterAirSpeed (knots) Speed (m s)1) Reynolds number Speed (m s)1)0.5 0.257 4.66 105 9.31.0 0.514 9.32 105 18.61.5 0.772 1.40 106 27.92.0 1.029 1.86 106 37.1M. A. Passmore and G. Rickers Drag levels and energy requirements 2002 Blackwell Science Ltd Sports Engineering (2002) 5, 173182 175Reynolds number data is shown in Table 1, thereference length is 0.74 m.The maximum tunnel working speed isapproximately 35 m s)1 so in practice the highestequivalent swimming speed is of the order1.9 knots.The frontal area of the model when in theswimming position (prone) is 0.015 m2. This rep-resents a blockage in this tunnel of only 2%. As themodel incidence is increased, the blockage increa-ses to a little under 5% at an incidence of 15.Diver configurationsWith the huge range of designs of equipment nowon the market it is clearly not possible to test everyconceivable configuration. The tests have thereforebeen limited to three main configurations followedby tests of subsidiary equipment. The baselinediver consists of a single 12 l cylinder fitted with afirst stage regulator, plus a standard waistcoat stylebuoyancy control device (BCD) with air supplyhose, contents gauge and hose, single regulator andhose, weight belt, mask and fins. Note that thecylinder capacity is quoted in terms of its watercapacity as cylinders have various working pres-sures when charged with compressed air. Thisconfiguration is shown in Fig. 1. Although thereare many designs of BCD in regular use, the oneselected for this work is a generic version of thetype most commonly found.The second and third configurations representtwo alternative methods of improving safety. Eithera second (octopus) regulator is added which, in anemergency can be used by another diver. Or asecond pony cylinder (water capacity 3 l) with aseparate contents gauge and regulator is added.Similarly this could be used by another diver in anemergency, but has the added advantage that it actsas a completely independent air source, and maytherefore be used by the diver carrying it. Thisarrangement can be seen in Figs 2 and 3. Thesefigures also show the additional items of equip-ment; a large torch, reel for an SMB and a knife.The additional items were tested as additions to thebaseline configuration and in a number of combi-nations to determine interference effects.Figure 1 Baseline diver. Figure 3 Fully equipped diver left view.Figure 2 Fully equipped diver right view.Drag levels and energy requirements M. A. Passmore and G. Rickers176 Sports Engineering (2002) 5, 173182 2002 Blackwell Science LtdThe diver model is largely constructed fromwood, with securing pins to attach the divingequipment. The Buoyancy Control Device wasmanufactured from a relatively fine weave material,and stuffed to take up the appropriate shape. Oncethe shape was achieved the BCD was attached to thediver using velcro and given a coating of lacquer. Asit is recognised that the routing of hoses will have anoticeably effect on the results obtained, all hoseswere made from 5 mm diameter PVC tubing oversoft copper rods. This construction allowed thehoses to be bent into a representative position andtests reliably repeated. For the tests reported herethe divers limbs were not articulated.Experimental procedureThe model is mounted on a support sting attachedto the under-floor balance and the tunnel run for ashort period to stabilize the temperature. With thetunnel switched off a tare reading is taken and alltransducers zeroed. Drag measurements are thenrecorded across the speed range of interest. Thespeed is taken from a pitot-static mounted atinlet to the working section and connected to adifferential pressure transducer. While makingmeasurements it is unnecessary to match the speedsexactly as the data is subsequently used to calculatenon-dimensional coefficients. All data wereacquired using a PC based data acquisition systemsampling at a rate of 100 Hz for 60 s. The data isthen averaged to eliminate the effects of anyunsteadiness in the flow. The averaged values werestored for further analysis.As the model is supported in the flow by a sting,the influence of this must be established and thedata corrected to determine the diver-only drag.With the support mounted to the balance and themodel mounted separately from above in order togenerate the interference effect, the contribution ofthe support sting to the total drag reading can bedetermined. This method of correction allows forthe direct contribution of the support and theinterference effect of the model on the support butdoes not account for the interference effect of thesupport on the flow around the model. To min-imize this latter effect the support is made from athin section bar with rounded leading edge andtapered trailing edge.The balance used was a three component virtualcentre strain gauged balance, located under theworking section. The balance is capable of provi-ding lift, drag and pitching moment, although inthis case the study is limited to drag.The averaged drag data is converted to a dragcoefficient (Cd) using the following definition.Cd D12 qAU2Where D is the drag force and q is the air density.The reference area (A) used is the projected frontalarea and in this work it is recalculated for eachconfiguration. This ensures that the drag coeffi-cients can be compared to determine which is themost efficient shape, but when assessing the addi-tional load on the diver the product CdA, or dragarea should be used. This is the standard approachwhen considering what are essentially differentshape bodies. In each case, the reference area iscalculated from the working drawings produced forthe model manufacture.Results and discussionReynolds number effects and overall accuracyBefore considering the effect of equipment changeson the drag of the diver the issue of Reynoldsnumber sensitivity is addressed. This is importantbecause if the tests are independent of Reynoldsnumber we can reduce the experimental work to asingle tunnel speed and compare the configurationsthrough a single drag coefficient or drag area value.A test of the baseline configuration, across the fullspeed range of the tunnel, allows a plot of dragcoefficient against Reynolds Number; Fig. 4.The variation exhibited arises from two sources.At the lowest Reynolds numbers tested themeasured drag force is very small so the errorsassociated with the tunnel speed measurement andbalance linearity and repeatability can result in aM. A. Passmore and G. Rickers Drag levels and energy requirements 2002 Blackwell Science Ltd Sports Engineering (2002) 5, 173182 177relatively large error in the drag coefficient. This isillustrated by the error bars given on the figure.However, where the uncertainty is greatest the dragon a real diver is small so it does not present theload problem seen at higher speeds. It is thereforeconcluded that the remainder of the tests should berestricted to Reynolds number above 7:5 105.The second source of variation arises because thecomplex nature of the body under test ensures thatdifferent parts of the model pass through transitionat different tunnel speeds, giving rise to coefficientchanges across the range. This suggests that allconfigurations should be tested across the rangerather than at a single tunnel speed.Diver configurations and accessoriesIn Fig. 5 the three main diving configurations arecompared.The addition of the octopus rig to the baselineincreases the drag coefficient across the range tes-ted, this is expected as the configuration involvesthe simple addition of an exposed hose and demandvalve. The effect of this could be reduced if thehose was more carefully routed, but as an item ofsafety equipment, it must remain readily available.The potential for improvement by careful routingof hoses is covered briefly later in the paper.The addition of the pony cylinder produces aninteresting result. In practical terms, it constitutesthe addition of a spherically tipped cylinder intothe region next to the main cylinder. The localReynolds number based on freestream velocity andpony cylinder diameter ranges from 5 104 to1.1 105. However, with the local flow accelera-tions likely in this region it falls into a criticalReynolds number range. The influence of this islikely to be a slow rise in Cd possibly followed by adrop as transition to a turbulent boundary layeroccurs, however this occurs as a contribution to theoverall characteristic seen in the figure.The data presented represents the efficiency ofeach of the configurations, but does not indicatethe effect they have on the drag on the diver. Thedrag area is therefore plotted against water speed inFig. 6.Figure 5 Main configurations against Reynolds number.Figure 6 Drag area against water speed for main configurations.Figure 4 Baseline diver Reynolds number run.Drag levels and energy requirements M. A. Passmore and G. Rickers178 Sports Engineering (2002) 5, 173182 2002 Blackwell Science LtdThis clearly illustrates the penalty associatedwith the additional equipment. The increasedfrontal area in the case of the pony cylinder coun-teracting the efficiency advantage it has over theoctopus rig. The average increase, across the Rey-nolds number range tested, in drag area andtherefore drag force, is 12% for the octopus rig and24% for the pony rig over the baseline configur-ation. Assuming that in the interest of safety nodivers would use the baseline configuration thenthe pony rig gives a 10% increase in drag comparedwith the octopus set-up.The effect of extra equipment items is illustratedin Fig. 7. Each item has been tested as an additionto the baseline diver. The knife is located on theoutside of the lower leg, the torch and SMB areattached to the chest area. These locations can beseen in Figures 2 and 3.The average increase over the range tested is 0%for the knife, 5% for the torch and 11.5% for theSMB. Finally, the items were tested in combinationyielding the results shown in Table 2. All config-urations tested are summarized in this table.In the final configurations tested it is seen that theOctopus rig with all accessories adds an additional32% drag and the pony rig with all accessories addsan additional 45%. Compared with the octopus set-up the fully equipped diver using a pony cylindersuffers a 29% increase in drag. The significance ofthis for the diver will be considered later.Incidence effectsIn the final programme of tunnel tests the inci-dence of the diver to the oncoming flow is con-sidered, Fig. 8. This is an attempt to simulate theusual requirement for the diver to swim in a slightlyhead up configuration although in this case, asthere is no articulation in the model, the completediver is inclined. In practice most divers swim headup at a slight incidence. Only the baseline diver isconsidered, and in line with usual practice the dragcoefficient is calculated using the baseline diverfrontal area. It is, therefore, unnecessary to consi-der the drag area.Over the range tested the average effect of inci-dence is to increase the drag coefficient by 0.013per degree. This amounts to 16% at 5 and 49% at15.A comparison of the results obtained with pub-lished material is difficult, as no study of this typeTable 2 Summary of resultsConfiguration Average Cd Frontal area (m2) Drag area (m2) Drag increase (%)Baseline 0.394 0.195 0.0770 Octopus rig 0.408 0.212 0.0864 12.3Pony rig 0.405 0.234 0.0951 23.5Baseline + knife 0.395 0.195 0.0771 0.2Baseline + torch 0.393 0.206 0.0809 5.1Baseline + SMB 0.414 0.207 0.0858 11.5Baseline + knife + torch 0.394 0.206 0.0812 5.5Baseline + knife + SMB 0.404 0.207 0.0837 8.8Baseline + torch + SMB 0.411 0.218 0.0896 16.4Baseline + knife + torch + SMB 0.413 0.218 0.0898 16.8Octopus rig + knife + torch + SMB 0.433 0.234 0.1015 31.8Pony rig + knife + torch + SMB 0.433 0.260 0.1112 44.5Figure 7 Drag area against water speed for auxiliary equipment.M. A. Passmore and G. Rickers Drag levels and energy requirements 2002 Blackwell Science Ltd Sports Engineering (2002) 5, 173182 179has been previously undertaken to the knowledgeof the authors. IAUECA (1987) provide approxi-mate forces on an average diver in the horizontalposition derived from water tow tests. The figuresquoted are approximately 15% higher than thoseobtained for the fully equipped diver reported here.However, it is difficult to draw further conclusions,as IAUECA (1987) does not report the exact con-figuration of the diver tested. It is also important tonote that Lyttle et al (1998) report that high de-grees of accuracy can be difficult to achieve withthe tow test. Lyttles work reports sophisticated towtests on elite swimmers at a range of depths andspeeds. At the deepest depth tested (0.6 m), wherethe wave drag is minimized, the mean drag coeffi-cient found is 0.33 (Cd values are not reported inthe paper but have been calculated from the datagiven). This result refers to the Reynolds numberrange 2.4 106 to 4.7 106. Given this result afinal test of the wind tunnel model was undertakenwith all SCUBA equipment removed. This ap-proximates to the configuration of the tow testsapart from the divers fins, which were not remov-able. The Cd value determined at the highestReynolds number possible (1.7 106) was 0.306.This gives some confidence in the results.Energy requirementsAlthough a detailed investigation of the energyrequirements of the diver are beyond the scope ofthis paper, an estimate of the likely increment inenergy input associated with the drag changes thathave been measured would be useful. The realsituation of a diver in water is clearly not directlycomparable with the fixed attitude tested in thewind tunnel. In practice, there is a dynamic situ-ation where the means of locomotion, the leg kick,generates vortex structures not seen in the passivecase. However, this does not preclude some furtheranalysis.The oxygen required for the process of respir-ation is, in the case of a SCUBA diver, limited bythe capacity of the compressed air cylinder used.The demand for oxygen depends on the BasalMetabolic Rate (BMR), the efficiency of the diverand the output work rate required. As the outputwork rate is the product of drag force times rel-ative water speed any increase in speed or dragwill increase the required oxygen input, and hencereduce the time that the diver may remain sub-merged.Basal Metabolic Rate has been widely studied; itis subject dependent, being particularly dependenton body mass and fitness and is effected by tem-perature and pressure. Nadel (1974) shows that notonly does the BMR increase with reducing tem-perature, but the oxygen consumption associatedwith activity can also increase. The work reportedshows that the oxygen consumption of a breast-stroke swimmer can increase by up to 60% for adrop in temperature from 33 C to 18 C.The mechanical efficiency of a swimming diverhas not been widely reported. Typical values forwalking and running are around 20%, McArdle(2001), but Toussaint (1990) suggests that theefficiency of a swimmer is significantly lower thanthis because of the transfer of kinetic energy to thefluid medium. Toussaints et al. (1990) measure-ments on a group of elite swimmers performingfront crawl yields efficiencies between 5 and 9.5%,with the higher efficiencies arising at the higherswimming speeds. Toussaint (1988) further sug-gests that dynamic measurements of the dragduring swimming correlate well with passivemeasurements. It is concluded that the use of thepassive drag forces, measured in the wind tunnel,will generate realistic power input and henceFigure 8 Effect of incidence.Drag levels and energy requirements M. A. Passmore and G. Rickers180 Sports Engineering (2002) 5, 173182 2002 Blackwell Science Ltdoxygen consumption figures if combined with anappropriate efficiency figure (g).The power input in Watts is calculated as thedrag power divided by the efficiency:Pin qACDU32gThe oxygen consumption in litres/minute at thesurface is the sum of the BMR and the oxygenrequired to generate the power:O2consumption BMR 0:002826Pinwhere the constant 0.00286 is the conversion factorbetween Watts and litres per minute O2 con-sumption.If the breathing gas is compressed air containing21% oxygen, then the total oxygen available to thediver is:Available O2Cylinder capacityworking pressurereserve0:21As the ambient pressure increases with depth, at therate of (approximately) one atmosphere for each10 m, the endurance time (Et) in minutes of thediver at a depth h in metres is given by:Et Available O21 h=10O2consumptionIn Fig. 9 the bottom times (duration of dive) areestimated for the baseline and fully equipped diverat constant depths of 20 and 40 m. The followingassumptions have been made: A 12 l capacity cyl-inder with a working pressure of 230 bar andreserve of 50 bar, a BMR of 0.37 l min)1 and anefficiency of 5%. The calculation does not accountfor the increased oxygen consumption associatedwith exercise at low temperatures, the increase inbreathing resistance caused by the apparatus anddepth, or the increased stress experienced by diverswhen under high work loads. These factors arelikely to reduce the bottom times significantly. Theability of the diver to maintain the required workrate is also not addressed.The influence of the additional drag is seenclearly in the graph. The reductions in availabledive time are, apart from the BMR, proportional tothe increase in measured drag. At the higherspeeds, the BMR accounts for approximately 15%of the total oxygen consumption.Drag reduction methodsThe relatively simple calculations of enduranceillustrate the dramatic effect the additionalsources of drag can have. Although it has notformed a significant part of this study, it istherefore natural to suggest means by which theeffects of the additional equipment may beameliorated. The effect of the hoses was seen withthe addition of the octopus rig to the baselinediver. This resulted in a 12.3% increase in drag.Therefore, this is clearly an area for potentialimprovement. For each of the three main con-figurations an alternative configuration was testedwhere all the hoses were restrained closer to thebody by taping them to the top of the shoulder.Such an arrangement is practical, as it is usual forBCDs to have a number of simple hose restrain-ing points. For the baseline diver shown in Fig. 1restraining the hoses reduced the drag area by11%, for the Octopus configuration the drag areais reduced by 6% and for the pony by 8%. Fur-ther reductions would be achieved by removingsome hoses entirely. For example remote aircontents sensors are available which remove therequirement for the console and its connectionFigure 9 Bottom times for constant depth dives at varying waterspeeds.M. A. Passmore and G. Rickers Drag levels and energy requirements 2002 Blackwell Science Ltd Sports Engineering (2002) 5, 173182 181hose. The further potential for drag reduction is agood area for further work.Conclusions A wind tunnel model of a SCUBA diver has beentested in an open-section wind tunnel over arepresentative range of Reynolds numbers, andin a number of configurations. Some Reynolds number dependency is seen forall configurations of diver tested. Relative to the baseline diver described theaddition of an octopus rig increases the drag by12% and the addition of a pony rig by 24%.Assuming that for safety reasons no divers woulduse the baseline configuration then the pony riggives a 10% increase in drag compared with theoctopus set-up. When added in isolation the addition to the totaldrag of a diving knife, large torch and an SMBreel were 0, 5 and 12% respectively. The fully equipped diver employing the ponycylinder and all the additional equipment itemsincreased the drag by 45%. When tested in a head up configuration theaverage increase in the drag coefficient is 0.013per degree. This amounts to 16% at 5 and 49%at 15. Some reduction in the drag penalties incurredcan be achieved by ensuring that the connectinghoses are secured close to the body. The results obtained compare well with thepublished literature. Estimated bottom times have been presented.For a more accurate indication, further work onthe efficiency of the swimming diver is required.However, as the BMR contributes a relativelysmall amount to the total oxygen requirementthe drag increases are a good indication of theincrease in overall oxygen consumption andhence bottom time.AcknowledgementsThe authors would like to thank Mr PeterStinchcombe for manufacturing the model of thediver and Mr James Ambrose for carrying out theadditional configurations reported in the section onDrag reduction methods.Appendix 1 Principal model dimensionsDiver standing height 0.58 m (representing a50% percentile male, height 1.75 m)Shoulder width 0.17 mFin length 0.165 m (from heel to tip)Model reference length 0.74 m (total length ofmodel with fins extended as in Fig. 1)12 l cylinder diameter 0.060 m height0.216 mPony cylinder diameter 0.034 m height0.170 m.ReferencesHoerner, S.F. (1958) Fluid-dynamic drag. Published by theauthor.IAUECA (1987) The Effects of Underwater Currents on DiversPerformance and Safety. AODC047. The InternationalAssociation of Underwater Engineering ContractorsAssociation (IAUECA).Lyttle, A.D., Blanksby, B.A., Elliot, B.C. et al. (1998) Theeffects of depth and velocity on drag during the stream-lined glide. J. Swimm. Res. 13, 1522.McArdle, W.D. (2001) Exercise Physiology Energy, Nutritionand Human Performance. Williams and Williams, Lippin-cott.Nadel, E.R. (1974) Energy exchanges of swimming man.J. Appl. Physiol., 36, 465.Toussaint, H.M. (1988) Active drag related to velocityin male and female swimmers. J. Biomechanics, 21,435438.Toussaint, H.M., Knopb, W., DeGroot, G. (1990) Themechanical efficiency of front crawl swimming. Medicine,Sci. Sports Exercise, 22, 402.Drag levels and energy requirements M. A. Passmore and G. Rickers182 Sports Engineering (2002) 5, 173182 2002 Blackwell Science Ltd


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