527121 research-article2014
POI0010.1177/0309364614527121Prosthetics and Orthotics InternationalDyer
INTERNATIONAL SOCIETY FOR PROSTHETICS AND ORTHOTICS
Original Research Report
The importance of aerodynamics for prosthetic limb design used by competitive cyclists with an amputation: An introduction
Prosthetics and Orthotics International 2015, Vol. 39(3) 232–237 © The International Society for Prosthetics and Orthotics 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0309364614527121 poi.sagepub.com
Bryce Dyer
Abstract Background/Objectives: This study introduces the importance of the aerodynamics to prosthetic limb design for athletes with either a lower-limb or upper-limb amputation. Study design: The study comprises two elements: 1) An initial experiment investigating the stability of outdoor velodromebased field tests, and 2) An experiment evaluating the application of outdoor velodrome aerodynamic field tests to detect small-scale changes in aerodynamic drag respective of prosthetic limb componentry changes. Methods: An outdoor field-testing method is used to detect small and repeatable changes in the aerodynamic drag of an able-bodied cyclist. These changes were made at levels typical of alterations in prosthetic componentry. The field-based test method of assessment is used at a smaller level of resolution than previously reported. Results: With a carefully applied protocol, the field test method proved to be statistically stable. The results of the field test experiments demonstrate a noticeable change in overall athlete performance. Aerodynamic refinement of artificial limbs is worthwhile for athletes looking to maximise their competitive performance. Conclusion: A field-testing method illustrates the importance of the aerodynamic optimisation of prosthetic limb components. The field-testing protocol undertaken in this study gives an accessible and affordable means of doing so by prosthetists and sports engineers. Clinical relevance Using simple and accessible field-testing methods, this exploratory experiment demonstrates how small changes to riders’ equipment, consummate of the scale of a small change in prosthetics componentry, can affect the performance of an athlete. Prosthetists should consider such opportunities for performance enhancement when possible. Keywords Prostheses, amputee, paracycling, aerodynamics Date received: 20 November 2013; accepted: 11 February 2014
Background Competitive cycling with a disability is typically referred to as ‘Paracycling’.1 In the case of paracyclists with an amputation, such participation often warrants the use of prosthetic limbs for either the upper body to provide support or for the lower body designed to help transfer power through to the pedal/crank interface of the bicycle. While the development of specific prostheses for sports such as running has developed notably with innovations such as energy storage and return technology,2 radical
innovations in cycling prostheses have been far less visible. There is a lack of attention with respect to cycling prosthetics design.3 However, the governing body for Faculty of Science and Technology, Bournemouth University, Poole, UK Corresponding author: Bryce Dyer, Faculty of Science and Technology, Bournemouth University, Poole, BH12 5BB, UK. Email: [email protected]
Downloaded from poi.sagepub.com at UNIV NEBRASKA LIBRARIES on December 10, 2015
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Dyer cycling has still determined that all prostheses used for paracycling will need to be formally approved for use from 2014.4 From this it can be assumed that while underdeveloped in terms of empirical research, the design and subsequent impact of prosthetics upon competitive cycling is of value for exploration. Unlike walking or running, rigidity and stiffness are prime consideration for cycling prosthetic limb design.5 Such stiffness is typically provided in the basic form of a rigid pylon connected directly to the pedal. Traditionally, this pylon was manufactured from metals, but more recently, composites such as carbon fibre have become increasingly common.5 This material allows extensive weight saving compared to steel or aluminium for the same strength.6 In addition, the advantages of using composites are that they allow greater flexibility in the resulting form of the pylon region. This provides an opportunity to consider design solutions utilising improved prosthetic limb aerodynamics. The aerodynamics plays a vital role in competitive cycling.7 At racing speeds, aerodynamic drag can represent up to 96% of the cyclists’ power.8 It has also been found that 31%–39% of the wind resistance or drag is due to the bicycle equipment.9 It is suggested that relatively small modifications to one aspect of a rider’s set-up can influence frontal area and therefore the aerodynamic drag.10 This could ultimately lead to substantial performance improvements.10 However, no study to date has identified the impact of such changes to a rider’s set-up, at a level unique to a paracyclist with a prosthetic limb. Several methods have been proposed as being statistically robust enough to evaluate the aerodynamic properties of cyclists and/or their equipment. Some of these include the use of wind tunnels,11 computational fluid dynamics (CFD) or field testing using linear regression analysis.7 However, while both wind tunnels and CFD with their high degree of accuracy and repeatability could be considered the ‘gold standard’ of aerodynamic measurement, these can both be extremely expensive. Furthermore, wind tunnels are geographically few in number. Finally, a criticism of wind tunnel–based studies is that they do not always have an athlete cycling at a physical intensity respective of competitive events.12 Alternatively, while harder to control the experiment boundary conditions, field testing has been proposed as a more affordable method of assessment, only requiring a power meter device fitted to the bicycle and an environment conducive to such testing.13,14 These environments comprise a flat surface that is undisturbed by traffic such as an aircraft runway or a cycling velodrome.8 Velodromes provide an enclosed and a relatively controllable environment. Like wind tunnels, cycling velodromes are few in number but this can be increased if outdoor velodromes could also be utilised. No study to date has attempted the utilisation of an outdoor velodrome for aerodynamic assessment.
Outdoor field testing has been demonstrated to be statistically robust7,15 and successfully correlated to wind tunnel testing of able-bodied riders.8,15 The model for deriving the aerodynamic drag from field testing was proposed,14 refined8 and finally produced in the form of a spreadsheet for expediency.16 This field-testing model was defined as follows: P× E −
∆PE ∆KE 1 − = CD A ρ S S + µ S g FN ∆t ∆t 2 2 a
g
(
)
P is the power measured at the crank-based power meter, E is the efficiency of the chain-based drivetrain assumed by Martin et al.8 to be 97.7%, PE is the potential energy, t is the time, KE is the kinetic energy, CDA is the combined frontal area of rider and bike, ρ is the air density, Sa2 S g is the product of air speed squared and ground speed, µ is a specified global coefficient of friction (assumed as 0.04), Sg is the ground speed and FN is the force exerted by the bicycle tyres on the road surface (typically the total rider + bike weight). The limitations of outdoor field testing are that it has typically only evaluated large rider position–based changes and not those akin to the sort of component volume a prosthetist would be considering when designing an upper or lower body prosthesis. This introductory study will investigate the projected impact on a rider’s performance when making a controlled change in the frontal area of a cyclist at a smaller level akin to a change in the componentry of a prosthesis using outdoor field-testing methods.
Methods A single male able-bodied candidate who was an experienced competitive cyclist undertook two aerodynamic field experiments. The test candidate was male, 195 cm tall and had a mass of 90 kg. The test rider rode a time trial bicycle with aerodynamic wheels inflated to 827.4 kPa (120 lbf/in2) using a riding position that utilised aerobars, typical of an athlete riding in timed events in competitive cycling. The combined mass of rider and bicycle was 101 kg. All trials were conducted with the same rider, bicycle, clothing and helmet, and institutional ethical approval was obtained for these experiments. A 250 m outdoor cycling velodrome was used as the test environment to assess controlled aerodynamic changes. While an indoor velodrome environment has been proposed as being suitable for aerodynamic field testing,15 no study to date has used an outdoor velodrome using this method. A white line evident around the base of the banked track signified a 250 m circumference which the rider adhered to during the test runs to ensure a repeatable riding distance. Test runs on the velodrome were all performed at a targeted steady-state speed over four
Downloaded from poi.sagepub.com at UNIV NEBRASKA LIBRARIES on December 10, 2015
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Prosthetics and Orthotics International 39(3)
complete laps of the velodrome. One lap (250 m) was used to establish the targeted steady-state speed, two laps (500 m) were then used as the measurement window and one final lap (250 m) was used to allow the rider to slow down to rest and then perform a full dismount/remount of the bicycle. The experiments fell into two parts. The first part involved an experiment set-up to ascertain the participant’s ability to provide repeatable data from the proposed method. This involved 10 runs of the four lap protocol performed at a steady-state speed of 8.94 m/s (20 mile/h). Any potential variability of the experiment was expressed as the average power of the test run divided by the average speed output of the test run and defined as the power/speed ratio (PSR). The absolute consistency of the 10 runs is defined using the coefficient of variation (CV) of the speed/power ratio. The second part of the experiment saw two different conditions used to illustrate the aerodynamic drag changes from a baseline condition (BC) to one whereby a controlled minor aerodynamic penalty is added. These two conditions were as follows: BC. A 10-mm-diameter wooden dowel was mounted across the handlebar which was 1 m in total length with 0.56 m exposed to the side of the bicycle. Change condition (CC). A 10-mm-diameter wooden dowel was mounted across the handlebars which was 1 m in total length with a 120 mm polystyrene sphere mounted on the end of it, and 0.51 m of the dowel is exposed to the air. The sphere was mounted outside the projected aerodynamic influence of the rider themselves by being positioned to the right of the rider as shown in Figure 1. This decision to mount the sphere clear of the rider’s direct influence was based on the fact that the aerodynamics of the rider themselves are highly individual.11 This experiment’s result would therefore not be as relevant to a wider research community if the known change in frontal area was influenced by the individual characteristics of the test participant. A 120-mm polystyrene sphere was selected as its diameter was similar to that which could be evident from a prosthetics socket component used by a paracyclist. This is considerably smaller than gross changes in riding position previously reported using field-testing methods.8 A spherical object was used as this would mean that a consistent frontal area would always be presented to forward motion, irrespective of any movement induced by steering or changes in the wind direction. The model proposed by Martin et al.16 suggests that six steady-state range speeds are obtained across as wide a range as possible. The resulting aerodynamic drag of each run is then averaged overall. This is expressed as a
Figure 1. Sphere mount design.
consequence of the drag coefficient (dimensionless) and the surface area of the shape moving through the air. This is defined as the CDA and is measured in metres squared.7 In these trials, 7 runs were undertaken with 6 being selected for CDA calculation using the method proposed by Martin et al.16 The defined speed targets were in 6–12 m/s range with approximately 0.894 m/s (2 mile/h) difference between each run. These are speeds typical of competitive cyclists with a disability and allowed completion of all runs without the impact of accumulative fatigue to the rider. Higher speeds of 13.41 m/s (30 mile/h) (such as those seen in short-distance paracycling events like the kilometre time trial) would also be desirable but the effort to achieve this proved to be too physically demanding to be able to complete all of the required trials and to maintain the required riding path on the velodrome. However, the final run of both conditions was attempted at the highest sustainable range the rider could complete to ensure the assessed speed range was as wide as possible. To minimise any inconsistency caused by atmospheric changes, the two conditions were alternated through the seven targeted speed ranges. This meant that after each test run, the cyclist stopped, dismounted and then either affixed or removed the 120 mm sphere. A published linear regression technique tool16 was used for the calculation of the CDA. The required field test data captured using this method were the total mass of bike and rider (kilograms), the track length (metres), the velocity at the start of the test interval (metres per second), the velocity at the end of the test interval (metres per second), the average velocity of the test interval (metres per second), an estimation of the friction coefficient of the track surface, average power output (watts) and the rider test interval duration (seconds). The power was recorded at 1 Hz using a bicycle crank power meter (Quarq Technology, Spearfish, SD, USA) which has a manufacturer’s proposed accuracy of ±1.5%. This meter was also calibrated by the author using a 20 kg known mass prior to these experiments.
Downloaded from poi.sagepub.com at UNIV NEBRASKA LIBRARIES on December 10, 2015
235
9.0 8.9 8.8 8.7 8.6 8.5 8.4 8.3 8.2
120mm Sphere R² = 0.997
450 400
No Sphere R² = 0.9954
350 Power (w)
W/m/s Rao
Dyer
1
2
3
4
5
6
7
8
9
300 250 200 150
10
100 50
Figure 2. 10-run test stability.
0 6.00
The 10-run test stability method results are shown in Figure 2. It can be seen that test run 10 exhibited a very low PSR compared to the previous 9 runs. The PSR CV of all 10 runs was 2.1%. However, it was surmised that the boundary conditions of the experiment in run 10 must have significantly changed. If run 10 is excluded from the analysis, the calculated CV of the test variability is greatly reduced to 1.5%. Considering the human/cycle relationship and that the experiments take place outdoors with large scope for environmental condition change, these scores are extremely low, thereby suggesting very high test protocol repeatability. The calculated obtained CDA values were 0.283 for BC and 0.293 for CC. The difference in CDA was therefore 0.01 m2 between BC and CC. It should also be noted that the outboard dowel was 50 mm longer with BC than CC. This is due to 50 mm of the dowel being covered when the sphere is mounted. The impact of this was assumed to be negligible prior to the experiment but for clarification, the extra length of the dowel aerodynamic penalty was calculated theoretically as 0.0005 m2. Therefore, the difference between BC and CC would be proposed as 0.009 m2. A graph of the obtained speed and resultant power of all trials is shown in Figure 3. The obtained fit of the data to a polynomial line (R2) is shown in Figure 3 for both the BC and CC. In addition, as per Experiment 1, any variation in weather or the experiment boundary conditions can be implied by calculating the PSR of each test run. If any divergence in this score is
9.00 10.00 Speed (m/s)
11.00
12.00
13.00
BC: baseline condition; CC: change condition.
35.00
120mm Sphere
30.00 25.00 20.00 15.00 10.00 5.00 0.00
Results
8.00
Figure 3. Power and speed of BC and CC.
w/ m/s
The calculation of air density for the exact time of the test is also required.16 The components for this calculation include the air temperature (degrees Celsius), relative humidity (percentage) and pressure (millibars). They were recorded as 2°C, 100% relative humidity and an air pressure of 1010 hPa. These data were obtained from the closest possible weather station to the test venue. The calculated air density value was 1.276 kg/m3. The wind strength was recorded as very light and
POI0010.1177/0309364614527121Prosthetics and Orthotics InternationalDyer
INTERNATIONAL SOCIETY FOR PROSTHETICS AND ORTHOTICS
Original Research Report
The importance of aerodynamics for prosthetic limb design used by competitive cyclists with an amputation: An introduction
Prosthetics and Orthotics International 2015, Vol. 39(3) 232–237 © The International Society for Prosthetics and Orthotics 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0309364614527121 poi.sagepub.com
Bryce Dyer
Abstract Background/Objectives: This study introduces the importance of the aerodynamics to prosthetic limb design for athletes with either a lower-limb or upper-limb amputation. Study design: The study comprises two elements: 1) An initial experiment investigating the stability of outdoor velodromebased field tests, and 2) An experiment evaluating the application of outdoor velodrome aerodynamic field tests to detect small-scale changes in aerodynamic drag respective of prosthetic limb componentry changes. Methods: An outdoor field-testing method is used to detect small and repeatable changes in the aerodynamic drag of an able-bodied cyclist. These changes were made at levels typical of alterations in prosthetic componentry. The field-based test method of assessment is used at a smaller level of resolution than previously reported. Results: With a carefully applied protocol, the field test method proved to be statistically stable. The results of the field test experiments demonstrate a noticeable change in overall athlete performance. Aerodynamic refinement of artificial limbs is worthwhile for athletes looking to maximise their competitive performance. Conclusion: A field-testing method illustrates the importance of the aerodynamic optimisation of prosthetic limb components. The field-testing protocol undertaken in this study gives an accessible and affordable means of doing so by prosthetists and sports engineers. Clinical relevance Using simple and accessible field-testing methods, this exploratory experiment demonstrates how small changes to riders’ equipment, consummate of the scale of a small change in prosthetics componentry, can affect the performance of an athlete. Prosthetists should consider such opportunities for performance enhancement when possible. Keywords Prostheses, amputee, paracycling, aerodynamics Date received: 20 November 2013; accepted: 11 February 2014
Background Competitive cycling with a disability is typically referred to as ‘Paracycling’.1 In the case of paracyclists with an amputation, such participation often warrants the use of prosthetic limbs for either the upper body to provide support or for the lower body designed to help transfer power through to the pedal/crank interface of the bicycle. While the development of specific prostheses for sports such as running has developed notably with innovations such as energy storage and return technology,2 radical
innovations in cycling prostheses have been far less visible. There is a lack of attention with respect to cycling prosthetics design.3 However, the governing body for Faculty of Science and Technology, Bournemouth University, Poole, UK Corresponding author: Bryce Dyer, Faculty of Science and Technology, Bournemouth University, Poole, BH12 5BB, UK. Email: [email protected]
Downloaded from poi.sagepub.com at UNIV NEBRASKA LIBRARIES on December 10, 2015
233
Dyer cycling has still determined that all prostheses used for paracycling will need to be formally approved for use from 2014.4 From this it can be assumed that while underdeveloped in terms of empirical research, the design and subsequent impact of prosthetics upon competitive cycling is of value for exploration. Unlike walking or running, rigidity and stiffness are prime consideration for cycling prosthetic limb design.5 Such stiffness is typically provided in the basic form of a rigid pylon connected directly to the pedal. Traditionally, this pylon was manufactured from metals, but more recently, composites such as carbon fibre have become increasingly common.5 This material allows extensive weight saving compared to steel or aluminium for the same strength.6 In addition, the advantages of using composites are that they allow greater flexibility in the resulting form of the pylon region. This provides an opportunity to consider design solutions utilising improved prosthetic limb aerodynamics. The aerodynamics plays a vital role in competitive cycling.7 At racing speeds, aerodynamic drag can represent up to 96% of the cyclists’ power.8 It has also been found that 31%–39% of the wind resistance or drag is due to the bicycle equipment.9 It is suggested that relatively small modifications to one aspect of a rider’s set-up can influence frontal area and therefore the aerodynamic drag.10 This could ultimately lead to substantial performance improvements.10 However, no study to date has identified the impact of such changes to a rider’s set-up, at a level unique to a paracyclist with a prosthetic limb. Several methods have been proposed as being statistically robust enough to evaluate the aerodynamic properties of cyclists and/or their equipment. Some of these include the use of wind tunnels,11 computational fluid dynamics (CFD) or field testing using linear regression analysis.7 However, while both wind tunnels and CFD with their high degree of accuracy and repeatability could be considered the ‘gold standard’ of aerodynamic measurement, these can both be extremely expensive. Furthermore, wind tunnels are geographically few in number. Finally, a criticism of wind tunnel–based studies is that they do not always have an athlete cycling at a physical intensity respective of competitive events.12 Alternatively, while harder to control the experiment boundary conditions, field testing has been proposed as a more affordable method of assessment, only requiring a power meter device fitted to the bicycle and an environment conducive to such testing.13,14 These environments comprise a flat surface that is undisturbed by traffic such as an aircraft runway or a cycling velodrome.8 Velodromes provide an enclosed and a relatively controllable environment. Like wind tunnels, cycling velodromes are few in number but this can be increased if outdoor velodromes could also be utilised. No study to date has attempted the utilisation of an outdoor velodrome for aerodynamic assessment.
Outdoor field testing has been demonstrated to be statistically robust7,15 and successfully correlated to wind tunnel testing of able-bodied riders.8,15 The model for deriving the aerodynamic drag from field testing was proposed,14 refined8 and finally produced in the form of a spreadsheet for expediency.16 This field-testing model was defined as follows: P× E −
∆PE ∆KE 1 − = CD A ρ S S + µ S g FN ∆t ∆t 2 2 a
g
(
)
P is the power measured at the crank-based power meter, E is the efficiency of the chain-based drivetrain assumed by Martin et al.8 to be 97.7%, PE is the potential energy, t is the time, KE is the kinetic energy, CDA is the combined frontal area of rider and bike, ρ is the air density, Sa2 S g is the product of air speed squared and ground speed, µ is a specified global coefficient of friction (assumed as 0.04), Sg is the ground speed and FN is the force exerted by the bicycle tyres on the road surface (typically the total rider + bike weight). The limitations of outdoor field testing are that it has typically only evaluated large rider position–based changes and not those akin to the sort of component volume a prosthetist would be considering when designing an upper or lower body prosthesis. This introductory study will investigate the projected impact on a rider’s performance when making a controlled change in the frontal area of a cyclist at a smaller level akin to a change in the componentry of a prosthesis using outdoor field-testing methods.
Methods A single male able-bodied candidate who was an experienced competitive cyclist undertook two aerodynamic field experiments. The test candidate was male, 195 cm tall and had a mass of 90 kg. The test rider rode a time trial bicycle with aerodynamic wheels inflated to 827.4 kPa (120 lbf/in2) using a riding position that utilised aerobars, typical of an athlete riding in timed events in competitive cycling. The combined mass of rider and bicycle was 101 kg. All trials were conducted with the same rider, bicycle, clothing and helmet, and institutional ethical approval was obtained for these experiments. A 250 m outdoor cycling velodrome was used as the test environment to assess controlled aerodynamic changes. While an indoor velodrome environment has been proposed as being suitable for aerodynamic field testing,15 no study to date has used an outdoor velodrome using this method. A white line evident around the base of the banked track signified a 250 m circumference which the rider adhered to during the test runs to ensure a repeatable riding distance. Test runs on the velodrome were all performed at a targeted steady-state speed over four
Downloaded from poi.sagepub.com at UNIV NEBRASKA LIBRARIES on December 10, 2015
234
Prosthetics and Orthotics International 39(3)
complete laps of the velodrome. One lap (250 m) was used to establish the targeted steady-state speed, two laps (500 m) were then used as the measurement window and one final lap (250 m) was used to allow the rider to slow down to rest and then perform a full dismount/remount of the bicycle. The experiments fell into two parts. The first part involved an experiment set-up to ascertain the participant’s ability to provide repeatable data from the proposed method. This involved 10 runs of the four lap protocol performed at a steady-state speed of 8.94 m/s (20 mile/h). Any potential variability of the experiment was expressed as the average power of the test run divided by the average speed output of the test run and defined as the power/speed ratio (PSR). The absolute consistency of the 10 runs is defined using the coefficient of variation (CV) of the speed/power ratio. The second part of the experiment saw two different conditions used to illustrate the aerodynamic drag changes from a baseline condition (BC) to one whereby a controlled minor aerodynamic penalty is added. These two conditions were as follows: BC. A 10-mm-diameter wooden dowel was mounted across the handlebar which was 1 m in total length with 0.56 m exposed to the side of the bicycle. Change condition (CC). A 10-mm-diameter wooden dowel was mounted across the handlebars which was 1 m in total length with a 120 mm polystyrene sphere mounted on the end of it, and 0.51 m of the dowel is exposed to the air. The sphere was mounted outside the projected aerodynamic influence of the rider themselves by being positioned to the right of the rider as shown in Figure 1. This decision to mount the sphere clear of the rider’s direct influence was based on the fact that the aerodynamics of the rider themselves are highly individual.11 This experiment’s result would therefore not be as relevant to a wider research community if the known change in frontal area was influenced by the individual characteristics of the test participant. A 120-mm polystyrene sphere was selected as its diameter was similar to that which could be evident from a prosthetics socket component used by a paracyclist. This is considerably smaller than gross changes in riding position previously reported using field-testing methods.8 A spherical object was used as this would mean that a consistent frontal area would always be presented to forward motion, irrespective of any movement induced by steering or changes in the wind direction. The model proposed by Martin et al.16 suggests that six steady-state range speeds are obtained across as wide a range as possible. The resulting aerodynamic drag of each run is then averaged overall. This is expressed as a
Figure 1. Sphere mount design.
consequence of the drag coefficient (dimensionless) and the surface area of the shape moving through the air. This is defined as the CDA and is measured in metres squared.7 In these trials, 7 runs were undertaken with 6 being selected for CDA calculation using the method proposed by Martin et al.16 The defined speed targets were in 6–12 m/s range with approximately 0.894 m/s (2 mile/h) difference between each run. These are speeds typical of competitive cyclists with a disability and allowed completion of all runs without the impact of accumulative fatigue to the rider. Higher speeds of 13.41 m/s (30 mile/h) (such as those seen in short-distance paracycling events like the kilometre time trial) would also be desirable but the effort to achieve this proved to be too physically demanding to be able to complete all of the required trials and to maintain the required riding path on the velodrome. However, the final run of both conditions was attempted at the highest sustainable range the rider could complete to ensure the assessed speed range was as wide as possible. To minimise any inconsistency caused by atmospheric changes, the two conditions were alternated through the seven targeted speed ranges. This meant that after each test run, the cyclist stopped, dismounted and then either affixed or removed the 120 mm sphere. A published linear regression technique tool16 was used for the calculation of the CDA. The required field test data captured using this method were the total mass of bike and rider (kilograms), the track length (metres), the velocity at the start of the test interval (metres per second), the velocity at the end of the test interval (metres per second), the average velocity of the test interval (metres per second), an estimation of the friction coefficient of the track surface, average power output (watts) and the rider test interval duration (seconds). The power was recorded at 1 Hz using a bicycle crank power meter (Quarq Technology, Spearfish, SD, USA) which has a manufacturer’s proposed accuracy of ±1.5%. This meter was also calibrated by the author using a 20 kg known mass prior to these experiments.
Downloaded from poi.sagepub.com at UNIV NEBRASKA LIBRARIES on December 10, 2015
235
9.0 8.9 8.8 8.7 8.6 8.5 8.4 8.3 8.2
120mm Sphere R² = 0.997
450 400
No Sphere R² = 0.9954
350 Power (w)
W/m/s Rao
Dyer
1
2
3
4
5
6
7
8
9
300 250 200 150
10
100 50
Figure 2. 10-run test stability.
0 6.00
The 10-run test stability method results are shown in Figure 2. It can be seen that test run 10 exhibited a very low PSR compared to the previous 9 runs. The PSR CV of all 10 runs was 2.1%. However, it was surmised that the boundary conditions of the experiment in run 10 must have significantly changed. If run 10 is excluded from the analysis, the calculated CV of the test variability is greatly reduced to 1.5%. Considering the human/cycle relationship and that the experiments take place outdoors with large scope for environmental condition change, these scores are extremely low, thereby suggesting very high test protocol repeatability. The calculated obtained CDA values were 0.283 for BC and 0.293 for CC. The difference in CDA was therefore 0.01 m2 between BC and CC. It should also be noted that the outboard dowel was 50 mm longer with BC than CC. This is due to 50 mm of the dowel being covered when the sphere is mounted. The impact of this was assumed to be negligible prior to the experiment but for clarification, the extra length of the dowel aerodynamic penalty was calculated theoretically as 0.0005 m2. Therefore, the difference between BC and CC would be proposed as 0.009 m2. A graph of the obtained speed and resultant power of all trials is shown in Figure 3. The obtained fit of the data to a polynomial line (R2) is shown in Figure 3 for both the BC and CC. In addition, as per Experiment 1, any variation in weather or the experiment boundary conditions can be implied by calculating the PSR of each test run. If any divergence in this score is
9.00 10.00 Speed (m/s)
11.00
12.00
13.00
BC: baseline condition; CC: change condition.
35.00
120mm Sphere
30.00 25.00 20.00 15.00 10.00 5.00 0.00
Results
8.00
Figure 3. Power and speed of BC and CC.
w/ m/s
The calculation of air density for the exact time of the test is also required.16 The components for this calculation include the air temperature (degrees Celsius), relative humidity (percentage) and pressure (millibars). They were recorded as 2°C, 100% relative humidity and an air pressure of 1010 hPa. These data were obtained from the closest possible weather station to the test venue. The calculated air density value was 1.276 kg/m3. The wind strength was recorded as very light and
