Aero testing without a wind tunnel
- 1. Aerodynamic testing without a wind tunnel: from the simple to the sublime Andrew R. Coggan, Ph.D.
- 2. Outline of talk Wind tunnel testing/the physics of cycling Alternatives to wind tunnel testing
- 3. Wind tunnel testing: how do you do it?
- 4. Wind tunnel testing: advantages and disadvantages Advantages Accuracy Precision/sensitivity Speed Ability to test at multiple yaw angles Disadvantages Cost!
- 5. CdA as a function of yaw angle 0.250 CdA (m2) 0.200 0.150 Std aero position Superman position 0.100 0.050 0.000 0 5 10 Yaw angle (deg) 15
- 6. Validity of wind tunnel testing Martin, Milliken, Cobb, McFadden, and Coggan. J Appl Biomech 1998; 14:276-291
- 7. Mathematical model of the physics of cycling PTOT = (PAT + PKE + PRR + PWB + PPE)/Ec PTOT = (0.5ρVa2Vg(CdA + Fw) + 0.5(mt + I/r2)(Vgf2 - Vgi2)/(tf - ti) + VgCrrmtgCOS(TAN-1(Gr)) + Vg(0.091+0.0087Vg) + VgmtgSIN(TAN-1(Gr)))/Ec Where: PTOT = total power required (W) PAT = power required to overcome total aerodynamic drag (W) PKE = power required to change kinetic energy (W) PRR = power required to overcome rolling resistance (W) PWB = power required to overcome drag of wheel bearings (W) PPE = power required to change potential energy (W) ρ = air density (kg/m3) Va = air velocity (relative to direction of travel) (m/s) Vg = ground velocity (m/s) Cd = coefficient of drag (dependent on wind direction) (unitless) A = frontal area of bike+rider system (m2) FW = wheel rotation factor (expressed as incremental frontal area) (m2) mt= total mass of bike+rider system (kg) I = moment of inertia of wheels (kgm2) r = outside radius of tire (m) Vgf = final ground velocity (m/s) Vgi = initial ground velocity (m/s) tf = final time (s) ti = initial (s) Crr = coefficient of rolling resistance (unitless) g = acceleration due to gravity (9.81 m/s2) Gr = road gradient (unitless) Ec = efficiency of chain drive system (unitless) Martin, Milliken, Cobb, McFadden, and Coggan. J Appl Biomech 1998; 14:276-291
- 8. Alternatives to wind tunnel testing Methods not requiring a power meter Frontal area measurements from photographs Coast-down testing Methods requiring a power meter Steady speed/power “Classical” regression method Robert Chung’s virtual elevation method Adam Haile’s short track regression method
- 9. Measuring frontal area: how do you do it? Kyle CR. Cycling Science 1991; Sept/Dec: 51-56.
- 10. Frontal area measurements: advantages and disadvantages Advantages Easy Inexpensive (free) Disadvantages Only provides a value for A, not CdA
- 11. Cd (not CdA) of cyclists at 0 deg of yaw Subject 1 2 3 4 5 Height (m) 1.63 1.80 1.80 1.75 1.80 Weight (kg) 47.6 77.0 74.0 59.9 69.0 Yaw angle (degrees) 0 0 0 0 0 Frontal area (m2) Total 0.272 0.279 0.290 0.334 0.358 Cd (unitless) 0.793 0.718 0.680 0.652 0.655 CdA (m2) 0.216 0.200 0.197 0.218 0.234 6 1.86 81.0 7 1.93 87.0 8 1.80 74.0 0 0 0 0 0 0 0.284 0.264 0.310 0.280 0.310 0.285 0.705 0.719 0.712 0.763 0.703 0.672 0.200 0.190 0.221 0.214 0.218 0.192 Mean S.D. 0.707 0.043 Kyle CR. Cycling Science 1991; Sept/Dec: 51-56.
- 12. Relationship of CdA to frontal area 0.250 0.200 y = 0.380x + 0.096 R² = 0.595 CdA (m2) 0.150 0.100 0.050 0.000 0.000 0.100 0.200 Frontal area (m2) 0.300 Kyle CR. Cycling Science 1991; Sept/Dec: 51-56. 0.400
- 13. Cd of model rockets DeMar JS. National Asssociation of Rocketry Report NAR52094, July 1995.
- 14. Coast-down testing: how do you do it? Method 1: coast down a long, steady hill and record either time or maximal speed. Method 2: coast down from a higher to a lower speed on a constant (flat) grade and record rate of decelleration.
- 15. Coast-down testing Advantages Can be inexpensive (free) Disadvantages Requires idealized venue and weather conditions Can be difficult to achieve high precision Time-consuming
- 16. Coast-down testing: indoors CV across 4 trials for CdA: 0.56% (n = 30 per trial) CV across 4 trials for Crr: 0.59% (n = 30 per trial) CV across 4 trials for CdA: 1.16% (n = 15 per trial) CV across 4 trials for Crr: 1.83% (n = 15 per trial) Candau et al. Med Sci Sports Exerc 1999; 31:1441-1447.
- 17. Coast-down testing: outdoors CV across 12 trials for CdA: 9.2% CV across 12 trials for Crr: 138% Cameron. Human Power 1995; 12:7-11
- 18. Coast-down testing using power meter as high frequency data logger Trial 1 Trial 2 14 12 Speed (m/s) 10 8 6 4 2 0 0 10 20 30 Time (s) 40 50 60
- 19. Coast-down testing using power meter as high frequency data logger Trial 1 Trial 2 60 80 0.0 -0.2 Acceleration (m/s2) -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 -1.6 -1.8 -2.0 0 20 40 Speed2 (m2/s2) 100 120 140 160
- 20. Steady speed/power method: how do you do it? Ride at a steady speed (or power) on a constant (flat) grade while recording average power (or average speed).
- 21. Steady speed/power method Advantages Data analysis is simple Disadvantages Requires idealized venue and weather conditions Does not differentiate between Crr and CdA
- 22. Steady speed/power method employed on an outdoor track Trial No. Distance (m) Time (min:sec) Velocity (m/s) Power (W) 1 2000 2:43.7 12.22 317.0 17.2 2 2000 2:44.3 12.17 318.6 3 2000 2:43.1 12.26 4 2000 2:43.1 5 2000 2:44.2 Temperature Baro. Press. (mm Hg) (C) Air density (kg/m3) CdA (m2) 29.98 1.200 0.248 17.7 29.98 1.198 0.254 316.4 18.1 29.98 1.197 0.246 12.26 318.1 18.2 29.98 1.196 0.248 12.18 301.6 18.4 29.98 1.196 0.238 Average 0.247 Std. Dev. 0.006 CV (%) 2.3% Modified from Table 1 in Coggan AR. Training and racing using a power meter: an introduction. In Level II Coaching Manual: USA Cycling, Colorado Springs, CO, 2003, pp. 123-145.
- 23. “Classical” regression method: how do you do it? Ride at a range of steady speeds on a constant (flat) grade while recording average power (and speed).
- 24. “Classical” regression method Advantages Disadvantages High accuracy and Time-consuming precision attainable Differentiates between CdA and Crr (mu) Requires idealized venue and weather conditions
- 25. Accuracy of the regression approach Subject Wind tunnel CdA (m2) Field test CdA (m2) Difference (m2) Difference (%) 1 0.247 0.252 +0.005 +2.0% 2 0.291 0.269 -0.022 -7.6% 3 0.240 0.241 +0.001 +0.4% 4 0.251 0.251 0.000 0.0% 5 0.252 0.253 +0.001 +0.4% 6 0.285 0.283 -0.002 -0.7% 7 0.198 0.198 0.000 0.0% Mean 0.252 0.250 -0.002 -0.8% S.D. 0.031 0.027 0.009 3.1% Data for subjects 1-6 are from Martin JC et al. Med Sci Sports Exerc 2006; 38:592-597, whereas data for subject 7 are unpublished observations of the presenter.
- 26. Taking the Tom Compton challenge: the experiment
- 27. Taking the Tom Compton challenge: results Expected Measured Difference in aerodynamic drag (N) 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 6.4 cm sphere 10.2 cm sphere
- 28. Determination of Crr via regression testing Crr from Andy's field tests (regression method) 0.0060 y = 1.087x + 0.000 R² = 0.949 Y=X 0.0050 0.0040 0.0030 Continental SS (clinchers) Continental SS + Bontrager RXL TT (clinchers) VF Record (clinchers) Bontrager RXL TT (clinchers) Bad cassette bearings! 0.0020 0.0010 0.0000 0.000 0.001 0.002 0.003 0.004 0.005 0.006 Crr from Al's roller testing VF Record + Tufo S3 Pro (tubulars) Michelin Pro Race 2 SC (clinchers) VF Record (tubular) + Vred Fortezza Tricomp (clincher) Continental Ultra 2000 (clinchers) Bontrager RXL TT (clinchers)
- 29. Aerodynamic comparisons 2005-2010 1) Elbow pad height -10.5 vs. 16.5 vs. 20.5 vs. 24.5 cm of drop 2) Forearm angle -Down-angled vs. level vs. up-angled 3) Elbow width - Wider vs. narrower 4) Saddle height - Normal vs. John Cobb’s “low sit” position 5) Framesets -Javelin Arcole vs. Cervelo P2T vs. Cervelo P3T 6) Wheels - Zipp 808 vs. Hed H3 vs. Campagnolo Shamal (clinchers) - Zipp 808 vs. Mavic iO (tubulars) 7) Tires -VF Record vs. Bontrager RXL TT vs. Continental SS (± caulk) 8) Helmets - Troxel Radius II vs. LG Prologue - LG Rocket vs. Bell Meteor II - LG Rocket (small and medium) vs. Spiuk Kronos vs. UVEX 9) Clothing - standard skinsuit vs. CS Speedsuit - no shoe covers vs. Lycra shoe covers 10) Miscellaneous other tests - other framesets, wheels, helmets, water bottle placement, etc.
- 30. Centaur Road in Chesterfield, MO The Centaur Road “natural wind tunnel”
- 31. Centaur Road: a “natural wind tunnel” Photo courtesy of Mark Ewers
- 32. Temperature data from 11/2/2008 25 Brunton removed from car and hung on sign Temperature (deg C) 20 15 Brunton removed from sign and placed in skinsuit Period of data collection 10 5 Sun reaches into woods 0 6:45:00 7:15:00 7:45:00 8:15:00 Time 8:45:00 9:15:00
- 33. Beware of local variations in environmental conditions! Airport temperature (deg C) 30 25 y = 1.151x - 0.711 R² = 0.952 20 15 10 5 0 0 5 10 15 20 Brunton temperature (deg C) 25 30
- 34. CdA and Crr determined using the regression method (non-linear fit) West East 450 400 y = 0.1339x2 + 2.924 R² = 0.9989 350 Power (W) 300 250 200 150 CdA = 0.233 ± 0.004 m2 Crr = 0.00387 ± 0.00039 100 50 0 0 2 4 6 8 Speed (m/s) 10 12 14 16
- 35. CdA and Crr determined using the regression method (linear fit) West East 30 25 y = 0.134x + 2.889 R² = 0.997 Force (N) 20 15 CdA = 0.233 ± 0.003 m2 Crr = 0.00382 ± 0.00029 10 5 0 0 25 50 75 100 Speed2 (m2/s2) 125 150 175 200
- 36. CdA and Crr determined using the regression method (worst case scenario) East West 30 y = 0.135x + 4.064 R² = 0.941 25 Force (N) 20 15 CdA = 0.232 ± 0.017 m2 Crr = 0.00515 ± 0.00135 10 5 0 0 25 50 75 100 Speed2 (m2/s2) 125 150 175 200
- 37. CdA and Crr determined using the regression method (assuming constant wind) East West 30 y = 0.1356x + 4.000 R² = 0.9975 25 Force (N) 20 15 CdA = 0.233 ± 0.003 m2 Crr = 0.00506 ± 0.00027 Est. wind = 0.49 m/s 10 5 0 0 25 50 75 100 Speed2 (m2/s2) 125 150 175 200
- 38. Using a power meter as a wind meter 0.5 0.4 y = 0.646x - 0.0331 R² = 0.413 P<0.05 Relative apparent wind speed from regression (m/s) 0.3 0.2 0.1 0 Average wind speeds (m/s) iBike: -0.06 ± 0.18 Regr: -0.06 ± 0.18 -0.1 -0.2 -0.3 -0.4 -0.5 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 Relative wind speed from iBike (m/s) 0.3 0.4 0.5
- 40. Wind is thine enemy!!
- 41. Robert Chung’s “virtual elevation” (VE) method: how do you do it? The VE method is really more of a post-hoc analytical approach than it is a formal means of performing field tests. Typically, however, it applied to data collected while riding out-and-back along the same stretch of road or around and around the same loop, while allowing speed and power to vary. Changes in kinetic and potential energy are then taken into consideration in the calculations, leveraging the knowledge that the same point on the road is always at the same elevation to calculate a “virtual elevation” that reflects the true elevation plus any unexplained variability due to, e.g., wind.
- 42. Robert Chung’s VE method Advantages Disadvantages Allows use of wider Data dropouts can be a variety of venues Often faster than regression testing High precision attainable PITA Can often be difficult to differentiate between Δ in CdA and Δ in Crr (mu) Accuracy? Does not account for wind
- 43. City Hall Drive in Ballwin, MO
- 44. Speed, power, and virtual elevation during a representative lap of City Hall Drive Speed (m/s) Virtual elevation (m) Power (W) 500 10 400 5 300 0 200 -5 100 -10 -15 0 3.15 3.35 3.55 Distance (km) 3.75 3.95 Power (W) Speed (m/s) or virtual Elevation (m) 15
- 45. VE profile of 8 laps of City Hall Drive Crr: 0.0038 (assumed) CdA: 0.305 m2 15 Virtual Elevation (m) 10 1 2 4 3 5 5 6 7 8 0 -5 -10 -15 0 1 2 3 4 Distance (km) 5 6 7
- 46. VE profile of 8 laps of City Hall Drive Crr: 0.0057 (assumed) CdA: 0.280 m2 15 Virtual Elevation (m) 10 1 2 5 4 3 5 6 7 8 0 -5 -10 -15 0 1 2 3 4 Distance (km) 5 6 7
- 47. VE profile of 8 laps of City Hall Drive Crr: 0.0019 (assumed) CdA: 0.331 m2 15 Virtual Elevation (m) 10 1 2 5 4 3 5 6 7 8 0 -5 -10 -15 0 1 2 3 4 Distance (km) 5 6 7
- 48. Effect of wind on CdA estimated using the VE approach 150 2007 Actual CdA: 0.208 m2 Apparent CdA: 0.237 m2 Chung CdA: 0.242 m2 100 Virtual Elevation (m) 50 0 2004 Actual CdA: 0.228 m2 Apparent CdA: 0.234 m2 Chung CdA: 0.248 m2 -50 -100 2008 Actual CdA: 0.225 m2 Apparent CdA: 0.238 m2 Chung CdA: 0.231 m2 -150 -200 -250 0 5 10 Distance from start (km) 15 20
- 49. Wind is thine enemy!!
- 50. Adam Haile’s short track regression method: method: how do you do it? Similar to the classical regression approach, Crr and CdA are derived by regressing force on velocity. However, rather than utilizing average values obtained during each “run”, the short track regression method uses each lap-length segment of data extractable from multiple short laps. Since each lap starts and ends in the same place (at least theoretically), variations in potential energy can be ignored. On the other hand, speed is allowed to vary within laps (and must vary across laps), with variations in kinetic energy accounted for in the calculations
- 51. Adam Haile’s short track regression method Advantages Disadvantages High precision Data dropouts can be a attainable Differentiates between CdA and Crr (mu) Allows use of wider variety of venues Faster than regression testing (?) PITA Accuracy? Does not account for wind
- 52. Example data from short track regression testing on an indoor track
- 53. Summary and conclusions A wide variety of methods exist for estimating CdA without use of a wind tunnel. Each has its advantages and disadvantages, with the quality of the data depending more upon attention to detail and access/selection of an appropriate test venue than upon the exact method used. The best choice will therefore depend upon an individual’s specific circumstances.