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 multipleyaw angles Disadvantages Cost! 5. CdA as a function of yaw angle 0.250CdA (m2)0.200 0.150 Std aero position Superman position0.100 0.050 0.000 0510Yaw angle (deg)15 6. Validity of wind tunnel testingMartin, 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 = (0.5Va2Vg(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) = 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 Chungs virtual elevation method Adam Hailes 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 forA, not CdA 11. Cd (not CdA) of cyclists at 0 deg of yawSubject 1 2 3 4 5Height (m) 1.63 1.80 1.80 1.75 1.80Weight (kg) 47.6 77.0 74.0 59.9 69.0Yaw angle (degrees) 0 0 0 0 0Frontal area (m2) Total 0.272 0.279 0.290 0.334 0.358Cd (unitless) 0.793 0.718 0.680 0.652 0.655CdA (m2) 0.216 0.200 0.197 0.218 0.23461.8681.071.9387.081.8074.00 0 0 0 0 00.284 0.264 0.310 0.280 0.310 0.2850.705 0.719 0.712 0.763 0.703 0.6720.200 0.190 0.221 0.214 0.218 0.192Mean S.D.0.707 0.043Kyle CR. Cycling Science 1991; Sept/Dec: 51-56. 12. Relationship of CdA to frontal area 0.2500.200 y = 0.380x + 0.096 R = 0.595CdA (m2)0.1500.1000.0500.000 0.0000.1000.200 Frontal area (m2)0.300Kyle CR. Cycling Science 1991; Sept/Dec: 51-56.0.400 13. Cd of model rocketsDeMar 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 idealizedvenue and weather conditions Can be difficult to achieve high precision Time-consuming 16. Coast-down testing: indoorsCV 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: outdoorsCV 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 1Trial 214 12Speed (m/s)10 8 6 4 2 0 0102030 Time (s)405060 19. Coast-down testing using power meter as high frequency data logger Trial 1Trial 260800.0 -0.2Acceleration (m/s2)-0.4 -0.6 -0.8-1.0 -1.2 -1.4 -1.6 -1.8 -2.0 02040Speed2 (m2/s2)100120140160 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 idealizedvenue 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)120002:43.712.22317.017.2220002:44.312.17318.6320002:43.112.26420002:43.1520002:44.2Temperature Baro. Press. (mm Hg) (C)Air density (kg/m3)CdA (m2)29.981.2000.24817.729.981.1980.254316.418.129.981.1970.24612.26318.118.229.981.1960.24812.18301.618.429.981.1960.238Average0.247Std. Dev.0.006CV (%)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-consumingprecision attainable Differentiates between CdA and Crr (mu) Requires idealizedvenue and weather conditions 25. Accuracy of the regression approach SubjectWind tunnel CdA (m2)Field test CdA (m2)Difference (m2)Difference (%)10.2470.252+0.005+2.0%20.2910.269-0.022-7.6%30.2400.241+0.001+0.4%40.2510.2510.0000.0%50.2520.253+0.001+0.4%60.2850.283-0.002-0.7%70.1980.1980.0000.0%Mean0.2520.250-0.002-0.8%S.D.0.0310.0270.0093.1%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 ExpectedMeasuredDifference in aerodynamic drag (N)0.35 0.30 0.25 0.20 0.15 0.100.05 0.00 6.4 cm sphere10.2 cm sphere 28. Determination of Crr via regression testing Crr from Andy's field tests (regression method)0.0060y = 1.087x + 0.000 R = 0.949Y=X0.0050 0.0040 0.0030Continental 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 testingVF 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 drop2) Forearm angle -Down-angled vs. level vs. up-angled3) Elbow width - Wider vs. narrower4) Saddle height - Normal vs. John Cobbs low sit position5) Framesets -Javelin Arcole vs. Cervelo P2T vs. Cervelo P3T6) 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. UVEX9) Clothing - standard skinsuit vs. CS Speedsuit - no shoe covers vs. Lycra shoe covers10) Miscellaneous other tests - other framesets, wheels, helmets, water bottle placement, etc. 30. Centaur Road in Chesterfield, MOThe Centaur Road natural wind tunnel 31. Centaur Road: a natural wind tunnelPhoto courtesy of Mark Ewers 32. Temperature data from 11/2/2008 25 Brunton removed from car and hung on signTemperature (deg C)2015Brunton removed from sign and placed in skinsuitPeriod of data collection105Sun reaches into woods0 6:45:007:15:007:45:008:15:00Time8:45:009:15:00 33. Beware of local variations in environmental conditions!Airport temperature (deg C)30 25y = 1.151x - 0.711 R = 0.95220 15 10 5 0 0510 15 20 Brunton temperature (deg C)2530 34. CdA and Crr determined using the regression method (non-linear fit) WestEast450 400 y = 0.1339x2 + 2.924 R = 0.9989350 Power (W)300 250 200 150CdA = 0.233 0.004 m2 Crr = 0.00387 0.00039100 50 0 02468 Speed (m/s)10121416 35. CdA and Crr determined using the regression method (linear fit) WestEast30 25y = 0.134x + 2.889 R = 0.997Force (N)20 15 CdA = 0.233 0.003 m2 Crr = 0.00382 0.0002910 5 0 0255075100 Speed2 (m2/s2)125150175200 36. CdA and Crr determined using the regression method (worst case scenario) EastWest30 y = 0.135x + 4.064 R = 0.94125Force (N)20 15 CdA = 0.232 0.017 m2 Crr = 0.00515 0.00135105 0 0255075100 Speed2 (m2/s2)125150175200 37. CdA and Crr determined using the regression method (assuming constant wind) EastWest30 y = 0.1356x + 4.000 R = 0.997525Force (N)20 15CdA = 0.233 0.003 m2 Crr = 0.00506 0.00027 Est. wind = 0.49 m/s105 0 0255075100 Speed2 (m2/s2)125150175200 38. Using a power meter as a wind meter 0.5 0.4 y = 0.646x - 0.0331 R = 0.413 P