Badger 3

  • July 2020
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Step 1: Calculate your Drag Coefficient (CdA) with an assumed Crr V1.0 prepared by Robert Jordan ([email protected]) October 2007

Input known variables Change assumed values if you want (Crr might range from .004 to about .007 for racing tires) Don't mess with calculated values Example Data (replace with yours) Bike Orca Cervelo MTB Wheels FP40 Am.Cl.60s Knobby Skinsuit? N Y N Aero Helmet N Y N Test Course Course 1 Course 2 Course 2 Date 10/30/2007 10/1/2007 10/2/2007 Weight of bike and rider (lbs) 173.0 174.0 180.0 Air temperature (celcius) 18.30 26.67 79.00 Relative humidity (%) 50 70 62 Barometric pressure (hPa) 1028 1030 1028 Start Speed (mph) 18.5 20.1 15.0 Finish Speed (mph) 22.4 22.1 18.0 Distance (mi) 0.31 0.61 0.61 Time (sec) 49.5 85.0 110.0 Road slope (ft/ft) 0.0140 -0.0313 -0.0313 Transmission coefficient (efficiency) 0.97 0.97 0.95 Measured average power (watts) 354 0 0 Assumed rolling resistance (Crr) 0.01 0.01 0.01 0.01 Total weight (kg) 78.46 78.91 81.63 0.00 Acceleration (m/s^2) 0.079 0.024 0.027 #DIV/0! Accel Force = mass x acceleration (N) 6.2 1.9 2.2 #DIV/0! Effective average power (watts) 343 0 0 0 Air density (kg/m^3) 1.225 1.187 0.912 #DIV/0! Average speed (mph) 22.76 25.62 19.80 #DIV/0! Average speed (m/s) 10.18 11.45 8.85 #DIV/0! Rider propelling force, Fr (N) 33.74 0.00 0.00 #DIV/0! Gravity force on rider/bike, Fs (N) 769.67 774.12 800.82 0.00 Slope resistance force (N) 10.78 -24.23 -25.07 0.00 Rolling resistance force (N) 3.85 3.87 8.01 0.00 Wind resistance force (N) 19.04 20.34 17.03 #DIV/0! CdA (m^2) 0.300 0.261 0.477 #DIV/0!

0.01 0.00 #DIV/0! #DIV/0! 0 #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0.00 0.00 0.00 #DIV/0! #DIV/0!

Air Density Calculation Temperature (Tc) Relative Humidity (RH) Barametric Pressure (P) Temperature Kelvin (Tk) Saturation Vapour Pressure (Es) Vapour Pressure (E) Virtual Temperature (Tv) Air Density (kg/m^3)

18.30 50.0 1,028.0 291.3

26.67 70.0 1,030.0 299.7

79.00 62.0 1,028.0 352.0

0.00 273.0

0.00 273.0

21.00

34.89

453.83

6.11

6.11

10.50 292.4 19.4 1.225

24.42 302.4 29.4 1.187

281.38 392.6 #DIV/0! #DIV/0! 119.6 #DIV/0! #DIV/0! 0.912 #DIV/0! #DIV/0!

There are ways to measure Crr that I will add in later versions.

Sum Total

1.52 244.5 0.068 22.42 0.01 0.00 #DIV/0! #DIV/0! 0 #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0.00 0.00 0.00 #DIV/0! #DIV/0!

0.01 0.00 #DIV/0! #DIV/0! 0 #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0.00 0.00 0.00 #DIV/0! #DIV/0!

0.01 0.00 #DIV/0! #DIV/0! 0 #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0.00 0.00 0.00 #DIV/0! #DIV/0!

0.01 0.00 #DIV/0! #DIV/0! 0 #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0.00 0.00 0.00 #DIV/0! #DIV/0!

0.01 0.00 #DIV/0! #DIV/0! 0 #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0.00 0.00 0.00 #DIV/0! #DIV/0!

Distance (mi) Time (sec) Time (hr) Ave speed (mph)

0.00 273.0

0.00 273.0

0.00 273.0

0.00 273.0

0.00 273.0

6.11

6.11

6.11

6.11

6.11

#DIV/0! #DIV/0! #DIV/0!

#DIV/0! #DIV/0! #DIV/0!

#DIV/0! #DIV/0! #DIV/0!

#DIV/0! #DIV/0! #DIV/0!

#DIV/0! #DIV/0! #DIV/0!

Celcius % hPa Kelvin hPa hPa Kelvin Celcius kg/m3

Step 2: analyze courses or sections (I plagiarized a few parts of this page of the spreadsheet from the web several years ago, but I have

Typical A2 values 0.356 standing

no idea where it came from. I've verified the equations and changed some parts of it).

Course: 41@Old Forsyth Rd to 41@King Road

Static Conditions(each segment below is a steady-state calculation)

0.267 upright (hands on bar tops)

Rider Name: Robert Jordan 0.233 crouch (hands on drops, elbows locked) Rider weight (lbs): 154.0 (rider, clothes, etc.) 0.167 racing crouch (hands on crops, elbows bent) If evaluating a variable course, use a segment for each climb, flat, descent, Rider weight (kg): 69.9 0.145 full downhill tuck etc. to model the entire course. Create more colums if you need them. Equip't weight (lbs): 18.5 (bike, bottles, bags, etc.) 0.120 end of pack of 1 or more riders Equipment weight (kg): 8.4 0.100 in the middle of a pack Temperature (F): 63 Go here to get your weather data: Enter 0 for distance in unused columns but Relative humidity (%): 43 Weather For You leave 100 watts in power row to prevent error Barometric pressure (P): 1022 29-Nov-07 4pm Air density (kg/m^3): 1.223 Transmission coefficient: 0.97 Use 0.95 for a dirty, greasy drivetrain with lower quality components; 0.975 for new clean Campy Record; 0.98 for track bike Rolling resistance coefficient (Crr): 0.01 Use .004 for best case, .005 for more realistic, and .006 or .007 for poor Segment: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Input conditions: Segment desc. 40k flat TT grade (ft/ft): 0 0 0 0 0 0 0 0 0 0 0 0 0 0 headwind: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24.85 distance (mi) 24.854 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 265 power (watts): 265 100 100 100 100 100 100 100 100 100 100 100 100 100 Iterate Cd and A toCd 0.6900 0.7720 0.7720 0.7720 0.7720 0.7720 0.7720 0.7720 0.7720 0.7720 0.7720 0.7720 0.7720 0.7720 get desired CdA A (m^2): 0.3750 0.3880 0.3880 0.3880 0.3880 0.3880 0.3880 0.3880 0.3880 0.3880 0.3880 0.3880 0.3880 0.3880 CdA 0.259 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300 A2: 0.158 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0 Climb, ft: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Aero force, N 19.39 9.58 9.58 9.58 9.58 9.58 9.58 9.58 9.58 9.58 9.58 9.58 9.58 9.58 Gravity force, N 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Results: Rolling force, N 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 3.84 24.76 Speed (mph) 24.76 16.17 16.17 16.17 16.17 16.17 16.17 16.17 16.17 16.17 16.17 16.17 16.17 16.17 1:00:14 Time (h:m:s) 1:00:14 0:00:00 0:00:00 0:00:00 0:00:00 0:00:00 0:00:00 0:00:00 0:00:00 0:00:00 0:00:00 0:00:00 0:00:00 0:00:00 1003 KCalories 1003 0 0 0 0 0 0 0 0 0 0 0 0 0 266.0 watt-hrs: 266 0 0 0 0 0 0 0 0 0 0 0 0 0

headwind Six iterations of Newton's method:

f6 0.0000 headwind (m/s) 0.0000 starting v: 20.0000 f 1085.6453 f' 193.7311 v1 (m/s) 14.3961 f 270.3188 f' 102.2249 v2 (m/s) 11.7518 f 44.8639 f' 69.3996 v3 (m/s) 11.1053 f 2.2887 f' 62.3849 v4 (m/s) 11.0686 f 0.0071

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 21 1680.08 246.20 14.18 479.24 114.27 9.98 123.50 58.60 7.87 22.65 37.91 7.28 1.51

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

15

16

17

18

0 0 0.000 100 0.7720 0.3880 0.300 0.183 0 9.58 0.00 3.84 16.17 0:00:00 0 0

0 0 0.000 100 0.7720 0.3880 0.300 0.183 0 9.58 0.00 3.84 16.17 0:00:00 0 0

0 0 0.000 100 0.7720 0.3880 0.300 0.183 0 9.58 0.00 3.84 16.17 0:00:00 0 0

0 0 0.000 100 0.7720 0.3880 0.300 0.183 0 9.58 0.00 3.84 16.17 0:00:00 0 0

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

f' v5 (m/s) f f' v6 (m/s)

61.9987 11.0685 0.0000 61.9975 11.0685

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

Weight, rider (N): 685.02 Weight, bike (N): 82.29

efficiency: basal metab

0.25 4.02 1.4 w/kg

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

Rider, kg (rider weight, kg Total wt (N)=Crr*N(total) x 1.4?) 767.31 70 98 3.84 Crr (N)

32.94 7.23 0.01 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

Air Density Calculation Temperature (Tc) Relative Humidity (RH) Barametric Pressure (P) Temperature Kelvin (Tk)

17.22 43.0 ### 290.2

Saturation Vapour Pressure (Es) 19.62 19

20

21

0 0 0.000 100 0.7720 0.3880 0.300 0.183 0 9.58 0.00 3.84 16.17 0:00:00 0 0

0 0 0.000 100 0.7720 0.3880 0.300 0.183 0 9.58 0.00 3.84 16.17 0:00:00 0 0

0 0 0.000 100 0.7720 0.3880 0.300 0.183 0 9.58 0.00 3.84 16.17 0:00:00 0 0

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

0.000 0 20 1445.25 223.66 13.54 409.50 104.56 9.62 103.11 54.72 7.74 17.55 36.74 7.26 0.95

Vapour Pressure (E) Virtual Temperature (Tv) Air Density (kg/m^3)

8.44 291.1 18.1 1.223

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

32.80 7.23 0.00 32.57 7.23

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