Introduction to Firearms and Ballistics - John Eric Goff

Three-Year Study of Tour de France Modeling John Eric Goff Lynchburg College CS-AAPT Fall 2005 American Center for Physics College Park, MD November 5, 2005 History of Research Ben Hannas (LC 03) Computational Physics Course Project (Spring 03) Ideas from Giordanos Computational Physics Ben Modeled Two Stages of 2001 Tour de France for Project After May 03 Graduation, Ben and I Modeled Entire 2003 Tour de France American Journal of Physics (May 2004) Ben and I Modeled Entire 2004 Tour de France European Journal of Physics (February 2005) Contacted by Richmond Times-Dispatch and Asked to Model 2005 Tour de France Bens Seminal Idea

Stage 16 of 2005 Tour de France Get stage profiles from www.letour.fr . Convert each profile into a series of inclined planes. Forces on Bike-Rider Combo Weight: W = mg Normal Force: FN = mg cos Bikers Force: Fb = Pb/v Retarding Forces: FR = FD + Fr FD = CDAv2/2 (Drag Force) Fr = rFN (Rolling Friction) Physicists LOVE the Inclined Plane! Parameters Bike-Rider Mass: m = 77 kg Coefficient of Rolling Friction: r = 0.003 Air Density: = 1.2 kg/m3

Drag Coefficient Cross-Sectional Area: CDA = 0.35 m2 ( 0, uphill) CDA = 0.25 m2 ( < 0, downhill) Bikers Power Output 2003 Tour de France Bikers Power Output 2004 Tour de France Other Changes for 2004 Short Stages 0, 4, 16, and 19 Reduce CDA by 20% for Drafting and Sleek Clothing (except stage 16) Model Successes Actual Model Differenc e

% 2003 82h 33 53 82h 32 37 - 01 16 - 0.03% 2004 82h 47 07 82h 44 38 - 02 29 - 0.05% 1h 27 41 1.77%

2003 (2004 82h 33 53 84h 01 34 model ) Angles for 2005 Tour de France Bikers Power Output 2005 Tour de France (Not much change!) On to 2005s Tour de France Differenc Model e Stage Actual 1

0h 20 51 0h 21 59 0h 01 08 5.44% 2 3h 51 31 4h 16 51 0h 25 20 10.94% 3 4h 36 09 4h 57 23

0h 21 14 7.69% 4 1h 10 39 1h 18 23 0h 07 44 10.95% 5 3h 46 00 4h 18 31 0h 32 31

14.39% 6 4h 12 52 4h 45 29 0h 32 37 12.90% We are too slow!!! % What Happened?!? Tailwinds permeated the first week of the race. Wind speeds measured in the 10-20 mph (16-32 km/hr) range. Easy way to account for tailwind increase power input.

How much??? Add Power from Tailwind Terminal speed reached when forward force matches sum of retarding forces. Tailwind means bikers speed relative to air goes down. Only considering the dominate air drag: P b ~ v t3 Add about 50W to main 325W power. Results Stage 1 2 3 4 5 6 7

8 9 10 11 Actual Model Difference % 0h 20 51 0h 21 59 0h 01 08 5.44% 3h 51 31 4h 04 05 0h 12 34 5.43% 4h 36 09 4h 42 43 0h 06 34

2.38% 1h 10 39 1h 18 23 0h 07 44 10.95% 3h 46 00 4h 05 43 0h 19 43 8.72% 4h 12 52 4h 30 49 0h 17 57 7.10% 5h 03 45 5h 04 44 0h 00 59 0.32% 5h 03 54 5h 21 13 0h 17 19 5.70% 4h 08 20 4h 00 41 - 0h 07 39

- 3.08% 4h 50 35 5h 01 39 0h 11 04 3.81% 4h 47 38 4h 26 26 - 0h 21 12 - 7.37% Results (continued) Stage Actual Model Difference % 12

13 14 15 16 17 18 19 20 21 TOTAL 4h 20 06 4h 12 43 - 0h 07 23 - 2.84% 3h 43 14 3h 55 34

0h 12 20 5.52% 5h 43 43 5h 37 48 - 0h 05 55 - 1.72% 6h 06 38 5h 34 42 - 0h 31 56 - 8.71% 4h 38 40 4h 39 00

0h 00 20 0.12% 5h 41 19 5h 22 59 - 0h 18 20 - 5.37% 4h 37 36 4h 36 08 - 0h 01 28 - 0.53% 3h 33 04

3h 37 44 0h 04 40 2.19% 1h 11 46 1h 06 06 - 0h 05 40 - 7.90% 3h 40 57 3h 08 13 - 0h 32 44 - 14.81% 85h 09 17 84h 49 22 - 0h 19 55

- 0.40% Lance Armstrong 7th Straight Tour de France Win! Winning Time: 86h 15 02 3593-Kilometer Race: vave 11.6 m/s 41.7 km/hr 25.9 mph vmax 15.9 m/s 57.2 km/hr 35.5 mph (average for stage 4) Other Tour Races in 2004 (Use 2004 Model) Thanks Brett Taylor at Radford University! Race Actual Differenc Model e

% Giro 3h 41 56 3h 30 21 (stage 1) 0h 11 35 - 5.22% ParisTours 5h 33 03 5h 49 10 (stage 3) 0h 16 07 4.84% LiegeBastogne 6h 20 09 6h 10 52 -Liege (stage 2)

- 0h 09 17 - 2.44%

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