Can Lance Armstrong Beat a Healthy Young Male in a Hill-Climbing Bike Race?

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In summary, the estimated power output of Tour-de-France champion Lance Armstrong and a healthy young human male (HYHM) is 500 Watts and 300 Watts respectively. Both riders, with similar weight, frontal area, and coefficient of drag, race up a 6% incline for 5 miles. The winner is Lance, with a margin of victory of 2 minutes and 37.898 seconds. However, the effect of air density at the higher elevation is not accounted for in this problem.
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jpark31
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Homework Statement


1. It has been estimated that Tour-de-France champion Lance Armstrong could generate a sustained 500 Watts of power over a 20-minute period, while a healthy young human male (HYHM) can generate about 300 Watts of power for 20-minutes. Lance and HYHM are going to race (on bicycles) up a hill with a 6% upgrade, that is five miles long, and the elevation at the top of the hill is 5000 feet. Both rider/bicycle combinations weigh 170 lbs, with frontal area 0.36m2 and coefficient of drag 0.88 (values being typical of bicyclists in crouched racing positions). The coefficient of rolling resistance for both bicycles is 0.01. (1) Who gets to the top first? (2) How much longer does it take the loser to make it to the top?

(1) The winner is ______________________________
(2) The winner's margin of victory is:
________________hours __________________minute _________________seconds


Homework Equations


P= FxV
Resistance of Air = ρ/2(coefficient of drag*Frontal area*v^2
Rolling Resistance = coefficient of rolling resistance*W
Grade Resistance = Weight*Grade
p=1.0567 kg/m^3



The Attempt at a Solution


I converted all the units to meters and Newtons. I added all resistances together to find F but since velocity is not known I left it as F=0.16738v^2+12.0092
I then applied P=Fxv equation by plugging in the power for both persons and the force equation above to find the velocity of each.
500=0.16738v^3+12.0092v
300=0.16738v^3+12.0092v

I got
v(lance)=12.7496 m/s
v(HYHM)=10.1982 m/s

With the distance of 5 miles = 8046.72m, I divided the distance by each velocity and got
t(lance)=631.135 seconds
t(HYHM)=789.033 seconds

After subtracting both, the margin of victory is

t= 2 minutes and 37.898 seconds.

Did I do this correctly? Thank you for your responses.
 
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  • #2
Where do you consider the incline? 12N is certainly too low to account for that.
It is probably beyond the scope of this problem, but you could consider that the air at this height won't be as dense as at sea level (with an average height of the track).
 
  • #3
I can't help but wonder now old this problem is!
 

1. How did Lance Armstrong's body adapt to cycling and improve his performance?

Lance Armstrong's body adapted in several ways to cycling. One major factor was his high red blood cell count, which allowed his body to carry more oxygen to his muscles and improve endurance. He also had a lower body fat percentage and a larger heart, which helped him maintain a high power output for longer periods of time.

2. How did Lance Armstrong's training routine contribute to his success?

Lance Armstrong's training routine was extremely rigorous and focused on building endurance and power. He would often train for over 6 hours a day, incorporating both long distance rides and high intensity interval training. Additionally, he would regularly participate in altitude training to increase his red blood cell count and improve his performance at higher elevations.

3. What role did aerodynamics play in Lance Armstrong's success?

Aerodynamics played a crucial role in Lance Armstrong's success. He was known for his aerodynamic body position on the bike, which reduced drag and allowed him to maintain high speeds with less effort. He also used specialized equipment, such as aero helmets and bikes, to further improve his aerodynamics.

4. How did Lance Armstrong's use of performance-enhancing drugs affect his physics performance?

Lance Armstrong's use of performance-enhancing drugs, specifically erythropoietin (EPO), artificially increased his red blood cell count and allowed his body to carry more oxygen. This gave him a significant advantage in endurance events, but it also put extra strain on his body and could have had negative effects on his overall health and performance in the long run.

5. Can Lance Armstrong's success be solely attributed to his physical capabilities?

No, Lance Armstrong's success cannot be solely attributed to his physical capabilities. While his physical abilities and training certainly played a major role, his success was also influenced by factors such as his mental toughness, strategic race tactics, and access to advanced training techniques and equipment. Additionally, his use of performance-enhancing drugs has called into question the integrity of his accomplishments.

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