如果其他所有条件都相同（并且我的计算是正确的话），那么仅空气密度就会对速度产生相当大的影响。
根据方程式和本页关于循环空气动力学的信息，以及Wolfram Alpha的空气密度值，我得出了：
At 300 watts, at 0*C, will travel at 39.34 km/h
At 300 watts, at 10*C, will travel at 40.06 km/h
At 300 watts, at 20*C, will travel at 40.77 km/h
At 300 watts, at 30*C, will travel at 41.46 km/h
At 300 watts, at 40*C, will travel at 42.14 km/h
这是基于“滴中”阻力系数/额叶面积值的，该值位于海平面上的一致水平上（我认为是在海平面上，尚不确定）
换一种方式：
To travel at 13.8m/s in 0*C requires 478.45 watts
To travel at 13.8m/s in 10*C requires 461.43 watts
To travel at 13.8m/s in 20*C requires 445.52 watts
To travel at 13.8m/s in 30*C requires 430.72 watts
To travel at 13.8m/s in 40*C requires 417.03 watts
（13.8m / s约为50km / h，任意数）
为了“展示我的工作”，这是我用来计算上述内容的Python脚本：
#!/usr/bin/env python2
"""Impact on air-density on cycling speeds
Written in Python 2.7
"""
def Cd(desc):
"""Coefficient of drag
Coefficient of drag is a dimensionless number that relates an
objects drag force to its area and speed
"""
values = {
"tops": 1.15, # Source: "Bicycling Science" (Wilson, 2004)
"hoods": 1.0, # Source: "Bicycling Science" (Wilson, 2004)
"drops": 0.88, # Source: "The effect of crosswinds upon time trials" (Kyle,1991)
"aerobars": 0.70, # Source: "The effect of crosswinds upon time trials" (Kyle,1991)
}
return values[desc]
def A(desc):
"""Frontal area is typically measured in metres squared. A
typical cyclist presents a frontal area of 0.3 to 0.6 metres
squared depending on position. Frontal areas of an average
cyclist riding in different positions are as follows
http://www.cyclingpowermodels.com/CyclingAerodynamics.aspx
"""
values = {'tops': 0.632, 'hoods': 0.40, 'drops': 0.32}
return values[desc]
def airdensity(temp):
"""Air density in kg/m3
Values are at sea-level (I think..?)
Values from changing temperature on:
http://www.wolframalpha.com/input/?i=%28air+density+at+40%C2%B0C%29
Could calculate this:
http://en.wikipedia.org/wiki/Density_of_air
"""
values = {
0: 1.293,
10: 1.247,
20: 1.204,
30: 1.164,
40: 1.127,
}
return values[temp]
"""
F = CdA p [v^2/2]
where:
F = Aerodynamic drag force in Newtons.
p = Air density in kg/m3 (typically 1.225kg in the "standard atmosphere" at sea level)
v = Velocity (metres/second). Let's say 10.28 which is 23mph
"""
def required_wattage():
"""What wattage will the mathematicallytheoretical cyclist need to
output to travel at a specific speed?
"""
position = "drops"
for temp in (0, 10, 20, 30, 40):
v = 13.8 # m/s
F = Cd(position) * A(position) * airdensity(temp) * ((v**2)/2)
watts = v*F
print "To travel at %sm/s in %s*C requires %.02f watts" % (v, temp, watts)
def speed_from_wattage():
"""Given a specific force output, how fast will a
mathematicallytheoretical cyclist travel?
"""
from math import sqrt
position = "drops"
for temp in (0, 10, 20, 30, 40):
# Calculate some reasonable number for F... I think..? Made
# sense when I wrote it, but now slightly confusing
v = 13.8 # m/s
watts = 300
F = watts/v # because watts=v*F
# "F = CdA p [v^2/2]" solved for "v" with sympy:
"""
from sympy import symbols, solve, Eq
F, Cd, A, airdensity, v = symbols("F Cd A airdensity v")
solve(Eq(F, Cd * A * airdensity * (v**2/2)), v)
"""
v = sqrt(2) * sqrt(F / (Cd(position) * A(position) * airdensity(temp)))
v_in_km_h = ((v * 60*60)/1000)
print "At %s watts, at %d*C, will travel at %.02f km/h" % (
watts, temp, v_in_km_h)
if __name__ == '__main__':
speed_from_wattage()
required_wattage()