cycling_physics.py

import math

def to_deg(angle):
    return angle * (180 / math.pi)

def to_rad(angle):
    return angle * (math.pi / 180)

# Environment
airDensity = 1.2234 # kg/m^3
frictionFactor = 0.004 # -
dragCoefficient = 0.7 # -
gravityFactor = 9.81 # m/s^2
windDirection = 310.0 # -
windVelocity = 2.94 # m/s
rollingResistanceCoefficient = 0.0032

# Bike and rider
bikeMass = 10 # kg
riderMass = 80 # kg
dragValues = [{
    "yawAngle": 5,
    "dragArea": 0.258
  },
  {
    "yawAngle": 10,
    "dragArea": 0.257
  }
]

wheelAerodynamicFactor = 0.0044 #-
distanceCovered = 471.8 # m
initialVelocity = 8.27 # m/s
finalVelocity = 8.45 # m/s
rideDirection = 340.0 # -
grade = 0.003 # -
timeToCoverDistance = 56.42 # s
momentOfInertiaOfWheels = 0.14 # kg/m^2
outerTireRadius = 0.557 # m
chainEfficiencyFactor = 0.976 # -
groundVelocity = distanceCovered / timeToCoverDistance # m/s

# Air velocity (V_air)
tangentWindVelocity = windVelocity * math.cos(to_rad(rideDirection) - to_rad(windDirection)) # m/s
airVelocity = groundVelocity + tangentWindVelocity
print("V_air:", airVelocity)

# Yaw angle
normalWindVelocity = windVelocity * math.sin(to_rad(rideDirection) - to_rad(windDirection)) # m/s
yawAngle = to_deg(math.atan((normalWindVelocity / airVelocity)))
print("Yaw angle:", yawAngle)

# Aerodynamic power (P_ad)
cda = ((dragValues[1]["dragArea"] - dragValues[0]["dragArea"]) / (dragValues[1]["yawAngle"] - dragValues[0]["yawAngle"])) * (yawAngle - dragValues[0]["yawAngle"]) + dragValues[1]["dragArea"]
aerodynamicPower = math.pow(airVelocity, 2) * groundVelocity * airDensity * 0.5 * (cda + wheelAerodynamicFactor)
print("P_ad:", aerodynamicPower)

# Rolling resistance power (P_rr)
rollingResistancePower = groundVelocity * math.cos(math.atan(grade)) * rollingResistanceCoefficient * (bikeMass + riderMass) * gravityFactor
print("P_rr:", rollingResistancePower)

# Wheel bearing friction power (P_bfl)
wheelBearingFrictionPower = groundVelocity * (91.0 + 8.7 * groundVelocity) * math.pow(10, -3)
print("P_bfl", wheelBearingFrictionPower)

# Power related to changes in potential energy (P_pe)
potentialEnergyPower = groundVelocity * (bikeMass + riderMass) * gravityFactor * math.sin(math.atan(grade))
print("P_pe", potentialEnergyPower)

# Power related tochanges in kineticenergy (P_ke)
kineticEnergyPower = 0.5 * (bikeMass + riderMass + momentOfInertiaOfWheels / math.pow(outerTireRadius, 2)) * (math.pow(finalVelocity, 2) - math.pow(initialVelocity, 2)) / timeToCoverDistance
print("P_ke", kineticEnergyPower)

# Total power (P_total)
totalPower = (aerodynamicPower + rollingResistancePower + wheelBearingFrictionPower + potentialEnergyPower + kineticEnergyPower) * chainEfficiencyFactor
print("P_total", totalPower)