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Speed correction for the bicycling model

This correction uses a physical biking model based on air resistance, gravity and frictional force. If the user selects the travelling mode "bicycling" within an anisotropic analysis, AccessMod estimates the power needed to achieve the velocity (and therefore, speed) entered by the user in the travelling scenario. Using this power, along with the slope derived from the DEM, AccessMod can predict the final speed at which the cyclist will cross a given cell.

The model implemented in AccessMod assumes that the increased speed due to negative slope does not exceed twice the speed obtained on a flat surface. A realistic mean value for the speed on flat surface can be around 12 km/h, but note that this can vary greatly with physical condition of the biker, the type of bike, and the road conditions.

The bicycle formula is based on a complex physical model in which several parameters were fixed in AccessMod (which cannot be changed by the user), as follows:

• Weight of the cyclist : 80 kg
• Weight of the bicycle : 15 kg
• Rolling resistance coefficient : 0.012
• Frontal area : 0.445 m2
• Wind velocity : 0 km/h
• Temperature : 20°C
• Elevation : 500m
• Transmission resistance coefficient : 0.9

A simplified description of the formula used can read as follows:

power = (velocity * resistanceBike + velocity * velocityTotal * velocityTotal * resistanceAir) / efficiencyTransmission

With:

• velocity =  velocity of the cyclist on a flat surface
• velocityTotal = velocity of the wind + velocity
• resistanceBike = Resistance of the tires and the gravity
• resistanceAir = Frontal area * air density
• efficiencyTransmission = Transmission resistance coefficient
• power = power necessary to have the bike move at the given velocity on flat surface

The final velocity (Velocity, below) is estimated by resolving a non-linear equation with the Newton's method. The non-linear equation is defined with the following: 

Tv = Velocity + Wind velocity

F   = Velocity * (resistanceAir * Tv² + resistanceBike) – efficiencyTransmission * power

F'  = resistanceAir * (3.0* Velocity + Wind velocity) * Tv + resistanceBike

For the Newton technique, we used a maximum tolerance of 0.05 and maximum 10 iterations. If there is no convergence, the result is set to 0.0 kmh. A graphical example of the corrected speeds in function of the slope for that particular speed is shown in Figure 8.

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