Monitoring system for electric vehicles (log various sensors, such as consumed power, solar production, speed, slope, apparent wind, etc.)
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Pt = Ph + Pm = max(0, Pp + Pa + k*v + f*wv²)
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Pp = -m*g*vv
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Pa = 1/2*m*(vdt² - v0²)/dt = m*a*(v0 + 1/2*a*dt)
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Pt: total power, in W
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Ph: mechanical human power, in W
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Pm: mechanical motor power, in W ; this is not the electrical power, as the motor has an efficiency lower than 1
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Pp: potential power (in W, due to potential energy change)
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Pa: acceleration power (in W, due to kinetic energy change)
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k: kinetic friction coefficient (dry friction)
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f: fluid friction coefficient (air friction)
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v: velocity, in m/s, assumed to be always positive or zero
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vv: vertical velocity (in m/s, positive when going uphill)
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wv: wind velocity, in m/s (velocity of the wind relatively to the vehicle, projected on the forward direction, can be approximated by wv = v)
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g: gravity constant (-9.8 m.s⁻²)
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m: mass in kg
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vehicle constants:
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- mass (m), including driver, passengers and other payloads ; easy to measure directly
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- kinetic friction coefficient (k) ; difficult to measure, needs to be estimated from monitoring data
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- fluid friction coefficient (f) ; difficult to measure, needs to be estimated from monitoring data
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