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Introduction

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• The force required for the car to accelerate to a certain velocity , using the force_req() method

• The maximum velocity of the car at after some time, starting from a certain point in the elevation map and starting from a certain velocity, using the max_velocity() method

• The energy used by the car to move through the course with the given elevation map and velocity profile, using the energy_used() method

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Crr: Rolling resistance coefficient of the car, defaulted to 0.0015

CdA: Drag coefficient of o f the car, defaulted to 0.15

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The force_req() function

• Parameters

  • v: (Numbersfloat) final velocity of the car to accelerate to, (m/s)

  • vwind: (Numbersfloat) velocity of the wind relative to the car, (m/s)

  • v_old: (Numbersfloat) initial velocity of the car, (m/s)

  • theta: (Numbersfloat) angle that must be climbed (radians) personally don’t understand why “climb” matters and not just angle of elevation

  • timestep: (Numbersfloat) Time between measurements, (s)

    • usually calculated dist / ((v + old_v)/2), dist being the distance between two points in elevation profile, e_profile.

• Returns

  • Fmotor: (Numbersfloat) Force of motors required to accelerate to a certain velocity in a certain time (N)

• Note

  • If v or v_old greater than maximum speed or less than minimum speed, it is caught in the function and whatever is out of bounds is set to maximum speed or minimum speed

  • Ffric, Fdrag , Fg , Fa, and ultimately Fmotor to be all calculated inside the function, using parameters and constants

The max_velocity() function

• Parameters

  • v_old: (Numbersfloat) final velocity initial speed of the car to accelerate to, (m/s)

  • vwind: (Numbersfloat) velocity of the wind relative to the car, (m/s)v_old: (Numbers) initial velocity of the car, (m/s)

  • theta: (Numbersfloat) angle that must be climbed (radians) personally don’t understand why “climb” matters and not just angle of elevation

  • timestep: (Numbersfloat) Time between measurements, (s)

    • usually calculated dist / ((v + old_v)/2), dist being the distance between two points in elevation profile, e_profile.

• Returns

  Fmotor: (Numbers) Force of motors required to accelerate to a certain velocity in

  Returns

  • max_v: (float) Maximum final velocity after a certain time (Nm/s)

• Note

  • If v or v_old greater than maximum speed or less than minimum speed, it is caught in the function and whatever is out of bounds is set to maximum speed or minimum speedFfric, Fdrag , Fg , Fa, and ultimately Fmotor to be all calculated inside the function, using parameters and constants

• We believe that this function has an error.

 max_v = v_old - self.force_req(v_old, vwind=vwind, theta=theta) + self.max_force * timestep

We are doing (velocity) - (force) + (impulse) to get final velocity. What are we doing here??

The energy_used() function

• Parameters

  • v_profile: (Numbers) final velocity of the car to accelerate to, float list) A list of the same length as the e_profile with each element representing the average velocity (m/s)

  • vwind: (Numbers) velocity of the wind relative to the car, (m/s)

  v_old: (Numbers) initial velocity of the car, (m/s)

  • theta: (Numbers) angle that must be climbed (radians) personally don’t understand why “climb” matters and not just angle of elevation

  • timestep: (Numbers) Time between measurements, (s)

    • usually calculated dist / ((v + old_v)/2), dist being the distance between two points in elevation profile, e_profile.

  Returns

  • Fmotor: (Numbers) Force of motors required to accelerate to a certain velocity in a certain time (N)required for the car to move at each section on the e_profile

  • e_profile: (2D float list)

    • Each row represents a section of a course

    • column 0: the pitch/slope/steepness of the section (rad)

    • column 1: the length/distance of the section (m)

  • distance: (float) distance of each section (m/s)

    • we never use this in the function, as we have length of each sections already stored in e_profile. Useless parameter?

• Returns

  • energy: (float) Total energy used if the entire v_profile was to be followed (J)

    • Calculated by summing force_req() * e_profile[point][1] (length of section at index point) for each point/section in v_profile and e_profile.

• Note

  • If v or v_old greater than maximum speed or less than minimum speed, it is caught in the function and whatever is out of bounds is set to maximum speed or minimum speed

  • Ffric, Fdrag , Fg , Fa, and ultimately Fmotor to be all calculated inside the function, using parameters and constants

Sample code

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• • .

  • Error if the length of v_profile and e_profile do not match

  • In the objective function (shown below) that we are trying to minimize, it basically returns the value of energy_used()function. Thus in Optimizer we are trying to minimize the return value of energy_used()

def objective(v_profile):
        energy = car.energy_used(v_profile, elev_profile, distance=dist_step)  
        return energy / 1000000