Car

Introduction

Car is an object defined in car_model.py that consumes a self, m, Crr, CdA, max_force, speed_min_ms, speed_max_ms

With a Car object, we can generate the following:

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

• The maximum velocity of the car at a certain point in the elevation map, 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

The object initialization

6 parameters (excluding self)

m: Mass of the car, defaulted to 720kg

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

CdA: Drag coefficient of the car, defaulted to 0.15

max_force: Max force of the car’s motors, defaulted to 100N

speed_min_ms: Minimum speed to travel, defaulted to 15m/s

speed_max_ms: Minimum speed to travel, defaulted to 45m/s

All values instance variables to be used in functions below, as well as

g = 9.81  # Acceleration due to gravity in m/s^2
rho = 1.225  # Density of air at room temperature

as static variable constants.

Functions

The force_req() function

• Parameters

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

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

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

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

  • timestep: (float) 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: (float) 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: (float) initial speed of car, (m/s)

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

  • theta: (float) angle that must be climbed (radians)

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

• Returns

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

• Note

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

• 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??

Also, considering that v_old is the initial velocity, and since timestepis usually calculated before the function call to be distance/v_old , it does not account for the gradual change of velocity. Throughout the code, we believe that the usage of velocity is inconsistent.

We propose that we use distance to calculate the maximum velocity.

The energy_used() function

• Parameters

  • v_profile: (float list) A list of the same length as the e_profile with each element representing the average velocity (m/s) required for the car to move at each point 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, 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)

• 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.

  • 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

Sample code