Overview of Article

This article will go over the Dynamics Project for Midnight Sun XIV as it stands on 6/18/2019, describing the the physics behind the system, inputs of the system, its projected outputs, and the work left TO DO.

Physics of System 

Midnight Sun can be, at a high level, seen as a vehicle with five forces acting upon it. The force of aerodynamic drag, friction, braking, motors and gravity. Since braking is intentional and no energy is expended in the change of state, it will not be considered for the system (the implementation of regenerative braking not being covered by this topic paper).

This means we can rewrite the state of the car at any given instance as Fmotor + ma = Ffric + Fdrag + Fg, where each of the forces are defined by the following equations

Ffric = Fn * Crr
Fn = m * g * cos(theta) 
Fdrag = 1/2 * rho * CdA * v^2
Fg = m * g * sin(theta)

Finally we get our equation, where m is the mass of cass, g is the acceleration of gravity, v is the vehicle velocity, vwind is the velocity of the wind, Crr is the coefficient of rolling resistance, CdA is the combined drag coefficient (essentially a fudge coefficient to relate the force experienced by the vehicle to its velocity squared), rho is the density of air, and theta is the angle between the ground and the car.
Fmotor = m * g * cos(theta) * Crr + 1/2 * rho * CdA * (v+vwind)^2 + m * g * sin(theta) + ma

With this equation, we can calculate the force requirement for any velocity and acceleration pair, which can then be integrated over time to get the energy requirement of the vehicle.

Inputs of System

With a series of velocities and elevations measured over distance, calculate the instantaneous force requirements (will likely need to calculate the accelerations over each velocity point to get the acceleration values)

Outputs of System

A series of force requirements, which can be queried and integrated to calculate the total energy consumption over a given time.