At the very highest level, a vehicle’s performance around any circuit applies Newton’s Second Law, F = ma, coupled with some equations of motion. The description that follows below is basically how vehicle dynamics simulations work.
Starting with the equations of motion, the motion of a vehicle around a circuit is dynamic, where the vehicle travels through three-dimensional space over time. If we break this motion through space into smaller and smaller time intervals, we can start to think about the vehicle’s state for each time interval as having a set of initial and final conditions.
When the time intervals are reasonably small enough, it is possible to approximate the change in the vehicle state from the initial to final conditions as a constant acceleration problem. Using this approximation, we can apply the SUVAT equations of motion from physics to get from the initial vehicle state to the final vehicle state. SUVAT is an acronym where s = displacement, u = initial velocity, v = final velocity, a = acceleration, and t = time.
For now, we will assume we already know the vehicle’s acceleration, so if we also know the initial velocity and time step, we can apply the second SUVAT equation to calculate the vehicle’s displacement during the time step, i.e. s = ut + ½ at2. In addition, we can apply the first SUVAT equation, v = u + at, to calculate the final velocity of the vehicle at the end of the time step. For the following time step, the initial velocity is the final velocity from the previous time step, and we can proceed to evaluate each time step sequentially. However, we cannot do this until we know the vehicle’s acceleration for each of these time steps!
We now need to consider Newton’s Second Law. From the above application of the equations of motion, we can see that the velocity of a vehicle at any point around a circuit is governed by the vehicle’s ability to accelerate; therefore, it is best to think of Newton’s Second Law expressed in terms of acceleration, i.e. a = F/m. We must consider this equation as the acceleration equaling the sum of all forces (total force) divided by the mass. These total forces include those available for propulsion and those forces resisting propulsion.
For example, a block sitting on an incline will have two forces acting on it: a gravitational force and a frictional force. The component of the gravitational force that is parallel to the incline’s surface will pull the block…
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