# Pinewood Derby Racecar

**Overall goal:** Use insights from solving dynamics equations to design and make a winning racecar propelled only by gravity on a set track. (We won second place!)

**Summary: **

In the Pinewood Derby car project, students design wooden cars with the intent of achieving maximum velocity (and the fastest race time) in a race down a pre-built track. Certain forces and moments, both conservative and dissipative, act on the car during its travel on the track. These forces and moments both accelerate and decelerate the car. The forces affect the change in energy of the car, which ultimately dictates the velocity of the car. Throughout the Dynamics course, the effects of such forces on moving bodies are studied in detail. Understanding these principles allowed us to design a car with optimum parameters to

maximize velocity.

The track is composed of one angled section, one curved section, and one flat section. The sections are continuous, but the exact equation of motion on each part of the track differs. Throughout the entire motion of the car, the car experiences a number of forces. These forces include gravitational force (weight), normal force, drag force, and frictional force exerted on the wheel as a moment. These forces contribute to changes in the carâ€™s energy and thus affect the motion of the car. Mathematical analysis of energy terms allows for derivation of the EOM for the car, which allows for understanding of how each parameter and force contributes to the motion of the car. Utilizing this information, the student can determine how to alter the parameters of the car in order to optimize its velocity.

Experiments were conducted in the lab in order to measure values for the center of mass, mass moment of inertia (MMOI), drag coefficient, and coefficient of kinetic friction of both a standard car (provided by instructor) and the custom designed car. Ultimately, it was confirmed that the values for each of these parameters were optimized in the custom design versus the standard car.

Through mathematical derivations of the EOMs, it was discovered that a low center of mass would increase the velocity of the car in angled parts of track, while a large mass moment of inertia would decrease the velocity of the car through the curved portion of track. A relatively high mass, however, allows the car a higher acceleration through the curved and angled section of track. Further, equations of motion confirmed that reducing surface area of the car exposed to air would reduce the magnitude of the dissipative drag force. Finally, reduction of the coefficient of friction via lubrication and sanding of axles corresponds to an increase in car velocity.