When we draw, we use a combination of lines and curves to form shapes and details to ultimately create a fun picture. Lines and curves can be used for more than just drawing though; they are used by engineers and scientists to understand and describe how things work! There are over 100 different types of curves that mathematicians have named and defined that are used to help understand our world.
Most of us are familiar with circles, lines, and probably ellipses. But have you ever heard of a hyperbola? A hyperbola is another type of mathematical curve that consists of a pair of identical curves that look like the limb of a bow and arrow. The two curves are mirror images about a central axis. Hyperbolas can be seen in space flight when using a maneuver called a gravitational slingshot. This maneuver uses the gravity of another planet or astronomical object to change the speed and path of a spacecraft. The path followed by the spacecraft is a hyperbola! A gravitational slingshot is typically used to reduce fuel consumption and save money.
In this project, the angled rod (part N) traces the shape of a hyperbola when rotated, which you can see in the vertical wooden board (A). How might the shape of the hyperbola change if you were to tilt the rod at a different angle? What shape would you draw if the rod was kept vertical? Horizontal? Test it out by carefully removing the vertical board! Make sure the central rod (M) is clamped well at the base to ensure the rod remains upright.