BPHO Computational Challenge 2024

Parabolas in Motion

15°30°45°60°75°

u = 10 m/s · h = 0 m · g = 9.81 N/kg45° lands furthest: 10.19 m

Tasks

Nine Simulations

My solutions to the nine tasks: each one's a simulation you can play around with. :)

01Simple ProjectileCalculates the trajectory of a projectile given its initial speed, launch angle, gravity and height.Open simulation 02Analytical ProjectileThe same trajectory, but this time using an analytical approach and plotting it like a parabola.Open simulation 03(X, Y) coordinatesShows the low and high ball curves that go through a pair of coordinates, as well as the minimum speed trajectory that still reaches them.Open simulation 04Maximum RangeShows the trajectory with the maximum horizontal range for a given speed, as well as a generic one whose angle and speed can be varied.Open simulation 05Bounding ParabolaCombines the previous two (Challenges 3 and 4), as well as including the bounding parabola.Open simulation 06Distances travelledBuilds on the previous simulation to include the distance (not vertical or horizontal displacement) travelled by the projectile.Open simulation 07Projectile RangesModels how the range of the projectile from the launch position varies over time, depending on the angle it's projected at.Open simulation 08Bouncing BallCompares the trajectories of multiple bouncing balls, taking into account the coefficient of restitution.Open simulation 09Air Resistance ModelCompares a drag-free model with one that takes air resistance into account - here it's modelled as proportional to velocity squared.Open simulation

Extensions

E13D Projectile From Spherical PlanetLong-range launches from a rotating planet, plotted on a 3D globe. This time gravity follows an inverse-square law.E2Atmosphere Density Projectile ModelAir resistance again, but now the air gets thinner as the projectile climbs, instead of a constant-density model.

About the code

Tools Used

JavaScript + Next.js

I used Javascript to create this website and its functionality, with NextJS - a React Framework that created modules for everything so that code could effectively be reused and make the site more efficient.

D3 for the Graphs

To create the simulations I used D3 - a NodeJS library that allows you to create custom graphs with more control than other high-level graphing libraries allow, which helped me to incorporate animations and interactivity into the plotting of the data.

Origins

This was originally my (Arushi Sachdeva’s) submission for the BPHO Computational Challenge 2024. In the end, I got a Gold award, and I'm maintaining the website so it can be used as an educational resource for anyone who needs it.