{"id":21955413,"url":"https://github.com/minhkhang1795/modsimproject3","last_synced_at":"2026-04-29T20:10:48.057Z","repository":{"id":101397232,"uuid":"110785267","full_name":"minhkhang1795/ModSimProject3","owner":"minhkhang1795","description":"Inspired by the famous scene in the movie, Indiana Jones and the Raiders of the Lost Arc, we set about to discover the optimal slope needed to slide a mass from the top of a hill to the position of a hapless grave robber.","archived":false,"fork":false,"pushed_at":"2017-12-12T22:31:39.000Z","size":15812,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":2,"default_branch":"master","last_synced_at":"2025-01-27T23:15:56.437Z","etag":null,"topics":["jupyter-notebook","modeling","modsimpy","python","simulation"],"latest_commit_sha":null,"homepage":"","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/minhkhang1795.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null}},"created_at":"2017-11-15T04:54:23.000Z","updated_at":"2017-12-12T18:53:03.000Z","dependencies_parsed_at":null,"dependency_job_id":"d58571ec-739a-4dd8-b910-e15608e0c0e5","html_url":"https://github.com/minhkhang1795/ModSimProject3","commit_stats":{"total_commits":11,"total_committers":1,"mean_commits":11.0,"dds":0.0,"last_synced_commit":"c5bc41e669c0129dbd84f559a979893c28bc3595"},"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/minhkhang1795%2FModSimProject3","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/minhkhang1795%2FModSimProject3/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/minhkhang1795%2FModSimProject3/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/minhkhang1795%2FModSimProject3/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/minhkhang1795","download_url":"https://codeload.github.com/minhkhang1795/ModSimProject3/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":245007240,"owners_count":20546142,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["jupyter-notebook","modeling","modsimpy","python","simulation"],"created_at":"2024-11-29T07:32:28.204Z","updated_at":"2026-04-29T20:10:48.011Z","avatar_url":"https://github.com/minhkhang1795.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"# ODEINT(iana Jones) and the Raiders of the Lost Semicolon\nInspired by the famous scene in the movie, Indiana Jones and the Raiders of the Lost Arc, we set about to discover the optimal slope needed to slide a mass from the top of a hill to the position of a hapless grave robber, while taking drag and friction into account. We found that a slope of -1.79 gets the mass in question from point A to point B in 1.97 seconds, faster than any other.\n\n![pic](https://github.com/minhkhang1795/ModSimProject3/blob/master/media/pic.jpg)\n\n## The Question\n\nIn order to protect the secrets hidden within the ancient crypts, you are building a trap that involves a large mass of stone sliding down an inclined plane, and towards a hapless intruder. Assuming that point A, the point from which the block is dropped, is 10 meters above the ori gin, and point B, the position of the intruder, is 10 me ters to the right, what slope of the plane gets the object from point A to point B the fastest?\n\n![fig1](https://github.com/minhkhang1795/ModSimProject3/blob/master/media/fig1.PNG)\n\n## The Brick, Mathematically\n\nAs the brick itself is the moving part in question, many\ncomponents of the system depend on the traits we as\nsigned to it. For the purpose of the simulation, we gave\nthe brick dimensions of a 0.15m cube, and assigned it a\nmass of 6.48 kg. We found that the coefficient of drag\non a cube is 0.8, and the coefficient of friction between\nthe brick and the ground, which we decided was made of\nwood, is 0.6.\n\n![free-body-diagram](https://github.com/minhkhang1795/ModSimProject3/blob/master/media/free-body-diagram.PNG)\n\nIn order to simulate this model, we defined a few key\npoints. The force of gravity was determined with the\ngravitational constant (g) and he slope of the hill (θ).\nFriction was calculated using gravity, the slope of the hill\nand the coefficient of friction (μ). Drag was determined\nby the density of air (ρ), object velocity (v), coefficient\nof drag (Cd), and the surface area of a single side (A).\n\n\n![math](https://github.com/minhkhang1795/ModSimProject3/blob/master/media/math.PNG)\n\n## Initial Validation\n\nIn order to make sure our model worked accuratly,\nwe first tracked the position of the brick, without\nfriction and drag, as it traveled down a single de\nfined slope.\n\nOnce we had gotten a reasonable output we com\npared it against hand calculations to make sure our\nmodel matched the actual physics. We then added\nin drag and friction while making sure the results\nremained plausible. We then manually tested a few\npoints between -5 and -1 before finally sweeping\nthrough all slopes within our previous boudaries.\n\n![fig2](https://github.com/minhkhang1795/ModSimProject3/blob/master/media/fig2.PNG)\n\nAfter sweeping through possible slopes, we plotted our results against the duration of the time it took for the brick to travel from point A to point B. We found the op timal slope of a brick cube traveling down a wooden in cline plane to be -1.79. Using this slope it took the brick 1.97 seconds to travel down 10m and right 10m. We found that the shortest past is not nessesarily the fastest when dealing with gravity, friction and drag.\n\n![fig4](https://github.com/minhkhang1795/ModSimProject3/blob/master/media/fig4.PNG)\n\n## Simplifications\n\nThe real world is never perfect, and because of this, we\nmust make a few generalizations about the situation.\n\n* The simulation uses a single, constant coefficient of\nfriction.\n* While the situation we are modelling likely has a curve,\nour model does not. We account for this by ensuring\nthat velocity is conserved from the slope to the hori\nzontal plane.\n* We are modeling a situation where the brick in question\nis perfectly flat, with no surface imperfections.\n* We set the air density and force of gravity equal to that\nat sea level.\n* We are using rough approximations for the drag coeffi\ncient of a cube, and for the coefficient of friction for\nbrick on wood.\n\n![fig5](https://github.com/minhkhang1795/ModSimProject3/blob/master/media/fig5.PNG)\n\n## Limitations\n\n* We only model two dimensions, removing the chance of\nmoving along the z-axis, as a three-dimensional object\nwould.\n* As the results are only tested with equivalent rise and\nrun, the optimal slope could be different under different circumstances.\n* The model fails to account for variations in the coefficient of friction that occur as material, humidity, and\nother similar variables change.\n\n## Future Steps\n\nThough our simulation came up with an answer, there\nare many possible improvements we could make, including:\n* Using a round object rolling down a linear ramp,\nwhich would involve including rotational physics\n* Finding the optimal curve between two points\n* Including a person running away from the sliding brick\nto bring our model closer to reality\n\n## Built With\n\n* [Jupyter Notebook](http://jupyter.org/)\n* Python 3\n\n## Authors\n\n* Kyle Bertram\n* Khang Vu\n* Mika Notermann\n\n## Acknowledgments\n\n* [ModSimPy](https://github.com/AllenDowney/ModSimPy) by Allen Downey\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fminhkhang1795%2Fmodsimproject3","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fminhkhang1795%2Fmodsimproject3","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fminhkhang1795%2Fmodsimproject3/lists"}