獨木舟物理模擬器 Canoe Physics Simulator
基於 2D 射影幾何代數的流體與剛體物理模型 Fluid & Rigid Body Physics Model based on 2D PGA
利用 2D PGA 幾何代數，模擬獨木舟在水流中的前進、側滑、旋轉與拉槳施力。您可以藉由調整各項流體力學參數，觀察獨木舟受力後的動態反應。
Simulate canoe translation, lateral slip, rotation, and stroke forces using 2D PGA. Adjust hydrodynamic parameters to observe dynamic behaviors of the canoe.
免責聲明：Disclaimer: 本模擬器為獨立開發之學用工具。其所模擬之船體在亂流、回流區 (Eddy) 或急流中之軌跡與力學回饋為二維剛體物理之簡化數學模型計算，不代表安全保證。實際划行時，亂流與湧浪為複雜的三維水力學動態，划行者不可將模擬器動態作為實際下溪之安全判斷依據。 This simulator is an independently developed academic modeling tool. Trajectories and mechanical responses in turbulence, eddies, and rapids are calculated via simplified 2D rigid-body mathematics; no safety guarantee is implied. Real whitewater involves complex 3D hydrodynamic dynamics and should not be judged solely from 2D simulated models.
方法論說明 (Methodology)：Methodology: 本模擬器基於 2D 射影幾何代數 (Projective Geometric Algebra, PGA) 框架開發，將船體模擬為剛體，並利用簡化的流體阻力與槳葉推力模型，計算旋轉力矩與漂移阻力之動態方程式。 Developed on the 2D Projective Geometric Algebra (PGA) framework, modeling the kayak as a rigid body with simplified hydrodynamic drag and stroke thrust equations to calculate dynamic torque and drift resistance.
即時物理模擬 Real-time Simulation
點擊下方按鈕以全螢幕啟動模擬器進行操作
Click the button below to launch the simulator in fullscreen mode
2D PGA 獨木舟物理模擬器 2D PGA Canoe Physics Simulator
此模擬器整合流線破水前進、船側阻尼、原地打轉等真實流體動力。
點擊啟動即可展開全螢幕並隱藏選單，進行極致順暢的物理演練。 Simulates forward hydrodynamic displacement, lateral hull damping, and pivot rotations.
Click to launch in full screen for an immersive physics simulation.
作者介紹 About the Author
蘇于瑞 (Yu-Jui Su)
台灣新生代極限運動冒險家 / 激流獨木舟選手 Extreme Adventure Athlete & Whitewater Kayaker
國立台灣大學數學研究所碩士，專長幾何分析。同時身為台灣極限運動冒險界頂尖新星，在激流獨木舟與戶外探索領域具備卓越實務技術。 M.S. in Mathematics from National Taiwan University, specializing in geometric analysis. An elite rising star in Taiwan's outdoor adventure community with expert skills in whitewater kayaking and alpine exploration.
曾多次遠赴日本、義大利及法國阿爾卑斯山激流河段進行深度遠征與極限探索，並在多項國內外業餘賽事中取得優異名次。他結合自身學術底蘊與運動專長，將流體力學與 PGA 幾何代數模型直觀呈現在網頁物理模擬中。 He has led expeditions across technical whitewater in Japan, Italy, and the French Alps. Blending deep mathematical rigor with practical kayaking mastery, he transformed fluid mechanics and PGA geometric algebra into an interactive web physics engine.
幾何代數物理引擎原理 Physics Design & Principles
本物理引擎簡化划船為剛體動力系統，由 面幾何代數 (Plane-based geometric algebra, PGA) 打造。PGA最有趣的地方在於幾何物件（點、線）也代表著變換（旋轉、鏡射），我們能不能想像划船的”力“是一個幾何物件呢？
對於一個剛體，我們用方向及起點來描述一個力，方向及起點可以決定一條線，當我們沿著這條線挪動力的起點時，我們發現對剛體產生的作用是一樣的，所以我們在此把力當作一條線吧！參考文章：bivector.net/PGADYN.html
This physics engine models paddling as a rigid body dynamical system built on Plane-based Geometric Algebra (PGA). The most fascinating aspect of PGA is that geometric objects (points, lines) also represent transformations (rotations, reflections). Can we imagine the "force" of paddling as a geometric object?
For a rigid body, we describe a force with a direction and a starting point, which defines a line. By sliding the force vector along its line of action, we find that the effect on the rigid body remains unchanged. Therefore, let us treat force as a line here! Reference article: bivector.net/PGADYN.html