🪂 终端速度计算器Terminal Velocity Calculator

使用说明与常见问题How-to & FAQ

「终端速度计算器」是什么？What is the Terminal Velocity Calculator tool?

按 v = √(2mg ÷ (ρ·A·C_d)) 计算物体在空气（或其他流体）中下落的终端速度，可选常见形状的阻力系数，结果给出 m/s、km/h 和 mph，以及达到约 95% 终端速度所需的大致时间。Calculate the terminal velocity of a falling object, v = √(2mg ÷ (ρ·A·C_d)), with drag coefficients for common shapes, in m/s, km/h and mph, plus the rough time to reach about 95% of it.

如何使用「终端速度计算器」？How do I use the Terminal Velocity Calculator tool?

在「终端速度计算器」中，填写「质量 kg」、「迎风面积 m²」、「阻力系数 C_d」、「自定义 C_d」、「流体密度 kg/m³（海平面空气 1.225）」等参数，结果会随输入实时计算并显示在下方。In the Terminal Velocity Calculator: Fill in "Mass kg", "Projected area m²", "Drag coefficient C_d", "Custom C_d", "Fluid density kg/m³ (sea-level air 1.225)"; results are recalculated instantly as you type.

用的是什么公式？What is the formula?

终端速度时重力等于空气阻力：mg = ½ρv²AC_d，所以 v = √(2mg ÷ (ρAC_d))。ρ 默认 1.225 kg/m³，是国际标准大气（ISA）海平面 15 °C 的空气密度。At terminal velocity gravity equals drag: mg = ½ρv²AC_d, so v = √(2mg ÷ (ρAC_d)). The default ρ = 1.225 kg/m³ is International Standard Atmosphere sea-level air at 15 °C.

跳伞者的阻力系数准吗？How good are the skydiver drag values?

只是粗略值。人体姿态、衣服和面积估计都会明显影响结果；默认值 80 kg、0.7 m²、C_d 1.0 只是示例，算出约 43 m/s，比常被引用的俯身跳伞约 55 m/s（Huang, The Physics Factbook, 1998；维基百科「Terminal velocity」引用）低约 20%，说明这组面积和阻力系数偏大，只能当粗略估计。They are rough. Body position, clothing and the area estimate all matter. The defaults (80 kg, 0.7 m², C_d 1.0) are only an example: they give about 43 m/s, roughly 20% below the about 55 m/s usually cited for a belly-down skydiver (Huang, The Physics Factbook, 1998, cited by Wikipedia's Terminal velocity article), so treat them as a rough estimate.

95% 时间是怎么来的？Where does the 95% time come from?

二次阻力下 v(t) = v_t·tanh(gt/v_t)，tanh 等于 0.95 时 gt/v_t ≈ 1.83。With quadratic drag v(t) = v_t·tanh(gt/v_t), and tanh reaches 0.95 at gt/v_t ≈ 1.83.

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「终端速度计算器」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Terminal Velocity Calculator uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「终端速度计算器」免费吗？需要注册吗？Is the Terminal Velocity Calculator free? Do I need an account?

「终端速度计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Terminal Velocity Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.