弹丸数学错误

Question

所以，基本上我是在尝试创建两种计算方法来执行以下操作：

1) 根据发射位置、速度和发射角度获取弹丸发射器的命中位置。

2) 根据速度和所需命中位置获取射击角度。

我目前有以下代码。

'use strict';

import Mortar from '../mortar/Mortar.js';

const GRAVITY = 9.8;
const MAX_RANGE = 1250;
const MIN_RANGE = 50;

/**
 * A class for the mortar calculator.
 */
class Calc {
    /**
     * Get Hit Location Data from Dial Data.
     * @param {*} dialData The current dialed in data
     * @param {*} mortarData The current Mortar Data
     * @return {*} Hit Location Data
     */
    static getHitLocData(dialData, mortarData = Mortar.getDefaultData()) {
        const {mrads, bearing} = dialData;
        const {velocity, x, y, elevation} = mortarData;

        const rads = Calc.getRadFromMils(mrads);
        const b = Calc.getRadFromDegree(bearing);

        const vx = (velocity * Math.cos(rads));
        const vy = (velocity * Math.sin(rads));
        const time = (2 * (vy / GRAVITY));
        const range = ((2 * vx) * (vy / GRAVITY));
        const yMax = (Math.pow(vy, 2) / (2 * GRAVITY));

        let canHit = true;

        // We need a modification for the difference in elevation

        // If the range wont hit
        if ((range < MIN_RANGE) || (range > MAX_RANGE)) {
            canHit = false;
        }

        const hitX = (x + (range * Math.cos(b)));
        const hitY = (y + (range * Math.sin(b)));

        return {
            bearing,
            'mrads': `${Math.round(mrads)}mrads`,
            'map': {
                'x': Math.round(hitX),
                'y': Math.round(hitY),
                'heightDiff': '0m',
                'distance': `${range.toFixed(2)}m`,
                'flight': `${time.toFixed(2)}sec`
            },
            'grid': 'A1-1-1-000',
            'misc': {
                'velocityX': `${vx.toFixed(1)}m/s`,
                'velocityY': `${vy.toFixed(1)}m/s`,
                'maxHeight': `${yMax.toFixed(2)}m`
            },
            canHit
        };
    }

    /**
     * Get Dial Data Data from Hit Location Data.
     * @param {*} hitLocData The current requested hit location
     * @param {*} mortarData The current Mortar Data
     * @return {*} Dial Data
     */
    static getDialData(hitLocData, mortarData = Mortar.getDefaultData()) {
        const {hitX, hitY, hitHeight} = hitLocData;
        const {x, y, mortHeight, velocity} = mortarData;

        const range = Math.sqrt(Math.pow((hitX - x), 2) + Math.pow((hitY - y), 2));
        const bearing = (Math.atan2((hitY - y), (hitX - x)) * (180 / Math.PI));
        const heightDiff = (hitHeight - mortHeight);
        let rads = 0;

        if (heightDiff) {
            // Height difference has not been math proven as 0,0 doesnt even work

            const v4 = Math.pow(velocity, 4);
            const gx = (GRAVITY * range);
            const gx2 = (GRAVITY * Math.pow(range, 2));
            const yv2 = (heightDiff * (Math.pow(velocity, 2)));
            const m1 = (GRAVITY * (gx2 - (2 * yv2)));
            rads = Math.atan((v4 - m1) / gx);
        } else {
            const gx = (GRAVITY * range);
            rads = Math.atan(Math.pow(velocity, 2) / gx);
        }

        const mrads = (rads * 1000);

        const vy = (velocity * Math.sin(rads));
        const time = (2 * (vy / GRAVITY));

        let canHit = true;

        // If the range wont hit
        if ((range < MIN_RANGE) || (range > MAX_RANGE)) {
            canHit = false;
        }

        return {
            bearing,
            'mrads': (`${Math.round(mrads)}mrad`),
            'heightDiff': (`${heightDiff}m`),
            'flight': (`${time.toFixed(2)}sec`),
            'distance': (`${range.toFixed(2)}m`),
            'spread': 0,
            canHit
        };
    }

    /**
     * Get the number of radians from Milradians.
     *
     * @param {Number} mrads The number of mrads
     * @return {Number} The new number of rads
     */
    static getRadFromMils(mrads) {
        return (mrads / 1000);
    }

    /**
     * Get the number of radians from degrees.
     *
     * @param {Number} deg The current degree bearing
     * @return {Number} The new number of rads
     */
    static getRadFromDegree(deg) {
        return (deg * (Math.PI / 180));
    }
}

export default Calc;

前者，获取命中位置是我知道的方法。如果我给它一个给定的方位角和 mrad 发射角，我可以找到我击中的位置与迫击炮位置的关系。

然而，尽管传递了与第一个函数相同的输出，但后者并不匹配。请参阅下面的输入和输出数据示例

输入：

var dialData = getDialData({
  'hitX': 1250,
  'hitY': 0,
  'hitHeight': 0
}, {
  'x': 0,
  'y': 0,
  'mortHeight': 0,
  'velocity': 110.75
});
var hitData = getHitLocData({
  'mrads': 800,
  'bearing': 0,
}, {
  'x': 0,
  'y': 0,
  'elevation': 0,
  'velocity': 110.75
});

输出：

{"bearing":0,"mrads":"786mrad","heightDiff":"0m","flight":"15.99sec","distance":"1250.00m","spread":0,"canHit":true}
{"bearing":0,"mrads":"800mrads","map":{"x":1251,"y":0,"heightDiff":"0m","distance":"1251.05m","flight":"16.21sec"},"grid":"A1-1-1-000","misc":{"velocityX":"77.2m/s","velocityY":"79.4m/s","maxHeight":"322.03m"},"canHit":false}

我一辈子都弄不明白为什么会这样。两者应该计算出相同的距离、mrads 和飞行。

Answer 1

我知道问题出在哪里了。问题是使用以下等式： Equation image 我的实现完全不正确。而不是计算 ± 的两边，我只是计算其中之一。您可以在检查 heightDiff 的 if 语句中看到这一点。

正确的解决方法是：

// Below are the two calculaitons we need to work out
        const dx = range;
        const v = velocity;
        const g = GRAVITY;
        const hd = heightDiff;

        const v4 = (Math.pow(velocity, 4));
        const gx2 = (GRAVITY * Math.pow(range, 2));
        const yv2 = (heightDiff * Math.pow(velocity, 2));
        const gx = (GRAVITY * range);

        const p1 = Math.sqrt(v4 - (GRAVITY * (gx2 + (2 * yv2))));
        const a1 = Math.atan((Math.pow(velocity, 2) + p1) / gx);

        rads = a1;
        const mrads = (rads * 1000);

弹丸数学错误

Projectile Mathematics error

javascript

math

game-physics

projectile