统一飞机物理

Question

我想做一个简单的飞行器控制器，在unity中看起来有点逼真。我看了一些飞机物理学的视频。并统一制作一个简单的脚本，但如果我开始，我的飞机就不能移动，或者如果我将阻力改为零，它就不能升起。我尝试使用真实数据并从 wiki（F22 Raptor）获取它。对于我的游戏对象，我给刚体组件质量 = 19670 千克。发动机推力 = 2 * 116000.0f 牛顿。

    private void calculateEnginePower()
    {
        EnginePower = engineThrust * ThrottleInput;
    }

    private void calculateForces()
    {
        angleOfAttack = Vector3.Angle(Vector3.forward, rb.velocity);
        angleOfAttack = Mathf.Clamp(angleOfAttack, 0, 90);

        coefficient = Mathf.Pow(1225.04f * rb.velocity.magnitude, 2) - 1; //M^2-2 where: M is mach.         

        if (coefficient > 0.0f)
            coefficientLift = (4 * angleOfAttack) / Mathf.Sqrt(coefficient);
        lift = 1.2754f * 0.5f * Mathf.Pow(rb.velocity.magnitude, 2) * coefficientLift * 78.04f; // densy1.2754 kg/m3, speed m/s , (F22)Wing area: 840 ft² (78.04 m²)

        coefficientDrag = 0.021f;
        rb.drag = coefficientDrag * 0.5f * Mathf.Pow(rb.velocity.magnitude,2) * 1.2754f * 78.04f;

        rb.AddForce(transform.up * lift);
        rb.AddForce(transform.forward * EnginePower);
    }

使用了这些公式：

升力： Lift formula 对于升力系数： Cl formula 对于拖动： Drag formula 以及风阻系数：我也使用了来自 wiki 的数据 (0.021f)。

Answer 1

所以您的代码存在很多问题。我在下面概述了它们；

计算力

Issue: angleOfAttack = Vector3.Angle(Vector3.forward, rb.velocity);

Vector3.forward和rb.velocity都在world-space中。 AoA 是机翼 local chord-line 与飞机 velocity 之间的角度。
Vector3.Angle 将 return 一个 无符号 角。 AoA 必须在 positive 和 negative 两个方向上工作，否则将无法实现负俯仰和倒飞。

Solution: Move rb.velocity to local-space and solve for AoA with trigonometry.

// *flip sign(s) if necessary*
var localVelocity = transform.InverseTransformDirection(rb.velocity);
var angleOfAttack = Mathf.Atan2(-localVelocity.y, localVelocity.z);

Issue: coefficient = Mathf.Pow(1225.04f * rb.velocity.magnitude, 2) - 1;

4α/sqrt(M^2−1)是M > 1的超声波系数。在零速度下，该方程将简化为 sqrt(-1)，这是一个虚数，将产生 NaN。 Mach 表示为 M=V/C 其中 V=velocity 和 C=the speed of sound。您的 1225.04f 常量必须以 km/h 为单位 C，而不是按要求 m/s。你也在乘法而不是除法，如等式中给出的那样。

Solution: Simplify your equations with Lifting Line Theory.

var aspectRatio = (wingSpan * wingSpan) / wingArea; 
var inducedLift = angleOfAttack * (aspectRatio / (aspectRatio + 2f)) * 2f * Mathf.PI;
var inducedDrag = (inducedLift * inducedLift) / (aspectRatio * Mathf.PI);

来源： Aerospaceweb.org

Issue: rb.drag = coefficientDrag * 0.5f * Pow(rb.velocity.mag,2) * 1.2754f * 78.04f;

rb.drag 不是必需的，因为我们正在手动计算和应用阻力。

Solution: Set the rb.drag property to the smallest possible value.

rb.drag = Mathf.Epsilon; // set in Awake

Issue: rb.AddForce(transform.up * lift);

transform.up 不适合 lift。升降机垂直至 velocity 而 drag 与平行 .

Solution: Compute the lift direction by crossing the normalized velocity vector with the aircraft's lateral direction and apply drag opposite to velocity.

// *flip sign(s) if necessary*
var dragDirection = -rb.velocity.normalized;
var liftDirection = Vector3.Cross(dragDirection, transform.right);
rb.AddForce(liftDirection * lift + dragDirection * drag);

你的升力方程看起来不错，所以把它们放在一起看起来像这样； (未测试)

public float wingSpan = 13.56f;
public float wingArea = 78.04f;

private float aspectRatio;

private void Awake ()
{
    rb.drag = Mathf.Epsilon;
    aspectRatio = (wingSpan * wingSpan) / wingArea;
}

private void calculateForces ()
{
    // *flip sign(s) if necessary*
    var localVelocity = transform.InverseTransformDirection(rb.velocity);
    var angleOfAttack = Mathf.Atan2(-localVelocity.y, localVelocity.z);

    // α * 2 * PI * (AR / AR + 2)
    var inducedLift = angleOfAttack * (aspectRatio / (aspectRatio + 2f)) * 2f * Mathf.PI;

    // CL ^ 2 / (AR * PI)
    var inducedDrag = (inducedLift * inducedLift) / (aspectRatio * Mathf.PI);

    // V ^ 2 * R * 0.5 * A
    var pressure = rb.velocity.sqrMagnitude * 1.2754f * 0.5f * wingArea;

    var lift = inducedLift * pressure;
    var drag = (0.021f + inducedDrag) * pressure;

    // *flip sign(s) if necessary*
    var dragDirection = rb.velocity.normalized;
    var liftDirection = Vector3.Cross(dragDirection, transform.right);

    // Lift + Drag = Total Force
    rb.AddForce(liftDirection * lift - dragDirection * drag);
    rb.AddForce(transform.forward * EnginePower);
}

统一飞机物理

Unity aircraft physics

c#

unity3d

math

air

physics