Unity 中的火箭模拟器：我不知道如何计算 delta V

Question

我在 unity 2d 中制作了一个非常简单的火箭模拟器，但在所有功能中，我无法让 delta V 工作。我在发射前就预先计算过了，但是当火箭燃料耗尽时，结果却不是这样。

这里是完整的代码：

using UnityEngine;
using UnityEngine.UI;

public class PhysicsScript : MonoBehaviour
{
    Vector2 weight;
    Vector2 thrustForce;
    Rigidbody2D rb;
    Vector2 netForce;
    Vector2 dragForce;
    float fuelConsumption;
    float altitude;
    bool enginesToggle;
    float dragRatio;
    bool TurnL;
    bool TurnR;
    float ThrustPercentage;
    bool shiftHeld;
    float yVel;
    float xVel;


    public float fuel;
    public float fuelDensity;
    public float g;
    public float rocketMass;
    public float massFlowRate;
    public float exhaustVelocity;
    public float dragCoefficient;
    public float maxAtmosphereAlt;
    public float TurningForce;

    public Text AltitudeText;
    public Slider thrustSlider;
    public Text Percentage;
    public Text VerticalVel;
    public Text HorizontalVel;
    public Slider fuelSlider;
    public Text FuelPercentage;
    public Text BTDisplayer;
    public Text WTRat;
    public Text WeightD;
    public Text ThrustD;
    public Text MassD;
    public Text DelataVD;
    public Image engineOnOff;
    public Text tti;
    public Text APoapsis;
    public Text dragD;

    float burnTime;
    float W_TRatio;
    float secondsBeforeHittingGround;
    float apoapsis;
    float deltaV;
    float finalMass;
    void Start()
    {
        rb = GetComponent<Rigidbody2D>();
        fuelSlider.maxValue = fuel;
        fuelSlider.value = fuelSlider.maxValue;
    }

    void Update()
    {
        yVel = rb.velocity.y;
        xVel = rb.velocity.x;

        fuelSlider.value = fuel;
        FuelPercentage.text = (fuel * 100 / fuelSlider.maxValue).ToString("0") + "%";

        VerticalVel.text = "Vertical Velocity: " + yVel.ToString("0") + " m/s";
        HorizontalVel.text = "Horizontal Velocity: " + xVel.ToString("0") + " m/s";

        if (Input.GetKeyDown(KeyCode.Space))
        {
            enginesToggle = !enginesToggle;
        }
        if (Input.GetKey(KeyCode.D))
        {
            TurnR = true;
        }
        else
        {
            TurnR = false;
        }
        if (Input.GetKey(KeyCode.A))
        {
            TurnL = true;
        }
        else
        {
            TurnL = false;
        }
        AltitudeText.text = "Altitude: " + altitude.ToString("0") + " m";

        float scroll = Input.GetAxis("Mouse ScrollWheel");
        shiftHeld = Input.GetKey(KeyCode.LeftShift);

        if (shiftHeld && scroll != 0)
        {
            thrustSlider.value += scroll / 10;
        }
        else if (scroll != 0)
        {
            thrustSlider.value += scroll / 3;
        }

        ThrustPercentage = thrustSlider.value;
        ThrustPercentage = Mathf.Clamp(ThrustPercentage, 0, 1);
        Percentage.text = "Thrust \n" + (thrustSlider.value * 100).ToString("F1") + "%";
    }

    void FixedUpdate()
    {
        rb.mass = rocketMass + fuel * fuelDensity;
        if (altitude > maxAtmosphereAlt)
        {
            dragCoefficient = 0;
        }
        dragRatio = altitude / maxAtmosphereAlt;
        //weight
        weight = rb.mass * g * Vector2.down;
        //drag
        dragForce = dragCoefficient * Mathf.Pow(rb.velocity.magnitude, 2) * -rb.velocity;

        //fuel and mass consumptions
        fuelConsumption = exhaustVelocity * massFlowRate * ThrustPercentage;

        altitude = transform.position.y;
        if (fuel > 0 && enginesToggle)
        {
            //thrust
            thrustForce = transform.up * fuelConsumption * exhaustVelocity * ThrustPercentage;
            fuel -= fuelConsumption * Time.deltaTime;
            engineOnOff.color = Color.green;
            apoapsis = 0;
            secondsBeforeHittingGround = 0;
        }
        else
        {
            thrustForce = Vector2.zero;
            engineOnOff.color = Color.red;
            apoapsis = Mathf.Pow(yVel, 2) / Mathf.Pow(g, 2);
            secondsBeforeHittingGround = apoapsis * 2 / g;
        }

        //net 
        netForce = (weight + thrustForce + dragForce) * Time.fixedDeltaTime;
        rb.velocity += netForce / rb.mass;

        fuel = Mathf.Clamp(fuel, 0, fuel);
        dragCoefficient = Mathf.Lerp(dragCoefficient, 0, dragRatio * Time.fixedDeltaTime);

        if (TurnR)
        {
            rb.AddTorque(-TurningForce * rb.mass);
        }

        if (TurnL)
        {
            rb.AddTorque(TurningForce * rb.mass);
        }
        rb.AddTorque(-4 * rb.angularVelocity * rb.mass * Time.fixedDeltaTime);
        burnTime = fuel / fuelConsumption;

        W_TRatio = (exhaustVelocity * massFlowRate * ThrustPercentage) / weight.magnitude;

        BTDisplayer.text = "Burn Time: " + burnTime.ToString("0") + "s";
        WTRat.text = "T/W Ratio: " + W_TRatio.ToString("F2") + "x";

        WeightD.text = "Weight: " + weight.magnitude.ToString("0") + "N";
        ThrustD.text = "Thrust: " + (exhaustVelocity * massFlowRate *   ThrustPercentage).ToString("0") + "N";
        deltaV = Mathf.Log(rb.mass / rocketMass) * massFlowRate * exhaustVelocity;
        MassD.text = rb.mass.ToString("0") + "kg";
        DelataVD.text = "work in progress..";

        tti.text = "Time to Apoapsis: " + (secondsBeforeHittingGround).ToString("0") + "s";
        APoapsis.text = "Distance Apoapsis: " + apoapsis.ToString("0") + "m";
        dragD.text = "Drag: " + Mathf.Clamp((100 - (altitude * 100 / maxAtmosphereAlt)), 0, 100).ToString("F1") + "%";
    }
}

希望它不那么难读。

我用计算器计算了delta V，当模拟火箭排空时，它的速度甚至没有接近我的预期。我对代码做了很多调整，这使它变得更糟，所以我撤消了它们。

所以，如您所见，我身上有 1000 燃料。燃料密度为0.3，燃料质量为300。火箭也有10kg。总共将是 310 公斤。火箭上没有阻力或重力。排气速度为100。若delta V = Ln(m0/mf)*ve，则deltaV = Ln(310/10)*100， deltaV = Ln(31)100，deltaV = 3.43100，结果 DeltaV = 343 m/s，而事实上，我的最大速度是 1150。 帮忙吗？