I have written scripts - projectile motion and armor penetration taken directly from physics equations:
/*
https://en.wikipedia.org/wiki/Projectile_motion
https://amesweb.info/Physics/Projectile-Motion-Calculator.aspx
https://www.weber.edu/wsuimages/mollysmith/3500Presentations/Kinematics%20of%20Projectile%20Motion.pptx
https://en.wikipedia.org/wiki/Terminal_velocity
http://www.calctool.org/CALC/eng/aerospace/terminal
https://demonstrations.wolfram.com/ProjectileWithAirDrag/#more
To Do:
- Further optimization ? (reduce trigonometry ?);
- Trajectory of a projectile with Newton drag (also read about Reynolds numbers), it is more difficult to be solved analitycally,
but may brings even more realistic behaviour.
*/
using System;
using UnityEngine;
public class ProjectileMotion : MonoBehaviour
{
public bool AirResistance = true;
public float Velocity = 300.0f;
public float Mass = 0.5f;
public float DragCoefficient = 0.3f;
public float Duration = 5.0f;
GameObject _Bullet;
Vector3 _StartPosition, _PreviousPosition;
float _Area, _Distance, _HorizontalAngle, _StartTime, _TerminalVelocity, _VerticalAngle;
MaterialPropertyBlock _PropertyBlock;
bool _UpdateProjectile = false;
float GetVerticalAngle(Transform t)
{
return (-1.0f) * t.eulerAngles.x;
}
float GetHorizontalAngle(Transform t)
{
float angle = 360.0f - t.eulerAngles.y + 90.0f;
if (angle > 360.0f) angle = angle - 360.0f;
return angle;
}
// Projectile motion in a uniform gravitational 3D field without air resistance:
// startPos = position of bullet, when bullet was shot;
// startTime = time, when bullet was shot;
// velocity = initial velocity (initial speed of bullet, when bullet was shot, for example 800 m/s);
// theta = horizontal angle of initial velocity in radians, computed from GetHorizontalAngle(projectileToShoot.transform) * Mathf.Deg2Rad;
// phi = vertical angle of initial velocity in radians, computed from GetVerticalAngle(projectileToShoot.transform) * Mathf.Deg2Rad;
Vector3 ProjectileDisplacement (Vector3 startPos, float startTime, float velocity, float theta, float phi)
{
float time = Time.time - startTime;
float x = velocity * time * Mathf.Cos(theta) * Mathf.Cos(phi);
float y = velocity * time * Mathf.Sin(phi) - 0.5f * 9.8f * time * time;
float z = velocity * time * Mathf.Sin(theta) * Mathf.Cos(phi);
return startPos + new Vector3(x, y, z);
}
// Mass = kg
// Drag coefficient (for bullets = 0.3)
// The density of air at sea level = 1.5
// Projected area of object (object with size 2 cm x 5 cm = 0.001 m2 etc.)
float TerminalVelocity(float mass, float drag, float density, float area)
{
float gravity = 9.8066f;
return (float)System.Math.Sqrt((2.0f * mass * gravity) / (density * area * drag));
}
// Projectile motion in a uniform gravitational 3D field with air resistance (Stoke's equation):
// startPos = position of bullet, when bullet was shot;
// startTime = time, when bullet was shot;
// v0 = initial velocity (initial speed of bullet, when bullet was shot, for example 800 m/s);
// vt = terminal velocity, computed from TerminalVelocity function;
// theta = horizontal angle of initial velocity in radians, computed from GetHorizontalAngle(projectileToShoot.transform) * Mathf.Deg2Rad;
// phi = vertical angle of initial velocity in radians, computed from GetVerticalAngle(projectileToShoot.transform) * Mathf.Deg2Rad;
Vector3 ProjectileDisplacementWithAirDrag(Vector3 startPos, float startTime, float v0, float vt, float theta, float phi)
{
float t = Time.time - startTime;
float g = 9.8066f;
double e = Math.E; // 2.7182818284590451
float x = (float)((v0 * vt / g) * Math.Cos(theta) * Math.Cos(phi) * (1.0f - Math.Pow(e, -g * t / vt)));
float y = (float)((vt / g) * (v0 * Math.Sin(phi) + vt) * (1.0f - Math.Pow(e, -g * t / vt)) - (vt * t));
float z = (float)((v0 * vt / g) * Math.Sin(theta) * Math.Cos(phi) * (1.0f - Math.Pow(e, -g * t / vt)));
return startPos + new Vector3(x, y, z);
}
void Update()
{
if (Input.GetKeyDown(KeyCode.Space) && !_UpdateProjectile) // initialize
{
_Bullet = GameObject.CreatePrimitive(PrimitiveType.Sphere);
_Bullet.transform.parent = Camera.main.transform;
_Bullet.transform.localScale = new Vector3(0.3f, 0.3f, 0.3f);
_Bullet.transform.localPosition = new Vector3(0.0f, 0.0f, 2.0f);
_Bullet.transform.localEulerAngles = Vector3.zero;
float radius = _Bullet.GetComponent<SphereCollider>().radius * _Bullet.transform.localScale.x;
_Area = Mathf.PI * radius * radius;
_StartPosition = _Bullet.transform.position;
_StartTime = Time.time;
_TerminalVelocity = TerminalVelocity(Mass, DragCoefficient, 1.5f, _Area);
_HorizontalAngle = GetHorizontalAngle(_Bullet.transform) * Mathf.Deg2Rad;
_VerticalAngle = GetVerticalAngle(_Bullet.transform) * Mathf.Deg2Rad;
_PropertyBlock = new MaterialPropertyBlock();
_Bullet.GetComponent<Renderer>().GetPropertyBlock(_PropertyBlock);
if (AirResistance)
_PropertyBlock.SetColor("_Color", Color.red);
else
_PropertyBlock.SetColor("_Color", Color.blue);
_Bullet.GetComponent<Renderer>().SetPropertyBlock(_PropertyBlock);
_Bullet.transform.parent = null;
_UpdateProjectile = true;
}
if (((Time.time - _StartTime) > Duration) && _UpdateProjectile)
{
_UpdateProjectile = false;
Destroy(_Bullet);
}
if (_UpdateProjectile)
{
_PreviousPosition = _Bullet.transform.position;
if (AirResistance)
{
_Bullet.transform.position = ProjectileDisplacementWithAirDrag(_StartPosition, _StartTime, Velocity, _TerminalVelocity, _HorizontalAngle, _VerticalAngle);
}
else
{
_Bullet.transform.position = ProjectileDisplacement (_StartPosition, _StartTime, Velocity, _HorizontalAngle, _VerticalAngle);
}
_Distance = Vector3.Distance(_PreviousPosition, _Bullet.transform.position);
}
}
void FixedUpdate()
{
if (_UpdateProjectile)
{
RaycastHit hit;
if (Physics.Raycast(_PreviousPosition, _Bullet.transform.position - _PreviousPosition, out hit, _Distance))
{
Debug.Log("Hit");
}
}
}
}
using UnityEngine;
// Physics equations taken from: "Physics for Game Programmers" by Grant Palmer
public class ArmorPenetration : MonoBehaviour
{
[Tooltip("Projectile mass [kg]")]
public float Mass = 0.0082f;
[Tooltip("Projectile (muzzle) velocity [m/s]")]
public float Velocity = 440.0f;
[Tooltip("Steel armor thickness [meters]")]
public float Thickness = 0.01f;
[Tooltip("Projectile diameter [meters]")]
public float Diameter = 0.009f;
[Tooltip("Angle of impact [degrees], angle is zero for projectile strike perpendicular to the steel plate")]
public float Angle = 0.0f;
// m - projectile mass [kg]
// v - projectile (muzzle) velocity [m/s]
// t - steel armor thickness [meters]
// d - projectile diameter [meters]
// phi - angle of impact [degrees], angle is zero for projectile strike perpendicular to the steel plate
bool IsArmorCanBePenetrated (float m, float v, float t, float d, float phi)
{
float f = 1.8288f * (t / d - 0.45f) * (phi * phi + 2000f) + 12192f; //armor resistance coefficient
float k = 0.5f * m * v * v; //kinetic energy of projectile
float s = Mathf.Cos (phi * Mathf.Deg2Rad);
float n = 8.025f * (t * d * d * f * f) / (s * s); //minimum kinetic energy required to penetrate armor
return (k > n);
}
void OnGUI()
{
if (GUI.Button(new Rect(10, 10, 100, 50), "Calculate"))
{
bool result = IsArmorCanBePenetrated (Mass, Velocity, Thickness, Diameter, Angle);
Debug.Log(result);
}
}
}
How would you extend it with penetration calculations and deflections if the angle and energy would allow the projectile to get deflected? Just some hints and Iāll try to do it.