//Force 2 - Pressure Drag Force
public static Vector3 PressureDragForce(TriangleData triangleData)
{
//Modify for different turning behavior and planing forces
//f_p and f_S - falloff power, should be smaller than 1
//C - coefficients to modify
float velocity = triangleData.velocity.magnitude;
//A reference speed used when modifying the parameters
float velocityReference = velocity;
velocity = velocity / velocityReference;
Vector3 pressureDragForce = Vector3.zero;
if (triangleData.cosTheta > 0f)
{
float C_PD1 = 10f;
float C_PD2 = 10f;
float f_P = 0.5f;
////To change the variables real-time - add the finished values later
//float C_PD1 = DebugPhysics.current.C_PD1;
//float C_PD2 = DebugPhysics.current.C_PD2;
//float f_P = DebugPhysics.current.f_P;
pressureDragForce = -(C_PD1 * velocity + C_PD2 * (velocity * velocity)) * triangleData.area * Mathf.Pow(triangleData.cosTheta, f_P) * triangleData.normal;
}
else
{
float C_SD1 = 10f;
float C_SD2 = 10f;
float f_S = 0.5f;
//To change the variables real-time - add the finished values later
//float C_SD1 = DebugPhysics.current.C_SD1;
//float C_SD2 = DebugPhysics.current.C_SD2;
//float f_S = DebugPhysics.current.f_S;
pressureDragForce = (C_SD1 * velocity + C_SD2 * (velocity * velocity)) * triangleData.area * Mathf.Pow(Mathf.Abs(triangleData.cosTheta), f_S) * triangleData.normal;
}
pressureDragForce = CheckForceIsValid(pressureDragForce, "Pressure drag");
return(pressureDragForce);
}
//The buoyancy force so the boat can float
private Vector3 BuoyancyForce(float rho, TriangleData triangleData)
{
//Buoyancy is a hydrostatic force - it's there even if the water isn't flowing or if the boat stays still
// F_buoyancy = rho * g * V
// rho - density of the mediaum you are in
// g - gravity
// V - volume of fluid directly above the curved surface
// V = z * S * n
// z - distance to surface
// S - surface area
// n - normal to the surface
Vector3 buoyancyForce = rho * Physics.gravity.y * triangleData.distanceToSurface * triangleData.area * triangleData.normal;
//The vertical component of the hydrostatic forces don't cancel out but the horizontal do
buoyancyForce.x = 0f;
buoyancyForce.z = 0f;
return(buoyancyForce);
}
//Add all forces that act on the squares above the water
void AddAboveWaterForces()
{
//Get all triangles
List <TriangleData> aboveWaterTriangleData = modifyBoatMesh.aboveWaterTriangleData;
//Loop through all triangles
for (int i = 0; i < aboveWaterTriangleData.Count; i++)
{
TriangleData triangleData = aboveWaterTriangleData[i];
//Calculate the forces
Vector3 forceToAdd = Vector3.zero;
//Force 1 - Air resistance
//Replace VisbyData.C_r with your boat's drag coefficient
forceToAdd += BoatPhysicsMath.AirResistanceForce(rhoAir, triangleData, boatDrag);
//Add the forces to the boat
boatRB.AddForceAtPosition(forceToAdd, triangleData.center);
//Debug
//The normal
//Debug.DrawRay(triangleCenter, triangleNormal * 3f, Color.white);
//The velocity
//Debug.DrawRay(triangleCenter, triangleVelocityDir * 3f, Color.black);
if (triangleData.cosTheta > 0f)
{
//Debug.DrawRay(triangleCenter, triangleVelocityDir * 3f, Color.black);
}
//Air resistance
//-3 to show it in the opposite direction to see what's going on
//Debug.DrawRay(triangleCenter, airResistanceForce.normalized * -3f, Color.blue);
}
}
//Force 3 - Air resistance on the part of the ship above the water (typically 4 to 8 percent of total resistance)
public static Vector3 AirResistanceForce(float rho, TriangleData triangleData, float C_air)
{
// R_air = 0.5 * rho * v^2 * A_p * C_air
// rho - air density
// v - speed of ship
// A_p - projected transverse profile area of ship
// C_r - coefficient of air resistance (drag coefficient)
//Only add air resistance if normal is pointing in the same direction as the velocity
if (triangleData.cosTheta < 0f)
{
return(Vector3.zero);
}
//Find air resistance force
Vector3 airResistanceForce = 0.5f * rho * triangleData.velocity.magnitude * triangleData.velocity * triangleData.area * C_air;
//Acting in the opposite side of the velocity
airResistanceForce *= -1f;
airResistanceForce = CheckForceIsValid(airResistanceForce, "Air resistance");
return(airResistanceForce);
}
//
// Resistance forces from http://www.gamasutra.com/view/news/263237/Water_interaction_model_for_boats_in_video_games_Part_2.php
//
//Force 1 - Viscous Water Resistance (Frictional Drag)
public static Vector3 ViscousWaterResistanceForce(float rho, TriangleData triangleData, float Cf)
{
//Viscous resistance occurs when water sticks to the boat's surface and the boat has to drag that water with it
// F = 0.5 * rho * v^2 * S * Cf
// rho - density of the medium you have
// v - speed
// S - surface area
// Cf - Coefficient of frictional resistance
//We need the tangential velocity
//Projection of the velocity on the plane with the normal normalvec
//http://www.euclideanspace.com/maths/geometry/elements/plane/lineOnPlane/
Vector3 B = triangleData.normal;
Vector3 A = triangleData.velocity;
Vector3 velocityTangent = Vector3.Cross(B, (Vector3.Cross(A, B) / B.magnitude)) / B.magnitude;
//The direction of the tangential velocity (-1 to get the flow which is in the opposite direction)
Vector3 tangentialDirection = velocityTangent.normalized * -1f;
//Debug.DrawRay(triangleCenter, tangentialDirection * 3f, Color.black);
//Debug.DrawRay(triangleCenter, velocityVec.normalized * 3f, Color.blue);
//Debug.DrawRay(triangleCenter, normal * 3f, Color.white);
//The speed of the triangle as if it was in the tangent's direction
//So we end up with the same speed as in the center of the triangle but in the direction of the flow
Vector3 v_f_vec = triangleData.velocity.magnitude * tangentialDirection;
//The final resistance force
Vector3 viscousWaterResistanceForce = 0.5f * rho * v_f_vec.magnitude * v_f_vec * triangleData.area * Cf;
viscousWaterResistanceForce = CheckForceIsValid(viscousWaterResistanceForce, "Viscous Water Resistance");
return(viscousWaterResistanceForce);
}
//Add all forces that act on the squares below the water
void AddUnderWaterForces()
{
//The resistance coefficient - same for all triangles
float Cf = BoatPhysicsMath.ResistanceCoefficient(
rhoWater,
boatRB.velocity.magnitude,
modifyBoatMesh.CalculateUnderWaterLength());
//To calculate the slamming force we need the velocity at each of the original triangles
List <SlammingForceData> slammingForceData = modifyBoatMesh.slammingForceData;
CalculateSlammingVelocities(slammingForceData);
//Need this data for slamming forces
float boatArea = modifyBoatMesh.boatArea;
float boatMass = boatRB.mass; //Replace this line with your boat's total mass
//To connect the submerged triangles with the original triangles
List <int> indexOfOriginalTriangle = modifyBoatMesh.indexOfOriginalTriangle;
//Get all triangles
List <TriangleData> underWaterTriangleData = modifyBoatMesh.underWaterTriangleData;
for (int i = 0; i < underWaterTriangleData.Count; i++)
{
TriangleData triangleData = underWaterTriangleData[i];
//Calculate the forces
Vector3 forceToAdd = Vector3.zero;
//Force 1 - The hydrostatic force (buoyancy)
forceToAdd += BoatPhysicsMath.BuoyancyForce(rhoWater, triangleData);
//Force 2 - Viscous Water Resistance
forceToAdd += BoatPhysicsMath.ViscousWaterResistanceForce(rhoWater, triangleData, Cf);
//Force 3 - Pressure drag
forceToAdd += BoatPhysicsMath.PressureDragForce(triangleData);
//Force 4 - Slamming force
//Which of the original triangles is this triangle a part of
int originalTriangleIndex = indexOfOriginalTriangle[i];
SlammingForceData slammingData = slammingForceData[originalTriangleIndex];
forceToAdd += BoatPhysicsMath.SlammingForce(slammingData, triangleData, boatArea, boatMass);
//Add the forces to the boat
boatRB.AddForceAtPosition(forceToAdd, triangleData.center);
//Debug
//Normal
//Debug.DrawRay(triangleData.center, triangleData.normal * 3f, Color.white);
//Buoyancy
//Debug.DrawRay(triangleData.center, BoatPhysicsMath.BuoyancyForce(rhoWater, triangleData).normalized * -3f, Color.blue);
//Velocity
//Debug.DrawRay(triangleCenter, triangleVelocityDir * 3f, Color.black);
//Viscous Water Resistance
//Debug.DrawRay(triangleCenter, viscousWaterResistanceForce.normalized * 3f, Color.black);
}
}
//Force 3 - Slamming Force (Water Entry Force)
public static Vector3 SlammingForce(SlammingForceData slammingData, TriangleData triangleData, float boatArea, float boatMass)
{
//To capture the response of the fluid to sudden accelerations or penetrations
//Add slamming if the normal is in the same direction as the velocity (the triangle is not receding from the water)
//Also make sure thea area is not 0, which it sometimes is for some reason
if (triangleData.cosTheta < 0f || slammingData.originalArea <= 0f)
{
return(Vector3.zero);
}
//Step 1 - Calculate acceleration
//Volume of water swept per second
Vector3 dV = slammingData.submergedArea * slammingData.velocity;
Vector3 dV_previous = slammingData.previousSubmergedArea * slammingData.previousVelocity;
//Calculate the acceleration of the center point of the original triangle (not the current underwater triangle)
//But the triangle the underwater triangle is a part of
Vector3 accVec = (dV - dV_previous) / (slammingData.originalArea * Time.fixedDeltaTime);
//The magnitude of the acceleration
float acc = accVec.magnitude;
//Debug.Log(slammingForceData.originalArea);
//Step 2 - Calculate slamming force
// F = clamp(acc / acc_max, 0, 1)^p * cos(theta) * F_stop
// p - power to ramp up slamming force - should be 2 or more
// F_stop = m * v * (2A / S)
// m - mass of the entire boat
// v - velocity
// A - this triangle's area
// S - total surface area of the entire boat
Vector3 F_stop = boatMass * triangleData.velocity * ((2f * triangleData.area) / boatArea);
//float p = DebugPhysics.current.p;
//float acc_max = DebugPhysics.current.acc_max;
float p = 2f;
float acc_max = acc;
float slammingCheat = DebugPhysics.current.slammingCheat;
Vector3 slammingForce = Mathf.Pow(Mathf.Clamp01(acc / acc_max), p) * triangleData.cosTheta * F_stop * slammingCheat;
//Vector3 slammingForce = Vector3.zero;
//Debug.Log(slammingForce);
//The force acts in the opposite direction
slammingForce *= -1f;
slammingForce = CheckForceIsValid(slammingForce, "Slamming");
return(slammingForce);
}
