Catapult Physics for Game Programming

[anupgupta]

hello

I am a game programmer..and working on a game which has a player attached to the catapult arm. now when the arm is released the player gets thrown in the air.. while in air..the air resistance could make the player rotate left or right... and then glides and lands on the ground.

i have written the code for player getting thrown at random angle and then following a projectile and touching the ground..but want to know about the rotation in air and gliding part.

the game physics is similar to this link
http://www.miniclip.com/games/catapult/en/

can anyone please let me know what physics formulas be required to achieve this
Any help is highly appreciated

//currently the code is here what i have written
float _velocityAngle;
b2Vec2 _linearVelocity, _orientation;
float torque;
float torqueFactor = -100.0f; //set this to whatever works for your units -100
float torqueDamping = 2; //this is a good starting place, but experiment 2
float _airGripFactor = 1.0f; //1

_orientation.Set(cos(gameSceneRef->gameBodies[BOD_ANIM_PLAYER]->GetAngle()), sin(gameSceneRef->gameBodies[BOD_ANIM_PLAYER]->GetAngle()));

_linearVelocity = gameSceneRef->gameBodies[BOD_ANIM_PLAYER]->GetLinearVelocity();

_velocityAngle = (float) (atan2f( _linearVelocity.y, _linearVelocity.x ));// + (b2_pi / 2));
float angVelDelta = gameSceneRef->gameBodies[BOD_ANIM_PLAYER]->GetAngle() - _velocityAngle;

//Constrain to -PI -> PI
while (angVelDelta > b2_pi)
{
angVelDelta -= 2*b2_pi;
}
while (angVelDelta < -b2_pi)
{
angVelDelta += 2*b2_pi;
}

float absVel = _linearVelocity.Length();
torque = absVel * torqueFactor * (angVelDelta) - absVel * gameSceneRef->gameBodies[BOD_ANIM_PLAYER]->GetAngularVelocity() * torqueDamping;
gameSceneRef->gameBodies[BOD_ANIM_PLAYER]->ApplyTorque(torque);


float32 proj = b2Dot(_linearVelocity, _orientation);
b2Vec2 targetVelocity = b2Vec2(_orientation.x * proj, _orientation.y * proj);
b2Vec2 force = (targetVelocity - _linearVelocity);
force = b2Vec2(force.x * _airGripFactor, force.y * _airGripFactor);

gameSceneRef->gameBodies[BOD_ANIM_PLAYER]->ApplyForce(force, gameSceneRef->gameBodies[BOD_ANIM_PLAYER]->GetWorldCenter());

 

[Valerie Park]

You need to use the equation of motion of a projectile, which is a special case of Newton's second law of motion. As the player is in the air, they experience a force due to air resistance. The equations of motion for this situation are as follows: F = ma Where F is the force on the player due to air resistance, m is the mass of the player, and a is the acceleration of the player in the x and y directions. To calculate the air resistance force, you can use the equation: F_air = -1/2 * C_d * A * p * v^2Where C_d is the drag coefficient, A is the cross-sectional area of the player, p is the density of the air, and v is the velocity of the player. You can also calculate the torque on the player due to the air resistance by using the equation: T = 1/2 * C_d * A * p * v^2 * RWhere R is the radius of the player's body. Finally, you can calculate the gliding position of the player using the equation for the trajectory of a projectile: x = x_0 + v_0 * t * cos(theta) y = y_0 + v_0 * t * sin(theta) - 1/2 * g * t^2Where x_0 and y_0 are the initial position of the player, v_0 is the initial velocity of the player, t is the time since the launch, theta is the angle of launch, and g is the acceleration due to gravity. I hope this helps!