by XennoX » Thu Nov 24, 2011 11:55 am
Thread necro.
Gravity, being considered a vertical force, will have NO influence over the horizontal velocity and distance. You cannot add orthogonal vectors to each other as their influence on the other is zero.
The equation(s) you would have to develop would be the trajectory/ballistic equation, but you would have to add in the angular momentum of the golf ball and the drag force on the ball.
FD = 0.5·CDrag·Dfluid·AProjected·v², where:
FD is the Drag Force;
CDrag is the Coefficient of Drag;
Dfluid is the density of the fluid;
AProjected is the projected area of the object;
v is the velocity of the object.
Please note, Force is a vector and so if Velocity, the rest are all scalars.
Angular Momentum (aka Backspin) is given by the equation:
L = I·w
Angular momentum is a Vector, known as a moment. (Like Torque and Bending)
L represents the quantity for the angular momentum
I is the moment of inertia of the object
w is the angular velocity, often given as Radians Per Second (Rad/s)
The units of Angular Momentum are N·m·s as opposed to N·m for Torque and Bending
Your equation would also involve the use of Calculus, to find the maxima you would have to differentiate your function, but you would also probably have to integrate to find the total displacement.
Newton's equation of motion F = ma CAN be used, as this is a Newtonian problem. (Note I bold the quantities that are vectors)
It also may be easier to use a polar co-ordinate system as opposed to a cartesian co-ordinate system.
So it would look something like this:
Vertical Displacement = Initial Vertical Velocity - Gravitational Acceleration + The Lift created due to the Magnus Effect (aka Backspin) - Vertical Drag
Horizontal Displacement = Initial Horizontal Velocity - Horizontal Drag
Thread necro.
Gravity, being considered a vertical force, will have NO influence over the horizontal velocity and distance. You cannot add orthogonal vectors to each other as their influence on the other is zero.
The equation(s) you would have to develop would be the trajectory/ballistic equation, but you would have to add in the angular momentum of the golf ball and the drag force on the ball.
[b]F[/b]D = 0.5·CDrag·Dfluid·AProjected·[b]v[/b]², where:
FD is the Drag Force;
CDrag is the Coefficient of Drag;
Dfluid is the density of the fluid;
AProjected is the projected area of the object;
v is the velocity of the object.
Please note, Force is a vector and so if Velocity, the rest are all scalars.
Angular Momentum (aka Backspin) is given by the equation:
[b]L[/b] = I·[b]w[/b]
Angular momentum is a Vector, known as a moment. (Like Torque and Bending)
L represents the quantity for the angular momentum
I is the moment of inertia of the object
w is the angular velocity, often given as Radians Per Second (Rad/s)
The units of Angular Momentum are N·m·s as opposed to N·m for Torque and Bending
Your equation would also involve the use of Calculus, to find the maxima you would have to differentiate your function, but you would also probably have to integrate to find the total displacement.
Newton's equation of motion [b]F[/b] = m[b]a[/b] CAN be used, as this is a Newtonian problem. (Note I bold the quantities that are vectors)
It also may be easier to use a polar co-ordinate system as opposed to a cartesian co-ordinate system.
So it would look something like this:
Vertical Displacement = Initial Vertical Velocity - Gravitational Acceleration + The Lift created due to the Magnus Effect (aka Backspin) - Vertical Drag
Horizontal Displacement = Initial Horizontal Velocity - Horizontal Drag