Welcome to the PF.Katie Smith said:I need an equation that solves for the height of a projectile at a specific x position. The known variables are spin of the ball, initial position, initial velocity, initial launch angle and the drag and lift coefficients.
berkeman said:Welcome to the PF.
How does a projectile have "lift"? Do you mean like a golf ball with backspin?
I googled projectile motion with air resistance, and got lots of good hits...
https://www.google.com/webhp?source...UTF-8#q=projectile+motion+with+air+resistance
The equation for projectile with drag and lift is given by:
m*ddot{r} = F_{grav} + F_{drag} + F_{lift}
Where m is the mass of the projectile, ddot{r} is the acceleration vector, F_{grav} is the gravitational force, F_{drag} is the drag force, and F_{lift} is the lift force.
Drag and lift forces act in opposite directions and can significantly affect the trajectory of a projectile. Drag force reduces the horizontal velocity of the projectile while lift force changes the vertical direction of the projectile's motion. These forces can cause the projectile to deviate from its expected path and result in a curved trajectory.
The magnitude of drag and lift forces depends on various factors such as the shape and size of the projectile, the velocity of the projectile, the density and viscosity of the surrounding medium, and the angle of attack of the projectile. These factors can significantly affect the performance and accuracy of a projectile.
To calculate the trajectory of a projectile with drag and lift, we can use numerical methods such as Euler's method or Runge-Kutta method. These methods involve breaking down the projectile's motion into small time intervals and using the equation of projectile with drag and lift to calculate its position and velocity at each interval. By repeating this process, we can plot the trajectory of the projectile.
In most cases, it is not recommended to neglect drag and lift forces in projectile motion calculations. These forces can significantly affect the accuracy and performance of a projectile, especially at high velocities. However, in some cases where the projectile's velocity is low or the medium's density is negligible, these forces can be ignored without significant impact on the results.