Projectile Motion with Lift and Drag

[Padj01]

I need an equation to solve for the distance traveled of a projectile. The variables that I have are lift coefficient, drag coeficient, launch angle and initial velocity. Could someone please help me find the formula I need. Thank you.

 

[demothenes]

First, isolate the initial movement in the x and y axes. For X, use cosine multiplied by the angle, and for Y, use sine multiplied by the angle. Then, take the sum of the forces in each axis.

X=(Forward{X} movement - drag {Coefficient*normal force})

Y=(Upward{Y} movement - gravity + lift {coefficient*normal force})

Then, you can use a time-in-air formula.

 

[Crosson]

Then, you can use a time-in-air formula.

You are a far ways aways from the end of the problem, at this stage it is certainly not obvious which ""time-in-air formula" you are talking about.

This is a tedious exercise in differential equations, solve these:

$$x'' + \frac{A}{m} x' = 0$$

$$y'' - \frac{L}{m} x' + g = 0$$

To get position x and y as functions of time. From here these, you can figure out how far things go (answer: find t @ y = 0 and solve for x(t).)