Optimal axis of rotation of a baseball for lateral movement Suppose a baseball travels at $90\;\mathrm{mph}$; what is the ideal axis of rotation for lateral movement of the ball? (two-seamer or cutter).
So far I think that the following factors play a significant role in determining lateral movement: Magnus Force, $\mathrm {RPM}$ (Suppose $\mathrm{RPM}=1700$), the height of seams (MLB official ball, I couldn't find the height of the stitches), air pressure ($1020$ millibar ($\mathrm{hPa}$)). 
Even though I think these variables play a role in determining lateral movement I do not know whether they interact with the axis of rotation in such a manner that it matters for the optimization of the axis of rotation.
 A: It seems to depend mainly on the spin. See the comsol.com simulation at https://www.comsol.com/blogs/physics-behind-baseball-pitches/
For the slider, in essence a lateral motion, Just spin it laterally, right to left if you are righty, and it'll curve to the left. The axis of rotation would be vertical, if righty the direction of the angular momentum vector is up. See the comsol.com simulations for all spinning cases.
The seams do make a difference, they effectively cause more movement due to a greater Magnus force from the same spin, something about creating some boundary effect I don't follow. The same thing happens with the dimples in golf. The air pressure and temperature contribute to more or less force, and of course the greater the spin the better. Apparently a slower velocity forward makes it curve more (maybe to a limit), probably just more time with that force, so curves are slow, sliders some what faster. Some of that may have to do with the mechaniscs of creating those spins, some can be created higher and some slower, both in spin and in translational velocity
An interesting thing pointed out in a few sites is that some of the motion perceived is due to perception effects as the ball moves from the central vision to peripheral, I did not understand it but it seems reasonable
The interesting one is the knuckleball, comsol.com has a link to a gif which show it and it is amazing. It hardly spins and moves a bit randomly, they said something as to why but I don't understand it. The forkball is another not clear to me (I know two fingers widely separated, I think, Elroy Face won 17 games or so and lost only 1 in 1960 with it - I remember it)
