I've attached the intake calcs for my teams robot this year. Our robot was geared for 14.5 fps so our intake was geared according. We spent weeks upon weeks testing on what intake was the fastest and best and came out with 6, 4" mecanum wheels (3 on each side) and 2, 4" stealth wheels in the middle. Our intake was very very quick. We took inspiration from 118 and worked with them a bit to understand how theirs worked.
As stated earlier in the thread, 2x your robot's ground speed is a good start for your intake speed. We then also threw power at it. We used 2 versaplanetary each with a 775pro to power our intake. We put about 1.75" of compression on the ball to grab it but when the ball came into the robot it would compress down from about 10" to 4" to get into our catapult. We had no issues with jamming or anything all season.
Here is some video of it in action.
https://www.youtube.com/watch?v=Y13rcqgDcBU
