I was thinking about that it is a 13“ swing was stuck between a 8” or a 10” 4 jaw thank youTypically, with a body diameter about 3" to 4" less than the swing. Much larger than that and you are paying for capacity that you will never be able to use because the jaws will hit the bed when they get a little bit outside of the chuck body..
Thank you looking into one nowNot many companies make a 13" lathe. It is sorta a bastard size. And unfortunately, even fewer will make a 9" diameter chuck. However, given the choice I would probably go for the 10" chuck assuming that I could afford it. And adopt a paranoid attitude about always slowly rotating the chuck and spindle by hand before engaging the motor.