To the printer! Then the machinist!
Only joking
My printers broken
Not entirely sure GGDT will work properly as this valve works in the opposite way to the valves intended for it but here goes:
So thats a 1" hole through which the air escapes from the chamber. Taking into account theres a 0.5" piston rod also sharing that space I get 0.785 - 0.196 = 0.589"sq. The 'seat diameter' of a circle of that area is 0.866".
The piston diameter would be the large disk which is about 1.5" after the o-ring is on.
The vent diameter is where you need to put the diameter of the pilot hole.
The piston mass is for the whole moving section of the valve.
The pilot volume is whatever volume the compressed air has to fill before it gets to that 1.5" piston face
and the volume created by the piston moving forwards.
Once you've got all that in you can find the flow co-efficient using the GGDT
Cv/Kv/Eff Calculator which is in GGDT but thats a help page for it.
Hope that helps.