Selig Z Chair Cushion Dimensions?  

Just measure the frame.
Seat:
width = from the far side of the seat frame to the other side
depth = front edge of frame to back edge of frame
Back:
width = side to side as above
height = base of seat to top of back frame, minus the thickness of the seat cushion
THICKNESS:
This is where a bit of personal preference comes in.
I like 3" for the seat and 2" for the back.
If you do an image search, you'll see everything from that to 3" and 3", 4" and 3", 4" and 4" and maybe even 2" and 2". I think the chair looks top heavy when the back is the same thickness as the seat. And I think 4" on the seat is too chunky for this chair. But that's only my personal opinion.
The first photo is 3" and 2".
Second is 3" and 3" or maybe closer to 4" and 4"--either way, it looks top heavy to me.
Third is I think 3" and 4" but also the back cushions are too tall. You can go an inch or so taller but more than that starts to look odd.
Some people might argue that 3" and 4" is more comfortable but if the webbing isn't saggy and the foam density is chosen to work with the amount of support of the webbing, a 3" seat cushion will be very comfortable.

Thanks Spanky!
Thanks Spanky!

I like the following specs:
seat: 22" x 22" x 4" thick, medium firm foam
back and ottoman: 22" wide x 17" deep x 3" thick, medium foam
On a side note, these sizes fit many of the other Selig Danish lounge chairs of the era as well.

Thank you cdsilva!
Thank you cdsilva!

I am formally educated in...
I am formally educated in the art of fine woodwork and custom furniture makeing. I hand craft Poul Jensen Selig-inspired Z couches, Z chairs and Z love seats. I have made several improvements and modifications from the original Poul Jensen Selig Z Chairs. We use only select Black Walnut heart wood for the frames. Each piece of black walnut is chosen for its color and grain quality. The chairs are more works of art than factory-assembled furniture; they are individually-produced. All joints use traditional single or double mortis and tenon joinery, we use only formaldehyde-free glue. The arm rest now has a hand carved relief. Its smooth stippled surface is a mark of craftsmanship and artistry. The remarkably comfortable original seat geometry remains. A love seat is finally available.
Natural OSMO brand oil, hand rubbed http://www.osmona.com/
Upholstered using German Natural tanned leather http://www.vegetable-tanned-leather.com/
Made in the USA Lenzip brass zippers http://www.lenzip.com/
(edited by DA - no advertising please)

While there are some...
While there are some interesting pieces in your collection, your Z chair is quite a clunky version of the original, and even clunkier than the current Room and Board version.
Nice pillow dresser though.

I like the yellow pine coffin...
I like the yellow pine coffin.

I like the brain matter panels
or whatever they're called. I like them very much. The armless lounge chair is nice too, in a sturdy sort of way.
I'd love to know what are "improvements" in that Z chair over the original. It looks like high quality porch furniture. What is the purpose of the rough chiseled part of the arm rest?

Straps
I've been asked to fix a friends Z chair. Can anyone recommend the straps I should be using?
Also, the finish on the arms seem to be alligatoring of sorts. How can I fix this?

Most Selig chairs have slots...
Most Selig chairs have slots cut at a 45-degree angle to accommodate Fagas Straps. They're available at the link below, and are made from Pirelli webbing I believe.
Some have larger (1/2" x 3") slots, and use regular Pirelli webbing from a roll, wrapped around dowels. If you post pics, someone here can tell you which to use.
Pirelli webbing, as near as I can deduce, is a combination of rubber, fabric, and strands of 24 karat gold. That joke will make more sense when you start pricing it.
http://fagasstraps.com/

If my memory serves me correctly,
I think I remember seeing one dowell rod on each side.

Here's an example of the...
Here's an example of the dowel-type seat. The original dowels are smaller diameter and are one per side, but we didn't know that when we did this chair.
We use Pirelli webbing because it's supposed to last longer. Maybe someone on here can turn you on to the secret stash of Pirelli webbing for
http://themidcenturybeehive.com/post/60220643686/happy-holidays

I prefer the black elastic...
I prefer the black elastic webbing with the red stripe down the middle. The last time I did a search, Vogue Fabrics was among the cheapest prices at $3 per yard (down to $2 per yard with bulk purchase).
This material has good "grab" for your dowel tensioning system. Just make sure to cut a little more than you think in order to have enough end material to grab and tighten with your pliers.
http://www.voguefabricsstore.com/Upholstery-Elastic-Webbing.html

I used this kit on a Larsen r...
I used this kit on a Larsen recliner a little while ago. Happy with the results and a lot cheaper than the fagas straps.
Looks like they sell the red striped stuff by the yard too...
http://www.ebay.com/itm/WEBBING-REPAIR-KIT-CLIPS-FAGAS-STRAP-PIRELLI-KOF...