I do these large pie shaped winders fairly often, and most of the time we glue and spline additional stock onto the width of stair blanks to get a piece of solid stock large enough.Never had any problem with movement. You are correct in that this looks better than using flooring in the middle of a run of stairs.

Hi,
The expansion/contraction of 3' of oak will be at least 1/4" seasonally. Do you want this to manifest at one point, or be distributed evenly among 15 or so individual planks? At some point a landing or winder becomes so large that gluing up one big board is not a good idea. At some point, the shrinking stresses will split the big board at a nail. (board tries to shrink, nail prevents movement, stress is relieved destructively.)
Assuming a three foot triangle, my estimate is that you are at the point where planks make better sense than one big board. I'm east coast, BTW, where we see a wide variation of humidity from winter to summer.
Casey

Perhaps if I provided measurements, it would help in solving this problem.

First (and bottom) step: 33.5 X 20 X 29.5 (29.5 side includes small rectangular cutout at one end)

Step 2: 29.5 X 30 X 47

Step 3: 47 X 24 X 40

"The expansion/contraction of 3' of oak will be at least 1/4" seasonally. "

Wood barely moves parallel to the grain in length for any humidity.
Movement is perpendicular to the grain.
See chapter 3 of the Wood Engineering Handbook.

Here is a link that might be useful: Wood Handbook

Yes, Brick, that's what I'm talking about. Previous answer suggested gluing up a one-piece pie shaped winder tread, I was pointing out that it will exhibit a good deal of movement, and that it could have bad consequences.
Casey

As long as the design is correct to allow for the movement all that happen is the back of the tread moves.
The expansion is on the concealed side behind the riser, just like it is on all the other treads.

We have 3 pie shaped stair treads in ours where we used oak flooring strips - I have attached a link. The dye stain we used helps minimize the grain of the oak as compared to pigment stain - and they blend nicely with the solid treads.
Kathy

Here is a link that might be useful: oak staircase

Yea, I know all about wood movement theories, but from experience I have done many of these, spline the joint, use two part epoxy, and have never had one crack. As suggested, the movement will take place to the rear, under the riser. The point is well taken about nailing though. I only nail at the front edge, and set the tread in construction adhesive, which allows some lateral movement.
I am in New Orleans, so there is no lack of humidity here.

And the key to a successful wide board glue up as I am sure that all above know. Is that the board have to be dry and acclimated. As long as that is done you should have no problems with your step. The other thing that could be done is a sheet of 3/4" oak veiner with a bull noise glued on. All though I would go with the glue up of wider boards.

"Is that the board have to be dry and acclimated."

No matter how dry and acclimated a wide board is going to move.
Finishes will slow the movement, but it is going to move over the heating and cooling seasons.

The secret ios corect construction that allows the wood to move in a less visible place without creating a problem.
Stair trads have classically been held in with wedges and only nailed at the leading edge.
This forces the movement to occur on the back edge of each tread behind the riser. A nice hidden place in most cases, or not very noticable if the back of the stair case is exposed.
Wood splits normally when it shrinks and is held in place across the width (perpendicular to the grain).
Sometimes the splitting shows up after it expands and binds tightly, then shrinks and cannot move freely.
I routinely glue up winders from matching wood without any problem, as long as the carriage is designed correctly and the treads installed correctly.

Thanks Kathy for the pictures. Your stairs are beautiful, however I plan to have a light oak stain which I expect will display more of the grain differences between the winder steps and the regular tread steps. I spoke with the carpenter about my wishes/concerns. He will only guarantee the results if I use his original plan for oak flooring on the winder steps. He also does not do the finish work, i.e., staining, painting, varnishing; though he can connect me to people who do this. Is this the usual process? I expected to hire someone to come in and do everything. I visited a new home under construction and viewed his unfinished wood trim work (window trim, door trim, etc.) as well as new staircase. He is very meticulous about his work and got praise from others working on the site (he was not there). One of the reasons I am doing the staircase over is that it is narrow and I need a railing that can be removed when large pieces of furniture need to be moved up/down stairs. He seems to have a good design to handle this problem, so I wasn't expecting to have these concerns about the winder steps. Will using oak flooring on these steps become a resale issue?