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Number 4 turnout would do it, but be aware not everything goes through it.
Sizes are measured by how many frog sections it takes to complete a diverging. Or by radius in model railroading.
I use large switches myself and sacrifice a few tracks to gain the ability to run anything through them.
Presuming you're talking about 3-rail and Ross turnouts, #4 turnouts are fine in yards and for industrial spurs as these are taken at slow speeds. #6's will be fine for your mainline crossovers (#8's or #10's would be better aesthetically and for high-speeds, but take up a lot more real estate.) All 3-rail equipment produced to date can negotiate a #4 turnout as Ross uses 36" radius (O-72 class) points.
Obviously, larger equipment looks better negotiating larger turnouts. Some 2-rail steam locomotives will not negotiate anything smaller than a #6, so a lot of the operators with layouts featuring large steam will have nothing smaller than a #6 for the yards a industry spurs and #8's and 10's on the mainlines.
Hope this helps.
Mr. Johnson
Matt Jackson gave you good advice here.
All 3-rail equipment produced to date can negotiate a #4 turnout as Ross uses 36" radius (O-72 class) points.
Numbered switches are available in 3 rail from three manufacturers, Atlas, MTH in the ScaleTrax line and from Ross. Any numbered switch will handle any 3 rail train requiring O-72.
On a numbered switch the curved portion of the diverging route is between the points and the frog. Beyond the frog the diverging route is strait. The ratio of divergence to distance past the frog defines the switch number. So a #4 diverges 1 inch for every 4 inches traveled past the frog, a #6 diverges 1 inch in 6 inches traveled, etc.
Since you mention #4s and #6s I assume you are looking at either Ross or MTH Scaletrax switches. Be aware that a Ross #4 is not the same as an MTH #4. The Ross #4 is tighter. The Ross Regular switch has an 11 1/4 degree frog and is equivalent to a #5 switch. The MTH ScaleTrax #4 is an 11 1/4 degree switch and would most accurately be described as a #5.
Atlas makes a #5 that is an 11 1/4 degree switch like the Ross Regular and MTH Scaletrax #4. The Atlas # 7 1/2 is a 7 1/2 degree switch like the Ross #8.
That all makes sense, doesn't it?
The Ross #4 or Ross Regular, MTH ScaleTrax #4 and the Atlas #5 are all good choices for use in a yard and can handle all O gauge trains. You don't need #6s in a yard unless you are moving away from traditional 3 rail equipment to 3RS. Three and a half inch centers work well for yard tracks with numbered switches.
I'd be a bit less conservative, using Atlas O-54 shorts you can probably achieve 4 1/4" center to center spacing. Allowing 3" for edge of layout, whether it's 3 1/2" or 4 1/4" it's either 3 or 4 sidings in the 1 foot available.
Add 3/4" to center of your inner loop. Total 1' 3 3/4" (15 3/4") to edge of layout.
3 1/2" center to center. (4 tracks)
Siding #1, 3 1/2",Siding #2, 7",Siding #3, 10 1/2", Siding #4, 14", 1 3/4" from the center of the rail to edge of layout.
4 1/4" center to center (3 tracks)
Siding #1, 4 1/4",Siding #2 8 1/2",Siding #3 12 3/4", 3" from the center of the rail to edge of layout.
I've used a Ross 204 three way before, a #4 switch I believe. It was in that 4 1/4" spacing range for the three tracks.
Three tracks is a safe bet, (4) tracks is gonna take some work. IMO
4 1/4" spacing. A Ross 204, a #4, combined with Ross 100/101s which I believer are #5 switches.
Mike