031 FasTrack figure 8 without cutting track?

Generally, the clearance issues between an O31 and an O36 loop will prevent their interoperation.  But, since you will only be running smaller pieces on the inside loop, if you add a short straight section on the 2 four foot ends of your O36 loop, you should be fine.  To answer your question about "cut" pieces, I suggest you download either SCARM or AnyRail track planning software to test build your figure 8.  Both are free to use with a limited number of pieces (not a problem in your situation) and both have good FasTrack libraries that you can use to test designs.

Chuck

Here are 2 options. The first has 4.5" or more center rail to center rail clearance. The second has just under 4.5" clearance. If needed, the Gold tracks in both can be squeezed together by removing the 10" straights or replacing them with shorter pieces. The Blue tracks in both can be widened a bit by replacing the 2 1 3/4" straights on each end with a single 4.5" straight depending on how close to the edges you're willing to go.

"031 FasTrack figure 8 inside an 036 loop without cutting track on a 4'X10.2' layout?"

According to SCARM you would use 8x of the Lionel short 1 3/8 inch pieces, 4X 10inch pieces to make the smallest possible figure 8 using 12x 031 Fastrack curves. Also the 90degree cross Fastrack piece.

Then the outer 036 track is 8x 036 curves, 2x 30 inch straights, 2x 10 in straights, and then 2 4.5inch straights. This measured in right at 82 inches, but you want more table than that and could ever so slightly extend that outer loop with some more straights in both directions to give more breathing room.

BTW, those short little pieces of Fastrack add up quickly. I noticed a minor difference in how I created the X crossing VS Dave's and while his is very exact, the cost is much higher. He used 2 each 4.5 inch straights to make a 9 inch piece, then the smaller 2 smaller (guessing 1 3/4) pieces. Also then using 4 more short pieces along the straight lengths, again, just know those little pieces cost nearly the same as a full 10 inch piece. Again, my X is just every so slightly off on alignment, but easily would mate up in real life given the distances. The center cross difference is 4 more pieces of track to get perfect ideal alignment and at lets say $5 each, that's $20 cost difference. Same thing on the straight legs down the sides, that 4 more pieces, another $20. You could shift the X crossing left or right and use 2 less pieces or just omit them entirely. Again, the problem is, Fastrack is sold by the piece and it does add up and matter when designing on how "exact" you want to be.

VS

Again, yes, I'm technically off in 2 spots, but the difference is easily made up by minor flexing of the total sum of joints in the circle.

Here is a 4x8 version using RailModeller express

Vernon. I did that too, but I always strive for proper joints because I often run the simulator. Did you measure the track clearance. If he runs 2 trains in opposite directions, he needs enough so they don’t hit. I can’t really tell from the photo, but it looks kind of close. At any rate, I think Bobbie’s got enough info to work with.

Assuming a 3.5" width for Fastrack, the outside diameter of an O-31 circle (31 inches is measured at the center rail) would be 32.75" (31 + 1.75).

The inside diameter of the O-36 FT circle (again, 36 inches is measured at the center rail) is 34.25" (36 - 1.75).

So the clearance would be 1.5" (34.25" - 32.75") inches if my math is correct ?

I believe that's why a short straight piece is typically added in the middle of each O-36 circle - to space it away from the O-31 loop.