According to NEC Chapter 9 Table 5 Dimensions of Insulated Conductors and Fixture Wares
for 1/0 THWN-2 the O.D. is 0.486".
NEC 392.20 Cable and Conductor Installation. See sub.D.
392.22 Number of Conductors or Cables.
(B) Number of Single-Conductor Cables, Rated 2000 Volts or Less, in Cable Trays.
(d) Where any of the single conductor cables are 1/0 through 4/0 AWG, the sum of the diameters of all single conductor cables shall not exceed the cable tray width.[ that means minimum 4.86"]
So, in order to state the ampacity of the cable as per NEC you need a Ladder or Ventilated Trough Cable Tray of 5"[6"] minimum.
As I can see no requirement for single-core cables in solid bottom cable trays.
392.80 Ampacity of Conductors.
(A) Ampacity of Cables, Rated 2000 Volts or Less, in Cable Trays.
Informational Note: See 110.14(C) for conductor temperature
(2) Single-Conductor Cables.
(b)Where installed according to the requirements of 392.22(B), the ampacities for 1/0 AWG through 500 kcmil single-conductor cables in uncovered cable trays shall not exceed 65 percent of the ampacities in Table 310.17 and Table 310.19. Where cable trays are continuously covered for more
than 1.8 m (6 ft) with solid unventilated covers, the ampacities for 1/0 AWG through 500 kcmil
cables shall not exceed 60 percent of the ampacities in Table 310.17 and Table 310.19.
I=260*0.65 =169 for copper and 205*0.65=133.25 for aluminum.
Exception to (c): For solid bottom cable , the ampacity of single conductor cables shall be determined by 310.14(B ).See attachment.
However, the Rca -effective thermal resistance -calculation for cable trays is not indicated nor in Neher McGrath article neither in IEEE 835/94[as NEC Chapter B explains].
In my opinion it has to be in
ANSI/NEMA WC 51 ICEA P-54-440 AMPACITIES OF CABLES INSTALLED IN CABLE TRAYS
