Why the radius rating?

I would think maybe there are flanges on all drive wheels that restrict it to larger curves.  Usually on the tighter curve engines there is no flange on the middle drive wheels, just the outer ones.  

The number and placement of "blind" aka flangeless wheels affects the curves that a car or engine can navigate.   The placement of the pivot for the truck or frame also comes into play.  The size of the drivers also affects the wheel base and that can mean the turning radius on a given wheel arrangement can be quite different.  A freight engine with smaller diameter drivers will have a shorter wheel base than a passenger engine with 70+ inch drivers.  

Unless they start making the boiler castings like a slinky I suspect long wheel base engines that are also scale are going to be problematic on O-36.

O-36 is a 36"diameter.  O-72 is 72" diameter, 36" radius. I'm not sure why, in three rail, diameters are listed and in 2 rail, radius is the point of discussion.  Most of my steam locomotives do well on a layout that is limited to O-54. Surprisingly the "Klunk and Bang" issue is more with the switches than anything else.   Engine overhang on the curves is interesting.  I do well with a Weaver Pennsy M1a Mountain on the layout. I have to restrict speed through some of the O-54 switches.
Best wishes
Here is a small video of switching with a Weaver 0-8-0 Pennsy C1. Switches are O-54. My one O-27 curve is noted on the siding where the switching is being done. The K-Line 0-6-0 B6 switcher does not have the flex--- to negotiate the O-27 curve and hook to the box car to the right.  The long ugly coupler on the Pennsy C1 seems to be an advantage on the tight curve.  Inner loop is O-45. Outer loop is O-54.  Curve pictured with the crossing gates is O-54. 



Mike CT

Rigid wheelbase, side-to-side play in the drivers, pivot point of the pilot and trailing trucks and even the drawbar all have an effect.

Also, on something like a 4-8-4, the pivot piont of the pilot truck is generally at or near the centerline of the cylinders, but on a 2-8-4, the pilot truck's pivot point is futher back, generally between the cylinders and lead axle.

Rusty

Guess I never thought of drive wheel side play nor lead or trailing truck swing. All of the engines that are "-8-" driven that I've seen, the two center sets of drivers are blind - that's what got me to wondering.

Now the tender with a centipede truck and "all flanged"...yeah, I can see a curve restriction sans blind wheels there.

probably the 2-8-2 and 2-8-4 you have looked at, are the Lionel traditional sized engine (not scale) like the Jr Berk, Jr Mikado etc...they will run on O-27...the Weawer model is a scale one, reason why it need 0-72..specially with a centipede tender...

Not aware of any scale 2-8-2 or 2-8-4  running on smaller  than 0-54 curves.

In my experience, the Mallet and Articulated locomotives track the best on sharp curves. The Rail King 30-1163-1 N&W Y6b is excellent on 031 curves. So too are the electrics such as the GG1 and EP5.

Lafondue, truth be told, I'm hunting primarily MTH for the proto sounds sytems{origonal/1/2}...nothing against lionel or others, I just happen to have 2 proto2 engines already and plan on a DCS system controller. The weaver engine was just mentioned because I was curious about it's driver configuration capability , but not to buy it{no full sound - I want full sound}.

And yeah, most of the 1/48th berks or miks I've seen do need 0-54 or better...that sized curve is planned on the outer run of our planed layout when it gets built....carpet for now.