Do actual trains operate on banked curves?

[Ralph S]

If Yes, then has anyone tried to run their HO scale trains on banked curves?

The reason I'm asking this, ... I'm working on an incline that is curved and wondering if I bank the curve inward toward the curve, and the incline is 3 to 4 percent, then placing the train in a moderate speed (before the incline curve, in order to get the loaded train to the top of the incline), will the train and its cars fall over at slow speeds, or will the momentum of the train at moderate speed be maintained and the train cars make it to the top of the hill.

I believe it'll be quite an intrigue to see the train cars leaning as they go up the incline.  If I leave the incline tracks flat, it becomes none sensational (same as any train curve).

I've seen images and watched many trains moving in curved sections that look like they-re on a banked curve, but isn't that an illusion cause -aren't train tracks always set flat, even in curves?

[trainman203]

Prototype curves are banked according to the speed limit on that section.

[Ken Clark]

  The amount of super elevation used is based on the degree of curvature and speed limit planned for the line.

  example  20 degree curve radius 286 feet (HO 3 feet 3 inch's) 25 MPH outside rail 7 & 13/16 inch's higher. 

[jward]

While the real railroads bank their curves I would advise against it on a model railroad, particularly using small radii on a steep grade. The physics is far different for model trains than real ones, and long trains can roll over on banked curves. I t was a well known hazard on my grandfather's layout, where one 24" radius curve was unintentionally banked. Unless you were very careful starting a long train on this curve, it would roll over. Since the curve was near the entrance to a yard, trains often stopped there. And to make matters worse, much of the curve was in a tunnel which meant a trip under the layout to reach up inside the mountain to retrieve the derailed cars. We didn't have that problem on the unbanked curves, or any of the unbanked ones on subsequent layouts our family has built over the years.

[Ralph S]

Note: I usually log in about once a week more or less, but this was one topic I am fully engaged in. 
So, I if got this correct, real railroads actually do bank some of their curves.  The images and actual observations that I've witness (because I couldn't actually verify that the track was banked) that curved and banked track is not an illusion.     

Now, I have enough room for this inclined curve.  Your experience with 24-inch radius I'm thinking may be to tight.   I have the 33.25-inch radius 18 Degree (model 44504), or should I use the 33.25-inch radius 12 degree (model 44509) or should I use the 28-inch radius 18 degree (model 44506).    Of course, I could use flex track, but that would bring up issues that I'd prefer not to delve into, like cork bedding, nailing track to prevent movement, etc.

The illustration below shows how maybe the EZ track would be angled just enough to give that impressive look of the train leaning in the curve.  The question I haven't been able to resolve is the difference in the rail height compared to the other rail (orange question mark ?).   My mathematical calculations can't seem to solve it. Therefore, I must be missing something.  I'm going to try to do an actual measurement once I get the incline setup.

Lastly, if all else fails, then I'll take your recommendations and move to flat unbanked, unimpressive track curves.

[Len]

Some info on superelevation.

https://www.trackplanning.com/superelevation.htm

Len

[Ralph S]

This is a godsend!  I was scratching my head as to my calculations.  I didn't think about the speed of the train as being part of the calculation.  Thanks for the website.  This clears up a lot. 
Again thanks!