How much room will I need (in Feet) for 3 percent? grade to raise up 4 inches?
11 feet 1 inch from theoretical level 0" to theoretical level 4" plus about an additional foot on each end for the necessary vertical easement. Figure thirteen feet total. If there is a curve on the grade, good practice is to ease the grade to compensate - which will add to the length.
I have a couple of uncompensated three percent grades on my under-construction layout, which have proven to be challenging for some of my motive power. You might want to test yours, to see if you will require doubleheading or a helper. (All of my problem children are light steamers. My diesels and electrics have no problems on 3% grades.)
Chuck.
Gama, great rule of thumb for grades, is
100 inches, up 1 inch, 1%grade
100", up 2" 2% grade
100", up 3", 3% grade…
100" is equal to about 8 feet, 4 inches.
Do not forget the easement (transition) at each end. A good recommendation is no more the ½% change in grade per foot. Thus, to get to 3%, you will need 6 feet, and another 6 feet to get back to flat. If you are running short cars and locomotive, you may be able to get away with faster transitions.
For grade transitions, a combination of experience and theoretical calculations show that a minimum vertical radius of 14ft can handle any HO rolling stock. A 10ft vertical radius will handle anything that will go around 18" radius curves. This sounds big, but it isn’t because the change of angle between level and grade is quite small, even at 4% grades. I think I calculated an 8" easement for my 6% grades.
The ratio between minimum horizontal and minimum vertical radius seems to be around 1:7 on some traction prototypes specs I have looked at. Non-traction railroads use a parabolic easement on grades, with the convex easement (top of the grade) being gentler than the concave. Models seem to do OK with a slightly smaller ratio than our full-size traction brethern, but it’s a good starting point.
Reality is that if you use cookie cutter techniques with any reasonably stiff subroadbed, you will automatically build in enough of a transistion. By cookie cutter, I mean bending the subroadbed in the vertical dimension and raising it on risers and cleats fastened to the layout framework. Examples of subroadbed being cut and bent are plywood and foam.
Where you are most likely to have transition problems is when you build a ramp on top of a flat surface. This has become more prevalent today with the use of grade risers mounted on top of flat foam sheets. In this case, you do need to take care to get a decent transition. Cut a piece of cardboard for a transition template, and check your roadbed before laying track. If you see daylight under the cardboard at the transition point, adjust and recheck.
FWIW, John Allen developed a formula based on some experimentation that says the extra friction on a curve is equivalent to (in HO) 32 divided by the curve radius. This says that if you are using 22" radius curves, the effect is the same as (with small rounding error for doing this in my head) to a 1.5% grade. If the 22" radius curve is on a 2% grade, the effecti