Wouldn't the ballast

Disregard.  I misread what you were asking.

Transitions

2 different thicknesses of cork + belt sander

http://www.lkorailroad.com/cork-roadbed-part-iii/

how to make it look good and functional?

Don't make the transition too steep, you want the couplers to stay connected even if they are not all set to perfect height.   I recently did some transitions on my N scale layout and found that 3.5 inches long was enough to keep everything connected so that would equal about 6.5 inches in HO scale. You should be able to sand the transitions into the cork with some coarse sandpaper on a board if you don't have a power sander. for my N transitions I just sloped a piece of thin plywood roadbed down from high to low level and filled the gap under it with caulking compound( I don't like sanding so only do it on things I can't cut or plane to shape)......DaveB

Transitions

I used 1/8" Homabed for my mainline HO roadbed. They make transitions that slope from 1/4" thick to 0" in 16" of length. That is slightly less than a 1.6% slope. I cut off and used the "lower" 8 inches to make a transition from the 1/8" roadbed to 0". The 1.6% transition has been no problem whether running long E-8s with 85' passenger cars or an 0-4-0 or 2-8-2 with 40' & 50' freight cars. And, yes, I tested that slope first before making a commitment.

Dante

Here is an example on my

Here is an example on my unfinished inglenook.

The siding is on 1/8 inch roadbed and the mainline in the background is on a roadbed of 1/4 inch.

The transition is about 8 1/2 inches as seen between the two red pieces of foam. I have no idea on how to calculate what grade I have with these numbers. 

Shim stock?

Don't know details of costs and quick availability, but try comparing the Homabed taper stuff with a trip to your local hardware store. I have found at mine a pack of  wood shims intended for door and window frames. Near-zero thickness at one end, and can be cut off to give whatever thickness you want at the other. Lots of shims for no more than $4.

For near zero cost, building a taper from card stock or paper can work.

For such a short transition, why is grade important? A nice quick slope will accentuate transition from mainline to siding. I think more important is maintaining the couplers' function.

Belt Sander

Using a belt sander to transition between different thicknesses of cork is easy and fast.

I start the ramp down just after the turnout and  spread the vertical curve over a distance of a foot or more.

Do the maths...

Dear Deem,

EDIT: values changed, I missed the 1/8" and thoug the change in elevation way 1/4", my bad!

Let's do it:

Grade = Rise (vertical change) over Run (horizontal distance travelled)

Grade = 1/8" UP over 8 1/2" ACCROSS

Grade = 1" over 66"
(multiplied both values by whatever it needs be,
in this case a value of 8,
so the "UP" value becomes a "1".

Same maths used to calculate the angle of a turnout)

Therefore

Grade = "1 in 66" in UK terms

OR

Grade = "1.5%" in US terms
("1 in 66" approx = "1.5 in 100")

NB that the above assumes a hard "angle" at the top and bottom of the "grade",
if we added slight vertical curves or "transitions" the actual grade will wind up being slightly steeper than calc'd...
(the linear length taken up by the transition "curves" results in less horizontal "Run" for the same "Rise")

Happy Modeling,
Aim to Improve,
Prof Klyzlr

"...One doesn't need to know the maths to make it work,
but it gives comfort and confidence that your "theory" is likely to succeed if the math's matches up to expectation, and known-working values... "

PS Using foamcore as both the sub-base and the roadbed, it becomes easy to cut a trench in the sub-base,
let the roadbed "s-bend" down into the trench, with the natural flexibility of the foamcore forming the transitions...

Simple formula

Rise over the run. Or rise divided by the run. In your case the rise is 1/8 of an inch, the difference in height between the 1/8 of an inch for the siding and 1/4 inch for the main. The professor has a simple method for you to make sure you are using the same units of measure. Multiply 1/8 by 8 and it becomes one. 8 and 1/2 times 8 is 68 units. The actual units do not matter in this case they are 1/8 of an inch but the formula works in this simplified form easily as long as the units are the same. Had the actual difference been 1/2 inch you could have multiplied by two. You could also convert all fractions to their decimal equivalent but the above method uses the less math.

1/ 68 =.01470. or 1 divided by 68 equals .01470 which is a nearly 1.5 percent grade. The answer is read to the right of the decimal two places to the right is 1 through 9 percent, one place to the right is ten through 90 percent, and three places to the right is tenths of one percent. The actual percentage is one point four seven percent for your grade.

Rob in Texas

Rise (vertical change) over Run (horizontal distance travelled)

  continuing Prof's instruction. Here's another version of the same thing. .25 inch/ 8.5inch=.03 or 3% .  The way grades are calculated is normally the straight grade going in, the point of intersection of the grade, the grade going down the ramp, the point of grade intersection , and the straight  grade going out. A vertical curve would be centered over the points of grade intersection so half the length of the vertical curve extends into the grade going in and the grade going out. The maximum slope (3% in this case ) would stay the same since the center of the slope is not included  in the vertical curves....DaveB

thanks so much

Transition Calculation

The elevation change in Deemiorgos' example is 1/8" in a distance of 8.5" which is 68-8ths. The correct calculation is 1/68 as stated above or 1.47%, not 3% as stated by the Professor whose calculation was based on a 1/4" change in elevation, not the actual 1/8".

Dante

example is 1/8" in a distance of 8.5"

in that case  1/8"=.125" ( rise)/ 8.5"(run) =.0147 or 1.47%, simpler using decimals instead of 8ths or 12th or whatevers....DaveB

My bad... (should read more closely...)

Dear Dante,

Well spotted, I totally missed the 1/8" reference, and therefore the correct difference value between the Main and Passing roadbed heights. My initial post has been edited to correct the mistake.

(The maths was solid, the plugged-in values were amiss... ).

Apologies to all...

Happy Modelling,
Aim to Improve,
Prof Klyzlr

"...not the first time in my life I've been wrong about something,
and certainly won't be the last...
...however, as long as I learn from the mistake, it wasn't a waste..."

PS Side-question: anytime maths is required here on fora, 

does anyone actually follow the working, 
plug in their own values,
and thus learn how to "apply to their own situations",
IE "teach a man to fish and he'll eat forever"

or do we all expect to be handed the specific solution to our unique situation on a silver platter?
IE "expect someone to hand us a fish on demand"

Decimals and fractions...

Dear Dave,

I'd happily use decimal, except that being a majority US forum,
and the OP was in fractions,
it seemed logical to try and "stay in the comfy zone"...

Happy Modelling,
Aim to Improve,
Prof Klyzlr

"stay in the comfy zone"...

We're in the comfy zone, prof, me and my calculator :> )  BTW. I got another CCT SW1500 now I got 1504 and 1502. Not sure what I'll do with them since they don't usually use them to switch Lodi, maybe staging switchers? ....DaveB

A good SW1500 is a poor thing to waste...

Dear Dave,

O/T, but such a pity to relegate those cute SW1500s to staging work...
I say 1790 is down with a strange low-water issue, and the 1500s need to keep the show going...
(and if that means waltzing a load of syrup and sugar to Sweetener Co @ Lodi, then so be it... ).

Happy Modelling,
Aim to Improve,
Prof Klyzlr

Transition Length

AzBaja,

That has not been my experience with the slopes and dimensions I have. It would be a safe bet, however.

Dante

Very interesting. I never

Wood shingles for tapered shims

Just use wood shingles that they use for house siding and roofing.   The taper is already in them and if need be they can be sanded easily.

Cardstock shims and glue

Get some card stock material from the wife's shopping. Say .030. cut to width, stair step over the distance with glue, lay the track and ballast. No mess, no sanding, no noise, no trips to the box store.

Plywood Sub-roadbed

I used plywood on risers for my sub-roadbed and this makes it very easy to vary the height of sidings.

Notice the cut between the siding and the mainline, but not under the switch? This allows the siding to transition naturally to the siding and you can use the same roadbed everywhere.

In another place, where I wanted to drop all the way to my plywood base, I used a piece of masonite that I sanded with a belt sander to get a nice long taper.

Foam to the rescue

I've used a strip of foam (blue or pink) about six inches long by the width of roadbed plus another  .25 inch. With a sharp knife or hot knife then sliced the taper, guided by a steel rule.

siding height

I am in HO, and I use HO cork for the Main, and N cork for the siding. I run the HO about a foot past the turnout branch.  I use a Surform plane to make the taper. I also do the same from the siding down to the benchtop for spurs. Make the tapers at least a foot long, more is better! John Colley, Sonoma, CA