As others mentioned here, percentage of slope is what is typically used and not degrees. It is much easier to think in terms of inches instead of degrees or radians. A 2.5% grade is 2 1/2" over a 100" run. A 2% grade is 2" over 100" run. Now 100" is really close to 8 feet so you can guess-timate about 8 feet for each 2" rise. You want 12" at 2% you need 48 feet. A 12" rise at 2.5% requires about 38 1/2 feet. At 3" the run you need is down to 32 feet.
That's all well and good but there is no consideration for vertical easements on both ends. What I've come to understand is the length and number of transitions are functions of the length of the longest engine and what the final grade is at the end of the transition. For 2, 2 1/2" slope and with a engine length of about 20" I try to transition 2 times, every 30-40 inches. The first transition is about .6%, then about 1.3% and finally reach the 2.5% grade over a total of 6 or 7 feet. This is at both ends.
You can plug in what numbers you want but usually the run distance is restricted by physical limitations so you start compromising. You can use a steeper slopes and reduce the run distance but you may need more transitions to get to that grade, so you gain here and lose there, etc. and hopefully iterate to workable solution.
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