As with anything, the answers can be found with Google if you know the search terms.
Terms:
Approach Angle, Departure Angle, Breakover Angle.
There are numerous entries on how to calculate these for your rig. Note that virtually all of these discussions focus on 4WD off-road vehicles, but the math is the same.
There are also numerous types of "
angle gauges" out there. I personally like the Lexivon protractor...simple and sturdy, and the arms are long enough to line up well with 2"x4"s.
One might get a couple of 12' 2"x4"s and lay them at the angle...one on the flat, and one on the slope, then use the angle gauge to get the angle. Note that any "rounding off" of the road surface effectively reduces the angle, but the distance that matters most is the wheelbase of the rig...and the distance between the rear axle center and the rear bumper of the rig...for butt dragging.
Of course, this is all too much monkey motion...and still largely guesswork. All you really need to do is BACK down the hill with a spotter on each side. The most vulnerable point is likely to be the black/grey water dump valves. If the spotter says stop...stop. Have the spotter take a pic with her phone...do NOT try to set the brake and get out and look. Pull back up the hill. But if these clear, everything else should clear...depending, of course, on where the dumps are located relative to the wheelbase. Dumps near the axles won't ground out, but if they are somewhere in the middle of the wheelbase, they might.
ALSO VERY IMPORTANT: Eyeball the underside of your coach. Remember that you have a drive shaft from the rear of the transmission...not far behind the driver's seat...all the way back to the rear axle. In many cases, this drive shaft will be segmented and much of it will be carried high in the chassis, but not always. Other vulnerable soft points, like the fuel tank, exhaust system (including tail pipe), exhaust for your onboard genny, may also be down in harm's way. You can mark the location of these vulnerable points with masking tape on the side of your rig, and as your rig approaches the breakover point, your spotters can get on their hands and knees with flashlights to see if any of these soft points are in danger. (Give your spotters some throw rugs or floor mats to kneel on and to keep their hands out of the dirt...this will vastly improve their performance as spotters.)
Train your spotters well before you begin this experiment. Divorces have happened over much less than a bent drive shaft or punctured fuel tank or dump pipes cleaned off the rig.
If you BACK down the hill, weight transfer to the rear axle will give you all the traction you have available to "change your mind" and drive back up the hill if something is about to ground out. BUT HAVE A BACKUP PLAN. Bear in mind that it's one thing to be able to drive up a steep hill with a little head of steam, but starting on a steep hill from a dead stop demands a LOT from your engine and drivetrain and available traction. If you (or a buddy) have a 4WD pickup and tow strap or chain, have that equipment and a qualified operator on site to hook onto your rig and help pull you back up the hill if you start to spin. If you spin, you dig, and ground clearance disappears as you dig. Again, YOU do not get out of your rig...you MUST hold the brakes. Putting the transmission in park and adding the parking brake only applies brakes to the rear wheels. You want all 4 wheels locked tight until the rescue comes.
If you can't pull off the maneuver with things as they are, a small dozer or skid steer can probably recontour your driveway to make the transitions less severe...and perhaps "repave" with a material like crusher run (best) or road base (adequate) to give your rig solid footing if it's wet. If you "cut" into a slope leaving higher terrain on either side of your recontoured road, be sure to also cut in drainage on either side of the driving surface, and crown the road surface, or your newly contoured road will become a drainage ditch! You need ditches on either side of this roadway...if you reshape it.
I'm a big fan of math, but no amount of reasonable math will account for things like the dangling bits of the black/grey dump valves and other such soft points. Only several competent sets of eyeballs can handle this task.
You mention "driving" down the hill. Maybe. Once you are comfortable that you can back down the hill, you can perform the same experiment driving forward down the hill with spotters. But bear in mind that you have a very long wheelbase vehicle with low ground clearance. What works in one direction may not work as well in the other direction. The worst case scenario is that you always back down the hill. And with all due respect, if you plan on doing these maneuvers, you'd better be able to back down every time.
P.S. I imagine you thought of this, but watch your roof clearance backing into your "garage". Have your spotters on hand to make sure that you have plenty of room above the RV roof before you are going to make contact with the garage door or door header on your garage. Being wrong at any point in this process can get VERY expensive.
Good luck.
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