Determining Ramp Length for Ground Clearance

[Drakkith]

TL;DR

Trying to figure out how long of a ramp I need to ensure adequate clearance for my mower.

Hey all.

I'm looking to buy a zero-turn mower and I need to build/purchase a ramp to get it into my shed for storage. Exact model is this one.
I need to figure out how long of a ramp I need to make sure the mower doesn't bottom out when driving up and down the ramp.

Mower stats:

Wheelbase: approximately 76 inches.
Height: 4.5 inches (based off the highest setting on the deck height adjustment)

Shed entrance is 12 inches off the ground.

The manufacturer says that the mower can handle slopes of 15 degrees, and while I think it would be able to handle more slope when not actually mowing, I went ahead and used that to find a ramp length of about 48 inches. I just don't know how to determine clearance.

Any help would be appreciated.

 

[.Scott]

The worse case is the angle between the ramp and the floor when the tractor is about halfway through the wheel base.
It we ignore the diameters of the wheels - treating them as 2D edges in contact with the ramp or floor - then the worse case happens when are straddled 38 inches through your wheel base. at that point, you need 4.5 inches. So the tangent of the tractor slope at that point must be less than the arc-tangent of 4.5/38. So the ramp slop must be less than twice that.

That arctan is about 7.5 degrees. So your ramp slope can be as much as 15 degrees.
Sounds like the manufacturer did his math.
Of course, this presumes the tires are nicely inflated.
Also, this is an approximation. The 7.5 degree contact between the tires and the floor/ramp will buy you some small additional fraction of an inch.

 

[berkeman]

I need to build/purchase a ramp

What kind of ramps have you been looking at so far? What will be the combined weight of the mower and yourself when you are driving it up the ramp?

You might consider using two skinny ramps instead of a full-width one. That way you can have the ramps extend up a bit after entering the shed to help with clearance and then you just drop a couple inches off the end of the ramps once inside the shed.

Kind of like shorter versions of this ramp, with some 2x4 spacers under the right end to add the extra clearance height:

 

[Baluncore]

The manufacturer says that the mower can handle slopes of 15 degrees, and while I think it would be able to handle more slope when not actually mowing, ...

That 15° is not relevant to climbing or descending a straight ramp, it is the angle of slope over which the caster-lead of the steering will probably allow you, with good traction, to avoid a downhill uncontrolled trajectory while trying to turn. Wear the seatbelt provided when travelling on any hill. You will discover why.

I need to figure out how long of a ramp I need to make sure the mower doesn't bottom out when driving up and down the ramp.

The crest of the ramp is the only problem in determining ramp angle.
The wheelbase is 76", with clearance 3.5". Half wheelbase is 38".
Half ramp angle = arctan(3.5"/38") = 5.26° ; So ramp ≤ 10.53° .

An alternative is a longer rocking ramp, over 2x76" long, with the fulcrum at the crest, with the lower-part able to fold up into the doorway.

The worse case is the angle between the ramp and the floor when the tractor is about halfway through the wheel base.

That is crossing the crest of the ramp.

That arctan is about 7.5 degrees. So your ramp slope can be as much as 15 degrees.
Sounds like the manufacturer did his math.

No. That 15° quoted is more an exaggerated marketing limit to turning on a hill.

I have ridden ZT mowers on several "death plunges" while turning on hills more gentle than specified, and have now done the maths.

I mow up and down hills steeper than about 12°. At the top of the hill, I do a simple 180° turn and run back down the hill, and there is no problem with that. The problem comes at the bottom of the hill when I begin the turn. At about 45° into the 180° bottom turn, the weight has come off the high-side drive wheel, and has been transferred to the low-side front caster. That caster wants to point downhill, while the high-side drive wheel loses traction. The low-side drive wheel then pushes me faster downhill as the mower enters an uncontrolled plunge. To avoid that situation, I first drive straight, further downhill before slowly going into reverse and beginning a 180° turn, uphill, backwards. The casters are then trailing down the hill as I reverse uphill, loop 180°, then line up with the next row, and stop, before beginning the next up-hill row forwards. That technique extends the slope of the land I can mow, but not much beyond 15°, since drive-wheel traction is limited when backing up-hill.

 

[Drakkith]

What kind of ramps have you been looking at so far? What will be the combined weight of the mower and yourself when you are driving it up the ramp?

I haven't really started to look yet, as I didn't know how long they needed to be.

 

[berkeman]

I haven't really started to look yet, as I didn't know how long they needed to be.

In case you decide to make it/them on your own, I'll share my old design.

I built a very strong motorcycle ramp (strong enough for streetbikes) out of 2x4s and plywood. I still had my table saw back then, so I ripped dados lengthwise in the 2x4s and cut the 3/4" plywood to the correct width for the bike tires. I glued and screwed the 2x4s to the plywood to form an I-beam for the needed vertical strength, and put down the sandpaper-like floor tape on the plywood ramp parts to give good traction.

 

[Drakkith]

Thanks all!

 

[Drakkith]

Got some 6 ft ramps from a local store. Works perfect.

 

[Baluncore]

Got some 6 ft ramps from a local store. Works perfect.

It should do.
A 1' step, with a 6' ramp, has a slope of; arcsin( 1 / 6 ) = 9.59°.
That is just less than the maximum, 10.53°, as calculated in post #4.