Math/Trig Question

Easy. I need the following information.

1. Diameters of both wheels. Best to measure the distance from the wheel hub to the ground with the tractor on flat level concrete. This will take into effect any flattening of the tires due to the mass of the tractor.

2. The distance of the wheelbase from front to rear. Again, measure from the center of the hubs.

3. Distance from the ground to the bottom of the mower deck. Measure with the tractor on flat, level concrete or road.

That's it.

OK here goes.

Dia front wheels = 14.5

Dia rear wheels = 22

Wheelbase = 46.5

Deck to ground = 2.5

And the answer is?

Desired ramp length?

Do pay attention at the back!

Del

Ideal ramp length is 8ft. I'm thinking I'll need to make it curved since that angle is going to be pretty small.

Maybe it's just that I'm old, and slow, but wouldn't the ground to shed floor height also matter?

Keep quiet up front, cat!

Slinks off...

Del

What is the height of the ramp?

12° upward slope.

I would make it a bit shallower if you can to account for any variation in tire pressure and as such, overall height.

For a 8' long base of the ramp, the height works out to just shy of 17" for a 10° slope.

A 12° slope would get you 20.4" high.

If that is not enough you can make the ramp longer or with a compound set of angles to ease the mower over the end of the ramp.

........driverless tractors......who knew??

Of course, brought to you by Google!

you need some numbers!

See #1 - now I know what to measure...tomorrow, it's night here.

Cheater pad...

Since I have not yet built the ramp, a cheater pad is a bit useless!

It's a workaround if you are space confined....if not, a 10º incline should work....

...or you can build something like this with a transition...

http://zonalandeducation.com/mstm/physics/mechanics/forces/inclinedPlane/inclinedPlane.html

d= distance between wheels, note this distance becomes slightly smaller as it passes over the angle, referred to as allowance.

h= is height of mower minus clearance height and minus allowance.

Angle = [tan¯¹(d/2h)x2]-90.

Regards JD.

Can y'all do that in reverse Polish notation? I have this old Hewlett-Packard calculator....

No, I cannot, a bit over my head. I could programme my TANDY pocket scientific computer PC-6, going back a few years ago, but it's way out of date now. I'm working on it, but don't hold your breath?

Regards JD.

Our drive had a similar geometry as one drove uphill to the road. We had no trouble but an empty dumpster truck found itself stranded when the idler wheels near the middle of the rig lifted the rear, driving wheels off the ground.

Instead of a straight line ramp, build a curve with the tangent point at the apron.

Save yourself some brain ache. Make a small cut-out model and just see what angle of ramp works on paper. Allow some safety margin, things may not go too good if you design for minimum clearance and have just had a heavy meal. If you want some real pain, construct a curved ramp.

"Save yourself some brain ache."

He is. He's simply asking us for the solution. :-)

lol - he's got to decide which answer to run with .

Download DraftSight - Free CAD Software for your DWG Files and lay it out. It's just like AutoCad without the cost.

I'll try that too. Thanks!

This is what I've been doing...my rafter layout square works pretty good but when all is said and done...it will be trial and error that wins. The "landing" for the end of the ramp is not level with the ground under the shed...so that's kind of variable. A little fill here, a little fill there...then there's the fact ( forgot this) that the deck floats so it can move up a few inches if it hits. Since I have portable ramps to load the tractor on my pickup, I can use them to test. I know I know I should have said all this but my new, wonderful meds aren't helping the thinking process!

_{Why I need CR4 to help!}

Two feet,?!? ....just go with portable ramps....

just a slight modification://www.youtube.com/watch?v=T-LiC1WT9NU

That's the last resort...you are spoiling all the fun!

My builder really wanted to build a ramp out of railroad ties!

You know, now that I think about portable ramps, that may solve a few problems.

I'd be able to plow in front of the doors before I bring the tractor out in the winter,

And it makes it easier to turn the tractor, and easy to line up the ramps!

Tractor supply has arched ramps for $100, that are 90" long...might work for a short term solution.

I'd bet that if you buy those ramps, you won't ever need to build a permanent snake/skunk shelter.

You could even hinge them so they fold up out of the way when you don't need them.

1,500# capacity, one foot wide. Perfect!

How much would the wood cost if you bought it to build a permanent ramp? Labor/time?

And, the ramps will find other ways to justify their existence as time goes by.

Just beware of neighbors who just, "want to borrow your ramps for 15 minutes and I'll bring them right back".

Come on, admit it. You like going to TSC anyway, don't you.

just throw this in on the weekendhttps://www.youtube.com/watch?v=5r29R1tJRRw

That would require a bit of blasting...the ledge in this area is about a foot below ground level...they blasted a hole for the house basement, but I think I wouldn't be able to afford the new tractor to put in the disappearing garage!

Tom, I believe there's some high-level interest being shown in your math outcome:

https://www.youtube.com/watch?v=5icV_mctrkE

Mark Bingham
Relativity PL

I bet someone on the logistics team got fired!

Oh well, I drew a nice picture but it won't display correctly.

Well this has been a lot of fun, but the problem is solved. My ramps I use to put the tractor on the truck work great. The truck tailgate sits38" off the ground and the shed is only 16" off the ground, so it works pretty good. I will be putting some 2x8 planks on the floor of the shed, just where the tires go, and that will solve what little dragging I have now. Again, thanks to all for participating!

It drags a bit when I back in, but the boards will fix that.

Great choice. No permanent structure to get in the way and hide critters.

There is a small space under the sides all the way around the shed. I'm going to put 4 inches of 3/4 stone there to keep the critter out!

Watch out that you don't block some in instead!

Ramp problem

I considered that this problem is not for only one person so that it justifies a general solution.

In order to simplify I used for analysis the model in fig 1:

Fig.1

The simplification is that the reference is axis "X" =O0-O2 with origin in O1 and axis Y is vertical origin as well in O1 direction "+" down.

I considered the 2 circles stationary and defined the locus of point "P"= the edge of the ramp with slope "α". The condition is that the 2 sides are always tangent to the 2 circles.

For the given dimensions and for different slopes results are as in fig 2:

Fig.2

Slopes less 1/5 are accepted.

If anybody has again to find such an answer I can mail the EXCEL sheet.

I hope this will help.

As a side remark the solution is not the one already suggested.

Nick,

I like the picture and the graph but have a few questions:

1. ....you stated "... the reference is axis "X" =O0-O2 with origin in O1". Did you mean "... the reference is axis "X" =O1-O2 with origin in O1"?
2. What are the parameters on the x (horizontal) and y (vertical) axis of the graph?

1- typing error did not notice it, Origin in O1

x-axis horizontal through O2 y-axis vertical through O1 normal to "x" and direction down.

2- for x-y the parameters are length units in this case inches as the OP gave.

I am sorry that you did not like in fact the solution since I see on it no reaction neither from you nor from any body else !

Thank you.

Oh, I liked the solution too, sorry I was not clear about that (only said I like the graph and picture). The graph and picture contain the solution so it was my intent to compliment your solution...however, my wording was ambiguous.