math question

[rong]

If you have a road which is enclosed by walls on both sides, with a width of 109, and there is a gap in the wall of 85. You have a vehicle with a turning circle radius of 128.3, a vehicle length of 109.2, a width of 54 and a front to rear wheel axis distance of 100.

Can the vehicle make the turn and how the hell do you figure that out.

[a500lbgorilla]

Do your own homework.

You know the circle it can follow, you know the rectangle it is and its orientation to the gap, start doodling til you figger it out.

[MadMojoMonkey]

If you have a road which is enclosed by walls on both sides, with a width of 109, and there is a gap in the wall of 85. You have a vehicle with a turning circle radius of 128.3, a vehicle length of 109.2, a width of 54 and a front to rear wheel axis distance of 100.

Can the vehicle make the turn and how the hell do you figure that out.

When turning, the inner, rear wheel is on the turning circle, and is oriented on the line tangent to the circle at that point.

1) Draw your vehicle.
2) Create a circle that is tangent to the inner, rear wheel, and to scale.
3) Draw 2 circles, concentric with the constructed circle.
3a) 1 of the circles inscribes the vehicle.
3b) 1 of the circles circumscribes the vehicle.

The constructed circles represent the minimum wall spacing through which a godly-skilled driver could just barely scrape both walls getting through.

EDIT: for a rectangular car, with no overhang, and the wheels at the edges, step 3a is identical to step 2.

[MadMojoMonkey]

At a rough approximation, assuming a rectangular car, with wheels on the corners:
The inner wall needs to have a radius of AT LEAST r1, where r1 is the stated minimum turning circle radius.

The outer wall needs to be AT LEAST
r2 = SQRT( (r1 + x)^2 + y^2 )
where x is the width of the vehicle, and y is the length of the vehicle.

It is the Pythagorean formula for the circle which goes through the opposite corner of the vehicle.

***
The practical application of this is that this tells us how the wheels move to attain movement in the cabin. If you sketch this idealized picture with the corners of the rectangle at the center of the area where each tire meets the road, the diagram accurately represents the movement of those points.

[rong]

So I basically have to draw it, to scale. I was hoping their might be some other way. like perhaps this is a thing that maybe vehicle manufacturers have to be aware of and there is a formula to follow.

Ah well, ty anyway mmm.

[rong]

Oh, a 2nd mmm post, ignore the above.

[MadMojoMonkey]

For the inner wall, you can just subtract the distance from the center of the wheel to the innermost projecting surface of the vehicle in the direction of the turn.

Like, the wheel is prob. 8 inches wide, so 4 of those inches are inside. Add on another few inches for doors and quarterpanels and whatnot. Call it 12 inches, just for kicks. So whatever the stated inner turning circle is, probably the wall needs to be a bit smaller.

The outer wall also would need to be further out, but it's a trickier calculation, because we're measuring that radius on a diagonal through the car, and not parallel with the back axel, as in the former case.

Still, I think adding 12 inches is probably an OK low estimate of the error in our approx. I'd guess 36 inches is well too much, so add something between 1 and 2 feet to the r2 calc above.

As always, this is a mathematical model, and a practical application will need wide margins for human error.... so these rough guidelines should get you there.

[rong]

The wheels are actually on the corners. what we're actually referring to here is a mobility scooter, a hallway on a cruise ship and the door being the entrance to the cabin.

[MadMojoMonkey]

Oh. Well then you only need to add a few inches to the above, so that it's not something that you have to line up perfectly.

[OngBonga]

It's maths, dan, as you well know. You're no Merkin.

Maths.

[a500lbgorilla]

The point of the doodles is to derive the equations, as is witnessed by mmm. This ain't no cookie cutter problem that I'm aware of, so you'll have to put some brainwork behind it.

[MadMojoMonkey]

What rilla said is right. It's just a geometry problem.

I just visualized the problem, reduced it to a circle and a rectangle and then drew a picture.
Once I drew the picture, the Pythagorean theorem just jumped right out at me, so it was really as easy as that.

***
Interesting fact.

The turning circle described by the rear wheels is always smaller than the turning circle described by the front wheels.
(EDIT: for front wheel steering vehicles moving forward.)
This is even true for motorcycles and bicycles.
(If the trailing wheel is not in line with the front wheel, the bike will turn in the direction of the back wheel.)

This means that every time you turn, the front of the car travels further than the back of the car.
Over the life of the vehicle, this adds up. I wonder how much, really.
Anyway, point is... the front of your car has different mileage than the back of your car.

[MadMojoMonkey]

I presented the problem to my father, a landing gear specialist for the F-15 among other Boeing military jets.

He affirmed my notion that the rear axle is along the line of the turning circle radius.

The front axle would also be in line, and the angle between the 2 axles implies a point of intersection, which is the center of the turning circle.

Furthermore, no matter how many axles there are, they should all be aligned on the same point at any given time.
(accepting that when you are not turning, they are aligned at a point "infinity" away, and it's equally infinitely away to the left as to the right.)

Modern cars have 2 front axles and 1 rear axle (geometrically- not in terms of parts).
The steering that accommodates this must turn the front wheels at slightly different angles to prevent slipping, which is noisy and embarrassing in the best cases.
If you are on a slippery surface and your wheels are not properly aligned, then the vehicle will alternate between the available turning circles in a chaotic pattern.

[Keith]

Dan , just say it won't fit so you'll have to leave the motherin law at home and not take her on holiday with you .

MMM's formula just works in terms of a single reverse, if not possible in one go it may be possible with a bit of shunting back and forth.

[Renton]

Why don't you just look at ADA code for hallways?

http://www.ada.gov/2010ADAstandards_index.htm

A lot of this work has already been done for you, though as an architect I can state that most disabled access standards are too generous.

[MadMojoMonkey]

MMM's formula just works in terms of a single reverse, if not possible in one go it may be possible with a bit of shunting back and forth.

My formula tells you the minimum wall width at which no shunting will be possible.

To be fair, I've only considered a 4 wheeled vehicle with front wheel steering moving forward.

though as an architect I can state

TIL Renton is an architect.

[Renton]

Well, I have a 5 year bachelors degree in architecture. I haven't worked in the field in 8 years and I never have had a license to practice.