barryj
Homework Statement:: I have a shower and wheelchair as shown in the attached figure. The question is, how deep can the bench be made and still allow the wheelchair to enter the shower.
Relevant Equations:: x^2 + y^2 = r^2 ?

I need to know the maximum depth, d , of the bench that will allow the wheelchair to fully enter the shower stall.
Obviously, the chair can twist in any way as it enters. If the bench is too deep, the chair will not enter.
I know the problem, I do not know the solution. Help.

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2022 Award
Show what work you have done so far.

Gold Member
There is a measurement missing from your diagram: the location and width of the entranceway to the shower.

FactChecker
barryj
The door opening is 36 inches

DaveC426913
Gold Member
What constraints do you think you will run into getting the wheelchair in?
What will that do to the path of the wheelchair?
Can you quantify the constraints?
It might help you to start solving this if you sketch it.

barryj
Here is a better diagram. If I assume that I start with point A and B together and then swing the chair around, it will not go through the door. So, the chair must be put partially into the door, and rotated, some amount to get it through. I am unsure how to calculate this. I think this is an interesting problem in that how do furniture makers insure they can get their large refirgerators into a kitchen through many doors.

Mentor
Here is a better diagram. If I assume that I start with point A dn B together and then swing the chair around, it will not go through the door. So, the chair must be put partially into the door, and rotated, some ammount to get it through. I am unsure how to calculate this.
This does not seem like a homework problem -- is it?

Please add the placement and sizes of the front and back wheels for the wheelchair. Those are important. And have you thought about how the answer may be different whether the person rolls the wheelchair into the shower forwards or backwards?

Update -- and please show the wall to the left of the shower. Is it flush with the entry, or is there room to swing the wheelchair some in that direction to angle into the shower?

barryj
No, this is not a homework problem for me but it could be. It is probably too tough for homework, yes? I am assuming the chair has a footprint of 25 X 42 piece of plywood and can this be slid through the opening. If so, how much can I have for a bench?

Mentor
No, this is not a homework problem for me but it could be. It is probably too tough for homework, yes? I am assuming the chair has a footprint of 25 X 42 piece of plywood and can this be slid through the opening. If so, how much can I have for a bench?
Okay, I'll move it to the general technical forums then.

And the wheelchair is not a box with those outside dimensions. It is a 3-D shape that can fit under/over stuff. For example, the footrests stick out in front, and can easily pass under the bench as long as the bench supports do not go all the way to the base of the shower (which they don't usually). You should try to do a more complete 3-D analysis.

BTW -- fitting the footrests under the bench when going into the shower may be a big help, and lead more toward going in front-first instead of backing in. Are the shower head and shower controls on the left or right of your drawing?

Mentor
And you didn't comment yet about where the left wall is in your figure.

Gold Member
An easy way to get a general idea is to make a scaled drawing of the shower stall and the wheelchair footprint.

Then cut out the wheelchair footprint and see if you can slide it into the shower.

You could also sketch on the wheelchair cutout where the footrests, armrests, wheels, and the backrest are, checking to see what would fit under the shelf and how it can pivot.

If you don't have paper large enough for convenient scaling, you could use a cut-up cardboard box, or even newspaper and a marking (felt tip) pen.

Or lay out the shower with masking tape on a linoleum floor (kitchen or bathroom), then see if you can ride into it!

If you don't have a suitable floor, maybe a friend will let you "borrow" theirs for a bit.

Cheers,
Tom

BNC, Lnewqban and anorlunda
barryj
I have edit my diagram showing the solid wall.
I realize that I could do a cut out but isn't there a mathematical way to do this more precisely?
Also, I know that foot rests can be moved a bit but I look at this as a general math problem whether it is about a wheelchair or not. If I assume a piece of 25 X 42 plywood how would I find the distgance d?

Mentor
No, this is not a homework problem for me but it could be. It is probably too tough for homework, yes?
Please tell us more about your question if you can. If you are helping to design a shower for a disabled family member or friend, that is a great thing and we want to help.

In my EMS experience, nobody showers sitting in their wheelchair. They wheel into the shower and transfer to sit on the bench to shower, and push their wheelchair out of the waterstream path before turning on the water. So in your design, the wheelchair only needs to be wheeled into the shower enough for the person to lift themselves via the shower wall handrails from their wheelchair onto the shower bench, and then push their chair out of the path of the waterstream.

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2022 Award
... please show the wall to the left of the shower. Is it flush with the entry, or is there room to swing the wheelchair some in that direction to angle into the shower?
@barryj do you plan on answering this question? Do you see why it matters?

berkeman
There are two critical constraints during the 90°, two-step turn.

Consider the first part of the entry progress. As the 25” chair passes through the 36” door, it may turn through a maximum angle before it becomes too wide for the door;
Acos( 25" / 36" ) = 46°;
So the chair front can avoid any 45° internal shelf during the initial entry. That assumes the approach is not blocked by any external wall on the left.

The second part is another turn. The length of the front of a maximum shelf is;
36" * √2 = 50.9”;
The chair has a length of 42”, which is less than the available 50.9”, so there should be no problem.

berkeman
barryj
Please tell us more about your question if you can. If you are helping to design a shower for a disabled family member or friend, that is a great thing and we want to help.

In my EMS experience, nobody showers sitting in their wheelchair. They wheel into the shower and transfer to sit on the bench to shower, and push their wheelchair out of the waterstream path before turning on the water. So in your design, the wheelchair only needs to be wheeled into the shower enough for the person to lift themselves via the shower wall handrails from their wheelchair onto the shower bench, and then push their chair out of the path of the waterstream.
I am doing a bathroom remodel and want to make sure it is handicap accessible, in case I become in need of a chair in the future. I am 81 and doing good so far but who knows. When considering access, I thought this could be solved mathematically even though I might not need to access the shower completely with a chair. It is still an interesting problem.

barryj
There are two critical constraints during the 90°, two-step turn.

Consider the first part of the entry progress. As the 25” chair passes through the 36” door, it may turn through a maximum angle before it becomes too wide for the door;
Acos( 25" / 36" ) = 46°;
So the chair front can avoid any 45° internal shelf during the initial entry. That assumes the approach is not blocked by any external wall on the left.

The second part is another turn. The length of the front of a maximum shelf is;
36" * √2 = 50.9”;
The chair has a length of 42”, which is less than the available 50.9”, so there should be no problem.
But wait. I want to have a bench in the corner. How big can I make the bench before it prevents the chair from entering. The bench would take away from the 50.9 inches I think. Don't forget that the chair can be pushed into the opening as it is being turned. Does this make a difference? Hmmmmmm...

barryj
@barryj do you plan on answering this question? Do you see why it matters?
I think I answered it, yes??

Gold Member
I think I answered it, yes??
What's here? Wall?

Because...

BNC, BvU and berkeman
barryj
berkeman
But wait. I want to have a bench in the corner. How big can I make the bench before it prevents the chair from entering.
You are thinking about a difficult solution, I am showing that it is not necessary to analyse it to full depth.
There are two critical points during the process.
1. You enter the space by running at 45°, parallel with the front of the maximum sized bench.
2. Then, when completely in the space, you turn the remaining 45°.

Gold Member
I thought this could be solved mathematically...
It can with an ideal wheelchair. In particular, the location of the wheels would have to be on the very corners of the device and be of zero size. But that will have no bearing on any real scenario.

barryj
There is a wall I forgot to mention. It extends 24 inches. I see that this will affect the angle at which the chair can be rotated upon starting to enter the area.

Now, my previous analysis is invalid, because you have moved the goal posts and invalidated the specified external wall assumption.

Gold Member
Me, I would approach your problem from a different angle*.
* see what I did there?

I would avoid compromising the space in which the scooter has to maneuver; instead I would look at a shelf design that is out of the way.

Gold Member
Now, my previous analysis is invalid, because you have moved the goal posts.
OK, well, he placed a goalpost that hadn't been there before...

barryj
You are thinking about a difficult solution, I am showing that it is not necessary to analyse it to full depth.
There are two critical points during the process.
1. You enter the space by running at 45°, parallel with the front of the maximum sized bench.
2. Then, when completely in the space, you turn the remaining 45°.
I will look into this idea.

barryj
Given my latest diagram (I did not intentionally hide the "goal post", I just didn't consider it. I will try to put pt A on B, then rotate the chair, then shove it in as far as I can to try to see how large a bench I can have. Seems like this is becoming an interesting problem. I'll wonder the next time I buy a piece of furniture if it will fit through a door of my house given my house layout. Surely this problem has been solved many times.

barryj
You are thinking about a difficult solution, I am showing that it is not necessary to analyse it to full depth.
There are two critical points during the process.
1. You enter the space by running at 45°, parallel with the front of the maximum sized bench.
2. Then, when completely in the space, you turn the remaining 45°.
I will look into this idea.

barryj
I tried to reply to DaveC4259 and got an error msg saying the post was not available.?

Surely this problem has been solved many times.
Yes it has.
But finding occasions of interference, during the manipulation of arbitrary 2D or 3D linked objects, through arbitrary 2D or 3D geometric passages, is not usually mathematically analytic, it is numerical and involves FEM with intrusion detection.

Mentor
I am doing a bathroom remodel and want to make sure it is handicap accessible, in case I become in need of a chair in the future. I am 81 and doing good so far but who knows.
In my EMS experience, nobody showers sitting in their wheelchair. They wheel into the shower and transfer to sit on the bench to shower, and push their wheelchair out of the waterstream path before turning on the water.
Okay, Barry please stop and take a deep breath. Whew.

Nobody showers sitting in their wheelchair, please trust me on this. I work in EMS and help folks with wheelchair disability issues all the time. So the question for you is really how to best design your new shower to accommodate future needs where you will maybe need to access the shower sitting in your wheelchair, and most comfortably transfer to the bench using handrails and push your wheelchair out of the shower so you can turn on the water stream.

So make your bench big and wide and make your handrails sturdy and make it easy to reach the shower door handle after you push your wheelchair just outside of the door.

More resources: https://www.abilities.com/

Last edited:
BvU and Lnewqban
Gold Member
I tried to reply to DaveC4259 and got an error msg saying the post was not available.?
Surely the one I deleted, having decided it had little to contribute.

Homework Helper
Gold Member
berkeman
Staff Emeritus
Any house modification of that nature should comply with the current Accessibility Building Code of your state, if located in USA.

Just for a guide on the basic dimensions, please see that current code for Florida:
https://codes.iccsafe.org/content/FLAC2020P1/chapter-4-accessible-routes
That is the real answer. In the modern world, the calculations the OP seeks to do have been done in advance. Also, other considerations the OP didn't think of are included. The result is embodied in a code like the one @Lnewqban linked.

Failure to follow the codes can result in making your house uninsurable, or unable to be resold in the future.

berkeman