# Wheelchair ascending a carpet/step

#### danielp3

Summary
Free body diagram and forces applied
When a wheelchair is about to ascend a carpet or a small step, which forces acts on the wheel(s)?
Say the wheelchair is about to ascend the carpet with both two front wheels, will it be easier to analyze both of the wheel at once or just one? which force will act then?
Say the wheelchair have 4 driven wheels, how will the FBD change when the only driven wheels is the 2 front wheels?

(no slip between the surfaces and all is done very slowly so the acceleration won't be felt and)

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#### BvU

Homework Helper
Hi,
no slip between the surfaces
No chance of surmounting even the smallest step, given the 'very slowly'.
You will have to compromise there.

For calculations, looking at one wheel with half the load is a start.
An even better start is making some sketches of cases you have in mind and drawing FBDs

#### berkeman

Mentor
Summary: Free body diagram and forces applied

When a wheelchair is about to ascend a carpet or a small step
And can you please clarify what you mean by "ascend" a carpet? Do you mean going from a hard surface to a soft carpeted surface at the same level, or over a bump or something? Thanks.

#### danielp3

No chance of surmounting even the smallest step, given the 'very slowly'.
You will have to compromise there.
Of course there will be some sort of acceleration.
'Very slowly' in means of a=0 just to ease the calculations.
I've done some calculation my self and got some freaky results (really high moment required to ascend a carpet.

#### danielp3

And can you please clarify what you mean by "ascend" a carpet? Do you mean going from a hard surface to a soft carpeted surface at the same level, or over a bump or something? Thanks.
Ascend in means of go upward.
Of course there will probably be a change in friction coefficient, but for now let's just assume ascend is going to a higher point (carpets height).

thanks!

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#### danielp3

I've come up with this FBD. where:
T1 - given moment to front wheel
T2 - moment created after moving the whole weight of the chair to the center of the wheel
beta - hit angle between the wheel and the carpet
fs1 - friction with the carpet
fs2 - friction with the floor
Fc - Reaction force from the carpet
N - Reaction force from the floor
mg - weight of the chair and one wheel (actually m+M/4)
(the whole chair and the user weight divided equally to all 4 wheels)
h - height of a carpet
d - distance to the center of gravity of the chair and the user

This analyze led me to some ridiculously results.

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#### BvU

Homework Helper
This analysis led me to some ridiculous results
Do you want us to check your analysis ? If so, you need to post it ...

Since $mg$ can be quite hefty, the torque around the edge of the step as axis of rotation can come out quite big.

But is that really what's happening when a wheelchair has to lift its front wheels to negotiate a step ?

#### danielp3

Do you want us to check your analysis ? If so, you need to post it ...
I can post it of course, but I thought that maybe my approach is wrong, then all calculations will go wrong.

Since mgmgmg can be quite hefty, the torque around the edge of the step as axis of rotation can come out quite big.
The result I got is really high, I mean like 100+ [Nm] torque needed to the front wheels
But is that really what's happening when a wheelchair has to lift its front wheels to negotiate a step ?
What do you mean?

#### BvU

Homework Helper
he result I got is really high
Sounds reasonable to me.
What do you mean?
I see wheelchair riders give a jerk to lift the front wheels in such situations (grant you it's not the oldies -- they get pushed and the pusher gently tilts the chair backwards by pulling while blocking the rear wheel)

#### danielp3

Sounds reasonable to me.
The motor I intend to use should be quit small to fit under a chair.
A motor with such power will be huge.

Sounds reasonable to me.
I see wheelchair riders give a jerk to lift the front wheels in such situations (grant you it's not the oldies -- they get pushed and the pusher gently tilts the chair backwards by pulling while blocking the rear wheel)
Ok, but that's not the case in my analysis.
I cannot assume that.

#### berkeman

Mentor
The motor I intend to use should be quit small to fit under a chair.
A motor with such power will be huge.
The situation is different for standard motorized wheelchairs. And yes, they have to be a bit heavy to accommodate the moderate-size motor (with low gearing) and the battery that lasts long enough to make the wheelchair useful.

EDIT -- Although this class of motorized wheelchairs that I found with a Google Images search doesn't look too crazy heavy. I wonder what it's specs are for battery life and climbing ability...