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Dansercoer

Physics Questions

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3D-Drawing.jpg

Hi people,

 

Above is a proposal for a human wheel I would like to make, the inner cylinder would be perforated.

The difference with a hamster wheel is that it wouldn't be stationary and is able to take ( large ) bends.

 

There will be a first estimation of the thickness of the materials (the rings shouldn't be able to amputate a hand, but shouldn't destroy too much grass either), the amount of crossbars and the diameter of the outer rings (wider than the palm of a big hand) using the Cosmos-software. The structure as drawn above would weigh ±80kg in TIG welded aluminium AW-5083, maybe fibreboard is an option too.

 

 

But I was wondering how to define the:

- width of the cylinder a

- diameter of the two rings in the middle b

 

to make sure:

1) the wheel is not too heavy to make it roll

2) it is not too difficult to make the wheel lean to one side

3) the wheel is unlikely to fall

( 4)the bends it can take are not too large )

 

 

1)

1.jpg

The two forces that I think decide whether the wheel is going to roll or not - friction and gravity on the person - seem to work in different directions?

 

 

2)

2.jpg

The wheel will lean to one side when the combined centre of mass of the wheel and the person in it is not positioned above the resting surface.

(mw.xw - mp.xp) / (mw + mp) = 0

This can be reduced to a function of a and b.

 

 

3)

3.jpg

The wheel will not fall when the combined centre of mass is positioned above the resting surface. But what is the influence of inertia - as a result of the leaning movement - on the position of the combined centre of mass?

 

All of these could result in a graph with a and b as axes from which I could deduct their ideal value.

 

Thank in advance!

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Guest kaiza

it does when you're talking about engineering design....

 

firstly to qualify (or disqualify) my answers - i've only done very basic engineering studies, so I could be well off on some things here.

 

for the first question:

http://en.wikipedia.org/wiki/Rolling_resistance

 

You could probably work out the force of the person's weight acting on the cylinder by instead working out the force acting on the tangent to the cylinder where the foot meets the surface, and substituting the rolling friction coefficient for normal friction coefficient ( http://en.wikipedia.org/wiki/Friction )

 

As for the second question - you have inertia acting on the body as you tilt it from upright when at rest - i would liken this to stepping on a rake with your foot - if the cylinder is too heavy it will simple keep tilting over due to inertia.

 

You also have inertia and centripetal acceleration acting on the body when you are moving, similar to how cyclists and motorcyclists lean in at steeper angles the faster they go around a corner. So the likelihood of the vehicle tipping is dependent on how fast you're travelling.

 

This ties in with your internal and external cylinder diameters. With only two different diameters, the turning circle would be determined by creating an imaginary cone, with the two circles as sections. The size of the turning circle is simply the length of the side of the cone.

 

I don't know how to calculate the inertia as you start cornering, although I'm sure it would be relatively simple - consider trying to bribe an engineering student with some beer for some help.

 

A couple of more practical questions - what surface is the person going to be running on? Also, I'm a bit wary of the running at a tilt because if the inside surface is flat then when turning you will effectively be running on a slope, which is difficult (and bad on your ankles)

 

Also, the ribs you've drawn are rounded, but these will only cause the vehicle to bump or jump as it rolls over them. Perhaps consider using a steel mesh? And instead of creating a cylindrical surface, forming the mesh into a section of a sphere - the spherical section may be easier to run on too.

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Thanks a lot for the extensive reply!

 

Some further clarification;

The ribs seem rounded, but that's only an optical illusion.

The intention of the wheel is to give an alternative to the walking paths in parks, a new experience with more freedom. Parks are not perfectly flat, this means that safety margins will need to be built in.

 

My reasoning:

For the first question I compared the wheel to a seesaw with rolling ;) resistance rather than a pivot; it can roll even when the person is just standing. I couldn't find the horizontal force component, maybe you can?

For the third question I didn't involve centripetal force because even when the wheel is not moving forward it shouldn't fall. But I did take it into account for the walking surface, a bit like indoor running/cycling tracks. Maybe the slope is a bit exaggerated, but wouldn't a spherical walking surface increase the cost? I will use anti-slip paint though. (http://www.protectakote.co.uk/)

 

Rounding the cross-section would make the turning smoother and add strength, but it would destroy more lawn, it would make it harder to counter the inertia and I have the impression that the speed won't be high enough to get proper control over the wheel. Strength could always be improved by using thicker rings and more crossbars.

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Guest Evanzo

You may also want to think of how the person is going to stop the wheel. Say they get going in an area with a downward slope. Even if the ground angle is not very steep, unless the wheel is extremely lightweight it will be difficult to stop while inside of it.

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Guest Grant Howarth

Who is this for? The diameter may be 2200mm which is generally much larger than most people, however, the position at which your guy is standing could be anything from 1600mm to 2000mm in height. This worries someone like myself who is 1930mm!!! also considering people lean forward when walking...

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Yes, when calculating the maximum weight I’ll have to choose the most extreme out of both situations: stopping on a downwards slope or starting on an upwards slope. But it seems that they are equally difficult as the absolute values of both accelerations are equal.

It is for this calculation that I’ve drawn the person in such an extreme position (he could even be a bit taller), the size should be fine for normal walking.

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What is this for? You talk about having this form parks as an alternative to walking?? Why? This would not work and frankly would be a major safety hazard. Why? Well let us assume you can move it. How does it steer? By you positioning to one side or the other to tilt it? How do you control speed? How do you avoid other people (2 year old wanders out in front of this thing......).

Sorry I just don't get it as a concept (reminds me of the inventor who came to me once and said he had a new idea that would revoltionize the automotive business - make cars spherical, because balls bounce off each other so these cars would be uncrashable! Yes that is true.)

 

Sorry some ideas should remain on the brainstorming sketchpad.

 

Now as an extreme sport where you run these things up and down hills and maybe make then inflatable........sister product to the zorb?

 

http://www.ballerhouse.com/2008/02/06/the-...ard-inflatable/

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I like your two examples.

But to answer your questions;

 

Why an alternative to walking paths?

Apart from the two reasons I already mentioned it will also keep your shoes clean without having to pave green space.

I am sure we have all heard of physics groups and classes in school building trebuchets or catapults. They are planning on storming a castle about as much as we are planning on giving extra large hamsters exercise.

By you positioning to one side or the other to tilt it?

Yes.

 

How do you control speed?

When your speed is slower/faster than the wheel's speed then you will be walking in the rear/front half which slows down/accelerates the wheel. The questions above are there to make this as easy as possible, I'm curious to hear your answers.

 

How do you avoid other people?

As described above. This wheel is not intended for hilly parks with high vegetation that limits sight.

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I'm still not convinced.

 

Keeping your shoes clean and avoiding paving green spaces? To run this thing you will need a track of some kind and it will destroy the green space you travel over. Get a pair of walking boots!

 

Tilting it to one side or another will not necessarily turn it. To turn it you need to move the centre of gravity to the inside and for the resulting force to act off centre (4 years of mechanical engineering degree). Or you need to physically rotate the wheel on its axis (like a car or motorbike - which is a combination of above).

 

With regards to speed I disagree. What will happen is you will fall out. This is not a flat treadmill where you can easily control speed, this is a cylindrical surface. For you to be able to do what you describe would require a diameter of maybe 5m or more. Hamsters, remember, have 4 legs and a low centre of gravity!

 

safety issues:

 

Will it roll off when empty?

if it hits a rock, it will throw the user off balance and they will stumble and fall.

You will still not see the path ahead so are more likely to hit something.

Tell me any parkland that is truely flat?

 

Like I said, for the stated application and design I see it as a non starter. As a fun sport item it has possibilities, but not exactly a new idea:

 

http://www.random-good-stuff.com/2008/04/0...-hamster-wheel/

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The wheel is able to change direction because it behaves like a chopped cone, not like a bicycle where you have to force a wheel to change direction. This same bicycle analogy proves that it won't sink that much into the ground; the wheel is heavier and the rings are thinner, but the contact surface is bigger because of the diameter and the fact that most of the time there is more than one ring touching the ground. Of course the tracks are deeper than footprints, but I have the impression that they are not as harmful to the lawn as a shortcut worn away by pedestrians, just think about lawn aerators. Small rocks shouldn't be a problem either, the diameter and width of the wheel are too big to feel much of an impact, large rocks can be seen.

I got some good advice though:

I'll keep the perforations in the metal mesh smaller than the smallest finger without making it non-transparent. I could flare the outer rims when the resting surface needs to be a few centimetres wider to achieve balance, I'm just a bit concerned about the price tag and the loss of support for the mesh.

 

I'll put the project aside for a little while to think about the worst case scenario, maybe I'm getting too attached to it as well. :D

You're right, there might be a storm (putting the wheel on its side helps), the angular momentum makes that the braking distance is relatively long and people could deliberately tip over the wheel.

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To turn it you need to move the centre of gravity to the inside and for the resulting force to act off centre (4 years of mechanical engineering degree).

May I ask what you meant with "move the centre of gravity to the inside and for the resulting force to act off centre" ?

 

 

I found three options for point 1:

http://webphysics.davidson.edu/faculty/dmb...on/rolling.html

-> Because the wheel is not rolling yet the rolling resistance should be orientated in the opposite direction acting from the bottom of the wheel in order not to contribute to the rotation of the wheel.

But down the bottom of the page there's "distribution of the normal forces creates a net torque negating the rotational contribution of the friction" ?

 

http://cnx.org/content/m14385/latest/

-> Here the formulas are completely different (no rolling resistance coefficient) and there's no deformation.

 

The rolling resistance force is (mw + mp)*g. I made the rolling resistance a vertically upward force acting at a horizontal distance b (= rolling resistance coefficient in units of length) in front of the wheel centre ground contact point, which creates a clockwise rolling resistance moment (mw + mp)*g*b. If you compute a horizontal force couple at the wheel centre and ground necessary to overcome this rolling resistance moment, then the force is F = [(mw + mp)*g*b]/r, pointing forward at the wheel centre, and backward at the ground.

I tend to go for the last option because there's no contradiction, but I would like a confirmation to be sure. Finding the rolling resistance coefficient is another issue.

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