[Karsten]

 What is the purpose of this contraption? Why not walk?

[Dansercoer (OP)]

Somebody told me my 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. I find this very confusing;
http://webphysics.davidson.edu/faculty/dmb/PY430/Friction/rolling.html [nofollow]
-> The first diagram agrees with the above because the wheel is not rolling yet.
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/ [nofollow]
-> Here the formulas are completely different (no rolling resistance coefficient) and there’s no deformation.

[Raghavendra]

Resistance for what?

[lyner]

Somebody told me my 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. I find this very confusing;
http://webphysics.davidson.edu/faculty/dmb/PY430/Friction/rolling.html
-> The first diagram agrees with the above because the wheel is not rolling yet.
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.

I think the confusion may arise because of Newton's Third Law and the need to choose the appropriate "action" or "reaction" force.
Also, for a vehicle to be driven forward, there is the necessity  of having a frame or chassis to allow for a torque to be applied. (It seems to be implied rather than explicit in the paper).  This is usually achieved by using another contact with the ground (the other axle) or, in the case of a unicycle - a forward tilt of the rider on the seat.

[Dansercoer (OP)]

I think the confusion may arise because of Newton's Third Law and the need to choose the appropriate "action" or "reaction" force.

How is the rolling resistance force orientated according to you, and what would be its origin?
In Physicsforums somebody told me the following: “I drew the rolling resistance force vector vertically upward, at the bottom of the wheel, at a horizontal distance b in front of the wheel centre ground contact point. Rolling resistance coefficient b would generally be much less than r.”

I hope I can find this rolling resistance coefficient in the first place...

[lyner]

The rolling resistance must be slowing the wheel down. If the wheel is not attached to anything then there must be a component of force pointing 'backwards' in addition to the reaction to the weight force.
This can only happen if there is some finite distortion of the wheel circumference of the ground (or the force would just be radial). In the diagram, the backwards component of the small diagonal force would be actually slowing the wheel down. I guess you'd call that the rolling resistance. This seems reasonable as the harder the surface / tyre, the lower the resistance because the reaction force is more vertical.

[lyner]

Perhaps a better way of drawing it would be:

[RD]

If the wheel was on a hard surface, (human-hamsterwheel isn't), the only "resistance" to rotation is from its moment of inertia.

BTW

 [ Invalid Attachment ]

A treadmill is a mill consisting of a large wooden cylinder with steps on the outside. It is worked by persons treading on the steps, their weight causing the cylinder to revolve. The treadmill was invented in China and originally used for raising water. The treadmill employed in British prisons as an instrument of torture or punishment was invented by Sir William Cubitt. The first penal treadmill was erected in Brixton Jail in 1817. The 'hard labour' of prison discipline was formerly the treadmill.

http://www.probertencyclopaedia.com/cgi-bin/res.pl?keyword=Treadmill&offset=0

At least the prisoners on the treadmill had something to hold on to and were kept dry, (roof over head), unlike human-hamsterwheel users.

[yor_on]

How about this? It's twice as good, possibly?

" A two-wheel man-powered vehicle having a frame, a steerable front wheel and a rear wheel, both rotatably mounted on the frame. A hand operable power lever has a lower end pivotally mounted on the frame so as to be capable of swinging back and forth in a vertical plane passing through the frame. The lever is constructed in such manner that an upper portion is capable of rotating about its own longitudinal axis. The power lever is provided with a handle at its upper end.

A seat for an operator of the vehicle is mounted on the frame so as to be movable back and forth with regard thereto. A flexible transmission mechanism has one end connected to the power lever and one end connected to one of the wheels through a unidirectional drive. The front wheel is connected to the rotatable portion of the power lever by flexible connecting cables so as to be steerable upon rotation of the power lever about its longitudinal axis. A first resilient spring urges backwardly the power lever, and a second resilient spring urges backwardly the operator's seat."

Not mine, but it sounds feasible?

[Dansercoer (OP)]

sophiecentaur: Thanks for your diagrams!
Assuming your last diagram is the correct one, how would you calculate where the origin of the rolling resistance force is?

Continuing the quote from the guy at Physicsforums: “The rolling resistance force is (mw + mp)*g. The rolling resistance moment is (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.”

RD: So playgrounds and gyms are for torture and punishment?
While googling for human hamster wheels I found this quote;
“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.”
I’m also surprised to see that your groundwater from before has been replaced by rain.
You should like the solution: why not just wear a coat?
Sorry but this was the last time I answered to destructive rather than constructive criticism,
I hope you can spot the “hold on to” differences by yourself.

[lyner]

RD

If the wheel was on a hard surface, (human-hamsterwheel isn't), the only "resistance" to rotation is from its moment of inertia.

MI is only a reaction - like Mass. It is not a 'resistance' because no energy loss is involved in increasing angular momentum. There will be (very) finite resistance due to friction on the spindle.
Without some way of dissipating the energy supplied by the prisoners, the wheel would soon spin so fast that they couldn't keep up.
I think it would be doing the hamster a favour to put a light brake on its wheel for the same reason, although, the hamster being inside rather than outside the wheel, it is in a more stable situation than the poor ol' prisoners. Aren't humans bastards?

yor_on
I'd rather have a bike, I think!

[lyner]

sophiecentaur: Thanks for your diagrams!
Assuming your last diagram is the correct one, how would you calculate where the origin of the rolling resistance force is?

Continuing the quote from the guy at Physicsforums: “The rolling resistance force is (mw + mp)*g. The rolling resistance moment is (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 think you would need to know the modulus of the surface (assuming that is the majority source of resistance) and to estimate the amount of deformation. The geometry would then help to tell you where the reaction (non-vertical) with the ground would act and the resulting angle.

For rolling resistance to slow a vehicle down, there must, of course, be a force backwards on the axles and when he says that you need to counteract the rolling resistance with a force, applied backwards by the tyre, that makes sense to me. To accelerate, you would need to increase this force.

I feel that the easiest way to estimate the rolling resistance would be to think of the force that is needed, constantly applied, to get the wheel to climb up the lump of road which it keeps creating in front of it. I guess the loss of energy is due to the friction in the material of the road being constantly distorted as the vehicle goes over it. I, frankly, don't feel like doing the actual sums, tho' - far too hard!

[RD]

RD: So playgrounds and gyms are for torture and punishment?

I’m just trying to point out that your unsafe impractical design will be “hard labour”.
My criticism is constructive: I’ll save you from financial ruin if I can dissuade you from manufacturing this device.