Wheelbarrel MA?

[TheTreeSpyder]

Originally posted by murphy4trees
Spidy,
Anyhow.. back to wheelbarrow.. I know it's easier to go over bumps with a larger wheel.. That has been my experience an it is unquestionable empirical data in my thinking.. Therefore I look for the explanation in phsics.... where is the MA... In my thinking the wheel acts as a rounded inclined plane... the larger the wheel, the longer the plane.... However an inclined plane cannot exist on a flat surface.. therefore on a flat surface there is no added MA from wheel size... That the size of the wheel has no effect on the ease of movement on a flat surface has also been my empirical observation..
So thanks again and God Bless,
Daniel

i think that a bigger wheel is better over bumps because of the MA ever present, and the weight is being carried at the axle, so it has a better chance of not slamming into an obstacle that squarely meets the height of the axle (shoving and locking straight into the obstacle).

i think that pushing the weight bearing area (axle) forward is the work to achieve, as more weight is added, there is more friction at the axle. i think that no matter how big the tire, the same amount of work is required to turn the bearing/axle one revolution, having a bigger tire, allows you to spread that work out over a longer distance, thereby requiring less efffort per foot of travel, over a longer distance.

i think of it it as funneling a given amount of work into a smaller space, like if 500# of force hits the ground in 1 sqaure foot, it strikes with 500# of force per square foot, if it covers 5 square feet of area, that is 500# of force, but 100# per square foot. Both are exactly the same but diffrent; both only have so much force, and trade off distance (speed)for power like any ramp, screw, transmission, 10 speed, lever, pulley on load, wheel/axle, gear, wedge etc. all are under the Law of Conservation of Energy. All are the same, seeing these in all forms i beleive helps understand all kinds of motions and locks in tree work, as we prolly deal with these raw forces of nature always.

 

[Nickrosis]

A larger tire will cover more distance per rotation. As long as the axle can handle it, it helps you.

Also, a larger tire will float better instead of burying itself like a skinny wagon wheel might.

Nickrosis

 

[murphy4trees]

That's not quite how I see it....
I think I saw this discribed on a site pertaining to physycs and lever classes etc...
The MA of the wheel turning on the axle would only give you an advantage on the friction on the axle.. which isn't much.
The real benefit of the larger wheel has to do with the inclined plane effect.
And that only really makes a difference at changes of slope..
Trace the hieght position of the axle over time as the wheel is pushed over a curb... The larger the wheel, the higher the axle.. but the axle must rise the same distance, no matter the size of the wheel. However with a larger wheel, the angle of rise is less steep, as the rise is spread out over a greater distance.. Thus the larger wheel ats as a longer and therefore less steep inclined plane.
That to me makes..
Hey.... what does this have to do with treework anyhow..
Perhaps we should expand the subject to all of MA.
God Bless All.
Daniel

 

[Nickrosis]

UNIScienceNET
http://www.unis.org/UNIScienceNet/MECH_knowledge.htmlThe wheel and the axle are a type of lever

A wheel can be rotated by applying a rotating force to its axle. The force applied to the axle is close to the point about which the axle turns. This is like the short arm of a lever. This is the effort arm. The wheel is like the long arm of the lever. The distance between point where the wheel touches the ground (in a wheel on a vehicle) and the point about which the wheel turns is the resistance arm.

Since these distances will be equal to the radius of the axle and the radius of the wheel, the ratio of these two will be equal to the mechanical advantage (MA = radius of axle/radius of wheel). Since the ratio of the two radii, is the same as the ratio of the two diameters, MA = diameter of wheel/diameter of axle.

In this case, the mechanical advantage is less than one, because when the wheel turns the point at which the effort is applied to the axle moves less than the point on the rim where the resistance is overcome.

The steering wheel on a car has a mechanical advantage greater than one, because the effort is applied at the rim and the resistance is overcome at the shaft of the steering wheel.

To explain it using the inclined plane principle seems much harder than to understand it as a lever. To me, the thinner the axle (without it breaking), the larger the wheel, the better.

Nickrosis

 

[TheTreeSpyder]

"In this case, the mechanical advantage is less than one, because when the wheel turns the point at which the effort is applied to the axle moves less than the point on the rim where the resistance is overcome." -Nick

Great to see ya back Nick!

Wouldn't this be MA more than 1? ie. 36" of wheel travel/4" of axle travel?

"The MA of the wheel turning on the axle would only give you an advantage on the friction on the axle.. which isn't much."- Murph

i think that friction is your base fight, besides inertia, small wheel misshaping.


All of positive MA is about funnelling more distance and it's related effort into yet a smaller 'box' of distance within th same ampount of time, there by concentrating your efforts into a smaller area, making those efforts yield more power.

This is from a discussion at ISA tree form years ago that someone mentioned privately, while trying to understand MA in all forms and disguises, for an exercise and insight into seeing it in all our work. OPening up to other MA examples can serve the same purpose.

The examination of axle type determining leverclass doesn't change leverage, but it is an example of how easily classes can be changed; this i feel is directly applicable to rigging, for recognizing it there can make a diffrence. Because, in that case the lever class does matter, by how you can use it, making seeing it in a wheelbarrel a lil'more relevant.

 

[murphy4trees]

Nick's example is based on a machine that is propelled by force turning the axle, which then turns the wheel, such as a bicycle or car.. In that case the energy used to make the axle turn x revolutions will move the machine farther with a larger wheel.. That is not applicable to the wheel barrow scenario.
In the WB, energy is used to move the load directly.. The wheel is just used to remove friction of the load dragging on the ground.

Spidy said "i think that friction is your base fight, besides inertia, small wheel misshaping"... Try pushing 100 lbs of stone up hill in a wheel barrow and tell me that your basic fight is with friction on the axle... If you removed that friction would the stone just float up the hill?
Common sense is in order here. Have you ever noticed the difference in wheel size while pushing a wheel barrow or trailer or log dolly on a flat surface? The answer is no...... If there was a difference in MA based on wheel size..... you would know it. Have you ever noticed a difference in wheel size when pushin a WB over a curb... YES... This is where you get a MA...
That's my story and I'm stickin to it.
And I suppose the fact that we use wheel barrows and Log dollies/ball carts in tree care makes this thread impunable...or would that impunible.. or maybe just OK.
God Bless,
Daniel

 

[TheTreeSpyder]

This leverage is also what makes a larger pulley more efficient, my understanding of leverage relates and is borne out of tree work, now try to use this common example to explain simple, elusive and powerful examples in tree work can be scene. Even through this one facet of the gem of MA/Motion, to see the rest from a diffrent view. So i try to lend that, because, i didn't grip on it overnight, nor by just viewing it from one angle. Also, by seeing these things around us all the time, the lessons are constantly reinforced and deepened, i think; for more cofident decisions.

Nick & i are saying the same thing i believe, that a wheel/axle (or toothed wheel) is a set of rolling levers. Whereby, the center point is the pivot (that doesn't move). The axle is a moving point, as well as the wheel. So an eliptical gear would vary it's MA on the shaft. In Nick's example, the power moves from the axle to the wheel, mine is reverse, so Nick's reduces power, mine gains. Kinda like on a given lever, if you want to move 5x as much weight, or go to the other end and be able to move a load 5x as fast, as the pivot doesn't change in that example either. Just as to be in high speed on a 10speed bike, you use the largest sprocket in front and smallest on back, for in the front the force is powered from the larger arc, and in the rear, the input force is from the inside going out. So reverse arraingements of input/output require reverse gear choice strategy. The larger the tire powered by that rear sprocket, the faster still, all rolling levers.

That also has direct relation to a pulley being in any of 3 positions: the force input into the machine, the force output from the machine, or the pivot/machine (that doesn't move in these scenarios).

If a wheelbarrow had bushings like a less efficient pulley, that would increase friction/effort. For they are both large wheels moving around an axle, who's friction is determined mass and mating type. Both the wheelbarrow and pulley are powered by an outer wheel turning more distance than a smaller one in the same piece of time. A biggery sheave on the same axle is more efficient, just as wheelbarrow.

Removing friction here as Danniel suggests, would mean removing gravity, that pushes heavier masses down, causing more friction to be overcome by the leverage of the wheel over axle.

Cars and bikes, usualyy have one passive axle, so they have 1 that is powered by the axle as in Nick's example, and one powered by the wheel as in mine.

When i told a construction buddy of the discussion, he said let some guys grab that smaller tire size and see! Big guy (ie over 5'5" ), likes to laff a lot!

All this is bound by the Law of Energy Conservation, that governs ruthlessly so much of our work, there are ways it can get ya, and ways you can flow with it and make it work for you everyday, for once you recognize it it is everwhere, offering further examples.

 

[murphy4trees]

Spidy,
I just don't follow your logic here and guess I don't have a lot of patients with the concepts as I think they don't offer worthwhile benefit.
So you said "leverage is also what makes a larger pulley more efficient".. what does more efficient mean?
You also said "Removing friction here as Danniel suggests, would mean removing gravity, that pushes heavier masses down, causing more friction to be overcome by the leverage of the wheel over axle. " I went to a plant in Ohio that built cabins. They built the cabins on a steel frame that had a bunch of rubber pads that were hooked to air lines. When they wanted to move it around the shop they plugged in an air compressor and it would lift off the ground.... Now I could move this cabin with two fingers... pretty cool. So maybe friction on the axle does account for more force than I was thinking.... however if I was trying to move that cabin up a grade.. that would still take enough force to lift the wieght up to the new grade Regardless of friction on an axle.
More thinking on this subject later.
Good night and God Bless,
Daniel

 

[TheTreeSpyder]

A pulley loads up with 2xload on the axle, to move it must break friction between sheave and axle. This is done by lower friction mating and leverage of sheave on axle. Bushings take more stress longer, but present less efficiency as a trade off compared to bearings. Whereby a pro grade 1"pulley with bushing might have a 15+% loss (double loss in double pulley??), and a 4"bearing style pulley only 4%+Loss. Nothing is free, every conversion has a cost, otherwise there would be perpetual motion, and the JFK magic bullet would still be doing right angle turns!. Whereby, the bearing and the leverage of the sheave, lend the higher efficency, so that more of the power of the lacing can be realized. Pulleys too, are 2nd class levers in the way the force comes from the outside, and is leveraged against the friction on a smaller radius.

Also, the larger diameter sheave, lends less distortion to the line, for higher line strength % and life.

Better?

 

[murphy4trees]

How about...
When pullies are used for MA.. the less friction they create the less the loss in power... making them more efficient.
Daniel

 

[murphy4trees]

Just found this in my files.
God Bless All,
Daniel

"University of Arkansas - AgriScience Project
Simple Machines
Information Sheet
WHEEL AND AXLE
The wheel and axle is a simple machine consisting of a large wheel rigidly secured to a smaller wheel or shaft, called an axle. When either the wheel or axle turns, the other part also turns. One full revolution of either part causes one full revolution of the other part. If the wheel turns and the axle remains stationary, it is not a wheel and axle machine.
When the force is applied to the wheel in order to turn the axle, force is increased and distance and speed are decreased. When the force is applied to the axle in order to turn the wheel, force is decreased and distance and speed are increased.
The mechanical advantage of a wheel and axle is the ratio of the
radius of the wheel to the radius of the axle. In the wheel and axle illustrated below, the radius of the wheel is five times larger than the radius of the axle. Therefore, the mechanical advantage is 5:1 or 5.

 

[John Paul Sanborn]

ANd then you have the lever in the handles for lifting and holding the load.

 

[TheTreeSpyder]

i think that the lifting process is a seperate system of the wheel barrel; it is a second class lever for lifting the CoB over the axle, so that the load balances over the axle and is carried by the axle, instead of you. Thereby, also freeing up the legs.

"Wheel-and-Axle
Consists of a large diameter disk (the wheel), which is attached to a smaller diameter rod (the axle).
The effort is applied to the wheel.
The load force is exerted on the axle.
The function of this machine is to multiply the effort force.
This machine can be arrange to perform many different forms of work. " from
Physics Notes

A wheel only doesn't give mechanical advantage, until it connects with something. Placing an axle in the wheel (round gear), allows it to have 2 parts moving at diffrent speeds from the same power. "2 parts moving at diffrent speeds from the same power"; is the answer to many of our mechanical inqiries.

But, i don't think that it matters if a wheel slid around on bearings on an axle, or if the axle turned with the wheel, and then the axle floated in bearings. Both, would exert the increased leverage on the bearings when powered from the outside( ground friction causing wheel to turn). i don't think that whether the axle is fixed to the wheel or frame matters, the increased resistance from progressive loading, comes from the turning of mating surfaces under greater load, not the point of axle attatchment. That is why i made refrence to the 2 diffrent setups, an axle fixed to wheel would give a first class lever, and if the axle is seperate, i think that it is a 2nd class lever; but the leverage ratio is the same. The classes change because the resistance in an axle built into wheel mounts on top, resisting turning in the opposite direction as the input force, so 1st class lever. If the axle is part of the frame, the axle sits down into the bearings of wheels tighter, increasing resistance that turns in the same direction as the input force of the wheel turning on the ground. If the input force of the wheel turning is moving in the same direction as the output against the mounting resistance of loading, it can't be a 1st class lever. Seeing as MA increases it can't be a 3rd class lever.

Sand or grease, will not change the rolling resistance of the ground, but sand or grease will for the bearings, so i see them as what is to be overcome, what resists movement beyond inertia! Adding more weight increases traction that powers the wheel around the axle, but extra weight also loads the bearings more to resist movement; at least i think adding more resistance than the ground holding the tire down more because of the increased load!

i went on about comments about pulley before because, a pulley is the same machine of a wheel rolling on an axle, taking leverage over the resistance of the mating surfaces turning by the ratio of the changes from exterior to interior arcs. The resistance of the mating surfaces that this mechanics takes leverage on can be changed with material/arraningement (bushing, bearing). The type of mating and leverage of resistance on mating parts turning prolly determine the efficincey in both pulley and wheel barrel.

 

[Stumper]

Thanks Dan. I was intending to jump into this one but have been trying to remember the proper terminology from those classes oh so long ago.-I still can't but you have done a good job bringing this back in to perspective. You said "wheels almost defy gravity"--that is a key observation. The wheel takes most of the friction out of the scenario. It is no big deal for a man to move several thousand pounds on wheels. No, he cannot lift it, but if the friction from trying to slide it is largly removed then it becomes a question of overcoming inertia-which our muscles can handle because we can put the requisite energy into the problem over time. (Your truck is stalled on a hard, level surface. Put your shoulder to it . Strain ,pushing hard with your legs. S l o w ly it begins to roll.) .
A single pully inceases the load on its attachment point fecause it becomes the fulcrum or balance point (so that lifting 200 lbs straight up requires 200lbs pulling straight down for a 400 lb load on the pulley attachment)-I'm ignoring minor friction factors for simplicity.- Tackle arrangements increase applied forces by virtue of increasing the time/distance that a lesser force is applied. A 3/1 arrangement allows you to lift 300lbs with only 100lbs of force applied to the tail but to move the load one foot you must pull the tail 3 ft..
The gear effect of wheels on fixed axles is interesting and important but not a factor in wheelbarrows or pulleys.

Wheels have much in common with inclined planes in that they allow us to trade time and distance of input force for for a total force which we could not apply in a lesser ammount of time or distance.

 

[Joe]

Dear Dan;

I am now picking on you.

http://www.tpub.com/machines/1b.htm

Have fun with this link.

Joe

 

[TheTreeSpyder]

ummmmm, that link of Joe's isn't saying that lifting a wheelbarrow is a second class lever is it?

After overcoming inertia, with an increased load in the wheelbarrow, it takes more effort to push it than without. On hard tires and ground, does the increased resistance to rolling from this increased load come from the static friction(non-heat causing) of the ground on the wheel (not wanting to release the wheel from the ground), or the other to surfaces frictionalized under load (bearings) being forced to move?

 

[Joe]

.

 

[TheTreeSpyder]

i think that the tire on the road causes heat when it slips, that force is lost to heat. So it takes more effort to move something that is giving away it's energy to heat, and not focused on task. But i think that non-slipping /static friction is diffrent; in fact is probably a componenet of inertia, in that it provides the 'stickyness' of a body at rest, producing no heat then.

Joe, nice links; i refer questions like this to a bike expert locally. i think we can rule out the effect where a wheel spinning at 35mph effectively adds 3x it's weight to the load of effort (hence lighter wheels for racing), and the use of $200 bearings in a $50 wheel barrow.

From the 2nd link:

Larger wheels have less rolling resistance, for several reasons. First, they won't drop (as much) into a smaller hole as a smaller wheel would. Second, They have greater leverage for lifting the wheel over bumps. Third, there is less deformation of the tire at the contact patch on the ground. Fourth, smaller wheels require faster chain speeds, which will have higher frictional losses. Fifth, for similar reasons they will have higher hub friction.

i think that faster chain speeds refers to more revolutions for the same work, yielding more bearing/hub friction. i think there is less tire deformation, for a flatter track also; but i think that makes it harder to initate the motion slightly, i think it has greater leverage over bumps because it casts a higher percentage of it's force over the obstacle- rather than into it- due to it's wider radius. They don't drop into holes imperfections as easily, but that is kinda in line with not misshaping either mating surface ground or tire.

 

[geofore]

hot air

My thought was Joe posted the site refferance to elimanate the hot air or at least cool it off while the laughter died down. If you read far enough through you will see a bit of the block and tackle uses that are important to moving loads too heavy for one man to pick up without hurting his back. hey it may even improve the math skills a bit.