How's my logic/maths/physics - pulleys

[ChrisGreaves]

20231128_145742.jpg

To the right-hand side is a tree; one of seventeen that I want to yank out of the ground. (Don't worry, I have hundreds of fruit trees as replacements!)
A cable tied firmly to an anchor point (schematically represented by a stake in the ground) passes through a single pulley wheel which is chained to the trunk.
Just to the left of that we see "2:1" because I believe that single pulley with two strands gives me a mechanical advantage of 2:1.

But instead of hauling on that end of the cable, I attach a second pulley with two strands giving me another 2:1 mechanical advantage.
Now if I haul on this new end I get a mechanical advantage of 4:1.

And so on. My logic is that at the left hand end when I haul I get a 64:1 mechanical advantage.
That is this arrangement of pulleys gives me a mechanical advantage of two-to-the-^pulley

I believe that this is the highest mechanical advantage using pulley wheels.
If I built a single pulley block with eleven wheels I would then have (I think) twelve strands, giving a mechanical advantage of only 12:1.

Any other arrangement, say three pulley BLOCKS at 3:1, 5:1, and 3:1 (yielding a mechanical advantage of 45:1) is a less efficient use of pulley wheels.

And FYI it won't be me hauling on the end of the cable (not rope); it will be an electric motor (from an old vacuum cleaner) cunningly designed as a portable winch, and I will be inside the shed well out of the way if/when the cable snaps.

In essence I am suggesting that Binary systems gives us the fastest increase in value per digit.

Thanks in advance for any elucidation/confirmation/dissension.
Chris

[DocAElstein]

Hello,

Disclaimer: Although I was a Physicist, quite a good one, it’s rather a long time ago…

I think your logic is OK, ( to a first approximation, ignoring things like friction, momentum, acceleration, relativity theory, etc, etc.)
The Work stays the same, but you keep halving the distance you move, so the force keeps geting doubled
Work = Force x Distance

Practically there might be problems. For example, the last few anchor points will need to be very secure and stable. If they move a bit, the tree won’t. Trees are usually very stable anchor points. You will need a large distance between the first two stakes. So you will probably need to either use the neighbours gardens and/ or stop all the road traffic so you can use all that area.
(Personally I favour digging holes a lot to do things. After I have done that I wait a while before filling them in. New novel ideas seem to crop up in my mind then. Remember like that one you had to help Brenda with the problem of her dog eating the apple tree leaves…..

Spoiler

she told me that her dog has chewed the leaves off the apple trees I gave her last summer.
Me: Oh Brenda, you weren’t planting your trees properly; you have to plant apple and pear trees a special way if you want to make sure that your dog doesn’t eat the leaves.
Brenda: How should I have planted them?
Me (thinking on my feet, remember): Well, say the root ball is nine inches, how deep a hole have you been digging?
Brenda: Nine inches, of course?
Me: Wrong! You shoud add an an extra foot. In this case make the hole one foot nine inches deep.
Brenda: ?!!???
Me: Before you place the root ball in the hole, take the dog ...
Brenda: ?!!??? ?!!??? ?!!??? !!!!!!!!!!!!!
Me (scrabbling for the next phrase): ... and place it in the bottom of the hole. Quickly shovel twelve inches of soil on top and tamp it down firmly ...
Brenda: !
Me: ... then sit the root ball on top of the tamped-down earth and fill in the hole with the rest of the soil.
(silence)
Me: Make s small deperssion and allow about six gallons of water to run into the hole.
(pause)
Me: There are several benefits from planting an apple or pear tree this way
(i) Never again will your dog eat the leaves off your fruit trees
(ii) Your apple tree will produce fruit a year or two earlier on account of the great nutrients at its disposal and ...
(iii) You wont need to walk outside to get apples. Just stand at your back door and whistle, then call out “Pip! Here Pip! Come home Pip!”, and half a dozen applies will obediently drop to the ground and trot towards you.

)

Alan

P.S. I once needed to shift a very heavy Granit post a couple of cm once quickly before the concrete I had it set in dried. I did not think of the Work/ distance/ force advantage idea, which is a shame now that I think about it. I did have some Pulleys laying around. In Panic I was thinking more in Power, Energy and momentum at the time. What I tried did work, but I still got the dent to prove it in the back of my VW Bus, :(

[RonH]

Borrow a friends tow truck with its winch. That will easily 'sort it'.
One of our 80+ yo apples ... sorted (now cut up and removed) but too cold to remove root just now.

Apple tree.jpg

[ChrisGreaves]

Alan, thanks for the reply.

... the last few anchor points will need to be very secure and stable. If they move a bit, the tree won’t.

...
Quite so. This much I remember from my years harvesting wheat and winching trucks out of dust-holes. Knots, ropes, and chains all tighten up in quantum leaps while the load is being taken up.

...I did not think of the Work/ distance/ force advantage idea,

This is in my mind for the plough. I don't mind if it takes the winch five minutes to pull a root-cutting plough twenty feet; there are always roots, rocks etc to tidy up from an earlier pass, soil to sieve, ...
Time, in this case, is on my side.
Since the winch will be mobile, time is of no real significance if the winch/pulley system is dragging a V-shaped snow blade up my driveway.
Cheers, Chris

[ChrisGreaves]

Borrow a friends tow truck with its winch. That will easily 'sort it'.

Thanks Ron. If it were so - just one tree in an open space - that would do the trick. For the eight or ten trees in the front hard that might work. But (a) we can't get a tow-truck into the back yard and (b) the trees there are all close to the southern and eastern fences, so I want fine motor control. If I see a portion of fence moving, it is time to leap in and exercise with a serious wood-axe!

I see many uses for a portable winch based on an electric motor from an old vacuum; tree pulling, lawn ploughing, snow ploughing, and even dragging sleds of sawdust, grass, soil, and rocks back and forth. Over almost five years here i have amassed a lovely collection of old motors, gear wheels etc.
Cheers, Chris

[DocAElstein]

Your way, as well as a very interesting fun way, is also a nice safe way, making it more likely that you are a safe distance away. The distance needed often catches people out. I am going to post one of the most funniest YouTube videos I ever saw if I come across it again. The guy pulled the tree down with his car - pulled it down on top of himself.

Edit: Here i found it, the one that starts here
https://www.youtube.com/watch?v=4KE7cpyUn3o&t=166s

[John Gray]

You could try accelerating your truck towards the tree as fast as it can go.
Remember to jump out immediately before impact!
[Oh, you have 17 trees to remove. Better start buying more trucks?]

[ChrisGreaves]

You could try accelerating your truck towards the tree as fast as it can go.
Remember to jump out immediately before impact!
[Oh, you have 17 trees to remove. Better start buying more trucks?]

Oh now you're being silly, John
If I crash the town's only tow-truck, who you gonna call?
Cheers, Chris

[ChrisGreaves]

... that you are a safe distance away.

Often enough the pain of cable-snap can be alleviated by passing the cable through a ninety-degree turn (via pulley) which can remove the operator from the war-zone.

That said, now imagine the winch&cable mounted on a hinged platform.
A plug and a socket join the two plates at the far side from the hinge.
If the plough being dragged towards the winch stubs its toe on a tree root, embedded rock, or even the plank at the border of the bed, the winch now lifts itself (hinged, remember) and thus breaks the power connection.

That should reduce the likelihood of an excessive strain being imposed on the immediate cable.
And, if I'm thinking straight, the closer the cable snaps to the far pulley (chained to the tree or plough), the more energy will be absorbed by making spaghetti, right?

Cheers, Chris

[DocAElstein]

I suppose you have your reasons for wanting to rip it out completely.
Personally I am a great fan of cutting back trees to varying extents, even extreme extents in some cases. But being a hobby builder and general experimental hole digger, strong fundaments fan etc., deep foundation fan, solid building fan etc. etc. , I have a lot of respect for the strong way a tree is often rooted. I would do everything else first before pulling tree roots up. For example, I put a new sewage pipe in whose ideal route went through where there was a 13 meter high tree, so I tunnelled directly under it. I got away with it as the strongest roots went a bit sideways, as they often do, and only a few roots went directly vertical downwards

[ChrisGreaves]

I suppose you have your reasons for wanting to rip it out completely.

Hi Alan.
Not "it" but "them", all 15 or 17 of them.
Aspen trees send roots horizontally at least 50 feet, with a dozen or so suckers erupting every couple of feet or so.

Don't worry, I have hundreds of fruit trees as replacements!"

Cheers, Chris

[ChrisGreaves]

My logic is that at the left hand end when I haul I get a 64:1 mechanical advantage.
That is this arrangement of pulleys gives me a mechanical advantage of two-to-the-^pulley
I believe that this is the highest mechanical advantage using pulley wheels....In essence I am suggesting that Binary systems gives us the fastest increase in value per digit.

Oh! What a great Christmas this will be,
At the 9m38s point in this video the switch is made.
I am not sure whether to call this "serial to parallel" processing or "the power of binary power", but I think that the answer to my question is here.

Compare the situation between 4m38s and the 9m38s points in the video to see the difference.

What's the cost? I believe that the cost is "size of system". In the binary method the pulleys occupy a greater linear distance, whereas in the pulley-block system extra pulleys do NOT cost extra space.

If you've got enough space to use, go for the binary system; less pulleys, more power (which is energy-per-unit-time)
Cheers, Chris

[DocAElstein]

Nice. I like this example of taking an already great idea, the pulley advantage thing, but thinking about it and then improving on it.
(I have often thought how we would be if after the invention of the wheel, we had not then come up with pneumatic tyre. Some people would have stopped at the wheel. Most others would have got as far as rubber tyres and stopped there. But the pneumatic tyre invention and the development of it, IMO is what really helped push the idea a lot further)
I spent a bit of time trying to think of all the different advantages and disadvantages between the two, so as to make a choice if I had to choose, for example on a limited budget, or limited space and weight carrying capacity on my transportable universal tool box, etc.
I started getting frustrated after every time I had a choice, I thought of something else that switched it. So I stopped thinking, fixed a totally different problem, then thought of a better solution: I would spend the money on a few good pulley wheels, different length bolts, string, (anything else I need I could knock up at zero cost as good as anything I could buy). Then I would thread them up to suit.

Have a fun Xmas Chris, ( and everyone) :)
Alan

[ChrisGreaves]

I spent a bit of time trying to think of all the different advantages and disadvantages between the two, ...

My mode of operation is to think/mull/sulk for a few weeks making pencil&paper notes.

Apart from the pulley wheel used to change direction (so we can winch a tree from a vantage point ninety degrees to the right of the cabling), there seem to be just two basic pulley arrangements: Two pulley blocks, one (at the top) holding N wheels and the other (bottom) holding N-1 wheels; the mechanical advantage is N:1. I call this the Parallel arrangement.
The second style is a series of single-wheel pulley blocks, with the stub of cable emerging from the "top" block (of a single wheel) holding the next single-wheel pulley block. This type offers a mechanical advantage of Two raised to the power N. I call this the Serial arrangement.

Building a winch-and-plough system to till soil suggests that the serial arrangement offers the better power when the winch is the mains-power motor extracted from a vacuum-cleaner.
But the 2^N mechanical advantage comes at a price: a 24-foot garden bed, ploughed at a 2^6 mechanical advantage uses the full 24-feet of winched cable, but delivers only 24/64 feet of movement at the ploughing end.

A lower cost in pulleys is irrelevant in the long term (year after year use of the system).

Significantly, all the books, web pages and videos I've seen to date demonstrate pulleys operating against gravity, hence arranged in a vertical sense. "Lifting a concrete block".

Tilling/ploughing a field, towing a crashed vehicle out of a bog, or pulling out an isolated tree stump requires a horizontal arrangement, which might mean cables being dragged across/through soil.

More grist for the mill ...
Cheers, Chris