Any mathematics gurus that can figure a real world problem?.

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qikbbstang
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Any mathematics gurus that can figure a real world problem?.

Post by qikbbstang » Mon May 04, 2015 11:08 pm

Thirty years ago when I bought a piece land with large hardwood trees I set about what I thought would be a cool project. Recalling back when I was just a kid I enjoyed swing sets that were large enough so that I could really swing hard and achieve a brief free-fall followed by a jerk on the chains at the peaks of the swing path, really stress the swings frame and got astonishingly high. Being the proud land owner I first threw strings over a hefty hickory limb some 20-25ft high, used the strings to pull ropes with slip knots up the limb and fed the other end of the ropes into drilled holes in a 2x6 as a seat. All set to swing hopefully a mile-high, I sat on the swing and could not get it to swing at all. Next I figured perhaps if I had a good swinging start and changed the rhythm that might help so I included a ladder about eight foot high and launched the swing with my butt on it. Despite my actions the swing simply swung down to nothing regardless of how I tried to impart swinging action with my arms/legs etc. Worst part was I had to eat crow and climb up and out on that manster limb to get the blasted ropes down from the non-working swing. However I still think back on going on a swing that really packed a thrill, took you high and travelled a good distance.
So what gives, why can't a swing be blown up in scale and still work?.....................
Is there any way to predict what is the max length for a swing for it to be able to work?......................

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Re: Any mathematics gurus that can figure a real world probl

Post by lada ok » Mon May 04, 2015 11:12 pm

As with any thing, ... there's always swings and roundabouts :roll:

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Re: Any mathematics gurus that can figure a real world probl

Post by user-23911 » Tue May 05, 2015 2:42 am

It depends on how long your legs are.
I too spent many hours as a kid playing on swings.
To get the swing to work right you're moving the centre of mass closer to the pivot point at the correct time. You're also moving it away at the correct time.
You bend your legs to do that.
If you look at that as a % then the longer the swing ropes are, the less the % is which you can shift your centre of mass so the less effective the swing is.
likewise if you've got ducks disease, you're not going to be very good on a swing.

It's the same idea as spinning around on a spot with your arms out, you then pull your arms in and you spin quicker.
Like on a roundabout?

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Re: Any mathematics gurus that can figure a real world probl

Post by Dave Koehler » Tue May 05, 2015 8:03 am

Fun with swings.
1: Where is Tarzan when you need him?
2: You likely needed an Acme Rocket when leaving from the tall perch.
3: What goes up must come down, spinning wheel.........

Reality
Grandpa built a really tall swing set out of whatever pipe was laying around the farm. It was a beast.
Even as a strong teenager it was extremely difficult to achieve horizontal stall but we kept trying.
I don't think I ever got any higher as an 18 yr old as I did as an 8 yr old.
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Re: Any mathematics gurus that can figure a real world probl

Post by Kevin Johnson » Wed May 06, 2015 10:55 pm

Repeat experiment with a static rope rather than dynamic rope.

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Re: Any mathematics gurus that can figure a real world probl

Post by allencr267 » Thu May 07, 2015 5:39 pm

qikbbstang wrote: ...slip knots up the limb... Despite my actions the swing simply swung down to nothing regardless of how I tried to impart swinging action with my arms/legs etc. So what gives, why can't a swing be blown up in scale and still work?...............
If the branch isn't horizontal, 2 different rope lengths, plus the moving pivot points as they slide around the branch, makes for a 2 point pendulum that will fight against itself.

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Re: Any mathematics gurus that can figure a real world probl

Post by Kevin Johnson » Thu May 07, 2015 5:42 pm

Wrong type of rope is being used. The rope is acting as a damper and internally dissipating his torque input. Use the correct type of rope or switch to steel cable or chains.

Side note: related issue is if you use the wrong kind of rope in a tug-of-war -- it can stretch and break and then slice off fingers as it contracts. Look up the difference between static and dynamic rope.

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Re: Any mathematics gurus that can figure a real world probl

Post by MadBill » Sun Aug 09, 2015 10:43 pm

joe 90 wrote:It depends on how long your legs are.
I too spent many hours as a kid playing on swings.
To get the swing to work right you're moving the centre of mass closer to the pivot point at the correct time. You're also moving it away at the correct time.
You bend your legs to do that.
If you look at that as a % then the longer the swing ropes are, the less the % is which you can shift your centre of mass so the less effective the swing is.
likewise if you've got ducks disease, you're not going to be very good on a swing.

It's the same idea as spinning around on a spot with your arms out, you then pull your arms in and you spin quicker.
Like on a roundabout?

Ankle weights perhaps? :)
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Re: Any mathematics gurus that can figure a real world probl

Post by Greenlight » Thu Sep 10, 2015 12:42 am

The things that Joe90 mentioned are all correct. I will add one or two more things to his comments.

On a relatively short swing, the majority of the weight of the swing assembly is the human body and therefore the center of mass (COM), relative to the pivot point, is virtually the COM of the body (approximately the belly button). In order to add energy to the system and get the swing to increase swing height, the human needs to rotate his/her body about the COM. You basically do this by pulling on the tethers above the COM and rotating your body below the COM.

As the swing tethers get longer and longer the weight of the tethers are less and less negligible and the COM moves closer to the pivot point. When the human attempts to add energy to the system, the moment (torque) he/she is able to impose about the COM becomes much less. Standing on the swing seat will greatly improve the ability to increase the moment about the COM in this case.

Also, as the length of the tethers increase the swing angle of the seat is very small for an equal arc length of the swings seat, compared to a short tether. When you rotate about the COM to add energy to the system, the angle of the tether affects the restoring force because the gravitation force is always straight down. That's why it's easier to increase the swing "height" after you have gone through those initial small angles of rotation as you just begin to swing. The torque you are adding at small swing angles is the small at high swing angles. But the angle of the tether relative to the direct downward angle of gravity increases the restoring force and causes the swing to go still higher.

Adding length also increases the time period to complete one cycle of the swing. So, even at small swing angles (when you are just starting to get the swing to move), it takes 5 or 6 seconds to complete one cycle. You body and mind is not accustomed to this long time period and you try to force the swing to move quicker by tugging the tethers and rotating your body quicker. These motions are all in vein and contribute to the swing not moving at all.

The image below attempts to show how the COM changes with long, heavy tethers.

Image

Please forgive my crude sketch. I did it quickly using MS Paint.

I hope I have written this in a clear enough manner that makes it easier for you to understand the physics behind your swing.
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Re: Any mathematics gurus that can figure a real world probl

Post by Kevin Johnson » Thu Sep 10, 2015 6:52 am

As long as you use the correct type of rope.

https://en.wikipedia.org/wiki/Static_rope
A static rope is a rope that is not designed to stretch when placed under load, in contrast to a dynamic rope. Static ropes have a wide variety of uses, for instance in fire rescue operations[1] and caving.[2]

They have some applications in climbing, though lead climbing, for instance, is always done with a dynamic rope, since a fall on a static rope is stopped too quickly[3] and may lead to serious injury.[4][5] Abseiling [rappelling], however, is best done with a static rope or, alternately, with a dynamic rope with low elasticity.[6]
https://en.wikipedia.org/wiki/Dynamic_rope
A dynamic rope is a specially constructed, somewhat elastic rope used primarily in rock climbing, ice climbing, and mountaineering. This 'stretch' is what makes it 'dynamic', in contrast to a static rope that has very low elongation under load. Greater stretch allows a dynamic rope to absorb the energy of a sudden load such as from a fall more slowly, reducing the peak force and therefore the chance of catastrophic failure. Kernmantle ropes are the most common type of dynamic rope, and nylon has replaced all natural materials such as hemp since 1945 for durability and strength.
This also has application for people towing cars or attempting to pull people out of the sand or mud. You need to understand the material properties of the link between the two vehicles.

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Re: Any mathematics gurus that can figure a real world problem?.

Post by MadBill » Fri Feb 23, 2018 10:00 pm

A number of winters ago in my neighborhood, a guy was trying to pull a car out of a ditch with what was apparently a dynamic rope attached to his front bumper and the stuck vehicle's bumperette. He had his head out the window to observe when the bumperette tore out and the elasticity of the rope propelled it into fatal contact with his head..
Felix, qui potuit rerum cognscere causas.

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Re: Any mathematics gurus that can figure a real world problem?.

Post by Geoff2 » Sat Feb 24, 2018 3:44 am

Mention of Tarzan reminded me of a joke. The definition of a Hippie: Looks like Tarzan, walks like Jane, smells like Cheetah....

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Re: Any mathematics gurus that can figure a real world problem?.

Post by Kevin Johnson » Sat Feb 24, 2018 4:32 am

MadBill wrote:
Fri Feb 23, 2018 10:00 pm
A number of winters ago in my neighborhood, a guy was trying to pull a car out of a ditch with what was apparently a dynamic rope attached to his front bumper and the stuck vehicle's bumperette. He had his head out the window to observe when the bumperette tore out and the elasticity of the rope propelled it into fatal contact with his head..
Hi Bill,

I am very sorry to hear about the fatality.

I carry a tow strap which is designed to stretch and help snatch a vehicle out of a rut or to dissipate braking forces. If you have ever been towed by using a chain with little to no stretch you will know how abrupt and damaging the shock load can be; you need to be careful about matching vehicle speeds with judicious braking and even acceleration. Finding a suitable place to attach the strap on the stuck vehicle can be a pain because by definition the vehicle is often buried.

The verge on our street has sugar sand that has been repeatedly stripped of stabilizing vegetation by delivery vehicles and garbage trucks. For several years a number of people (pizza delivery vehicles, people stopping for various reasons) had gotten stuck and needed to be helped out. Gross but practical tip for people dealing with sugar sand: we have a number of cats and the used kitty litter helps to bind the loose particles whilst the feces provides nutrients for plants/weeds/grass to grow and further bind the small particles.

The Post Office threatened to stop delivering mail to our box after their small delivery vehicles without limited slip differentials a-l-m-o-s-t got stuck. I had a buy a few cubic yards of irregularly shaped gravel that interlocks and stabilizes the area. It is not an ideal solution because the individual stones can be driven into the street and be propelled by passing car tires and mowing the verge becomes hazardous owing to the potential of the blades striking and propelling the stones. Life in sunny Florida had some interesting challenges when first moving here.

Okay, I hope I have added sufficient tangential and interesting information to dilute the sad news of people being killed and fingers sliced off. :(

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Re: Any mathematics gurus that can figure a real world problem?.

Post by MadBill » Sat Feb 24, 2018 9:32 am

Quite so about the chain effect; I've 'veed-out' more than one bumper that way.. #-o

Good ole post office: Neither rain nor snow, etc., but soft shoulders and barking dogs are a different story.

Glad to see you back in action on S/T Kevin, hope you're firing on all cylinders now. =D>
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Re: Any mathematics gurus that can figure a real world probl

Post by j-c-c » Thu Oct 18, 2018 3:45 pm

Greenlight wrote:
Thu Sep 10, 2015 12:42 am
The things that Joe90 mentioned are all correct. I will add one or two more things to his comments.

On a relatively short swing, the majority of the weight of the swing assembly is the human body and therefore the center of mass (COM), relative to the pivot point, is virtually the COM of the body (approximately the belly button). In order to add energy to the system and get the swing to increase swing height, the human needs to rotate his/her body about the COM. You basically do this by pulling on the tethers above the COM and rotating your body below the COM.

As the swing tethers get longer and longer the weight of the tethers are less and less negligible and the COM moves closer to the pivot point. When the human attempts to add energy to the system, the moment (torque) he/she is able to impose about the COM becomes much less. Standing on the swing seat will greatly improve the ability to increase the moment about the COM in this case.

Also, as the length of the tethers increase the swing angle of the seat is very small for an equal arc length of the swings seat, compared to a short tether. When you rotate about the COM to add energy to the system, the angle of the tether affects the restoring force because the gravitation force is always straight down. That's why it's easier to increase the swing "height" after you have gone through those initial small angles of rotation as you just begin to swing. The torque you are adding at small swing angles is the small at high swing angles. But the angle of the tether relative to the direct downward angle of gravity increases the restoring force and causes the swing to go still higher.

Adding length also increases the time period to complete one cycle of the swing. So, even at small swing angles (when you are just starting to get the swing to move), it takes 5 or 6 seconds to complete one cycle. You body and mind is not accustomed to this long time period and you try to force the swing to move quicker by tugging the tethers and rotating your body quicker. These motions are all in vein and contribute to the swing not moving at all.

The image below attempts to show how the COM changes with long, heavy tethers.

Image

Please forgive my crude sketch. I did it quickly using MS Paint.

I hope I have written this in a clear enough manner that makes it easier for you to understand the physics behind your swing.
This was also my takeaway in red, but regardless, the period will remain the same for any chosen tether length, only the distance traveled and seat speed will change, correct?

I think aero drag starts to enter the equation based on higher speeds and maybe the ultimate limiting factor as tethers increase.

If I am restating the obvious, my apologies.

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