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Understanding The Physics of Slingshots


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#1 busySteve

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Posted 14 May 2016 - 09:52 PM


See attached PDF:
 
In an effort to understand the physics of a slingshot I had to learn some algebra, some calculus, and some basic physics. The most helpful book for an introductory crash course on these topics was the ”No Bull**** Guide to Math & Physics” by Ivan Savov. If you struggled with math in school or dropped out like I did, this book will give you all you need to begin understanding your slingshots.  After the math has been understood, the next step is to read retired physicist, Bob Yeats’, paper titled: 
 
”Physical modeling of real-world slingshots for accurate speed predictions”
 
His paper is a gateway of sorts. The why’s of what is needed to understand slingshots is covered very well, but the mathematical ways are not. At least that was my experience. So my hope is to help you by saving you the time it took me to build the foundation required to take this information in. In his paper, Bob Yeats refers to a method of calculating the speed called leapfrog. Believe it or not, this is a technical term in the physics world. The reference (#11) he sites from his paper goes very deep into the way it works, and was beyond me until I read Savov’s book and some Wikipedia items on the topic. I’ll try to explain in my own words how all this works together but I am not the source of this information. Bob and his references are where the credit goes. My focus here is on where I struggled.
 
I have written a web page that implements the math and methods:
 
I have also written a short paper that covers the basics of how I came to understand Bob Yeats' paper.
 
I hope this is of value to someone.

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Edited by busySteve, 14 May 2016 - 09:55 PM.


#2 Rayshot

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Posted 15 May 2016 - 07:42 AM

Never hurts to learn and exercise the brain.  

 

And that sometimes it helps when material is distilled or at least a process in which may be an easier way to assimilate the info.



#3 Tremoside

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Posted 15 May 2016 - 07:50 AM

Thank you very much Steve! Have a nice weekend!



#4 Phoul Mouth

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Posted 15 May 2016 - 12:05 PM

I don't think I have ever seen such an appropriate user name.  LOL



#5 Chuck Daehler

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Posted 15 May 2016 - 04:08 PM

Frankly, I've always used science/math to understand things that deal in physics, numerical values and calculating numbers.  Nice work!

 

It will be interesting when you get the calculator java script done...

 

There are other variables such as barometric pressure (denser air resists movement more than thinner air...i.e. I live at 9000 ft elev), temperature of the bands (warm bands are snappier than cool or cold bands in contraction speed), the pouch width (air resistance) and the ammo geometrics.  Lead, glass or steel?  Lead holds velocity better than steel which hold vel better than glass (marbles) due to the ratio of mass vs air resistive surface area. Many here shoot cylinders, while most shoot spheres, some shoot cubes and hex nuts...so velocity at release will be affected by the ammo type, say, 10 meters down range after air resistance has played its factor.   The lead/glass/steel and geometric shapes add about 8 variables, 64 combinations.

 

But all in all your calculator would be interesting to use vs a chronograph to see the similarities of calculated vs real time.  A chronometer is the last word.  I use a freeware sound program called "Audacity" on my laptop (I think it's Android compatible also) which measures the time from the sound of the bands at release to the target impact sound. it shows you the sounds on a graph like screen and you measure the time between sound peaks.  I use 4 meters as the range.   It's not as accurate as a real chrony but it's better than nothing and is for me at least, pretty good to compare band/ammo/draw length variables.


Edited by Chuck Daehler, 15 May 2016 - 04:19 PM.


#6 treefork

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Posted 15 May 2016 - 04:30 PM

The WKB approximation to the one-particle Schrödinger equation is used to obtain the wave function at a given point as a sum of semiclassical terms, each of them corresponding to a different classical trajectory ending up at the same point. Besides the usual, real trajectories, also possible complex solutions of the classical equations of motion are considered. The simplicity of the method makes its use easy in practical cases and allows realistic calculations. The general solution of the one-dimensional WKB equations for an arbitrary number of complex turning points is given, and the solution is applied to calculate the position of the Regge poles of the scattering amplitude. The solution of the WKB equations in three dimensions for a central analytical potential is also obtained in a way that can be easily generalized to N-dimensions, provided the problem is separable. A multiple reflection series is derived, leading to a separation of the scattering amplitude into a smooth “background” term (single reflection approximation) that can be treated using classical but complex trajectories and a second resonating term that can be treated using the Sommerfeld-Watson transformation. The physical interpretation of the complex solutions of the classical equations of motion is given: they describe diffractive effects such as Fresnel, Fraunhofer diffraction, or the penetration of the quantal wave into shadow regions of caustics. They arise also in the scattering by a complex potential in an absorptive medium. The comparison with exact quantal calculations shows an astonishingly good agreement, and establishes the complex semiclassical approximation as a quantitative tool even in cases where the potential varies rapidly within a fraction of a wavelength. An approximate property of classical paths is discussed. The general pattern of the trajectories depends only on the product ϵ = , and not on energy and angle separately. This property is confirmed by experiments and besides the signature it gives for the semiclassical behavior, it simplifies considerably the search for all trajectories scattering through the same angle. Finally, a general classification of the different types of elastic heavy ion cross sections is given.



#7 Rayshot

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Posted 15 May 2016 - 05:39 PM

The WKB approximation to the one-particle Schrödinger equation is used to obtain the wave function at a given point as a sum of semiclassical terms, each of them corresponding to a different classical trajectory ending up at the same point. Besides the usual, real trajectories, also possible complex solutions of the classical equations of motion are considered. The simplicity of the method makes its use easy in practical cases and allows realistic calculations. The general solution of the one-dimensional WKB equations for an arbitrary number of complex turning points is given, and the solution is applied to calculate the position of the Regge poles of the scattering amplitude. The solution of the WKB equations in three dimensions for a central analytical potential is also obtained in a way that can be easily generalized to N-dimensions, provided the problem is separable. A multiple reflection series is derived, leading to a separation of the scattering amplitude into a smooth “background” term (single reflection approximation) that can be treated using classical but complex trajectories and a second resonating term that can be treated using the Sommerfeld-Watson transformation. The physical interpretation of the complex solutions of the classical equations of motion is given: they describe diffractive effects such as Fresnel, Fraunhofer diffraction, or the penetration of the quantal wave into shadow regions of caustics. They arise also in the scattering by a complex potential in an absorptive medium. The comparison with exact quantal calculations shows an astonishingly good agreement, and establishes the complex semiclassical approximation as a quantitative tool even in cases where the potential varies rapidly within a fraction of a wavelength. An approximate property of classical paths is discussed. The general pattern of the trajectories depends only on the product ϵ = , and not on energy and angle separately. This property is confirmed by experiments and besides the signature it gives for the semiclassical behavior, it simplifies considerably the search for all trajectories scattering through the same angle. Finally, a general classification of the different types of elastic heavy ion cross sections is given.

 

Pretty good Marty, you learn fast.


Edited by Rayshot, 15 May 2016 - 05:39 PM.


#8 Chuck Daehler

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Posted 15 May 2016 - 05:47 PM

...and you copy/pasted that from where Treefork? I pass in awe if you just thunk that up.  Fresnel lenses?  You left me in your dust pahdner... the sence of humor on this forum reaches a high point when inventive and respectful use of it paints a picturesque yet amusing and contemporary image of intelligence. In other words, ROFFLMFAO!!! " :(I'll wash it down with a glass of prop wash served in a left handed cocktail glass.  As Albert always said, Yeeee Hawwww!  The square of the hypoteneuse is equal to the sum of the squares of the other two sides and zero value given the angle of the dangle.

 

Joerg Sprave made up a table of values pertaining to the elastic's pull, ammo weight and so on...I can't find it but found it most unuseful...impressive work however. Achtung.

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Edited by Chuck Daehler, 15 May 2016 - 05:57 PM.


#9 busySteve

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Posted 15 May 2016 - 07:26 PM

The goal of this effort is currently to make very close "approximate" predictions relatively easy before we start cutting rubber.  (get it... relative... E=mc2 )  The JavaScript page is semi functional right now for most browsers. When I am done with the predictive parts, I will work on the a band set recommendation tool that actually works.  The other part of this project is an Arduino controlled band stretcher that will establish accurate band type constants for material like pure latex and Thera-Band types to plug into the algorithms.  As for trajectory and wind resistance and where the moon is, and gravitational pull at various part of the earth, I currently have no intention on calculating those factors.  Mostly because even with all those numbers my aim kinda stinks.  



#10 Ibojoe

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Posted 16 May 2016 - 04:14 AM

I think slingshots are fun.

#11 busySteve

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Posted 16 May 2016 - 05:20 AM

Frankly, I've always used science/math to understand things that deal in physics, numerical values and calculating numbers. Nice work!

It will be interesting when you get the calculator java script done...

There are other variables such as barometric pressure (denser air resists movement more than thinner air...i.e. I live at 9000 ft elev), temperature of the bands (warm bands are snappier than cool or cold bands in contraction speed), the pouch width (air resistance) and the ammo geometrics. Lead, glass or steel? Lead holds velocity better than steel which hold vel better than glass (marbles) due to the ratio of mass vs air resistive surface area. Many here shoot cylinders, while most shoot spheres, some shoot cubes and hex nuts...so velocity at release will be affected by the ammo type, say, 10 meters down range after air resistance has played its factor. The lead/glass/steel and geometric shapes add about 8 variables, 64 combinations.

But all in all your calculator would be interesting to use vs a chronograph to see the similarities of calculated vs real time. A chronometer is the last word. I use a freeware sound program called "Audacity" on my laptop (I think it's Android compatible also) which measures the time from the sound of the bands at release to the target impact sound. it shows you the sounds on a graph like screen and you measure the time between sound peaks. I use 4 meters as the range. It's not as accurate as a real chrony but it's better than nothing and is for me at least, pretty good to compare band/ammo/draw length variables.



#12 busySteve

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Posted 16 May 2016 - 05:23 AM

Funny you mention Audacity. I did a quarky video on measuring speed some time back. Works very well compared to my Chrony.

#13 Susi

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Posted 16 May 2016 - 08:24 AM

That's what I wanted to see, an actual comparison of shots...thru the crony and with Audacity both on the same shots to compare them.  THANK you for that statement that they were pretty similar.  I'm not going to buy a crony, they don't sell them here in monkeyland anyway, I just wanted some approximation of vel to compare options of banding, pouch, ammo mass and draw lengths.  Whether it's pin point accurate to me isn't the goal...comparisons are.  Like you I like to putz a little.  Hats off to you the java programmer!!!! I only learned to tweek it and never learned the language.  You could expound on it as time goes on with temperatures.

 

One variable we didn't cover is that it's not just poundage of pull, it's the taper vs non taper, amount OF taper and type of rubber..this gets really complicated...but you could just use TBG as a base since that's the most popular rubber.  Next popular seems to be natural latex but that comes in varying thicknesses and from a number of manufacturers...and mixed with this and that polymer...geez it gets complicated...so just use TBG as your base is my suggestion with a temperature factor gleaned from experimentation with the crony.

 

Audacity is not however accepted as a standard for measuring velocity as would be a chronograph on this forum...evidently it's not considered legit or accurate since the sounds can be faked.  Nothing like a 2000 fps slingshot!

 

Wish we were neighbors, you and a number of others here.  A fine group to say the least.

 

L. Chuck (ask Matt what the "L" stands for, lol)

 

I'm posting some images to Susi's (wife) gallery right now hence I signed in with her avatar...Sam our deceased and beloved pit bull...there'll never be another Sammie.


Edited by Susi, 16 May 2016 - 08:53 AM.


#14 busySteve

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Posted 16 May 2016 - 09:03 AM

Another factor that weighs heavily on velocity is the time you hold the pouch back during the pull. There is a tendency of the rubber to form or adjust to the stretched state. The longer you hold back the slower your ammo will go. This band "acclimation" time varies too with temperature and is covered in the book "Physics of Rubber Elasticity", but I currently do not know how to interpret the differential equations that express this phenomenon.

#15 busySteve

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Posted 16 May 2016 - 11:53 AM

It was brought to my attention that the JavaScript in the web page was not functional in Explorer.  It is now.  Sorry about that.

http://busysteve.com...gshot_calc.html .  There is still much to do.  Let me know if there are any issues or questions.  I am open to more input too.  I am doing this for you all (and me), just be patient as I putts along with progress.  Many thanks folks!!! 



#16 Tremoside

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Posted 16 May 2016 - 01:17 PM

Hi Steve,

 

Sounds interesting and like the precise calculator. Maybe some factory data can help to make the usage easier and fast to give some real life functional data.

 

Elastics Wizard - Thera Band data, Natural Latex, Dankung, (Linatex)

Pouch Wizard - SimpleShot - SuperSure pouches

Ammo Wizard - weight picker

 

Estimated drop on 10m - 20m - 30m

Energy - thinking of hunting

 

Just a couple ideas, I was starting to use the calculator and found myself measuring rubber and checking weights etc. So it's just a user friendly addition to your generous work.

 

Cheers,

Tremo



#17 busySteve

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Posted 16 May 2016 - 02:04 PM

Hi Steve,

 

Sounds interesting and like the precise calculator. Maybe some factory data can help to make the usage easier and fast to give some real life functional data.

 

Elastics Wizard - Thera Band data, Natural Latex, Dankung, (Linatex)

Pouch Wizard - SimpleShot - SuperSure pouches

Ammo Wizard - weight picker

 

Estimated drop on 10m - 20m - 30m

Energy - thinking of hunting

 

Just a couple ideas, I was starting to use the calculator and found myself measuring rubber and checking weights etc. So it's just a user friendly addition to your generous work.

 

Cheers,

Tremo

 

These are great ideas.... was thinking to offer some presets but wasnt sure what.  This is great!  Thanks!



#18 busySteve

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Posted 17 May 2016 - 04:08 PM

Well, I just received the force sensor and driver board that will be used for the band measuring project.  Next, I have to select a robotic motor for the band stretcher.  If this is too far from a slingshot post let me know and I will be more reserved with the progress of this project.

 

gallery_11160_2175_246127.png



#19 crazymike

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Posted 17 May 2016 - 04:55 PM

We tell you the secret of all at the 2016 east coast slingshot. Shoot

#20 Jeb

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Posted 18 May 2016 - 03:23 AM

Well, I just received the force sensor and driver board that will be used for the band measuring project. Next, I have to select a robotic motor for the band stretcher. If this is too far from a slingshot post let me know and I will be more reserved with the progress of this project.

gallery_11160_2175_246127.png


Hi Steve,

I've been tinkering around a bit with Arduino myself recently. Just a newbie side hobby and never imagined applying it to slingshots (got a pretty spiff binary clock in the works at the moment though!). This is very cool. Really looking forward to your next update!

Happen to have a link to the force sensor you bought?




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