# Understanding The Physics of Slingshots



## busySteve (Apr 3, 2014)

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"
http://arxiv.org/pdf/1604.00049.pdf

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:
http://busysteve.com/slingshot_calc.html

I have also written a short paper that covers the basics of how I came to understand Bob Yeats' paper.
http://busysteve.com/Understanding_Slingshots.pdf

I hope this is of value to someone.


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## Rayshot (Feb 1, 2010)

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.


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## Tremoside (Jul 17, 2013)

Thank you very much Steve! Have a nice weekend!


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## Phoul Mouth (Jan 6, 2015)

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


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## Chuck Daehler (Mar 17, 2015)

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.


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## treefork (Feb 1, 2010)

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 = EΘ, 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.


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## Rayshot (Feb 1, 2010)

treefork said:


> 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 = EΘ, 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.


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## Chuck Daehler (Mar 17, 2015)

...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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## busySteve (Apr 3, 2014)

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.


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## Ibojoe (Mar 13, 2016)

I think slingshots are fun.


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## busySteve (Apr 3, 2014)

Chuck Daehler said:


> 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...
> 
> ...


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## busySteve (Apr 3, 2014)

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


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## Susi (Mar 3, 2013)

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.


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## busySteve (Apr 3, 2014)

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.


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## busySteve (Apr 3, 2014)

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/slingshot_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!!!


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## Tremoside (Jul 17, 2013)

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


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## busySteve (Apr 3, 2014)

Tremoside said:


> 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.
> 
> ...


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


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## busySteve (Apr 3, 2014)

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.


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## crazymike (May 8, 2011)

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


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## Jeb (May 6, 2014)

busySteve said:


> 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.


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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## busySteve (Apr 3, 2014)

Jeb said:


> busySteve said:
> 
> 
> > 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.
> ...


The aluminum bar looking thing is the actual sensor, sometime called a load sensor. The one here is 1kg max and was purchased on amazon with the driver board for $18.95, I am thinking I'll be using a 10kg sensor instead, otherwise I'll use leverage to reduce the load of the slingshot rubber by 10x. I'll post the arduino software I write and the supporting libraries I used to test it on GitHub and provide links if you plan on using one.

Here's the link to the sensor kit:

http://www.amazon.com/DFRobot-SEN0160-Gravity-Digital-Weight/dp/B014KYBHLW?ie=UTF8&psc=1&redirect=true&ref_=oh_aui_detailpage_o00_s00

Here's a link to my github for reference, but the code has not been posted yet:

https://github.com/busysteve


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## Jeb (May 6, 2014)

Cool. Thanks s bunch for that, Steve.


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## busySteve (Apr 3, 2014)

I received the 10kg sensor in the mail and hooked it up today. Works as expected. I started prototyping the software for the unit and will provided feature details when I demonstrate in a video. I have decided to use a windshield wiper motor to drive the band stretcher as suggested by my brother in law. I have an order of pure natural latex on the way too from rubbersheetroll.com. I ordered .030", .040", and .050" thick sheets. I will be comparing these bands with Theraband Gold, Silver, and Black. I plan to provide graphs of all data gathered. I'll share images and attach spreadsheets. However, the main goal is to build an accurate rubber calculator page to share with all, and be challenged by it. I have made some minor changes to the calculator page but it has a long way to go.

For some reason I thought Joules and FPE were the same thing... but learned otherwise. The site now shows both Joules and FPE. I am also working on making it metric or US compatible. Thanks for following along.

http://busysteve.com/slingshot_calc.html


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## busySteve (Apr 3, 2014)

Window motor for band stretcher




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busySteve


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Jun 13, 2016








I finally received an electric window motor. I will resume progress this week on the band stretcher tension measuring project. Thanks for your patience.


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## Greyman (Mar 9, 2016)

busySteve said:


> I finally received an electric window motor. I will resume progress this week on the band stretcher tension measuring project. Thanks for your patience.


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## aiping (May 31, 2016)

@busysteve:

what's about the approach 
energy transmittion is optimized when the impedance 
of the source is equal to the impedance of the sink

Something (rubber coefficient) x (taper coefficient) x (draw length) x (draw weight) = projectile weight


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## aiping (May 31, 2016)

Man, I was tired when I wrote that...

What I mean, can it be as simple as that:

weight of the rubber bands = weight of the ammo (considering the weight of the pouch and pouch fixing 1/10

(or less) of the ammo)

That does not mean maximum speed, but it should transfer optimum energy out from the rubber into the ammo.

Like this click-clack steel pendulum:

https://en.wikipedia.org/wiki/Newton%27s_cradle


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## busySteve (Apr 3, 2014)

aiping said:


> Man, I was tired when I wrote that...
> 
> What I mean, can it be as simple as that:
> 
> ...


Great point! This assumes energy transfer is the goal. Many times the goal is maximum energy(for Power Rangers) or penetration(not transfer) for hunters. But even if optimal transfer is the goal... how do you band your fork? How far do you pull back on the rubber for your given ammo mass?

The band stretcher is for measuring the stretch and retraction characteristics of differing types and cuts of rubber. To remove yet another unknown from the list. Remember, not all rubber is the same. Inner tubes stretch differently than pure latex which stretch differently than synthetics. Unless you know these differences it is less like you will be able to predict or guesstimate the outcome.


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## aiping (May 31, 2016)

Sure! Predicting the energy outcome by given information of the rubber type, banding, fork width!, taper, draw length, draw retention, ambient temperature, humidity, ammo mass, density and shape, (plus band lifetime..) , such an application would be the holy grale. Do it, please!


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## aiping (May 31, 2016)

to busySteve: This now is OT, but you have the technical background to verify my information, and if so spread it in your technical network. Here we go:

Warning: log_other_mode (Android)

This file is not only grewing by time and stealing precious
internal memory.

This file, when erased to the bone of 4 kB, is growing, when the Android
device is SWITCHED OFF. As long stwitched off, as bigger, proportionally!

For example I switched off after erasing 'log_other_mode' at 3:10 and switched on at 7:15, in this time it grew up to whopping 15.9 MB.

Growing proportionally within SWITCH OFF time makes only one sense:

The Android device monitors with its MICRO the surrounding OF YOUR HOME and SAFE THE SOUNDFILE in log_other_mode. From there it
can than sneak out when ONLINE.

Switched off, the Android device must be completly inactive, but its not!

You can check it by your own:
- root the Android device if it is not already
- install DiskUsage
- go into [root required] /data

NOW: WHO IS INTERESTED IN YOUR CONVERSATION WHEN YOUR ANDROID DEVICE IS SWITCHED OFF


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## aiping (May 31, 2016)

Add:

If you want to verify my claim, this is also important:

I modified the two! micros of my Android device in a way that they are generating continously 'white noise'.

So you check it in this way:

Erase log_other_mode to the bone of 4kB, switch off (preferable when you go to sleep) and put it beside a continous sound source. When you wake up switch on OFFLINE , than check the size of log_other_mode.

The next evening you repeat that but cover it under a pile of cloth(and don't forget where you put it!)


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## busySteve (Apr 3, 2014)

The initial prototype of the Band Stretcher is underway. I have built the basic platform of plywood. There is a flat base and a sled that holds the slingshot as it is slid away from the load sensor, in turn stretching the band(s). The load sensor is held be an anchor point. The software is not near ready. I also need to build the H-Bridge driver circuit for the window motor from four 3055 power transistors. That will probably be the next photo posted. Here's what I have built so far:





  








Band Strether Full View




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busySteve


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Jun 20, 2016












  








Electric Window Motor With a Fishing Reel Spool Attached




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busySteve


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Jun 20, 2016












  








The Slingshot Fork Sled




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busySteve


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Jun 20, 2016












  








Load Sensor and Pouch Hook




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busySteve


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Jun 20, 2016


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2


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## busySteve (Apr 3, 2014)

aiping said:


> to busySteve: This now is OT, but you have the technical background to verify my information, and if so spread it in your technical network. Here we go:
> 
> Warning: log_other_mode (Android)
> 
> ...


Sorry, I am not an Android expert. I suggest you seek Android assistance on Android forums.


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## aiping (May 31, 2016)

Dear BusySteve,

here are some links which are may be helpfull for
you to develope the Wholy Grale:






http://slingshot-shooting.de/techstuff/science/science.html


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## busySteve (Apr 3, 2014)

This is very good information. Thank you.


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## aiping (May 31, 2016)

thanks 

here what I posted in 'The quest of A-Ping..'
but I think it fits also in your thread:

About rubber science, the higher speed of thinner and tapered bands I
have my own explanation:

- as thin as fast=> the band consists of single molucular springs. These 
tiny springs are orientated randomly, but some of them are alligned
in stretch direction. These orientated springs are the most efficient,
the others pointed in worst case 90 degree to the stretch is dumb weight. Imagine, what is 'thin' for our eyes, but the elastic molecule
is some nanometer, a hair is for example about 100.000 nanometer.
So I think, the process to produce thin bands alignes more efficient molecules than dumb molecules as the process for thick bands. If you could manage to align ALL molecules into stretch direction by for example applying a magnetic or electric field, that would be a superband and probably very resistant to rupture.

- fast taper 
=> first, I think its all about direction of the force vectors, if
you focus the force vectors (taper) to one point you are most efficient, like a lense. A taper 1/0 is the perfect focus, but band life time...
=> second, taper cut off / eliminates the unefficient/non focused band area so reduces weight, which does not need to be accelerated


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## busySteve (Apr 3, 2014)

aiping said:


> thanks
> 
> here what I posted in 'The quest of A-Ping..'
> but I think it fits also in your thread:
> ...


This is pretty intense. I will not claim to understand it much either. I know more about physical measurements and experimentation than I do about theory. When it comes to nanometers... that's in the theory realm for me.


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## busySteve (Apr 3, 2014)

I built the first H-Bridge circuit this weekend of MJE3055 power transistors and no-go. The circuit did not supply enough current to drive the motor that stretches the bands so I may need to build it with power MOSFETs. I'll be ordering MOSFETs today.


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## busySteve (Apr 3, 2014)

The MOSFET hbridge didnt work either. Too much current draw.










I just ordered a relay pack with next day shipping. That will work for sure.

https://www.amazon.com/gp/product/B00KTEN3TM

I'll continue to keep ya'll posted.


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## woshiqinkaixin (Dec 2, 2014)

helpful, thanks!


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## nike (Oct 26, 2013)

good :violin:


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## busySteve (Apr 3, 2014)

After about almost a year, I have revived the band stretcher. I am nearing completion. Here is a video of the semi-functional prototype:


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## busySteve (Apr 3, 2014)

So the band stretcher phase 1 is basically complete. In this demonstration is measured the banding of my axiom champ and calculated a 221 fps velocity. When a measured it with the Chrony, I got 221 fps. That's pretty neat.


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## Dr J (Apr 22, 2013)

Are you guys serious! If you have to go through all of this to enjoy a slingshot then there is no way it can be fun.

Sent from my iPhone using Tapatalk


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## busySteve (Apr 3, 2014)

I am a computer scientist, this is how i have fun. But, it still does not equal plinking a can 20 meters.


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## treefork (Feb 1, 2010)

You need to take a break from the computer and truly enjoy what slingshots are about . No measuring devices or data needed . Allow a deeper part of your brain to engage and give you all the necessary data to shoot . When you shoot enough a chrony isn't needed . You know what your bands are doing . Most of all yo're have a pure child like fun .


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## busySteve (Apr 3, 2014)

I really appreciate that. I don't do this all day... when I take a break, which I do as often as possible , I shoot with no devices. But, I like to exercise my gray matter from time to time. Thanks again for the advice.


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## busySteve (Apr 3, 2014)

One sarcastic question though... how did ya'll respond to this post so quickly? Smoke signals or was it with a computerized device? Hmmmm.... have fun today folks!


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## Chesapeake Inuit (Jul 14, 2016)

Scientists recently made a "time crystal" at the University of MD. Really. Something about it being active (motion) in time but not in space. It hurts my head thinking about it and even some physics types do not understand it.

Even still I will eventually understand it if only in a very, very crude way.

I am glad there are scientists like you that work on fun projects like your band stretcher. Amazing that the prediction was dead nuts on!

A lot of the info in this thread hurt my head as well but it still very cool to work on it "just cause."

Not as much fun as shooting but still very interesting. I'm going to get that book your recommended.

Top marks to you for your work!


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## busySteve (Apr 3, 2014)

Prijon said:


> Scientists recently made a "time crystal" at the University of MD. Really. Something about it being active (motion) in time but not in space. It hurts my head thinking about it and even some physics types do not understand it.
> 
> Even still I will eventually understand it if only in a very, very crude way.
> 
> ...


Oh my, what a compliment, I nearly cried... but smiled instead. I must offer my thanks!

busySteve


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## TimR (May 22, 2011)

You're quite the craftsman, I am in awe.

FYI - well you probably know this but maybe it will help somebody - Middleton covered some of this, less technically, in Man Powered Bullets.

Google Amazon Practical Guide to Man Powered Bullets. I tried to link but this PC blocked it.

It's a must read for anybody who is into slingshots. I got it interlibrary loan but it's probably worth buying.


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## aiping (May 31, 2016)

Hi Steve, great job and achievement !!!

Can you also calculate tapered bands for example

Thera band black / length 27 cm / taper 9 cm to 3.5 cm ?

Thanks in advance and all the best from A-Ping


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## busySteve (Apr 3, 2014)

What is your draw length?


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## busySteve (Apr 3, 2014)

busySteve said:


> What is your draw length?


Aping,

I assumed 32in draw length and ran a test. I also assumed 10mm steel ammo. Photos and video are below.


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## busySteve (Apr 3, 2014)

treefork said:


> You need to take a break from the computer and truly enjoy what slingshots are about . No measuring devices or data needed . Allow a deeper part of your brain to engage and give you all the necessary data to shoot . When you shoot enough a chrony isn't needed . You know what your bands are doing . Most of all yo're have a pure child like fun .


I put your advice into practice and made it a point to have have today. The way I did was by way of a recently obtained G10 mini-champ from Rayshot. It is amazing!!!



















I spent hours shooting 1/4 inch and 5/16 steel at cans. I have no idea how fast I was shooting, or the tension of my bands, and that's ok with me  . Your advice went a long way and the kid inside is very glad I did it. So thanks again.

busySteve


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## aiping (May 31, 2016)

Hi Steve,

you did much more than I expected, thank you so much! 
I need to apologize as I did not specify the exact draw length and ball dimensions / weight:

- draw length 53-54 inch
- steel ball 9,5 mm

One thing maybe important to mention that the 9 cm TBB is wrapped around the fork of my Semi-tube slingshot so that there is no interference with the rubber itself. My latest results with ChronoConnect App :

9 x 3.5 cm taper / 26 cm length

- Thera Band BLUE => draw 150 cm for 9.5 mm steel will give you around 350 fps / livetime around 20 shots

- Thera Band BLACK => draw 135 cm for 13 mm steel will give you around 300 fps / livetime around 30 shots

http://slingshotforum.com/topic/54786-theraband%C2%A9-properties-changed/

I will repeat these tests ASAP.

Again thanks!!! A-Ping


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## busySteve (Apr 3, 2014)

aiping said:


> Hi Steve,
> 
> you did much more than I expected, thank you so much!
> I need to apologize as I did not specify the exact draw length and ball dimensions / weight:
> ...


That length of stretch is too long for my stretcher by several inches. It might be too tight as well. Let me see what I can do. I should make it butterfly friendly. So I'll have to set it up with cable and longer wood. I may make a floor mount version to eliminate these restrictions.

I'll keep ya'll posted.


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## busySteve (Apr 3, 2014)

busySteve said:


> aiping said:
> 
> 
> > Hi Steve,
> ...


I was able to shorten the hook cable an stretch to 51 inches. The numbers gathered resulted in a calculated 347.59 fps with 9.5mm steel. Here's a pic of the results:


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## aiping (May 31, 2016)

Steve! You're incredible fast. And I must promise my wife to clean up the attic before using it again as a shooting range, call it busy A-Ping. 
However, you proved that 350 fps with
9,5 mm is no black magic. Drawweight is about 10 kg? A draw of 150 cm should produce between 385 and 400 fps. So it's now up to me to deliver ☺.


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## Imperial (Feb 9, 2011)

i think theres a flaw in this study. how long are you holding the shot before letting go ? does it make a difference ?


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## busySteve (Apr 3, 2014)

Imperial said:


> i think theres a flaw in this study. how long are you holding the shot before letting go ? does it make a difference ?


There are many "flaws" in this study. The question is how much do they factor in? The draw time is about 3 or 4 times longer than a typical draw, due to the motor strength and speed. I have the hold time set to 1.5 seconds. And yes this time matters. And the retraction is very slow compared to real world because of the motor. Temperature is another factor. And my taper compensation algorithm is experimental at best. But i am learning and thinking about slingshots in a new way. I'd like to hear the flaws you've identified.


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## Viper010 (Apr 21, 2012)

I think you're doing amazing work there Steve. It quite boggles my poor little brain half the time, but I still enjoy the reading.

Thank you for investing your time, effort and expenses, and for sharing it here.

Really amazing your calculations are so bang on par with the shooting bench tests!


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## busySteve (Apr 3, 2014)

I'd like to take a moment to remind everyone that this endeavor was inspired by retired physicist Bob Yeats' own experimental research into an elastic retraction speed algorithm he was made aware of and shared on the good old Internet. His desired application was the study of slingshots. As a thanks to him and all of you, I will be compiling the requirements and instructions build a simular unit for your study, if you so desire. All I have accomplished is automating the stretching of the rubber. The rest of the credit goes to the physicists who have shared their knowledge and discoveries. I only tinker with it all.


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## Viper010 (Apr 21, 2012)

Don't sell yourself short there buddy - to effectively tinker with this stuff, one must be a real thinker!


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## Genoa Slingshot (Oct 29, 2015)

Hey Steve, your site worked only for TBG. Now do it work also with other kind of bands?
How can I use it? i.e. with a chinese flatband 1mm thickness or with theraband silver or natural latex .030?


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## busySteve (Apr 3, 2014)

Genoa Slingshot said:


> Hey Steve, your site worked only for TBG. Now do it work also with other kind of bands?
> How can I use it? i.e. with a chinese flatband 1mm thickness or with theraband silver or natural latex .030?


It is actually based on the elasticity measurements obtained, so it is not material dependent. I have done mostly latex testing, with some thera band tests here and there. Rayshot gave me some Chinese material to measure. I'll post all of that over the next week. That is part of the 2nd phase, to compare the various types and dimensions. I am assuming that you are using the http://busysteve.com/slingshot_calc.html site and not the Jorge version which is a thera band gold only - cut suggestion tool.


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## Genoa Slingshot (Oct 29, 2015)

busySteve said:


> Genoa Slingshot said:
> 
> 
> > Hey Steve, your site worked only for TBG. Now do it work also with other kind of bands?
> ...


Yes, I use yours.
I thought it was only for TBG.
Anyway, I don't know the "entry increments" on the new version.


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## busySteve (Apr 3, 2014)

Genoa Slingshot said:


> busySteve said:
> 
> 
> > Genoa Slingshot said:
> ...


The entry increments are the points of force/weight measured. It was 1 inch but my band stretcher measures at 0.8177 inch increments. I should've made mention of that when I made the update.


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## busySteve (Apr 3, 2014)

aiping said:


> Steve! You're incredible fast. And I must promise my wife to clean up the attic before using it again as a shooting range, call it busy A-Ping.
> However, you proved that 350 fps with
> 9,5 mm is no black magic. Drawweight is about 10 kg? A draw of 150 cm should produce between 385 and 400 fps. So it's now up to me to deliver ☺.


A-Ping,

I achieved a 59in (149.9cm) draw with a force of 9kg. The resulting calculation was a 397 fps with 9.5mm steel. Be careful and best of luck.

busySteve


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## Imperial (Feb 9, 2011)

busySteve said:


> Imperial said:
> 
> 
> > i think theres a flaw in this study. how long are you holding the shot before letting go ? does it make a difference ?
> ...


thats it, you have it covered. heat and room temp was my other concern that i forgot to mention. because by experience we all know that our bands/tubes seem to shoot better in the heat and drops some in the cold. any chance you could some shots set at different hold times ? im sure a difference of a couple of seconds wont matter much when held but an active shot compared to a long hold of maybe 5 seconds, may show some diffference. the other thing also that may make a difference is the distance between the bands/tubes at the forks. fork width dont matter, but the space between the rubber may. to where same slack length and pull length is the same but the only thing that changes is the distance between the rubber. 2 inch, to 4 inch, to 6 inch and so on. but either way, its your experiment and im just curious. good luck !


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## busySteve (Apr 3, 2014)

I intended this topic to be a community effort, which it has started to become with folks like you and A-ping, with me holding the test-tudes. If you come up with a test and I have the materials and the means, I'll run the test, my idea or not. As far as materials, I have thera band gold, silver, black, red. Latex .050, 0.040, .030, 0.025, .020, 0.010. Rayshot gave me some Chinese stuff to test that smells odd but still throws ammo that is .030. That's about the extent of my supply. So I will be testing varying widths and tapers and getting a feel for what does what. Then a banding advisor Web page can be written and I can turn this stretcher into a shelf. I've been test in a 72 to 74 degree F temperature room. I'll try the effects of temperature in the stretching.


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## TimR (May 22, 2011)

im sure a difference of a couple of seconds wont matter much when held but an active shot compared to a long hold of maybe 5 seconds, may show some diffference. the other thing also that may make a difference is the distance between the bands/tubes at the forks. fork width dont matter, but the space between the rubber may. to where same slack length and pull length is the same but the only thing that changes is the distance between the rubber. 2 inch, to 4 inch, to 6 inch and so on. but either way, its your experiment and im just curious. good luck !

Yes, it makes a huge difference.

Rubber heats up when stretched, it looses strength as soon as it cools, which happens fast (lots of surface area).

I did my first measurements tying a slingshot to the top of a step ladder and adding weights to a bucket, and they made no sense. After I read Man Powered Bullets, I started measuring with a luggage strap scale and reading it as fast as possible.


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## busySteve (Apr 3, 2014)

TimR,

I too have noticed a big difference in the impact of hold time on my Chrony tests when going for my Power Rangers badge. This point reminds me of a video that was shared of renowned physicist Richard Feynman speaking on the topic of rubber bands and he mentions heat:






If I had the bucks I would love to purchase an infrared camera for my phone and record the time it takes for various elastics to dissipate their heat after they are stretched and during "aim" or hold time.

The stretching I am doing is not optimal. The motor just isnt fast or strong enough. I've been tempted to sacrifice my DeWalt drill motor for this effort, but it is the only cordless drill I have and I use it too much to give it up for this contraption. Theoretically I'm losing heat during stretch just because the pull is not as rapid as us average humans playing with our slingshots. It is still striking to see how close the algorithm is to the Chrony in most cases. But with all that said I am looking to find the measurable stretch "characteristics" of the variety of elastics we use from day to day on our slingshots.

In the end I don't think I'll end up with a faster slingshot, its not always about speed, but I will understand why I am cutting the rubber to a given geometry as opposed to the trial and error I have been doing for so long. I have a fixed budget for slingshots or I'll go bonkers, so I am ordering a copy of Man Powered Bullets on Friday.


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## Ibojoe (Mar 13, 2016)

I've often thought of how important tiller ( the strength of the top and bottom limb) is in archery. I wonder how important the strength of each band is in Slingshots. If it would be worth testing each band and pairing it with bands of equal strength. Do you think it could make a difference?


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## TimR (May 22, 2011)

Middleton's experiments showed significant advantage to reducing the weight that the bands had to propel (outside of the projectile itself.) So he tapered bands, and also reduced pouch weight to very small levels.


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## treefork (Feb 1, 2010)




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## busySteve (Apr 3, 2014)

Ok, starting Phase 2. This is where I stretch various elastics to see their retraction characteristics. I have selected 10 for the first round cut to 10.5 inches long and 1 inch wide.










I also made a quicker change set up and have started with TBG. Where possible I will stretch 10, 20, 30, 40, 50 inches of pull from 9.5 inches of rest.


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## aiping (May 31, 2016)

Hi Steve, I am delighted to see that your building a huge parameter field !!

For my last results please refer to the pictures, average is 445 fps with 9.5 mm steel.

These are the read-outs from ChronoConnect, so only plausible. Physical impact

performance is piercing a water filled PET 600 ml Coke bottle with 9,5 mm steel

from 1 meter without exit, so the balls are in the bottle. These coke bottles are quite strong

and should be same all over the world as reference. All the best from A-Ping


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## busySteve (Apr 3, 2014)

Outstanding!!!


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## aiping (May 31, 2016)

Well, these numbers need to be verified from someone with a chrony (and a Semi-tube slingshot) . However I just shot a 13 mm steel ball from one meter distance through a water filled PET 600 ml coke bottle, in AND exit, and not centered.


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## aiping (May 31, 2016)

that's what I mean..


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## aiping (May 31, 2016)

besides, that was my last 13 mm, I am struggling to find it in all the mess of my attic..., the ball on the magnet is 9.5 mm


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## busySteve (Apr 3, 2014)

Current findings:

I kinda knew this but could not prove it until now... Below is a pic of two graphs, left is a pair of 1/2 inch x 10.5 TBG, and the other is a pair of 1 inch x 10.5 TBG. Both stretched to 50in total length:










The retraction curve is nearly identical. With the numbers in half proportions. When I run these values though the calculation the velocity is not double with the wider bands but the power is. It is almost exactly doubled:

FPS=276.322 / FPE=9.339
FPS=391.837 / FPE=18.779

This should lead us to predictable banding and a savings in rubber due to less trial and error cuts, once I write the banding Web page.


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## aiping (May 31, 2016)

Great prove! Will it be same for tapered bandsbands?


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## busySteve (Apr 3, 2014)

Don't know yet


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## busySteve (Apr 3, 2014)

Turns out I don't understand tapered bands. I did some testing and I can speculate but I can't express it in math... yet.

Here's the deal, I cut two band sets of TBG. 3/4 inch by 10.5 straight, and 1/2 inch to 1 inch tapered 10.5 long.

This equals the same surface area. See area images attached.

These had similar draw tension between them. The tapered set was actually a little lighter. After stretching then to a 50inch length (41 inch draw) I banded them on two hdpe Axiom Champs from Simple Shot OTT with BB kangaroo pouches. The straight band set clocked 190s FPS on the Chrony. The tapered set clocked 230s FPS. Each with 3/8 steel ammo.

I'd like to hear some theories of why this might be, if ya'll don't mind. I think weight offset is the biggest factor but there seems to be more.
















Sent from my SM-G920T using Tapatalk


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## oldasa (Apr 6, 2018)

busySteve said:


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


Being new and not inclined to drop a c note for a chronograph and Because of your post here I'm encouraged to go ahead and use a simple little audio program like Audacity to measure the milliseconds between sound peaks on the program's graft screen. (personally my favorite is Doninn Audio Editor for android) Today there are tons of little programs that will do that even on cell phones. Certain members here, I'm certain, have a set up to calculate velocity and might save me from presuming too much. But I'm thinking that shooting into a 3 foot long box cut to allow two thin papered over sizable holes on both ends will suffice. Thus allowing the pop sound of the paper penetrations to be recorded across the known 3 ft distance. If anyone thinks the 3 foot section is too short to get a good point to point reading on my little audio program please voice your opinions.

My calculations predict that a projectile traveling a 180 feet per second would pass over the 3 foot section in about 165 milliseconds. I think my little audio program on my tablet should clearly measure that. Your opinions Please? Of course this means protecting your tablet from any hits from the projectile but buy keeping everything inside the box should mitigate too much extemporaneous background noise I've heard others complain of.


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## oldasa (Apr 6, 2018)

busySteve said:


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


Seems someone aught to do an update on your idea of using audio editing software instead of dropping the money onto a chronometer.

The Idea I have only requires a box frame (like maybe 3 Ft long) to allow ammo to pierce both papered over holes or windows cut on either end. Also my software is easier to undersand than "Audacity" JMO. Its also free and runs on most any tablet or smart phone. It's called Doninn Audio Editor. It can sample the impact sounds of the paper penetration up to 2 million times a second so it aught to be pretty accurate. NOpe have not built it yet. Just got my first slingshot yesterday. Just checking to see if anyone is interested in tracking velocity this way?


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## MakoPat (Mar 12, 2018)

Thanks Busy Steve and all. This will make for good explorations and reads in my backpack. A small bit of math to generate a deeper understanding of slingshot connectivity then sort of wing the particular's effects. Cool stuff.


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## oldasa (Apr 6, 2018)

MakoPat said:


> Thanks Busy Steve and all. This will make for good explorations and reads in my backpack. A small bit of math to generate a deeper understanding of slingshot connectivity then sort of wing the particular's effects. Cool stuff.


That would be fine with me too if I knew what all that math was solving for. Did I miss something here? Perhaps someone would explain to me what all these letters stand for. A,a,b, and h?


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