# Speed calculation vs projectile weight.



## boyntonstu (Jul 16, 2010)

According to Richard Middleton's book, "Man-Powered Weapons and Ammunition", page 75; the speed of a projectile is inversely proportional to the cube root of its mass.

He points out that when calculating for a slingshot we must weigh the rubber and the pouch and add the result to the projectile.

My data is:

16 grains 220 fps
80 grains 200 fps
224 grains 165 fps

Using the attached spread sheet, I added a column for the weight of the rubber and the pouch.

What I found was that I could only match 2 adjacent data sets as I plugged in various values.

I could calculate 220 and 200 or 200 and 165, but never all 3.

It appears that my Red TB tube has a velocity of a little more than 220 fps.

Going up from 16 grains to 80 grains reduces the speed only 10%

Going up from 80 grains to 240 grains reduces the speed 17.5% more.

Any ideas why it does not scale according to theory?


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## Nico (Sep 10, 2010)

Maybe its because a theory is largely an educated guess?

Unfortunately when dealing things like rubber you cant always predict the final outcome as you are dealing with something that was harvested from a natural source and that leaves room for variations rubber is a moody material. Rarely can things be so measured and put into neat little boxes, its human nature to try and make things so easily measurable.

If you research Middleton's book you will see that he too found many variations in his experiments.. His is a great book and his chapter on catapults is research based on tubes and the man gained some serious velocities with his tubes.

I'm not sure what your main goal is in measuring projectile energy, mine is always for hunting and I can tell you by looking at that red theratube that it will easily do the job for hunting. If it were lead I'd use 45 cal with this stuff and steel I'd use 14mm and you'd have plenty of energy for killing small game optimal speed plus sufficient mass for impact. Plus you'd have a smoother shot as I understand the red theratube is medium pull and accuracy plus sufficient energy for hunting sounds like a recipe for success.

Great thread..


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## ZDP-189 (Mar 14, 2010)

boyntonstu said:


> If you research Middleton's book you will see that he too found many variations in his experiments.. His is a great book and his chapter on catapults is research based on tubes and the man gained some serious velocities with his tubes.


Middleton made no attempt to account for the mass or characteristics of the bands and pouch, which we know to be very important. However, his book is an inspiration to anyone who would follow him on his journey of learning in the world of slingshots. I love his book and I think he would be very happy that I am doing my own experiments.


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## Nico (Sep 10, 2010)

Its still an educated guess just one with some more crucial data for experimentation.. You said it yourself it can bed "tested" by others my point that a theory is based on some data, that does not provide solid facts hence tests and experimentation.

Thats great though that you would take the time to do such experiments and I will take the time check out your blog which I'm sure is filled with important data for these aspects of slingshot shooting.


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## ZDP-189 (Mar 14, 2010)

By the same token, we cannot be sure that the sun will rise in the morning, or of the path of the planets. It's just an educated guess based on a model that matches experimental data. The copernican model predicts the paths of the heavenly bodies better and simpler that the models that followed it, though it has been refined by Newton, Kepler, Einstein and others. We only know of this model because of one man's obsession for measurement, but we are now certain of it and able to predict observations far more accurately because of all those who refused to take existing dogma as a universal truth and added their own independent measurements and refinements. I hope that you and Stu will challenge my model with equal or superior rigour.

PS/ I concur with Middleton insofar as to say that velocity decreases with projectile mass with vanishing effect. However, I believe his mathematical derivation of velocity from the formula for kinetic energy is flawed and that he neglected to take account of the inertia of the bands and pouch, which is significant at small to medium mass projectiles, which is probably why his model is not borne out by Stu's experimental data.


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## Nico (Sep 10, 2010)

Now your talking amigo when you mentioned the intertia of a given set of bands and its pouch as used with medium projectiles I have found some serious impact from my slingshots. I have done this with a 9 inch bandset of an approximate 17 lb pull and the projectile weighing about 14 grams.

Some of my greatest kills came from using this particular combination and the shock/trauma alone as shown when having dressed the prey demonstrated some serious hydrostatic shock that went beyond the point of impact.

Most of my observations come from field experience as opposed to shooting gelatine or speed tests all of which are good to a certain point. To me in the end its about the most efficient killing energy always tested on living matter.

I like you Z your intellectually engaging you certainly have my attention with this discussion


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## ZDP-189 (Mar 14, 2010)

It's always gratifying to debate with someone that will participate with an open mind. Yes, I agree field results is what matters; experiments are more precise for modelling, but if one can't get a ball on target all the theory in the world will count for nothing.


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## boyntonstu (Jul 16, 2010)

ZDP-189 said:


> However, I believe his mathematical derivation of velocity from the formula for kinetic energy is flawed and that he neglected to take account of the inertia of the bands and pouch, which is significant at small to medium mass projectiles, which is probably why his model is not borne out by Stu's experimental data.


I quote from Middleton page 75, paragraph 3:

"I took this catapult and removed the pouch, and found that it weighed 91 grains. If the cube root hold true, then I have to re-calculate, adding 91 grains to the mass of the bullet in each case....

After adding the pouch weight, his prediction vs actual was 234.5 fps vs 236.3 fps.

Middleton proved that adding the weight of the pouch made his cube root calculation fit his data.

My calculation also fits, but only for 2 out of 3 data sets.

I will try yours.

Edit: This does not load http://slingshotforu...tion-resources/


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## ZDP-189 (Mar 14, 2010)

Try the web folder in root of the link. Failing that PM me your email address and I'll send it. It's only a few Kb.


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## boyntonstu (Jul 16, 2010)

ZDP-189 said:


> Try the web folder in root of the link. Failing that PM me your email address and I'll send it. It's only a few Kb.


I got a better fit using a pouch weight of 76 grains. (Middleton uses GRAINS!)

220 fps 16 grain Chrony vs 221.73 calculated
200 fps 80 grain Chrony vs 194.30 and 192.79 calculated
165 fps 224 grain Chrony vs 163.72 calculated


I scaled up from 165 fps and down from 220 fps

I am now happy with theory vs practice.


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## Tex-Shooter (Dec 17, 2009)

I just shoot them over the Chrony and find the results. Then I calculate the energy. Of course I don't shoot a slingshot for the specs involved, I shoot with a eye on is it easy to load, does it feel good when shooting, does it have a reasonable amount of energy to kill small game, does it cause my hand or elbow to hurt after 50 shots and is it fun to shoot. I have done test shooting for someone that has a lot more test equipment that I, but wanted a shooters opinion. A shooter ultimately makes the decision as to whether a slingshot and band set is right for him and with most shooters specs don’t play a large part in that decision. He just compares the slingshots and band sets that he has shot and make his personal decision whether the best or not. – Tex-shooter


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## ZDP-189 (Mar 14, 2010)

Tex, I agree most people try things out and settle on something that suits them. Experienced people like Gary and your self can probably give a sheet a few tugs and then go right ahead and cut a suitable bandset. That's how it always has been done. Both of you contributed so much to our sport, for example your championing of flatbands through the dark ages of factory tubes and Gary's encyclopedic knowledge of elastics.

I think where this becomes interesting for experimentalists like Middleton, Stu and myself is we want a deeper knowledge of how bands perform than what has been already published and in the public domain. I want to know how to make the optimal bands for a given weight and draw so that I get the best possible velocity for an acceptable weight of draw. I want to know if we can go off in new directions and find better ways of doing what we are doing. Without data and models, I would be tuning my bands in the dark, working by intuition and educated guess.

That doesn't mean everybody should do this, just the most passionately curious among us.


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## boyntonstu (Jul 16, 2010)

ZDP-189 said:


> Tex, I agree most people try things out and settle on something that suits them. Experienced people like Gary and your self can probably give a sheet a few tugs and then go right ahead and cut a suitable bandset. That's how it always has been done. Both of you contributed so much to our sport, for example your championing of flatbands through the dark ages of factory tubes and Gary's encyclopedic knowledge of elastics.
> 
> I think where this becomes interesting for experimentalists like Middleton, Stu and myself is we want a deeper knowledge of how bands perform than what has been already published and in the public domain. I want to know how to make the optimal bands for a given weight and draw so that I get the best possible velocity for an acceptable weight of draw. I want to know if we can go off in new directions and find better ways of doing what we are doing. Without data and models, I would be tuning my bands in the dark, working by intuition and educated guess.
> 
> That doesn't mean everybody should do this, just the most passionately curious among us.


Tex,

I would love for you to shoot and evaluate my Slingshot on a Stick.

I betcha that it is easier on the draw and steadier to aim than a conventional SS.

Stu


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## Nico (Sep 10, 2010)

Tex-Shooter said:


> I just shoot them over the Chrony and find the results. Then I calculate the energy. Of course I don't shoot a slingshot for the specs involved, I shoot with a eye on is it easy to load, does it feel good when shooting, does it have a reasonable amount of energy to kill small game, does it cause my hand or elbow to hurt after 50 shots and is it fun to shoot. I have done test shooting for someone that has a lot more test equipment that I, but wanted a shooters opinion. A shooter ultimately makes the decision as to whether a slingshot and band set is right for him and with most shooters specs don't play a large part in that decision. He just compares the slingshots and band sets that he has shot and make his personal decision whether the best or not. - Tex-shooter


Ah Tex,

We work in similar parameters.. I too have my own chrony and what I have done is similar some speed tests with known weighted projectiles and the elastics used and field proven to take small game and from here I both draw my own conclusions and do some of my own "field experiments" most importantly I look for a slingshot that will not hurt my tendons after too many shots and be more than capable of taking small game energy wise. You cant be accurate if drawing the bands is causing you pain.


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## boyntonstu (Jul 16, 2010)

Nico said:


> I just shoot them over the Chrony and find the results. Then I calculate the energy. Of course I don't shoot a slingshot for the specs involved, I shoot with a eye on is it easy to load, does it feel good when shooting, does it have a reasonable amount of energy to kill small game, does it cause my hand or elbow to hurt after 50 shots and is it fun to shoot. I have done test shooting for someone that has a lot more test equipment that I, but wanted a shooters opinion. A shooter ultimately makes the decision as to whether a slingshot and band set is right for him and with most shooters specs don't play a large part in that decision. He just compares the slingshots and band sets that he has shot and make his personal decision whether the best or not. - Tex-shooter


Ah Tex,

We work in similar parameters.. I too have my own chrony and what I have done is similar some speed tests with known weighted projectiles and the elastics used and field proven to take small game and from here I both draw my own conclusions and do some of my own "field experiments" most importantly I look for a slingshot that will not hurt my tendons after too many shots and be more than capable of taking small game energy wise. You cant be accurate if drawing the bands is causing you pain.
[/quote]

Try a Slingshot on a Stick to discover how easy it is to draw and how simple it is to hold your aim steady.

(I keep repeating this mantra in the hope that someone will try it)


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## stelug (Feb 6, 2010)

Nico said:


> You cant be accurate if drawing the bands is causing you pain.


coming to any weapon this is the ultimate truth. I like this discussion and rearly wish to improove my english for better undertsanding Dan's experiments. I think he is offering us a totally new and unespected way to understand one of the simplest weapon of theworld: combination of any kind human propelled item and a stone (or ball). But when hunting or plinking the most scientific tool wold not be also the more efficient because here come in play the special feeling ones developes with one weapon, and may be not with one other alothought if way more refinite. 
ps, the zdp's T1 is one of my favourites







))


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## Nico (Sep 10, 2010)

boyntonstu said:


> I just shoot them over the Chrony and find the results. Then I calculate the energy. Of course I don't shoot a slingshot for the specs involved, I shoot with a eye on is it easy to load, does it feel good when shooting, does it have a reasonable amount of energy to kill small game, does it cause my hand or elbow to hurt after 50 shots and is it fun to shoot. I have done test shooting for someone that has a lot more test equipment that I, but wanted a shooters opinion. A shooter ultimately makes the decision as to whether a slingshot and band set is right for him and with most shooters specs don't play a large part in that decision. He just compares the slingshots and band sets that he has shot and make his personal decision whether the best or not. - Tex-shooter


Ah Tex,

We work in similar parameters.. I too have my own chrony and what I have done is similar some speed tests with known weighted projectiles and the elastics used and field proven to take small game and from here I both draw my own conclusions and do some of my own "field experiments" most importantly I look for a slingshot that will not hurt my tendons after too many shots and be more than capable of taking small game energy wise. You cant be accurate if drawing the bands is causing you pain.
[/quote]

Try a Slingshot on a Stick to discover how easy it is to draw and how simple it is to hold your aim steady.

(I keep repeating this mantra in the hope that someone will try it)
[/quote]

Hi Stu,

Its not that I dont want to try it, simply its a matter of impracticality for a slingshot is always a "pocket poaching" tool for me so to speak.

For your sake I'm going to design something like what you have mentioned and I will need to look at your vid again for this to get the idea. Maybe I can make something that is still concealable in a "walking stick". Most likely this will be a wire frame slingshot of sorts.


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## Jaybird (Dec 20, 2009)

Slingshots are simple weapons.I think sometimes we get to technical,I'm guilty myself.I think we should find a slingshot we like to shoot and serves our purpose and shoot it.Don't try to make a high power rifle or bow out of it.Use it for what it is a low power hunting weapon and low cost fun shooter.Remember you can't make a silk purse from a sows ear.


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## Nico (Sep 10, 2010)

Jaybird said:


> Slingshots are simple weapons.I think sometimes we get to technical,I'm guilty myself.I think we should find a slingshot we like to shoot and serves our pourpous and shoot it.Don't try to make a high power rifle or bow out of it.Use it for what it is a low power hunting weapon and low cost fun shooter.Remember you can't make a silk purse from a sows ear.


Finally a man who speaks with sense...

They are simple low power hunting weapons and they work so who really cares about how much more you can get from it by crunching numbers weights vs speed or getting too technical with such a basic weapon.

Jay I'm going to quote you some day _you cant make a silk purse from a sows ear _thats beautiful


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## boyntonstu (Jul 16, 2010)

Nico said:


> I just shoot them over the Chrony and find the results. Then I calculate the energy. Of course I don't shoot a slingshot for the specs involved, I shoot with a eye on is it easy to load, does it feel good when shooting, does it have a reasonable amount of energy to kill small game, does it cause my hand or elbow to hurt after 50 shots and is it fun to shoot. I have done test shooting for someone that has a lot more test equipment that I, but wanted a shooters opinion. A shooter ultimately makes the decision as to whether a slingshot and band set is right for him and with most shooters specs don't play a large part in that decision. He just compares the slingshots and band sets that he has shot and make his personal decision whether the best or not. - Tex-shooter


Ah Tex,

We work in similar parameters.. I too have my own chrony and what I have done is similar some speed tests with known weighted projectiles and the elastics used and field proven to take small game and from here I both draw my own conclusions and do some of my own "field experiments" most importantly I look for a slingshot that will not hurt my tendons after too many shots and be more than capable of taking small game energy wise. You cant be accurate if drawing the bands is causing you pain.
[/quote]

Try a Slingshot on a Stick to discover how easy it is to draw and how simple it is to hold your aim steady.

(I keep repeating this mantra in the hope that someone will try it)
[/quote]

Hi Stu,

Its not that I dont want to try it, simply its a matter of impracticality for a slingshot is always a "pocket poaching" tool for me so to speak.

For your sake I'm going to design something like what you have mentioned and I will need to look at your vid again for this to get the idea. Maybe I can make something that is still concealable in a "walking stick". Most likely this will be a wire frame slingshot of sorts.
[/quote]

If pain is your game, use a pocket slingshot.

I developed the stick concept because of tennis elbow pain.

A Slingshot on a Stick uses a different set of muscles for the draw and it is much easier on your arms. ( see the video)

You have to try it to believe my words.

A walking stick and a pocket slingshot is a great combination.


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## Jaybird (Dec 20, 2009)

Nico
The silk purse saying is a lot older than I am.


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## Nico (Sep 10, 2010)

Jaybird said:


> Nico
> The silk purse saying is a lot older than I am.


Its an awesome saying one I was unfamiliar with as most of the sayings I was raised with were in another language, in which case I thank you for the education.


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