# The formula of kinetic energy,you must to know!



## GZK-CHINA

Since a few years ago,I found a lot of guys prefer heavy pull tubes,because they think that heavy pull slingshot with great power.In fact, there is a mistake.First of all, you have to understand how the power of a slingshot be produced and how to calculate. The ammo(steel or leadball,etc.) be catapulted by rubber tubes or bands, this process produce kinetic energy.lt's see the formula of kinetic energy:
Ek=1/2mv^2, just mean the kinetic energy(Ek) = the weight of ammo X a quadratic of moving speed ÷ 2. From the formula,we can know that,the power of slingshot has no direct relation with the pull of tubes.But,the speed of ammo moving and the weight of ammo are the two important aspects(Well,the speed has a greater impact).So now,you can understand why more and more guys begin to use flat band,which is thin and light pull,but could provide faster initial velocity for ammo!Of course, if you are infatuated with huge steel balls as your ammo,maybe the thick tubes are still your first choice! Here show you a real damage effect of thin 0.65mm flat bands with 7mm balls.


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## mr. green

Thank you for sharing.


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## BCLuxor

oooo taboo subject ! ding ding


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## Charles

Nothing taboo about the subject.

I would hope by now that it would be well known that the rate of retraction of the bands does not depend on the force necessary to draw them. For example, a set of bands made from neoprene rubber will be much harder to draw than a set of bands of the same dimension made from latex. But the latex bands will retract MUCH faster. Try cutting bands from a bicycle inner tube. They will be hard to draw but will give very disappointing velocity.

Cheers ...... Charles


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## tradspirit

The energy stored in the bands by drawing them is a function of the draw weight however it is only as useful as the retraction rate of the bands which is the determining factor in the energy or force with which the steel ball hits the target. Stated differently, it is the rate of retraction of the bands that accelerates the steel ball and causes blunt trauma to either a tin can or a rabbit. Lighter weight bands that retract more rapidly are more powerful than heavier bands that retract with less efficiency. The force of impact is realted to the acceration rate of the projectile (retraction rate of the bands) which in turn is highly dependanton the velocity imparted to the projectile.


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## romanljc

Back in the good old days when i was a kid all we had was rocks to shoot and they worked well against any small game a big 350 400 grain heavy river stone . Works really well and you dont need fast bands to get good power from them . In my experience.. heavy projectiles work best on game even at slower speeds compare to the size of a rabbet a 1inch 400 grain rock is like hitting a human with a cannon ball . If it does not die it will be nocked out for a fast kill shot .


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## KineticEnergy

I think Tradspirit you are correct. In terms of the total potential energy stored in the bands is a function of (force x distance=Work (joules) aka (draw weight x active draw length). This would set the maximum amount of energy (Joules) you could possibly to convert back to kinetic energy (K,E.) upon release. Assuming that the entire system is lossless, all of that energy would be converted back into kinetic energy upon release. Unfortunately, this is not the case.

Also Charles states, the conversion of the stored potential energy within the bands back into kinetic energy is dependent upon the properties of the elastic material and its ability to retract quickly because mass would be a constant in either scenario. Since the formula for kinetic energy is .5mv^2 maximizing velocity is the key to maximizing K.E aka maximizing retraction rate.

Therefore, it is important to use good band materials like (TBG) and to maximize draw weight and draw length length to something you can shoot comfortably and accurately. After all, having a high K.E. is not worth much if you can't deliver it on target safely.

Cheers.


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## Toolshed

Wow....Learn a lot of stuff here....I think I just need to search random stuff sometimes....

I just looked at ROMANLJC's content to get here....

Dead threads ain't really dead....Just buried....


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## truthornothing

Ok I have a question, I understand the rate of retraction is the determiner of speed but when does the Power part come in. I mean for bands that are better with heavy ammo? I do not know how to phrase my question properly. For example due to my injury i had to go to light bb bands until healed. Well as I am healing I can pull a little more weight. The bands I bought at simple shot deliver bb's and 1/4" with zippy speed I tried to shoot some 3/8 and of course they barely move down range. They are made of blue theraband so I bought some /...actually a lot 18 feet. I made some 3/4 bands. Really zippy on the 1/4 and too much for bb's but still 3/8 barely flies. I made some 1" to 1/2 tapers ( my first self cut tapers I was proud lol) and again too much for bb's 1/4" zippy and 3/8 slow/. I made 1" flats almost too much for 1/4 but 3/8 though it flies still a little slow. 1 1/4 to 3/4 taper, Too much for 1/4 ( though i like to shoot them anyway they are almost too fast to see but band life is nil) 3/8 flies about what I get out of 1/2 TBG. So my question is what part of the equation deals with ammo weight and how do I maximize speed vs draw weight? Is there a formula or a set of formulas. I like to hunt and kill cleanly so I want the throw the biggest ammo at the highest speed with the minimal draw(for accuracy's sake) Any research/ideas on this? thanks


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## Chuck Daehler

The power comes in here, and that's a very logical question.

But first let's look at "contraction" and "retraction".

http://www.merriam-webster.com/

Contraction:
: the act or process of making something smaller or of becoming smaller
e.g. The hot metal undergoes contraction as it cools.

Retraction:
: a statement saying that something you said or wrote at an earlier time is not true or correct

: the act of moving something back into a larger part that usually covers it : the act of retracting something

e.g.
His charges were false, and he was forced to make a retraction.
the retraction of the plane's landing gear

Rate of contraction of a thin band of the same rubber is same as a wide band. The power comes in where it over comes the standing momentum of the projectile. Any load on a band will slow it's contraction, that's obvioius, and a projectile and pouch are "loads". So the power comes in when the momentum of the projectile is partially overcome enough to attain a desirably high velocity. Obviously, heavy projectiles take more power to overcome the mass's standing momentum than do light projectiles.

Impact energy is where the target absorbs or otherwise overcomes the MOVING momentum of the projectile. This energy is dissipated in the form of imparting movement to the target and/or heating the target AND the projectile at the same time, or some of both.

A loss of impact energy results in air resistance on a projectile's path to the target. The larger the profile to the "wind" of both the projectile and pouch and bands themselves, the more slowing effect these factors have.

Somewhere in there the physics are "sweet" for a given band and a given optimum projectile to deliver what the shooter desires..sheer smack down or highest possible velocity/flat trajectory. You can't make a 20mm steel go worth a flip (pun intended) with a 5mm single TBG band set compared to a 25mm band set no matter what the contraction rate is and on the same hand, it's silly to band up with 25mm wide flats to propel a 1/4" ball, it would be a misuse of all that rubber.

This is why chrony tests abound..finding the holy grail of bands vs ammos...what is best for what.

Tapering a flat band and making pseudo tapers for tubes aids in the power factor for if you pull rubber to its maximum without breaking it, it has more power than if you pull to only 80% of its max. The band at the thinnest part is pulled to the max while the thicker part is not, this gives more snap as proven by chrony tests, to the bands (more power) than a flat taper using the same square inch/cm area of a given flat band. So it's the amount of pull's percent of max also that affects power and velocity both. But pulling to max wears out the bands faster, it separates those long molecules of polymer more (i.e. breaks the bands down) hence many opt for less than max pull to spend less money on banding per X shots.

Since heat is generated by stretching rubber, if a shot is fired at full draw without hesitation, that heat energy makes the rubber more elastic and therefore a slightly faster contraction rate, whereas a long pause between the time of full draw and release, allows some of that heat to dissipate by radiation and convection...resulting in a slightly lower velocity than a "snap shot". It is wrongly assumed that the heat energy propels the projectile faster, it is rightly assumed that the heat increases the elasticity and therefore the contraction rate.

I love it when members apply physics to slingshots. Science and elementary math are always useful to answer questions.

One more thing...edit... The rate of contraction of a band set UNDER X LOAD is all the velocity a band set can give a certain X projectile with acertain pouch. Air resistance of the pouch is also a factor as is its mass. A band set WITH pouch and WITH projectile will never contract the same speed as the same band set without the pouch or projectile, that's obvious or should be.

Therefore, velocities can only be that which the band set's contraction partially overcomes the mass and air resistance of pouch + ammo.

I have never seen actual proof of contraction of various naked (no load) bands, that doesn't mean this does not exist, it's just I haven't ever found it (have looked all over). If someone would like to provide an accurate definitive slo mo vid proving the actual contraction rate of various elastics, tube and flat, that would be highly productive to this forum. It would indicate what the goal for speed freaks would be, that which would approach (but never equaling) the actual naked band contraction rate.

Possibly new shooters don't know this so here it is... over banding, i.e. shooting light projectiles with stout rubber used for heavy projectiles, produces the likelihood of a "return to sender" episode, wherein the pouch captures the ball instead of releases it (ball momentum forward actually does the releasing and if there isn't enough momentum... a RTS may happen) and flips it back to the shooter as the bands rebound from the initial shot forward through the forks. Do not over band.





 is a prime video example.


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## Chuck Daehler

I love the ring magnets for holding ammo handy. For a few rounds it's really handy, say, in hunting when more than 6 or 10 rounds are seldom fired in quick sequence. I made a belt clip magnet version(s) that I dearly love out of some speaker magnets and a couple types of belt clips. Rather than try to pick off ammo from the ring on a finger of the other hand while it's trying to hold the slingshot frame, I'd use it as a belt attachment, i.e. belt through the hole, or sew it or tie it securely, no flop flop, onto a day pack shoulder strap.

I have yet to make a magnet dispenser in a hollowed out frame handle although it seems like the best way to keep ammo fastly handy. I've seen them numerous times on this forum, pictured my members. Since I use steel cylinder ammo I dunno if it would work as well as steel ball ammo...likely not, which is why I haven't made a frame with that feature.


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## Chuck Daehler

Thinner bands with a butterfly stance offer much more results than the same bands pulled only 30 inches. The longer the ammo is in the pouch distance wise, i.e. long draw, the faster it will go for the same bands but shorter..comparing percent of draw maximum to percent of draw maximum. Velocities of in excess of 250 fps are had with relatively low draw weight but full butterfly stance. New shooters often are not aware of this hence the post.

Mostly I post for newer shooters' benefit, highly experienced ones already know what I know and more and have for considerably more time than I have been a member here.


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