Physics of springers

[bennedose]

Please indulge me folks. I am neither a physicist nor an engineer but after taking apart and putting together my old SDB and accidentally tuning it in the process I had several questions that no one can answer for me because only I have the specific measurements of my rifle. So I did what I used to do as a schoolboy/junior college student and applied elementary physics and did a few calculations. I ignored friction inside the barrel and I ignored the effect of heating of air as it gets compressed by the piston.

The aim of my work was:
1. How long does it take my pellet to move from stationary position at breech to emerge 150 m/sec (500 fps approx) at the muzzle
2. What force is required to accelerate the pellet to that velocity
3. What is the air pressure that needs to be achieved by the piston to get that pressure?
4. What is the minimum speed the piston must travel at to get that pressure?

For the calculations I needed several measurements and I will simply list them here minus the calculation. If anyone is interested I will post the actual formulae I used in a separate post. Most 12th std kids will know them although most others forget - except engineers I guess. They can be used to do the same calculation for any air rifle if other parameters listed below are known.

1. Area of bore of rifle (0.22)= 0.16 sq cm
2. Length of barrel: 50 cm
3. Volume of air in barrel: 8 cc
4. Piston face area: 5 sq cm (from piston diameter of 2.5 cm)
5. Length of piston stroke: 7 cm
6. Volume of air in piston chamber (cocked): 35 cc
7. Muzzle velocity: 150 m/sec
8. Weight of pellet= 700 mg (approx 11 grains)

From these it is possible to calculate that:

1.The pellet takes just 7/1000 of a second (0.0066 sec) to exit the barrel at 150 m/sec
2. The piston has to be faster than that and assuming that the piston compresses the air in just 0.0025 sec it means that the piston is traveling at 96 kmph (60 mph). This fits in with some data I found on a Pyramid air site - but my calculation cannot be taken as exact. It is guesswork.
3. The pressure required to push the pellet out at that velocity is theoretically 97 times atmospheric pressure (97 bar). (The force is 157 Newtons). To make the pellet go supersonic (330 m/sec) I would need a force of 762 Newtons or 470 bar pressure - i.e 470 times atmospheric pressure.
4. A pressure of 97 bar can be achieved by the piston only when the air in the chamber is compressed to a volume that is 97 times smaller than the original 35 cc - i.e at a point when the piston is almost hitting the breech end of the chamber. But at 97 bar the air is pressing back at the piston face with a 500 kg force so the piston cannot slam into the back of the breech so easily. Even in the "worst case" scenario of pellet being very close to muzzle when the piston hits the breech, there will still be at least 20-25 kg force holding the piston back from slamming hard into the front of the chamber.
5. In reality the dynamics will be a little different because the air pressure will rise a lot more due to heating, but the pellet also will move forward tending to increase the volume and reduce the pressure.
6. The total time from release of sear to exit of pellet is in the region of 0.01 seconds (or less). Human nerves that sense touch at best transmit impulses at 50 m/sec (often slower). The distance from hand to brain may be 1 meter - so the sensation reaches the brain in 1/50 second - or 0.02 sec. This is a lot slower than the exit time of the pellet so the brain cannot register the time in which the pellet exits until after it is out.
7. Unfortunately I do not know the weight of the piston. If I guess that it is 250 grams and the piston moves at 96 kmph - an empty chamber with no pellet (dry firing) will ensure that the piston hits the front of the chamber with tremendous force. That is the force of a 1 kg weight falling on your toe from a height of 8 feet or so.

[brihacharan]

Hi Bennedose,
> Good food for thought
> But then this is like re-inventing the wheel......
> The laws of physics is endemic to the phenomenon called creation...it exists, will exist & will continue to exist
> The principle behind which an AR works is totally dependent on the laws of physics...easy to understand if one takes the pains to understand it...nothing mysterious about it....
> However there is something called the "The law of Variables'...which means the end result will vary depending upon the variations such as:
1. Size
2. Density
3. Hardness
4. Mass / weight
5. Velocity
6. Friction
> This is one reason why even the experts are at a loss as to why ARs that are manufactured in the same factory using the same materials and standard manufacturing procedures vary in performance - ARs coming out from the same batch & even having successive serial numbers
> BTW - The weight of an IHP piston is 285gms +/- 5% - This specs is arrived at taking into consideration the ID of the receiver, the swept volume, size of transfer port, the tenacity/ resilience of the spring & conformance to the legal limits of energy delivered.
> You had mentioned 'friction' - well this is one 'aspect' that prevails in any mechanism where 'contact' is essential / necessary. No physical movement is possible without being subjected to it (human body or mechanical devices etc)
> Now then the 'co-efficient of friction' can be controlled with the use of lubricants appropriate to the function, by using lubricants of which there are several varieties suitable for each function....the choice depends on the end use / what is desired.
> Come to think of it...
> Even today the components of a spring piston break barrel AR hasn't changed...what has changed is the composition of materials used, its dimensions & engineering process
Briha

[bennedose]

> However there is something called the "The law of Variables'...which means the end result will vary depending upon the variations such as:
1. Size
2. Density
3. Hardness
4. Mass / weight
5. Velocity
6. Friction
> This is one reason why even the experts are at a loss as to why ARs that are manufactured in the same factory using the same materials and standard manufacturing procedures vary in performance - ARs coming out from the same batch & even having successive serial numbers

Wise words sir. One of the reasons that made me go through all that calculation - albeit incomplete was this variation.

Another thing I am struggling to understand is energy transfer from pellet to target because of observations that are really weird. I happen to live very close to a scarp metal dealer who collects tin cans for me to shoot - so I have a plentiful supply of tin cans as reactive targets. One weird observation that happens too often for coincidence is that there are some cans that do not get punctured from 10 meters - but get a hole from 20 meters. I have never understood how or why this happens and this goes against all the "muzzle velocity" struggle and contortions that one can find all over the internet

[brihacharan]

> However there is something called the "The law of Variables'...which means the end result will vary depending upon the variations such as:
1. Size
2. Density
3. Hardness
4. Mass / weight
5. Velocity
6. Friction
> This is one reason why even the experts are at a loss as to why ARs that are manufactured in the same factory using the same materials and standard manufacturing procedures vary in performance - ARs coming out from the same batch & even having successive serial numbers

Wise words sir. One of the reasons that made me go through all that calculation - albeit incomplete was this variation.

Another thing I am struggling to understand is energy transfer from pellet to target because of observations that are really weird. I happen to live very close to a scarp metal dealer who collects tin cans for me to shoot - so I have a plentiful supply of tin cans as reactive targets. One weird observation that happens too often for coincidence is that there are some cans that do not get punctured from 10 meters - but get a hole from 20 meters. I have never understood how or why this happens and this goes against all the "muzzle velocity" struggle and contortions that one can find all over the internet

Hi Bennedose,
> The probabilities are:
1. The wall thickness of the cans could be different
2. The pellet may not have hit the can 'dead centre' - meaning concentration of energy at a single point
3. The configuration of the pellet & its dynamics, fitment in the breech etc. could create loss in the muzzle energy
> Well these are some points that comes to mind off hand...there could be others
> As you have rightly mentioned - no one expert gives a tangible answer when it comes to the performance of a Spring Piston air rifle.
> That's one reason I keep mentioning the word "Enigma" with reference to ARs.
> In a lighter vein ARs behave like women - their moods often betray their emotions
Cheers
Briha

[essdee1972]

One weird observation that happens too often for coincidence is that there are some cans that do not get punctured from 10 meters - but get a hole from 20 meters.

The probabilities are:
1. The wall thickness of the cans could be different
2. The pellet may not have hit the can 'dead centre' - meaning concentration of energy at a single point
3. The configuration of the pellet & its dynamics, fitment in the breech etc. could create loss in the muzzle energy
> Well these are some points that comes to mind off hand...there could be others

Apart from that, the material / method of producing the can (for example, steel or aluminium or alloy, which alloy, seamed or seamless), whether the pellet strikes the seam or the plain part of the can, etc. etc. etc. (ad infinitum). Some cans (esp the aerosol type) have bases slightly thicker than the walls, so, if the pellet strikes on / near the rim, you may not get penetration, the can might be spinning / moving after the last shot (if you suspend the cans).................

[brihacharan]

INFLUENCE OF CALIBER, WEIGHT & SHAPE OF PELLETS

CALIBER
By far the largest number of air-guns sold is in 0.177 and this is the pellet size of choice for nearly all target shooting, plinking and some small pest hunting. It offers the highest velocity for a given amount of energy and results in the flattest trajectory.

By comparison the 0.22 is heavier in weight & travels slower in velocity but has a greater retained energy at longer distances and might be the choice if you owned a single hunting rifle.

PELLET TYPE
The single most important factor in choosing a pellet is to obtain one that is accurate in your air-gun! Only personal experimentation will let you discover the most effective pellet for your air-gun. Each air-gun varies slightly in the way it handles different pellet types. Since the accuracy of pellets themselves will vary slightly from batch to batch, it is wiser to buy sufficiently large quantity of pellets at one time than to buy in smaller quantities.

Light pellets accelerate rapidly and leave the gun barrel at high speed. The light pellet's time-to-target is also short so gravity affects it only for a split second. As a result it undergoes a very flat trajectory.

Light pellets are ejected so rapidly that they do not dwell long enough to get the full energy transfer of the decompressing charge of air. While the same rifle can propel a 8.5gr 0.177 pellet to 850 fps and a 14gr 0.22 pellet to 700 fps, these figures reveal that the 8.5gr pellet only acquired 14 ft lbs of energy while the 14gr pellet obtained 15.5 ft lbs.

The speed of a heavier pellet is lower in the same air-gun versus a lighter pellet. Because of its slower speed, a heavy pellet takes a longer time to get to the target & this gives gravity a longer time to pull it down.

Note that the drop of any pellet has nothing to do with its mass or weight - all pellets are pulled down by gravity at the same rate. The only thing that counts is how much time gravity has to do the pulling. It is only because heavy pellets take longer to get to the target that their trajectory is more arched. A light-weight pellet traveling as slowly as a heavy weight would have an equally arched trajectory

AIR RESISTANCE
Once clear of the barrel, another 'energy factor' begins its work - Air resistance. Air resistance increases with the cube of a pellet's speed - double the speed and air resistance increases eight times! This means fast pellets lose energy more rapidly than slower pellets. Energy equals mass times velocity squared. Since the energy imparted to a pellet is about the same and a pellet doesn't lose mass, it can only make up for the different weight by changing velocity.

In fact fast, light pellets lose energy so rapidly that after 35 yards or so they can be traveling slower than heavy pellets. This is inconsequential in 10 meter target shooting, but it becomes a major disadvantage in hunting and field use.

WHAT PELLET SHOULD YOU USE?
Flat-nosed wad-cutters punch perfect holes in paper targets to aid in scoring and are required in competition. The slight effects of higher air resistance on accuracy due to the flat head are unmeasurable at 10-meter range, but do become noticeable at 35 meters and beyond.

Medium weight round headed pellets, offer the best of weight and flat trajectory for medium-powered hunting rifles (12 to 15 ft lbs.). The closer you can normally get to your prey, the heavier the pellet you should use because heavy pellets, 16gr / 18gr will penetrate much deeper and be less susceptible to wind deflection.

ACCURACY
Assuming an air-gun always exerts the same force on a pellet, the accuracy of a pellet's path, its trajectory is affected by three major and some minor factors:

CROWN
During its rush up the barrel, a pellet is constrained from going anywhere but straight forward. At the instant the pellet leaves the barrel, it is desirable that the barrel tip or "crown" always presents exactly the same surface to the spinning tail of the pellet. Ideally, the barrel loses contact with the entire circumference of the tail of the pellet at the same instant so that the pellet is not tipped one way or the other. Tipping the pellet imparts a wobble, increasing the cross-sectional area through the air.

The wobbling pellet causes more air resistance. This increased area will slow the pellet down more quickly than if it pierced the air perfectly head-on. Many foreign made air-guns are "button choked" at the crown of the barrel to assure a perfectly uniform grip on the pellet circumference the instant it leaves the barrel. Make sure not to damage the crown of your air-gun barrel.

UNIFORMITY
Spinning is what keeps a pellet from tumbling, and keeps it facing directly forward as it travels through the air. It has been pointed out by experts that if a pellet is the slightest bit unbalanced as it spins, the centrifugal wobble will lurch the pellet off course the instant it leaves the barrel. The direction of that lurch will vary with every shot depending on which direction the mass of the pellet is pointing at the instant it is released from the barrel. This is one major reason quality manufacturers of pellets pay great attention to pellet quality control.

WIND
Supersonic bullets get deflected by wind the slower they go. Surprisingly sub-sonic air-gun pellets are less deflected by wind when slower they go - this seeming anomaly is due to the higher weight of the slower pellet, assuming that both are shot out of the same air-gun.
For any air-gun, a pellet with a higher "ballistic coefficient" will be less deflected by wind. Generally, heavy pellets have a higher ballistic coefficient than lighter ones.

AIRGUN SHOT REPEATABILITY
An air-gun does not exert the same force from shot to shot. Without such high repeatability, even excellent pellets will not be able to do their job. Average pellets may safely exhibit a weight differential of up to a few percent in any one tin. When both pellets and air rifle vary randomly, you will find yourself hitting the target perfectly with some shots, while you miss it completely on others.

Every air-gun user should obtain a tin of high quality pellets to determine just what the air-gun is capable of with bench rest and what the shooter is capable of with hand held hold. You may use mid-grade pellets for practice, but always use the most accurate pellets you can find for competition and actual hunting.

Air-gun shooters should use this as a guide to select at-least three or four different types of pellet that seem closest to answering their own shooting needs. Then shoot these pellets for accuracy to get an idea of how well each type behaves in your own air-gun. There is no substitute for this personal testing which will quickly lead to the selection of the most effective pellet type for your own particular use which will eventually boost your accuracy and shooting pleasure to new highs.
HAPPY SHOOTING!!!
Briha

[bennedose]

It took me over 2000 shots to figure out the best pellet from each of my air rifles. The Orion was the easiest - I happened to discover that the standard round head GSmith were perfect.

My old SDB kept giving me nasty surprises. Elsewhere on this forum I had mentioned the light (700 mg/11 gr) Diana shot pellets as giving me the best grouping. But after my tune up it seemed like Mastershot round head was good but one day it would be fine and the next day I was hearing loud reports and having wild misses. I had to go though boxes and boxes of Masterhort round, export quality round, export quality sharp, Diana shot, Marshal shot round and sharp to discover that the SDB "likes" heavier pellets - particularly Mastershot Wadcutter with which it is quiet, pleasing and consistent at 20 meters. There is nothing more relaxing than setting up 3 targets at 20 meters, taking 3 pellets and hitting all of them with a clang. GSmith pellets don't fit into the SDB well.

In general I think it is best to go for medium to heavy pellets (As Brihacharanji had suggested elsewhere) despite the temptation of blistering muzzle velocity with light pellets. This is a lesson that is difficult to swallow and comes only after the frustration of firng off 10 shots at a tin can and missing all from 10 meters immediately after adjusting the sights.

[brihacharan]

It took me over 2000 shots to figure out the best pellet from each of my air rifles. The Orion was the easiest - I happened to discover that the standard round head G Smith were perfect.

In general I think it is best to go for medium to heavy pellets (As Brihacharanji had suggested elsewhere) despite the temptation of blistering muzzle velocity with light pellets. This is a lesson that is difficult to swallow and comes only after the frustration of firing off 10 shots at a tin can and missing all from 10 meters immediately after adjusting the sights.

Hi Bennedose,
> Its heartening to note that you 'went through the mill' - that's what experience is all about.
> Looking back it's a lesson well learned as now you know your weapons well
> Now coming down to pellets 0.22 cal - The Germans make their breech size to accommodate 5.5mm dia based on the metric system, while the Brits go by theirs and make it 5.56mm - that 0.06mm difference is what makes the SDB not accept G Smith pellets!!!
> This may sound trivial - but it matters.
> Moral of the story - Shooters obsessed by Velocity use lighter pellets thus compromising on accuracy - So stay with medium weight pellets and enjoy your shooting.
> A short while ago I came across 16gr Magna Shot Pellets - These fitted & performed exceedingly well in my Orion - In fact if I can lay my hands on 15gr pellets - Its Manna from Heaven.
Cheers
Briha

[bennedose]

Brihacharanji I had a box of 500 ELEY 5.6 mm pellets with me that used to fit only in my old Weihrauch. When I discovered that they were too big for my Orion I gave them away

But yes you are right about the light pellets and nowadays I am getting irritated with light ones. They are actually no good for anything over 10 meters IMO. It is so sooooo painful to shoot off a box of light pellets that you don't want - it's depressing to even look at them. The point you made about heavier pellets retaining energy over longer distances is vital. Now I feel like going back to a shop I had visited a few weeks ago - that guy had some huge pellets of some brand that I cannot recall - maybe I will pick up a few and report on here in due course.

You mentioned how a light pellet may have left the barrel even before available energy is transferred. I suspect that is exactly what is happening with my SDB. Once I use Masteshot Wadcutters the rifle is so pleasant I find myself with a high that lasts me a few hours

[bennedose]

http://www.kiledjian.elac.org/phys%2000 ... %20Gun.pdf

An absolutely fantastic research paper that analyses what happens when the spring of a springer is released.

Particularly fascinating is thet fact (as shown in 2-3 graphs in the paper) that in some rifles, the pellet moves faster in the middle of the barrel and then slows down - so those particular rifles will benefit from a shorter barrel with the same spring. That explains why Dr Shirsat of Precihole is a real scientist and the short barreled Orion kicks out more power than longer/bigger air rifles

[mercury]

WOW , that is one "heavy" theoretical paper...but applying the laws of pure science to a spring piston air rifle is not without risk as the variables are too high. studies in ballistics and not just on air powered guns but also cartridge guns imo , can also be touch and go , again because of the variables.

the term "long" and "short" barrels again are optimal and not to be loosely applied.

the paper does not deal with spring powered air guns

QUOTE...."The analysis is simpler for air guns because we can plausibly
make the assumption that temperature is constant during
the gas expansion phases, so that Boyle's law applies instead
of a more complicated temperature-dependent gas law.2"

temperature generated in spring powered air guns can never be a constant......( PCP's and CO2 can also not be TAKEN as a constant )

QUOTE...."There are several variants of air gun that differ in the
means by which air is compressed. The action of spring piston
airguns is complex to analyze, and so we will not consider
them further.f"

as to a shorter barrel having more power....I do not fully agree...as it is the power generated by the gun that determines the velocity not the length of the barrel. the length is an added factor. agreed a longer barrel in a high powered air gun could give one the extra 50 fps. in a low powered gun there could be some element of truth though ( shorter barrel).

long or short have an optimal standard.

get your hand on the book...."Airgun from Trigger to Target" by Cardew. I do not mean this in any "other" sense...just that for some one as interested as you in the theory/ behavior of air guns you will love it. it was written years ago but still makes for excellent reference study.

[brihacharan]

Particularly fascinating is thet fact (as shown in 2-3 graphs in the paper) that in some rifles, the pellet moves faster in the middle of the barrel and then slows down - so those particular rifles will benefit from a shorter barrel with the same spring. That explains why Dr Shirsat of Precihole is a real scientist and the short barreled Orion kicks out more power than longer/bigger air rifles

> Hi Bennedose,
> I fully endorse the last line of your statement...
> Sitting with him even for a few minutes - you come out having gained a wealth of knowledge pertaining to the "design mechanics" of an air rifle
> I consider myself lucky to know him - a veritable source of knowledge & inspiration....
Briha

[brihacharan]

Hi Guys,
> I came across this article while browsing for answers Short Barrels Vs Long Barrels....
Why shorter barrels may often be better
by
Eugene Nielsen

Quote:
There’s a growing trend to shorter barrels on tactical precision rifles. Today, it’s not uncommon to find rifles with significantly shorter barrel. Attitudes are changing and the desire for more maneuverable rifles for the urban setting has led a growing number of manufacturer's to come out with shorter-barreled precision rifles.

The appropriate barrel length is closely tied to the caliber and the load employed. If a shorter barrel provides equivalent or better accuracy and little or no loss in velocity, why go to a longer barrel? Why sacrifice maneuverability and add excess weight? While old attitudes may die hard, chronographs and ballistics don't lie.
Shorter barrels are often better. The proof is in the performance.
Briha