(Note: I can not be held responsible for your use or misuse of this information. Double check all this information against secondary and tertiary sources and double check to make sure loads are safe against a reloading manual from a reputable source before use).
A long time ago in a galaxy far far away computers were slide rulers and paper was used to make cheap computers. You don’t believe me? I find your lack of faith disturbing. No matter. You will. I’ll be doing some scans and YOU WILL.
Here they are…
Yes! I have recently found my old Powley’s Computer for Handloaders and PSI calculator and Bullet Drop and U.S.-Metric Measurement Converter Slide Rules! Also I found my old Powley’s High Velocity Trajectories drop chart. Wow. What a glorious treasure trove. And I wasted $20 buying another Powley’s Computer for Handloaders off Ebay only today having given up the search and only performed a last ditch effort afterwards searching literally on my hands and knees, which got really dirty, but no matter! I found not only the Computer but all those other things as well and the instructions! All perfectly preserved in a little translucent blue plastic envelope I had tucked them in about a decade ago. I’ll be writing some articles about these things and sharing them with you and I’ll be writing a ballistics program in Java. For now know only that while they are only paper what I found is incredibly rare and seldom come onto the market. They haven’t been made for decades. At one time they were sold by Hutton Rifle Ranch, a range in California, that moved their business to Idaho.
The Computer was a slide rule which was the product of research done by Homer S. Powley around 1960-61.
“Homer Powley, one of the greatest ballisticians of our time, developed these “tools” with the assistance of Robert Hutton, Technical Editor of Guns & Ammo magazine, and Robert Forker, former Guns & Ammo Handloader editor.” – The Gun Pro Course – Study Unit 7 Part 2
One source says…
“All are based on work done by Homer Powley circa 1960. His goal was to allow handloaders to estimate safe charges of IMR powders for modern rifle cartridges. Powley also helped develop a slide rule computer which handled much of the math. Davis presents equations which allow one to compute the results without that slide rule, and Howell gives a correction provided by Powley. Miller provides an equation which simplifies the calculations and also spells out some typos in Davis’s text. ” – http://kwk.us/powley_notes.html
I also found another reference to another source written by Geoffrey Kolbe which is more rare (goes for around $400 – eck!). He’s got a bullet drag calculator on his site that looks cool. http://www.geoffrey-kolbe.com/drag.htm and an external ballistics calculator too! http://www.geoffrey-kolbe.com/trajectory.htm Looks like great stuff.
Enough with the sidetrack: So where I did get the slide rules and the ballistic charts? Inheritance. They belonged to my father and I got them when he died in 1995. I’ve used them through the years, but more often I relied on the numbers in regular reloading manuals having received some of the manuals as part of the inheritance and purchasing others myself. And now of course there is a significant amount of information about reloading online available through the powder manufacturers own websites, but they only list a few loads per cartridge type, but most of the time it’s sufficient information. But for working out original loads the Powley Computer worked really well, especially for common rifles rounds when using IMR powders. Well I got to get scanning to preserve this stuff. I’ve scanned in the manual and an additional chart it came with already. The PDF is here. powleysmanuals1.pdf
One of the major points to note from information in the manual & the Gun Pro Course I have which included the slide rules and lessons on how to use them is that the computer was not designed for use with IMR 4831 as it was not available in canisters for home use until 1973. Instead the 4831 referred to is H-4831, which was made by Hodgdon which is slower than the IMR version.
“DU PONT IMR 4831 was introduced as a canister powder in 1973. In burning speed, it is slightly slower than 4350, but faster than H-4831. It is important that IMR 4831 not be used in charge weights recommend for H-4831.” Gun Pro Course – Study Unit 7 – Part 1 pg 20
This is verified in that the manual makes note that IMR 4831 was not available in canisters.
There is information in the course which explains how to convert from one of those kinds of powder to the other which I will supply along with other notes when I can.
Okay: Let’s start talking about how the computer works…
The computer was designed to work with IMR (Improvised Military Rifle) powder, but also included powders from Hodgdon and a few powders that only theoretically existed meaning they would have the ideal properties sought, but had never actually ever been made. The computer was designed to try to find the ideal powder for use and the amount to use in a particular case with the bullet seated to a particular depth so that the pressure was about 40,000 to 50,000 PSI which is within the safe range for most modern rifles.
The thing the user had to determine was how much space would be left in the case after the bullet was seated to the depth that was going to be used. This was called the “case capacity.”
Because each manufacturer made their cartridge cases a bit differently with different webbing and wall thicknesses the case capacity of one brand or even lot of cases could vary widely and so a process was developed for measuring this space that was fairly foolproof.
Because water can fit into any space a bullet would be seated in the case and the case would be filled with water and the weight of the necessary water to do this measured in grains.
Then this number could be mathematically related to how much powder would be used.
To follow the recommended process however the user had to have a cartridge, the bullet, water, a syringe, a reloading press with the appropriate seating die, and a powder scale. These items are used to make a dummy round that is used in conjunction with the computer. Most reloaders would have the necessary equipment, but not necessarily the syringe. I’ll explain the correct procedure for making the dummy round, which requires a syringe of some sort, which I’ll explain how to obtain, and after I’ll explain the process used for an estimated value first in case you don’t have a syringe.
Step 1: Depriming and NeckSizing the Cases –
In the correct procedure we must seat our bullet in an unprimed case. If the round has been fired it must be deprimed first. Ideally because we are trying to determine the case capacity of a round as it is being fired and the brass cartridge case expands to fit the chamber when this occurs a cartridge that has been fired and unsized, but deprimed is best, however not all bullets will remain seated in a case like this. Theoretically lead ones may, but jacketed will not. Personally I’ve never had much success with the bullets remaining in place unsized cases, so I go ahead and resize at least the necks when I deprime them, but try to avoid resizing the whole case body. That’s a good compromise since we need the bullet to stay in place in the case neck and what we are really measuring is the space inside the body of the case anyway. You can however use new unprimed cases for this step, but it is not optimal and will give you less than ideal results since fire-sized cases are going to tell you more about the true size of the chamber than new unfired cases.
Step 2: Seating the Bullet –
We must seat the bullet to the correct depth. Check any reloading manual to determine the finished round’s length (the distance from the base of the cartridge case to the tip of the bullet) which can be measured with a caliper. This length is called the cartridge overall length abbreviated as C.O.A.L. Reloading manuals will tell you to make the C.O.A.L longer when using more powder and likewise shorter for less powder and the manuals will give you an idea of what is ideal for higher or lower pressure rounds, but the computer is designed to help you determine how much powder to use for the bullet seating depth of your choice, so consult a reloading manual first to determine the C.O.A.L for either a higher or lower velocity load and use that depending on your preference. The main consideration however about C.O.A.L is that if a higher velocity is desired the length should be as long as possible a just a bit less than that so that you have more space inside the cartridge, but is can not be so long as to improperly cycle through the action of the firearm or be too close to the rifling of the barrel when the bullet is first fired. Either one of those things would be dangerous. It also can not be so long or short as to prevent the neck from grabbing onto the bullet correctly because that could cause the bullet to fall out of the cartridge or move back into the cartridge, which would not only be dangerous, but could be fatal to the firearm’s user. With a real round you’d also want to be conscious of the appropriate amount of crimp for safety to help prevent these scenarios also, but with the dummy round a light crimp is probably fine. Also remember that the recommended C.O.A.L not only depends on how much powder is going to be used, but also the general shape and length of the bullet itself. So just consult a good reloading manual to determine the optimal C.O.A.L for a particular kind of bullet. Trust the manual.
Step 3: Filling the Case with Water –
Subsection 3.A: The syringe –
Now that the primer has been removed and the bullet has been seated we can fill the case with water. We do this with a syringe. As I said most reloaders would have the necessary equipment for this process, but not necessarily the syringe. In older books it was recommended that the user ask a physician or veterinarian for one which could then be blunted with a file or sharpening stone. Obviously no doctor today would be willing to do that for anyone for legal reasons as a syringe, even a blunted one, could be considered drug paraphernalia by our unjust legal system even if it weren’t being used for illicit purposes.
But thankfully the free market provided a solution as syringes with plastic or metal pre-blunted tips came onto the market. Sometimes these are used for applying oil to machine parts, or glue in crafts, or to refill ink in printer cartridges and they are available at online retailers like amazon or craft supply shops or even Brownells.
A dropper bottle might also work and in a pinch a bulb syringe from a drug store will work, which I have used before, but not ideally as you want the injection device to fit into the flash hole of the cartridge case to be certain all the air pockets have been flushed out and the case is truly full of water.
The kind of commercially available syringes with the plastic tips are fine if the tip is tapered to a smallish point and most metal tips are fine too, but the tip should be pretty thin. One of the smaller tipped plastic ones at Brownells will probably work fine (the 10cc looks like it has the finest tip). http://www.brownells.com/gunsmith-tools-supplies/stock-work-finishing/stock-bedding-accessories/re-usable-syringes/re-usable-syringes-prod1056.aspx
The size of the flash hole varies between cartridge manufacturers and flash-hole the syringe should fit into say in a large rifle is about 0.080-.0802 inches in diameter but can be as small as 0.062. Our syringe doesn’t have to fit into that perfectly, but ideally it will so we want a small tip that would fit inside.
Most retailers don’t list the thickness of plastic tipped syringes, but the metal thickness of the metal tipped ones are usually listed by gauge. A 14 gauge syringe needle measures 0.083 and a 16 gauge measures .065 so while either would probably work the 16 gauge would be best as it is probably going to fit into the hole while the other would not. A gauge 17 (0.058) or 18 (0.050) most certainly would but when doing research those are less readily available. I figure those sizes are approaching the kind used in medical application and so are more restricted or just less useful to most people. If in doubt as to the correct size my research tells me it would be best to get something around a 16 or 17 gauge.
For health reasons however I would be very careful as to where I ordered metal tipped syringes from as retailers are very inconsiderate as to your health and often have bad personal habits that can jeopardize yours. I’d much rather use the plastic kind so that I do not have to worry about that kind of risk.
A direct shipment from trusted medical supplier would probably be a safer bet than a regular online retail outlet using second parties, but there are some risks I just will not take so I am going to see if I can make an appropriate sized plastic tip from a plastic syringe I have had for years that did not fit at all (but which I used effectively anyway just by being careful to flush out alk air bubbles in the case using liquid pressure while the case was inverted), which has a large tip that looks like it is designed for epoxy application. To modify it I am going to remove the plunger and slightly heat the tip over a candle while I pull it thinner with a pair of needle nose pliers and then cut it off. If it catches fire I can just blow it out. If the hole needs to be reopened a sewing needle heated over the candle will open it back up. Stretching plastic like that is a trick my father taught me when making plastic models which can be used to make antenna for military vehicles from the plastic trees you cut the models from. And if it works it should save me about $25 by not having to order a plastic syringe from Brownells and it is a safer option than ordering a metal tipped one from an untrusted source. I’ll let everyone know if this worked.
Now that we have our syringe and the bullet is seated we must weigh our dummy cartridge BEFORE we fill it with water. We’ll need our powder scale. Make sure it is set to measure in grains. Place a small piece of tape over the flash hole and weigh the dummy round and write the number down. Now remove the tape from opening of the flash hole and fill the case with water trying as best as you can with the kind of syringe you are using to get all the air bubbles out and then replace the tape. If some water drips out after you replaced the tape that is fine as long as it remains in the pan you are using to weigh the dummy round in so that the water is still being weighed. Write this greater number down.
Now subtract the less number from the greater number and you’ll know how much the water inside the dummy round weighed. That’s your case capacity measured in grains of water.
Subsection 3.B: What to do if you do not have a syringe –
Since rifle bullets are normally seated to a depth so that the body of the bullet begins about where the cartridge neck begins you can use a fired case with the primer still in it and without a seated bullet and fill it with water just to the beginning (very beginning) of the case neck. By measuring the empty case and the filled case you can get a rough estimate of the case capacity when a bullet is seated in this manner however you should repeat the process three or four times to get a good average. The other method with a syringe is much preferred.
Now that you have your case capacity make sure you write this number down. You’ll need it to use the computer.
Chapter 2: Loading Density –
Now that you have the case capacity of water weighed in grains you’ll need to know how much powder weighed in grains to use. The two numbers are related, but not equal. The relationship as a ratio is called the “loading density.”
The computer is designed to help you fill the case to only 80% (if using 4198 and 4427 powder) or 86% (if using all other powders) of the total case capacity.
If the case were completely filled with powder the fill could be said to be a loading density of 100% or 1.0 expressed as a ratio where 1.0 is 1 whole being even on a scale but that would be dangerous and not optimal in any case. You would think that filling the case all the way and picking an appropriate powder to do this would be best, but smokeless powder requires a little breathing room (unlike black powder which likes to be slightly compressed).
But if there is too much space left over that would also not be ideal because the loaded round lays horizontally inside the firearm and so if too little powder is used the primer will not uniformly ignite all the powder as some of the powder would settle to the bottom of the case which is laying horizontally and that is not good for ideally the primer’s blast should pass through the powder, not pass over it or around it. And so a semi-full case is best. Commercial rounds are loaded between 80% and 90% of the case capacity so the computer is designed also to use this range. And so we can easily determine how much powder to use since we know how much water the case can hold. We just need to use 80% of that if the final result of the computer computations were telling us to use 4198 or 4427 powder (and we’d refactor in that case which is something I’ll discuss later) or 86% of that for other powders the computer is designed for if it indicates we are to use any particular one of those. I know it sounds complicated so let me explain.
The computer begins calculations assuming and 86% fill, but if the end result is a recommended powder of 4198 or 4427 an adjustment is made and the fill reduced to 80%. This is because those powders are very powerful and so a reduction is needed for safety.
While the slide rule computer figures the appropriate powder charge automatically for us we can do a little calculation ourselves to help us understand how it works.
For example let’s say our case capacity was 50 grains of water. Well we know we shouldn’t use that much powder so we take 50 and multiply this by 0.80 which equals 43. That’s how much powder we could use for an 80 percent fill. We don’t know what kind yet, but we have a good idea of how much. We know that we won’t over or under fill our case if we used that much IMR type powder.
Pretty simple huh? Because the slide rule gives us an analog output instead of a digital one and it is difficult to read between the lines it is inferior to running calculations ourselves, but it is a handy tool and I still love it which is why I’m writing this article.
Alternatively we could make a custom load that fills the case to the amount we want calculating from any preferred loading density.
For example if the case can hold 50 grains of water and we make a load that fills the case by say 70% we could know that because 50 * .70 is 35 that we’ll need 35 grains of powder to do that. We can reverse the calculation too to determine what our loading density is if we used 35 grains of powder in a cartridge with 50 grains of water capacity using division like: 35 / 50 = 0.70. So .7 is our loading density which in decimals automatically represents 70% of 1 whole.
I hope that makes sense. So after finding your case capacity in water you’ll know how much powder to use (80-86% of that number is optimal), and the computer is designed to help you figure out the amount of powder to use for an 86% or 80% loading density since this is considered optimal and the computer will tell you that instantly but you still won’t know WHICH powder to use so let’s move on.
Chapter 3: Ratio of Charge to Bullet Weight –
With an acronym of RCBW the ratio of the powder charge to bullet weight is the first thing that tells us a lot about what kind powder we should use.
Again it’s a ratio. If the weight of the powder in grains and the weight of the bullet weight in grains were equal the ratio would be 1.0 or 100%.
We can double check our understand by use of the computer for on our computer if we were to have set our powder charge to say 100 grains and we had our bullet weight also 100 grains we can see that our ratio is 1.0
It’s always the powder weight divided by the bullet weight
RCBW = powderweight / bulletweight
If the powder weight were say 70 grains and the bullet weight say 140 grains the ratio would be 0.5 or 50%.
The higher the ratio number approaching the number 1 the higher the velocity will be since either more powder is being used or the bullet is lighter. Make sense right?
So the calculation to determine the RCBW is easy.
Another Example: 59 grains of powder and a 180 grain bullet becomes: 0.327777778
Usually RCBW is rounded off to the precision of three digits past the decimal point so 0.328 is fine or we could say about 33% rounded off.
Chapter 4: Sectional Density –
The last thing we’ll need to know to inform us as to what powder we should use is the sectional density of the bullet. This is a straight forward calculation that tells us something about the relationship between the bullet’s diameter and its weight which gives us some indication as to what kind of force it will take to get it moving and how much force can be applied to its base and it helps us understand how much resistance it will experience due to air drag in the barrel and in flight (although there is more information needed for that kind of ballistic workup).
Calculating the correct sectional density (with the acronym of SD) is found in various sources like The Gun Digest Book of – Gunsmithing Tools and Their Uses – John E. Traister page 225 C. 1980 ISBN 0-910676-08-9
The formula is: Bullet Weight in Grains / 7000 (to convert to pounds) / Bullet Diameter in Inches / Bullet Diameter in Inches = SD
An example would be a 180 grain bullet of .308 inches (called a 30 caliber bullet most of the time) where the solved formula would be: 180 / 7000 / .308 / .308 = 0.271064742 but we usually round this off to three digits of precision past the decimal point to 0.271.
There is a chart on the back of the computer for common bullets that give the numbers for the general calibers (not the precise diameter) and that chart works alright, but there is a little discrepancy as the published SD for that bullet is .272 and our calculated is .271. This small of a difference probably wouldn’t make much of a difference, but it appears the chart rounds up when it is not necessary to do so. There may be a reason for this and it may be accounting for the fact older bullets were mostly round nosed and flat based, but I don’t like it. I use the calculated number with correct rounding when possible although in truth it would make no perceivable difference.
Chapter 5: Powder Selection – (this chapter is under heavy construction, do not take it at face value at this time)
Powley’s Computer was designed to try to help a handloader select the right kind of IMR powder, but as I mentioned at least one of the powders it was designed for was NOT an IMR powder and this information has been almost lost to history, but luckily I know this fact. It was a Hodgdon powder with the same number. (Find out more by clicking this link.) And so a powder charge reduction is needed in that case if the computer recommends this powder. The information was in Gun Pro Course Study Unit 7 n2507 Part 3 Page 9.
It is written, “WARNING! The 4831 powder used by the computer is Hodgdon’s 4831. The newer IMR 4831 is faster. When actually loading cases, back off 5% on recommended loads if you are using the new IMR 4831.”
So there you have it folks. While it is true the computer was GENERALLY designed for IMR powders the IMR 4831 was NOT AVAILABLE in the kind of canisters that handloaders had to use at the time and so Powley used Hodgdon’s 4831 which is SLOWER. So if you use IMR 4831 with the computer you MUST reduce your load by 5% FOR SAFETY and to allow the math to work for you. This may explain some the discrepancies also between Davis’ math for powder selection and Powley’s slide-rule’s math for powder selection. Davis may have adjusted for this and not explained why or the information was lost to history or he may have noticed the discrepancy arising from using IMR 4831 with the computer in test data and not have even known why it existed and yet adjusted for it. Or it could be that Davis’ had the correct formula, but when Kleimenhagen tried to verify the formula against the slide rule he didn’t know that Hodgdon powder was used for the 4831 and so came to a different formula that he thought the card was using leading to a supposed discrepancy that may not have even existed. Those are some of my working theories to explain the discrepancy at this point and I’ll have to look at a lot of data and the mathematics to suss it out better as I gather more information, but I gave you the information for safety reasons and because we’ll be talking about the discrepancy between the two maths in a bit.
But for now let’s talk generally about how the computer tries to select powder.
It has been measured that one pound of IMR powder of any type produces 1,246,000 pounds of energy which is 178 pounds per grain by weight. It doesn’t matter which of the powders we are talking about in terms of how much potential energy is in them. That’s because the basic formula and process for creating the different powder types in their line is the same. What differs however is speed at which that potential energy can be released by burning because the IMR powders are created in granules of different lengths. By halving the length of a granule of cylindrical powder you double it’s burning speed. And so finer granules mean a faster burning powder and a higher peak pressure in a given amount of time. That means that if we need to drive a bullet faster in a shorter period of time we need a finer powder, but it also means increased danger as pressure will peak more suddenly. A finer grain of powder then it used for cartridges designed for shorter barreled guns which operate at a higher pressure and for cartridges which have less space inside them in which longer granules of powder would not fit well. That means we really have to be careful as to our powder selection and follow reloading manuals exactly. The computer was designed to help us select the most optimal powder for a given cartridge based on the IMR line of powders, but it wasn’t perfect for a number of reasons one of which is that there were IMR powders that were not available for home use at the time and another because some powders available have burning speeds which overlap a little and so there is some question as to which would be best in a given situation, and in some instances the computer might point between lines and so some other solution would need to be found which represented a compromise between what was optimal and what was safest. And lastly because there are some powders which only existed theoretically meaning their characteristics occupied space on the computer but they had never been created in real life and so substitution would be needed when the computer pointed to those so some other solution would need to be found which represented a compromise between what was optimal and what was available.
The theoretical powders were listed by letters A,B,D,F, and G.
Now the question is what lies beneath the powder selection in the first place? What are the mathematics involved?
Karl W. Kleimenhagen who programmed this…
used the a formula:
X = 20 + ( 12 / ( Z * Math.sqrt( A ) ) )
If the value of X is greater or less than or equal to a certain number a certain powder is recommended, but Kleimenhagen notes that the computer does not seem to use this formula. The formula he uses in his own version of the computer is like Davis’, but he says the computer uses is something more like:
x = 19 + 12 / ( SD * MR^0.6 )
Where MR is the mass ratio (A) and SD is the sectional density and the caret 0.6 means raised exponentially (just a way of showing superscript of the following number when the typesetting doesn’t allow for superscript).
So in one formula we have the RCBW being square rooted, which is the same as raised to the power of 0.5, and in the other raised to the 0.6 power.
His exact quote is from http://kwk.us/powley_notes.html and quotes as …
Looking at the scales on the slide rule, one can see the powder quickness equation there is not that presented by Davis. That given by Davis is
20 + 12 / ( SD * MR^0.5 )
where the Mass Ratio is charge weight divided by bullet weight. In the slide rule, the quickness is approximately
19 + 12 / ( SD * MR^0.6 )
I do not know when Powley changed this equation; perhaps Davis made the change. The equation on the slide rule is not cleanly reworked into terms of relative case capacity and SD, which to me suggests it is off.
As an aside, these equations have the correct “units,” namely area divided by mass. These “units” are directly related to those which express the rate of gas production from burning grains of powder. I found in an internet archive a quote by Steve Faber which helps explain: “the relative speed of the tubular IMR powders can be calculated based on the dimensions of the powder grains. This is outlined in the Firearms Pressure Factors book by Wolfe Publishing … [It is] the surface area to volume ratio for each powder.””
And so I am wondering if this discrepancy is because of the IMR 4831 versus Hodgdon’s 4831 difference and I’ll have to run some numbers later to find out and I’m not sure if I have all the information necessary to do that right now and I have other information to finish providing, but for now you have the information in case it is relevant for others in their research and as a note for myself to study later.
Now just to give you an idea of how x works if x is less than or equal to 145 the recommended powder would be IMR 3031. If x is less than or equal to 165 the recommended powder would be 4198 and so on. The higher x is the faster the powder recommended becomes but something very important happens if a powder of 4198 or above in speed is recommended.
In that case for safety reasons the powder charge is reduced from that which would be recommended by an 86% loading density to the lower 80% loading density and this is done by resetting the computer and working out all the numbers again. The reset is done by setting the case capacity instead of at the “START” line at the “4198-4227” line which is next to it, but to the right and the recommended amount of powder must be reread at the number “1” arrow again and the ratio of charge to bullet weight and sectional density and powder numbers reworked at though you are using the computer for the first time.
A good example of how the numbers might work out in a situation in which the computer might require such a reset is that say a case of 50 grains water capacity were used the computer would initially recommend a powder charge of just less than 43 grains, but if in the end of the computer’s use to the point of powder selection the computer ended up recommending 4198 or 4227 type powder the user would set the case capacity at the 4198-4227 line instead of the START line and the powder charge would now be reduced to something just less of 40 grains or so.
check back for more to this section… still working on this section… sorry.
Chapter 6: Expansion Ratio (ER)
Expansion ratio is a little harder to explain, but when powder burns it releases gases which expand accelerating the bullet until it leaves the barrel and because the properties of ideal gases are well known and the properties of the powders in question are well known we can estimate the velocity of the bullet when it leaves the barrel.
All that needs to be known is the space inside the barrel and part of the chamber not filled with the case and the space inside the case (which acts as a chamber sealing off the rest of the chamber around the case during firing). That will give us the necessary information that we need to estimate how far the gas can expand giving the bullet time to accelerate will it is in the barrel. This total space inside the gun in which the gas can expand outward from the case is called the “bore capacity.”
And so we’ll need to know the length of the barrel obviously to determine bore capacity, but the published barrel length of the firearm is not going to help us as what we need is the actual barrel length and manufacturers tend to exaggerate the length of their barrels or round off and the space inside the chamber from where the base of the bullet begins its forward travel is part of the barrel also for ballistic purposes.
So what we really need is the EFFECTIVE barrel length or what we call the “Ballistics Barrel” (different sources use different terms) to help us determine the Bore Capacity.
We already know the space inside of the case so that’s the first number we use to determine the expansion ratio.
And we know the diameter of the bore of the barrel so if we can measure the effective barrel length there is a way we can estimate the total space inside the bore and chamber in which the gas can expand. After all the dimensions of chambers and bores for particular cartridge designs are well known, so the real problem is just figuring out how to measure the real length of the barrel in terms of how far back the bullet is seated.
This isn’t really as difficult at it may sound. If we put our dummy round in the chamber we can measure from the tip of the bullet to the end of the muzzle and that’ll give us a lot of information because then we can add to that the length of the bullet and the result will be the “ballistics barrel length.” The process of doing this is fairly straight forward.
First we make sure all the water has been sucked and blown out of our dummy round. And then we insert it into the chamber of the gun making sure no other rounds are in the firearm or magazine for safety reasons.
And then we take a cleaning rod without a tip affixed in the end of the rod and insert it into the muzzle from the far side until the rod touches the tip of our bullet and we mark the rod right at the muzzle with a marker or a dot of paint.
We take the rod out and measure the length from the rod’s end to the mark we made and that tells us how long our effective barrel is. We write down this number in inches as precisely as we can, but usually a regular yard stick would probably provide enough precision for this part. We should round to the nearest 1/8th of an inch since that’s the precision allowed for on the computer but you could maybe round to the nearest 1/16th if you are willing to read between the lines, but I don’t round until the next step is complete.
And what is our next step? Well we might think we know the length of the barrel for ballistics purposes, but we still need to add the length of the bullet because the ballistic barrel length is actually from the BASE of the bullet, not the tip so get your calipers out. Measure the length of one of the bullets you haven’t used yet (calipers measure in inches to the nearest 100th at least) and add that to the length of the barrel you measured. Now you can round that to the nearest 1/8th or 1/16th. And you now know the ballistic barrel length to use with your computer.
Now the computer is fairly smart and can help us figure out the rest since the ballistic barrel length is know.
The math of area inside of a cylinder (the chamber and the bore are cylinders). It knows the diameter of the inside of a particular caliber’s barrel and so can estimate how much space the gas has to expand before the bullet can leave the barrel. The expansion ratio is an expression of this space as a number in relation to the original space inside the case.
For example rifles with low numbered expansion ratios around 5 to 6 have large chambers, but long narrow bores so the gas doesn’t have much room to expand beyond the original volume of the space inside the case/chamber. Rifles with expansion ratios of 6 to 8 are considered about medium and high expansion ratios would be something from about 10 to 11. All else being equal if the number is low the rifle is of a smaller caliber, but has a larger case the velocity achievable out of the round is generally higher and the bullet drag lower so less bullet drop would occur when shooting than gun than if the expansion ratio number were larger which it would be if the rifle had a small chamber, but large bore for a large bullet diameter. So then efficiency of the gun can be rated by how well balanced the chamber/case size is to the diameter and length of the barrel. It’s possible to increase the velocity of the round by lengthening the barrel or by increasing the chamber size but in the case of changing the chamber size efficiency decreases for more powder would be wasted not fully burning before the bullet leaves the barrel.
It has been measured that one pound of IMR powder of any type produces 1,246,000 pounds of energy which is 178 pounds per grain by weight. So if we know the velocity at the muzzle we can determine how well the powder is being used first finding the energy of the bullet by its weight and velocity and we can calculate how much energy should be in the grains of powder we are using and then using the formula: ME (muzzle energy) / potential energy of the grains.
For example: Say that 53 grains of powder may give us a velocity of 2,940 fps (feet per second) when the bullet leaves the barrel which means the bullet has the kinetic energy of 2,878 foot pounds. Now we can find out how much it could have had by multiplying 178 x 53 which equals 9,434, but because the barrel is of a limited length and due to other factors like friction we are not using all that energy to drive the bullet so we are less efficient than what would be ideal. We could figure out our efficiency of this machine we’ve created by taking the kinetic energy of the bullet at the muzzle (2878 ft lbs) and dividing it by how much energy our grains of powder could have produced in an ideal situation (9434 ft lbs) which gives us an efficiency of .30 or 30%. This is about medium efficiency for most rifles and is typical for a gun having an expansion ratio of about 7.5. Few approach 40% efficiency.
So what exactly is the expansion ratio number mean in terms of gases? Well if the gas has room to expand inside the chamber and barrel say 4 times the volume of the effective chamber size available to the trapped gases behind the bullet before firing when the bullet begins to move forward (being really just the total space inside the case) before the bullet finally leaves the barrel then we say that the expansion ratio is 4. That’s all. And so it is the ratio between the space inside the case and the space inside the whole of the interior parts of the gun which can allow the gases to expand and are trapped during firing. Again it sounds complicated but it is not. It is just a ratio between those two things. A ratio between the space available to the volume of gas before the bullet moves forward and that which is available just before the bullet leaves the muzzle. Since gas exerts equal pressure in all directions all the time we do not have to take directional forces into consideration. The bullet being the lightest and most moveable object having a path forward will move in that direction as a firearm’s design dictates even as gas fills the space behind it in an even manner as the bullet continues to move.
more to come in this secton
Chapter 7: Davis’ Formulas.
In the book “Handloading” – William C. Davis – National Rifle Association – 1981 the author gives a series of formulas which are similar to those used in the Powley Computer for Handloaders. As noted there seem to be some differences, but I’ll give them here as Davis did for reference.
The chapter is titled “Some Simplified Interior Ballistics For Handloaders” and begins on page 138.
Davis writes, “The methods described here are, in general, applicable only to DuPont IMR powders fired in strong centerfire rifles, capable of withstanding loads that typically develop pressures on the order of 50,000 c.u.p. A few handguns also fall into that category… The most important characteristics in determining the performance of a cartridge are the charge weight, the capacity of the powder chamber, the diameter and weight of the bullet, and the length of the barrel in which it will be fired. These basic characteristics are combined in various ways to derive some of the other terms commonly used in interior ballistics, such as loading density, expansion ratio, sectional density, and the ratio of charge weight to bullet weight.”
He includes four tables which are on pages 139, 140, 142, and 143 which is the last page of the chapter.
Table 1 is a list of common cartridges and the amount of water they can hold to the brim (not the case capacity of the loaded round mind you but rather the total amount of space within a typical cartridge of that type BEFORE a bullet is seated), the case length, and the maximum cartridge length after a bullet is seated (also known as C.O.A.L or Cartridge Overall Length). I’ll include it here once I retype it.
Table 2 is a list of variables (their names and descriptions) to be used in the calculations. The variables are:
A = Mass ratio (charge weight/bullet weight) – this would be the same as “ratio of charge to bullet weight” as it is named in the Gun Pro Course.
B = Bullet length (inches)
C = Case Length (inches)
D = Bullet diameter (inch)
E = Barrel length (inches)
F = Full water capacity of case (grains) – this would be the amount of water the entire case could hold to the brim without a seated bullet in it.
G = Bullet weight (grains)
H = Height (axial length) of boattail (inch) – that’s of a boat-tail shaped bullet
I = Charge Weight (grains) – that’s the weight of the powder being used
J = Tail diameter (small end) of boattail (inch)
K = Displacement correction for boattail bullet (grains)
L = Cartridge overall length (inches)
LD = Density of the loading (I/W ratio) – that’s the loading density
M = 1 / 4√R
N = (1 – M)
P = Water displaced by seating flat-base bullet (grains)
Q = Effective bore volume (cubic inches)
R = Expansion Ratio
S = Bullet seating depth (inch)
T = Bullet travel in barrel (inches)
U – Volume of cartridge powder chamber (cubic inch)
V = Muzzle velocity (ft/sec) – that’s in FPS or feet per second
W = Water capacity of cartridge powder chamber (grains)
X = Powder-selection index
Y = (G + I / 3)
Z = Bullet sectional density) (lb/in2)
We’ll use these later and they’ll be explained further.
Table 3 is a powder selection table so that X = what kind of powder to use. It says…
TABLE 3. POWDER-SELECTION TABLE
|Powder Selection Index (X)
|Less than 81
|Powder indicated is much “slower” than IMR-4831. There is no very suitable IMR canister powder available. Use only loads specifically pressure-tested, and do not experiment.
|81 to 91
|Powder indicated is “slower” than IMR-4831 and IMR-4350, and calculated charges must be reduced by about 5 to 10 percent if IMR-4831 or IMR-4350 is used.
|91 to 110
|Powder indicated is similar to IMR-4831 and IMR 4350.
|110 to 125
|Powder indicated is similar to IMR-4064, IMR-4895. and IMR-4320.
|125 to 145
|Powder indicated is similar to IMR-3031.
|145 to 165
|Powder indicated is similar to IMR-4198.
|165 to 180
|Powder indicated is similar to IMR-4427.
|More than 180
|Powder indicated is “faster” than IMR-4427. For lower pressures, IMR-4427 may be used, but velocities will be less than predicted.
And Table 4 is a Expansion Ratio table for various Mass Ratios (charge weight/bullet weight). Here’s a copy.
Davis writes (pg 141), “For the DuPont IMR powders, and some similar powders sold by Hodgdon, it will be found that the maximum charge weight which can be conveniently loaded into a cartridge case, without compressing the powder, is about 80 to 90 per cent of the weight of water required to fill the powder space. This concept is expressed in interior ballistics by the term “density of loading” (or “loading density”) which is defined as the ratio of the weight of powder charge to the weight of water required to fill the available volume of the powder chamber. Some powders pack more densely than others, owing mostly to the size, shape and surface characteristic is expressed by another term called “bulk density,” or “gravimetric density.” The bulk density of IMR-4227 and IMR-4198 is somewhat less than that of the other IMR canister powders, and for that reason, it will be found that a charge weight equal to about 80 per cent of the water capacity will nearly fill the available powder space. For the other IMR powders, a charge weight equal to about 86 per cent of the water capacity can be accommodated, without quite filling the available powder space. The “ideal” charge weight will therefore be about 80 per cent of the water capacity for IMR-4227 and IMR-4198, and about 86 per cent of the water capacity for the other IMR canister powders.”
He gives a formula I = .86 x W for all IMR powders besides 4227 and 4198
and the formula I = .80 x W for those two
He relates a “relative quickness” list where IMR 4350 is arbitrarily set at 100 and higher numbers indicate a faster powder.
And he explains that the data are based on laboratory tests instead of gun firings and serve as a general guide for expected performance, but powders which are placed fairly close together in their quickness number may changed their relative positions if ranked in accordance with their performance in actual gun firings. He says, “This is particularly true of IMR-4064, IMR-4895 and IMR-4320… IMR-4064 is often found to allow higher charge weights, and produce higher velocities at acceptable pressure, than do either IMR-4895 or IMR-4320, both of which rank lower (“slower”) on the relative-quickness scale. For that reason, it is impossible to say with certainty which of the powders in this group of three… will be found most suitable in a particular load in which all three have reasonable suitable characteristics. The same is occasionally true of IMR-4350 and IMR-4831, which are separated by only five points on the relative quickness scale. The choice among powders within these groupings cannot be reliably predicted by calculation, but must be determined by actual firing tests in the cartridge under consideration…. we will establish the approximate range 45,000 c.u.p. to 50,000 c.u.p. … If it appears that a powder “slower” than IMR-4198 will be required, we can proceed on the assumption that the density of loading should be .86… If it appears that a powder “faster” than IMR-3031 will be required, we can assume that the loading density should be .80.”
To find ratio of charge to bullet weight or “mass ratio” he says A = I / G and for sectional density Z = G / (7000 x D2) where z is sectional density, lb/in2.
The powder selection index (variable X) “has been empirically determined to yield numbers corresponding roughly to the Du Pont index of relative quickness, when the working chamber pressure is about 45,000 to 50,000 c.u.p. The correspondence with the Du Pont relative-quickness scale is not perfect, of course, partly because the behavior of powders in different cartridges and loads sometimes indicates a different ranking than that established by the relative-quickness numbers, as explained before. It should also be emphasized that the powder selected by calculation is an “ideal” IMR powder [for the pressure target & loading density]… [&] probably will not correspond exactly to any of the canister IMR powders actually available, since only eight powders could hardly be “ideal” for nearly 1000 cartridges and perhaps a thousand different bullets…[firing tests are required for final workups]…”
The formula for powder-selection index variable X is…
X = 20 + 12/(Z x √A) where A is mass ratio and z is sectional density (lb/in2).
Then he writes the final step, “… is to reexamine the choice of the loading density chosen to calculate the charge weight. If the charge weight was based on the loading density of .86, assuming that a powder “slower” than IMR-4198 would be used, but the powder-selection index was found to indicate IMR-4198 or IMR-4227, then the charge weight should now be recalculated using a loading density of .80… if a loading density of .80 was assumed, but the powder-selection index was found to indicate IMR-3031 or a “slower” powder, then the charge weight should now be recalculated at a loading density of .86…”
He writes of the Powley Computer, “…we are indebted to Homer S. Powley, for a key equation that he developed some years ago to predict the performance of rifle loads using the Du Pont IMR powders. The Powley Computer for Handloaders (available from Homer S. Powley, Petra Lane, RR 1, Eldridge, IA 52748) is an ingenious slide-rule device, having eleven scales on the front and give scales on the back, which canbe used to select an IMR powder, estimate a charge weight, and predict the velocity expected, all on the basis of input measurements similar to those described in this article. Powley’s equation is a semi-empirical one, which gives remarkably accurate results considering the complications of small-arms interior ballistics, and it has the great virtue of being simpler than any of the other methods so far devised. Even so, in its original form, the equation might appear formidable to those not accustomed to solving lengthy equations. We shall therefore break down the quation into simpler steps for solution…”
M = 1 / 4√R
N = (1 – M)
V = (G + 1 / 3)
“In terms of these variables, Powley’s equation for muzzle velocity (V) now becomes:
V = 8000 x SQR (I – N / Y)
(SQR indicates “square root of”)”
He explains the pressure of the load can be calculated from the “Powley psi Calculator”, an ingenious slide-rule device for calculatoing pressures of cartridges using the Du Pont IMR powders.”
“Though Powley’s final equation for calculating chamber pressure is one of the simplest yet devised, it might in its original form appear too formidable to those unaccustomed to dealing with lengthy algebraic expressions. It can however, be broken down into simpler steps, and solved quite easily by using a pocket calculator.”
“In addition to the parameters we have already found, the equation involves also an empirically determined factor which depends upon the expansion ratio (R) and the mass ratio (A). We will call this factor F2. It can be found from Table 4. The numbers in the body of Table 4 are the values of F2, corresponding to the values of R and A in the line and column in which they appear.
Finally, the muzzle velocity of the load (V) must be known.”
He derives three new variables (K1,K2,K3) by:
K1 = .0142 x 1 x F2 x V
K2 = .53 X (G/I) + .26
K3 = W x (R – 1.0)
Then, “…Powley’s equation for chamber pressure (P), in psi as measure by the crusher-type gage, is this:
P = k1 x K2/K3″
But later he gives an example equation and squares the velocity: “K1 = .0142 x I x F2 x V2
= .0142 x 53.6 x 1.74 x 26202” etc. So I’m pretty sure the velocity is supposed to be squared as it often is in energy calculations in ballistics and physics generally e=mc2 (which was a formula stolen from ballistics and classical physics by the way).
And there is a very important part when he said, “by the crusher-type gage” which means that current psi measurements as we use them today is not what Powley used, but rather something equivalent to c.u.p because at the time psi used in ballistics and c.u.p. were roughly equivalent, however today psi is a universal scientific standard across multiple disciplines and so psi and c.u.p are no longer equivalent. That is important because otherwise you may think that the Powley Psi Computer gives you an output in PSI as we understand it today. It doesn’t. It gives you a PSI roughly equivalent to c.u.p. If you need PSI as currently measured for some reason you’ll need to convert it.
Article still unfinished, check back for more…
MISC. Information: In order to calculate bullet energy an old formula is used which Einstein stole by saying E=MC2. That had been known since the 1700s. A form factor is always involved an in Einstein’s he used the known speed of light (which varies by the way, but don’t tell your physics teacher that or he’ll have a heart attack). But in ballistics we use the form factor of 450240. The formula can be expressed as velocity in feet per second squared (acceleration or “C” squared as Einstein put it), multiplied by the mass in grains (7000 grains to a pound) adjusted to coincide with the way we want to express the energy, which in this case is foot pounds. So the procedure could be said to be Velocity x Velocity x Mass / 450240 = Energy in ft-lbs. This formula appears in “Gunsmithing Tools and Their Uses” but was known as I said back in the 1700s after the ballistic pendulum was invented by Benjamin Robins. It was just a weight that would swing when shot and by measuring the amount of swing the velocity of the bullet could be calculated. The amount of energy could be expressed as how far the pendulum would move weighing a certain amount of pounds hung by a lever of a certain length (foot pounds). And so Einsteins formula was known in the 1700s to ballistic technicians and WIDELY known by the 1800s by all physicians. Newtonian physics has always been superior to the theoretical physics of Einstein and the moderns. Unfortunately statistical guesswork has infected even the study of ballistics. But I’ll write about that some other time.