Summary: Both Computers provide useful information for handloaders, and both demonstrate the underlying trends of internal ballistics. Predictions for the internal ballistics of small arms are not reliable, so be wary.
This version is based on the following works:
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.
These notes are divided into five main sections:
The Load Computer does not cover all possible reloads. It was meant to predict safe and accurate loads approaching full power with modern cartridges in modern rifles. These limitations are imposed:
Regarding pressures, at the time Powley did his work, the copper crusher was the usual method used to measure peak chamber pressure. Modern SAAMI procedures for pressure measurement with copper crushers use the term "CUP" to denote the results. However, Powley's work may not have been based on SAAMI spec. tests. Instead, they were likely based on an earlier copper crusher standard, which would not always correspond to modern CUP readings. In general, copper crushers do not accurately record true peak psi, and the distortion this measurement method introduces is thus built into the Powley equations. Crusher measurements of psi are generally low; 44,000 CUP is usually near 50,000 psi. More information on this topic can be found in the page on Pressure Standards. While not technically correct, pressures in the Powley Computers will be referred to as CUP to distinguish them from true pressure.
I would advise another limitation: use only standard primers and jacketed bullets of conventional construction. Components have unpredictable effects on pressure.
Powley did suggest one could use the Load Computer to help select charges for certain lower pressure cartridges, and this is covered below.
Powley's equations are semi-empirical. They use some simplified thermodynamic theory with the numbers altered to fit the results to lab data. In the Powley Computer section of his site, Steve Faber gives an analysis of the theoretical form of the velocity equation, and he concludes it assumed a complete and nearly instantaneous burn followed by an expansion without losses to friction or heat transfer.
The calculations are simple. The volume under the bullet, as measured in gn of water, is multiplied by 0.86 (or by 0.80, for 4198 and faster powders) to give a charge which will nearly fill the case. This calculation is related to the average density of the IMR powders. A separate, empirical equation is then used to determine which IMR powder will produce a peak pressure of about 44,000 CUP using this load. Finally, the equation considered by Faber is used to estimate the muzzle velocity.
The physics behind the Load Computer equations can be described simply. The volume under the seated bullet determines how much powder can be loaded. The charge determines how much chemical energy is available to propel the bullet. The expansion ratio determines how much of the chemical energy is converted to kinetic energy.
The computer gives a value for the "relative quickness" of the powder required. These comments on the reference scale are from Davis (the scale is in the Computer's help pop-ups, at Quickness in the third column):
Relative quickness data are based on laboratory tests instead of on gun firings, and serve as a general guide for the expected performance in cartridges, but it is found that powders which are placed fairly close together in the relative quickness range may change their relative positions if ranked according to their performance in actual gun firings. This is particularly true of IMR 4064, IMR 4895 and IMR 4320, which rank in that order according to relative quickness, from "fastest" to "slowest." In actual firing, however, 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 ... will be found most suitable... The same is occasionally true of IMR 4350 and IMR 4831... The choice among powders within these groupings cannot be reliably predicted by calculation...
Davis's comments regarding the differences between 4064, 4895, and 4320 are born out in numerous load books. In general, if the computer suggests these powders, one should probably just try 4064, or maybe 4895 if a smaller grained powder is desired. If the computed Quickness (third column) is near 95, 4831 is a better bet than 4350.
The computed quickness is compared to a table given by Davis to determine which powder to recommend. For instance, a quickness of 165 is the border between an indication for 4227 or 4198. If the reported quickness is between two powders in the Quickness table, I think it prudent to begin load development with the slower powder. This is especially important for the border between faster the powders. If the case fills before the predicted speed is reached, the faster powder can be tried.
Results from the Load Computer can be compared to the loads in the IMR Handloader's Guide, 05/01. Portions of this guide can be found on their site. IMR's data doesn't include the case capacity nor the length of the components, so these values had to be estimated using data from various sources.
Chosen for comparison were those loads from IMR's data which provided the best velocity without resorting to compressed charges. IMR's data often shows nearly equal performance when using smaller charges of a slightly faster burning powder. Again, the Powley computer tries to find the powder which nearly fills the case.
To gauge the accuracy of the predictions, one might begin with the medium pressure cartridges. These operate at pressures near that of the nominal operating pressure for which the Powley computer was designed, namely 44,000 CUP. The available cartridges range from the .222 Rem to the .444 Marlin. Ideally, the Computer would predict the correct velocity and charge for these. For the bottle neck cases in this group, the appropriate powder is selected and the charge and velocity are within a few percent.
The references I have for case capacity of the .444 Marlin differ by over 3 gn. Using the smaller value causes the computer to predict a charge of 4227 which IMR's data shows would be dangerous. Using the larger value gives a fair match to IMR's data for 4198. (I should note the more sophisticated internal ballistics simulator QuickLOAD has similar trouble here.) In general, I feel that if the Computer indicates either 4227 or 4198, one should begin testing with the next slower powder. So far, this is the only example of a dangerous load I've found.
Also tried was a lower pressure cartridge, the .30-40 Krag, which is limited to 40,000 CUP, a pressure a bit below that assumed by the Computer. The computer suggests charges and velocities a bit above that shown in the IMR book, which was to be expected.
Cartridges which operate at high pressures, from the .17 Rem to the .458 Win Mag, are those for which the Load Computer was designed. In general, I've found the computer selects a safe charge and predicts a velocity somewhat below maximums, in keeping with the reduced pressures. However, it would be wise to reduce the suggested charge at least 5% and watch velocity with a chronograph, for the Computer seems to be better at predicting the velocity possible than the charge weight needed to reach it. Starting development with the next slower powder (eg. 4350 instead of 4064 and 4895) would not be foolish.
For comparison, I obtained a slide rule Powley Computer from:
Hutton Rifle Ranch
P.O. Box 170317
Boise, ID 83717-0317
In early 2004, the cost for both slide rules was $24. I've seen a picture of the originals (1960's), and these from Hutton's appear to use the same equations. The two slide rules are labeled the "Powley Computer for Handloaders" and the "Powley psi Calculator" (even though the latter estimates CUP, not true psi).
Davis's equations do not try to predict loads of 7828 powder, but Hutton's slide rule does. 7828 was released long after the Powley computer was and several years after Davis's article. (The original Powley computer also did not consider 4895.)
I've found the slide rule can indicate different charges than the equations given by Davis. While charge weight and fps predictions agree, the powder indicated sometimes differs. When they disagree, the powder speed from the slide rule seems to always be fast, which would create higher pressures. Using the slide rule to predict a load for the .444 Marlin with 240 gn bullets indicates a powder faster than 4227 is needed. This is dangerously wrong, for 4198 is the correct powder. As noted above, the powder selection equations used in the computer here are not infallible, but I have found them more reliable than those in the slide rule.
If one does not use it to try to predict charges of powders faster than 3031, the slide rule does ok, and it is more handy to take to the shooting range.
For rifles using bottleneck cartridges with operating pressures of 52,000 CUP or greater, the Powley computer generally selects a load which is safe and has the potential for good accuracy and long barrel life.
Do not use the Load Computer for cartridges having a pressure limit below 52,000 CUP. It is not accurate enough to provide a reasonable margin of safety.
This solves a different problem in internal ballistics. As mentioned above, small changes in the initial motion of the bullet can have large changes on the pressures developed. Davis provides an article documenting pressure changes of 7000 CUP due to seemingly minor changes in bullet construction.
With greater pressures, more kinetic energy can be extracted from a given charge of powder. One might, then, use velocity to estimate the peak pressure generated. Modern chronographs are accurate and fairly inexpensive.
Davis provides the equations, but Howell provides a correction to one of the numbers. This correction was pointed out by Powley and lowers the CUP estimate 5%. In comparing results to IMR's current data, I found that values from Davis's version were generally closer, but Lyman's recent data seems to match better with Howell's; Howell's version is used here.
Miller mentions Powley's equation was constructed for loads like those of the Load Computer, namely a nearly full case of IMR rifle powder producing a peak pressure in the vicinity of 44,000 CUP. He offers a correction he devised for lower load densities, ie. cases less full of some faster burning powder. This he based on an analysis of the pressures predicted by Powley's equations as compared to those in the 1996 IMR Handloader's Guide. While I didn't find his suggested change especially useful, it did help some for powders much faster than recommended by the Load Computer.
Miller also offers an equation to replace a look up table which Powley gave. This table can be thought of as giving the ratio of peak pressure to average pressure. As inputs, the table uses mass ratio (charge weight to bullet weight) and expansion ratio. When compared to Powley's table, Miller's equation creates a maximum error of less than 1%. The equation also provides ready extrapolation for expansion and mass ratios outside the ranges given by Powley. Miller's equation is used in this version of the Powley Computer.
As mentioned, Davis presents an article showing the large change in pressure which can occur with changes in bullet construction. The table of pressure and velocity from this article (both the charge and the seating depth were kept the same) was compared to the output of the Pressure Computer. The equations used in the Pressure Computer predict that for a fixed charge, pressure rises with the 2nd power (square) of the velocity. In other words, each 1% increase in fps means about a 2% increase in pressure. However, the lab data shows a far more pronounced pressure rise, with percentage changes in pressure rising more than 5 times as fast as in velocity. The A-Square Handloading and Rifle Manual documents a similar pressure rise rate.
The 47th edition of the Lyman Reloading Handbook has a table of typical shot to shot variation in pressure and muzzle velocity for a given load. There, pressure rises about 4 times as fast as velocity. The A-Square Manual gives both the standard deviation and the extreme spreads in velocity and pressure found in their tests. Comparing the extreme spreads, one again finds pressure rising much faster than velocity, about 6 times so, but in some cases much higher.
Primer substitution can also cause drastic changes in pressures, with all other components the same. John Barsness, writing in the June, 2004 issue of Handloader tested different primers in a given load for the .300 Win., and his numbers suggest pressure can rise 10 times as fast as velocity. The A-Square Manual shows even greater pressure rise rates.
These rates of pressure rise with velocity are considered on a separate page on this site.
Clearly, then, the Pressure Computer is not suitable for estimating pressures resulting from either typical shot to shot variations or from component substitutions. It might, though, be useful in relating the pressure and velocity of normal loads. If it is reasonably accurate at predicting the typical pressure for a given fps, then it could be used "in reverse" to predict fps from a pressure limit. In other words, it might be useful for estimating cartridge performance at any pressure, even if it doesn't tell you which powder, primer, and bullet to use.
A source for data to test this is the 48th edition of the Lyman Reloading Handbook. For many cartridges, charge, pressure, and velocity are given for full and reduced power loads. Powders used include IMR's and similar, single base powders from Hodgdon and VihtaVouri. Similar information for Hodgdon's single base, extruded powders is found in their 2004 Annual Manual for reloading. The A-Square Manual also gives very complete load information for IMR powders over a range of high and low pressure cartridges. With all these books, the loads considered were those which nearly filled the case, and I had to estimate case capacities from other sources.
Davis did similar Pressure Computer calcuations on the loads found in the 1975 Du Pont Handloader's Guide for Smokeless Powders:
The results indicated that the calculated pressures for cartridges from about .25-caliber to .338-caliber were usually within about 10% of the measured pressures, about equally divided above and below. For the smaller calibers, the calculated pressures were typically somewhat below the measured pressures, the average being about 4% lower for the 6mm calibers, and about 8% for the .22 calibers. For calibers larger than the .338, the calculated pressures were typically somewhat higher than the measured pressures, the average being about 7% higher for the .35-caliber cartridges, and about 15% higher for the .458 Winchester Magnum. The .375 H&H Magnum, in exception to the trend, gave calculated pressures in very good agreement with the measure pressures.
The reason for the apparent caliber-dependence of the difference between calculated and measured pressures is not known. It is not certain that it truly exists, since some of the details for the Du Pont test loads were not known, and typical values for the cartridges were used in the calculations. It is possible to improve the agreement between calculated and measured pressures, for these particular data, by introducting another factor into the equation for pressure calculations, but it is doubtful if the accuracy of the data warrant that refinement. Experimenters should be aware, however, that some such trend might exist, and treat their calculations accordingly.
I ran similar calculations with this version of the Powley Computer, covering over 120 loads in more than 35 cartridges. The pressures estimated for small bores (below 28 caliber) are indeed usually low; however, this appears to be related more to low SD bullets (below .200) than to caliber. In a few loadings it was 10,000 CUP low, such as with very low SD bullets (around .150) in the larger cases (Relative Capacity over 4.0). (Do not condemn the old Powley Computer based on this single number. Even the best of the modern computers for internal ballistics, QuickLOAD, is known to miss pressure by 10,000 psi at times; see Barsness' article in the 06/2004 issue of Handloader.)
I did not find the predicted pressures to be high for the large bores. In general the pressure estimations are low for most cartridges near 50,000 CUP, but when the SD is high (over .330), the pressure estimate is often good. I did notice the computer is often high when the measured pressure drops below 35,000 CUP.
Davis did not speculate on why the Computer's estimates of pressure were low with the smaller bores. However, with the smaller bores, it seems possible bullet engraving and friction forces will be higher relative to the bullet's inertia. The Powley equations for pressure estimation do not consider this, and the relative effects of inertia and engraving are thus fixed, likely for the popular 30 caliber. The problem of low SD bullets in large cases may be due to the underlying theoretical equations being "stretched" a bit too far (especially in velocity) from their fit to cartridges proportioned like the popular .30-06. Another possibility is that the theoretical portion of Powley's equations were warped by the use of CUP instead of true psi pressures.
On the whole, I've found the Pressure Computer not too bad at predicting typical lab pressures for loads which nearly fill the case. I use it only for estimating cartridge potential, and this version of the Computer will estimate a velocity if given the cartridge dimensions and a pressure limit.
As with the Load Computer, I have compared the results of this Pressure Computer to those from the Hutton slide rule. For cartridges of the proportions (Relative Capacity) of the .30-06 and longer, the slide rule seems to do a better job of estimating pressures. It is not so low near 50,000 CUP, and it is a bit better at the lower pressures as well. However, it more greatly underestimates pressures for relatively short cartridges, such as the .358 and the .444. The equations provided by Davis are more complicated than can be readily implemented with a slide rule, and they do a better job over the entire range of pressures and cartridges.
While higher velocities do come with higher pressures, estimating pressures with a chronograph and this Pressure Computer cannot be very accurate. If it is to be tried, I believe velocity should be averaged over several rounds. Use only bullets of standard construction, namely jackets of gilding metal or copper over fairly soft lead cores. Also, use with powders which can be safely loaded for a nearly full case over a standard primer.
If its limitations are taken into account, the Pressure Computer will do a respectable job of predicting cartridge performance at a certain pressure, but it can't tell you what components to use.
While the Powley Computers were designed for modern high pressure cartridges, it might be possible to use them to estimate loads for lower pressure rounds. However, Powley suggested only one of these extensions.
All the other extensions presented in this section are speculative and would involve much work at the range with a chronograph. These are based on the observation that the Pressure Computer is pretty good at matching CUP to velocity for charges which nearly fill the case. In my comparisons with published loads, the computer's estimate of CUP is generally on the safe side, being somewhat high for low pressure cartridges and about right for medium pressure cartridges. However, because the Pressure Computer tends to underestimate the pressures with low SD bullets, I certainly would not attempt these with bullets of SD .200 and below.
One starts by using the Pressure Computer to estimate velocity for a loading density of 0.86 at the cartridge's pressure limit. Because components can alter pressure with little change in velocity, it would be prudent to back off on the velocity prediction at least 5% (or more, your target will not notice the difference). Further, I would use CCI or Remington standard rifle primers, because in the reports I've read, these tend to generate more modest pressures.
The Load Computer ideally predicts a charge delivering a pressure of about 44,000 CUP. It is not wise, though, to use Load Computer charges for cartridges which are limited to this pressure, for these charges can produce pressures near 50,000 CUP. Instead, one could begin load development with the next slower class of powders, and if the case fills before the expected velocity is reached, then try working up with the class of powder recommended by the Load Computer.
At the range, testing would begin with a charge of a very slow powder at a loading density of about 0.80. If this chronographs too slow, increase the loading density somewhat and chronograph again, and so on until a compressed charge is reached. If the velocity is still lower than expected, start again with the next faster powder, and so on until the expected velocity is reached.
An important caveat: there is at least one pitfall in trying to work up a load by working down through the slowest powders. Nominal burning rates are established with high pressure tests, and at lower pressures, say 30,000 CUP, it is quite possible the order changes. Further, there is no guarantee any powder in the IMR line—or any other line—will be able to deliver the velocity predicted by the Pressure Computer (or any other such software).
In principle, one could run through the complete range of powders—7828, 4831, 4350, 4064, 3031, 4198—seeking the expected velocity, but using the Load Computer can shorten the process. The Load Computer tries to select the best powder for a nearly full case at pressures near 44,000 CUP. If it suggests a charge using powders such as 4895 or faster, one might simply cut its suggested charge weight, an approach Powley did offer. In a separate article, Davis mentions that 4895, 3031, and 4198 work nicely for reduced charges. (Using H-4895 for reduced loads of medium speed powders might do, for Hodgdon reports this powder generally works well in reduced charges. Many shooters report Reloder 15 works well for reduced pressure loads in big cases, such as the old Nitro Express rounds.)
Powley suggested a 10% reduction in charge reduces pressure in CUP about 20% and velocity about 10%. If the needed reduction in charge leaves too much space in the case, one would have to use nearly full cases of the slowest powders. (Using greatly reduced charges of 4350 and slower powders is not safe.)
Above 50,000 CUP, it would be best to lower the pressure limit by at least 3000 CUP when having the Pressure Computer estimate velocity, for the Computer tends to be overestimate fps at these pressures. Further, if bullets below SD .220 are to be used do not attempt to work up to the velocity suggested by the Pressure Computer. To reach the expected velocity, one might try working up through the charge of the powder suggested by the Load Computer. If the case fills before the expected velocity is reached, back off on the loading density and switch to the next faster powder class.
For many of the old British African cartridges, such as the 450 NE, the Pressure Computer isn't too bad at predicting performance, which is surprising. These were loaded with Cordite, which had a quickness similar to 3031. Cordite's long, stiff strands allowed consistent ignition at lower load densities, but the Powley Computer assumes high load densities. Today, many reloaders of these will use a nearly full case of 4831, H4831, or Reloder 22; the A-Square manual covers this well. Some of these classic cartridges are in the provided list of cartridge dimensions. You'll find the Load Computer recommends for many of these a powder Quickness near 100, about that of 4350. Because their operating pressure is lower than 44,000 CUP and because 4350 should not be reduced too far, 4831 or 7828 would be the powder to choose instead, to keep the loading density high.
Ken Howell, author and friend of the late Homer Powley, often posts at a shooter's forum, and in early 2005 he wrote:
Homer Powley, Bob Forker, and Bob Hutton collaborated on the ballistics slide rules. Homer provided their math, Bob Forker arranged for their production, and Bob Hutton financed their production and owned the rights for them. Marian (Mrs. Homer) bought them from Hutton and sold them while Homer worked for the Army. ... Recent software—some of which includes refined later versions of Homer's math—makes them obsolete.
The software Load from a Disk is based on Powley's equations. The software QuickLOAD operates on quite different theoretical principles, and LoadTech appears to be strictly empirical.
Another interesting comment of Howell's on the same forum in late 2007 was in regard to the Pressure Computer calculations:
Homer Powley devised... a way to postulate average peak pressures from chronograph data... I'm not sure how practically useful it is. Homer wasn't sure, either.
A few image files are used as well, but having these is not essential. You can, of course, have your browser save a copy as a "complete" page.
As mentioned, I've compared Powley Computer outputs to values from various load books. I want to provide this information, but I'm still working on a clear presentation.
Before using these Computers to develop loads, you should compare their outputs to loads found in reputable reloading manuals. (Using the cartridge and bullet lists provided makes this somewhat easier.) Only by doing so can you get a feel for the accuracy of (and lack thereof) the Computers. I also urge you to use a chronograph, for it appears the computers are better at predicting velocities than charges. Strong guns with sterling reputations for gas handling, such as Remington 700 and Ruger No. 1 rifles, would be good choices for developing loads, for while generally reliable, both Computers can seriously underestimate pressure—a statement which applies to all software which attempts to predict the internal ballistics of small arms.
It might be useful to summarize in one place the known deficiencies of these Computers. In general, these problems span all calibers and can be categorized in terms of bullet SD and relative case capacity.
This Powley Computer tries to conform to W3C standards. Except where noted, it works in Firefox 3, Opera 9, Safari 4, Chrome 2, and IE 8, all tested under WinXP.
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."
04/2003 - 10/2007