The Relative Burning Speed of Smokeless Powders

By Roberto Serino


Unfortunately, reloaders can't do without some mathematics, but if you have understood the specific impulse concept, you are ready to get more. The Du Pont Index is a very useful figure in order to choose the right powder. It's seven times the Relative Quickness, or seven hundred times the ratio between the Energy Potential (ft.lbs/gr) and the Specific Impulse (lbs/sq.in*fps):

DPI = 7*RQ = 700*EP/SI

As a matter of fact, it is not exclusively connected to Du Pont powders, but it can apply to other powders, too. In this way it can be even more useful, a true comparison being possible, whereas manufacturers throughout the world still use their own indexes.

Concerning Du Pont powders, IMR 4350 is rated at 100; 3031 is rated at 135, while 4831 is rated at 95. 4198 is rated at 160; between 3031 and 4350, you can find 4064 rated at 120, 4895 rated at 115 and 4320 rated at 110. Finally, at the extremes, 4227 is rated at 180 and is the fastest rifle powder and the slowest pistol powder at the same time, while 7828, rated at 84, is the slowest rifle powder.

Now let's have a look at the IMR Handloader's Guide, listing data about the .30-06 cartridge loading, with reference to the standard 4350 powder, and to the heaviest bullet (220 gr.), so that the propellant could be thought of spreading its full specific impulse:

 

30-06 Cartridge Load Data

Starting Loads

Maximum Loads

Bullet Weight (gr.)

Bullet Dia.

C.O.L.

Powder

grs.

Vel. (fps)

Pressure

grs.

Vel. (fps)

Pressure

220 GR. HDY JRN

.308"

3.230"

IMR 7828

53.0

2288

48,600 PSI

58.0

2476

59,700 PSI

220 GR. HDY JRN

.308"

3.230"

IMR 4831

50.0

2275

47,300 PSI

54.0

2438

57,200 PSI

220 GR. HDY JRN

.308"

3.230"

IMR 4350

49.0

2287

49,500 PSI

52.5

2425

57,300 PSI

220 GR. HDY JRN

.308"

3.230"

IMR 4064

43.0

2241

52,200 PSI

45.5

2325

56,700 PSI

First of all let's calculate the Sectional Density (lbs/sq.in) of the bullet; in this case the Bullet Weight (gr.) will be divided by the actual cross section area, not the simple squared Diameter (in):-

SD = (4/p)*(BW/7000)/D2 = 1.27*(220/7000)/(.308)2 = .422 lbs/sq.in

The specific impulse being unknown, it only can be estimated by the maximum load velocity. In this case it can be supposed the load has been completely burnt when the bullet leaves the muzzle of a barrel 22" long.

The burnt gases momentum and the friction along the bore must be taken into account, too, because burnt gases propel themselves as well as the bullet, and the friction acts against the bullet motion.

So let's multiply Sectional Density by Muzzle Velocity developed at the maximum load conditions; then increase the result with half the ratio between Powder Weight and Bullet Weight, and with a Friction Coefficient (which can be extimated about .2 for rifled bores, according to Hatcher's Notebook):

SI = (1 + FC + PW/BW/2)*SD*MV = (1 + .2 + 52.5/220/2)*.422*2425 = 1350 lbs/sq.in*fps

The meaning is: if you want to drive a bullet having a sectional density of .422 lbs/sq.in, at 2425 fps, in a barrel 22" long, the powder burning behind it must provide a specific impulse of 1350 lbs/sq.in*fps at least.

Physically, IMR 4350 is a single-base, extruded, tubular propellant (as are most Du Pont IMR powders). Its particles are made of colloided nitrocellulose, coated with DNT to retard burning, and heavily graphited to flow better through powder measures.

Its Energy Potential is about 1,246,000 ft*lbs/lb, or 178 ft*lbs/gr (according to the NRA Firearms Fact Book), so that Relative Quickness and Du Pont Index can be calculated:

RQ = 100*EP/SI = 100*178/1350 = 13.2 (extimated) DPI = 7*RQ = 92.3 (extimated)

This result is less than 100, due to the fact that probably the actual Specific Impulse is a bit smaller than 1350, or the actual Energy Potential is a bit greater than 178. Nevertheless, as you can see, it's very close to the IMR 4350 standard rating.

All of the powders in IMR family have approximatively the same Energy Potential, so their Specific Impulse can be derived simply dividing this figure by their Du Pont Index, and then multiplying the result by 700:

SI = 700*EP/DPI

Subsequently the above formula yields to the following estimated value for the specific impulse, from fastest to slowest (SI estimated):

Powder.....DPI....RQ....SI (est.)

IMR4227...180...25.7...692

IMR 4198...160...22.9...779

IMR 3031...135...19.3...923

IMR 4064...120...17.1...1038

IMR 4895...115...16.4...1083

IMR 4320...110...15.7...1133

IMR 4350...100...14.3...1246

IMR 4831...95...13.6...1312

IMR 7828...84...12.0...1483

Alliant Powders (formerly Hercules Powders) are double-base, extruded propellants, with nitroglycerin ranging from 4% to 40%. Some of rifle powders are coated with DBP to retard burning. Alliant own index is just Relative Quickness as defined above, rating as follows from fastest to slowest:

Powder.......DPI...RQ

2400............189...27.0

Reloder 7....136...19.4

Reldr 10X...118...16.9

Reloder 15...96...13.7

Reloder 19...79...11.3

Reloder 22...78...11.1

Reloder 25...74...10.5

According to the tables above, IMR and ALLIANT rifle powders can be located as follows:

Powder.......DPI...RQ

2400............189...27.0

IMR 4227....180...25.7

IMR 4198....160...22.9

Reloder 7....136...19.4

IMR 3031....135...19.3

IMR 4064....120...17.1

Reldr 10X...118...16.9

IMR 4895....115...16.4

IMR 4320....110...15.7

IMR 4350....100...14.3

Reloder 15...96...13.7

IMR 4831.....95...13.6

IMR 7828.....84...12.0

Reloder 19...79...11.3

Reloder 22...78...11.1

Reloder 25...74...10.5

The matter seems quite simple, but unfortunately DPI and RQ are not the only tips for choosing the right powder, because bulk density, specific gravity and case capacity play a role as well as bullet sectional density and expected muzzle velocity (in a word, the specific impulse).

So various Burn Rate Charts display powders in a somewhat different order, taking into account the bulk density of powders, their specific gravity and the average case capacity of peculiar cartridge loading.

This happens especially to powders showing very close value of RQ, like IMR 4064, 4895 and 4320, or Reloder 15 and IMR 4831, or IMR 7828, Reloder 19, Reloder 22 and Reloder 25, or Unique, Herco, PB and SR 7625.

Just for comparison, find here DPI and RQ of pistol and shotgun powders by IMR and Alliant:

Powder.......DPI...RQ

Bullseye.......700...100

Red Dot.......659...94.1

700X............635...90.7

Green Dot....545...77.9

Unique.........431...61.6

Herco...........393...56.1

PB................390...55.7

SR7625.......340...48.6

SR4756.......305...43.6

Blue Dot......265...37.8

SR4759.......210...30.0

WARNING! NEVER determine a load from this, or any burn rate chart. Employ only the newest published data for the specific powder you intend to use.




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Copyright 2006 by Roberto Serino. All rights reserved.


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