Powder measure equation

[Canute Rex]

I was just looking around in the back 40 on my computer and came across this. I had taken measurements from some powder measures I had when I wanted to make my own out of antler. I think I also looked up some volumetric numbers somewhere. Anyway, I worked out this nifty equation for designing your own powder measure.

Capacity in grains = (Pipe_ID/2)^2 * pi * Pipe_Length * 248.

where:
Pipe_ID is inside diameter of pipe (or cavity) in inches.
pi = 3.14159...
Pipe_Length is unobstructed length inside pipe (or cavity) in inches.

So what I'm really saying here is that the throw in grains is equal to the internal volume of the measure in cubic inches multiplied by 248. Or 248 grains per cubic inch.



You can also start with the capacity desired and ID of cavity and determine the length necessary by rearranging things.  

Pipe_Length = Capacity_in_Grains/((Pipe_ID/2)^2 * pi * 248)

Just as an example, let's say you want a half inch hole in the material (antler or whatever) and you want a 100 grain powder measure. How deep do you drill?

Length = 100 divided by (0.5"/2) squared times 3.14159 times 248

That's 100 divided by 48.69, or 2.054 inches. I'd say 2" would be close enough.

What if you wanted a 100 grain measure with a 3/8" hole? 100/(.375/2) squared * pi * 248 = 3.65" deep

Check this out on your own commercial powder measures and tell me if I have missed the boat on this one.

Now I just looked around the intertubes again and found numbers for grains per cubic inch from 230 to 248. It varies with granulation, finer being denser. But really, if you run the equation again for a 1/2" measure with 230 you get 2.21". a bit over an eighth-inch difference from 248. If you were to pick a number around 239 you'd never be more than a sixteenth off (3.6 grains in a half inch tube), and how many of us can get the powder level within a sixteenth?

[Canute Rex]

Here's a chart using 239 grains per cubic inch:

   Length of cylinder in inches   
Grains   5/16" Dia.   3/8" Dia.7/16" Dia.1/2" Dia.
10            0.55    0.38             0.28   0.21
15            0.82    0.57             0.42   0.32
20            1.09    0.76             0.56   0.43
25            1.36    0.95             0.70   0.53
30            1.64    1.14             0.83   0.64
35            1.91    1.33             0.97   0.75
40            2.18    1.52             1.11   0.85
45            2.45    1.71             1.25   0.96
50            2.73    1.89             1.39   1.07
55            3.00   2.08              1.53   1.17
60            3.27   2.27              1.67   1.28
65            3.55   2.46              1.81   1.39
70            3.82   2.65              1.95   1.49
75            4.09   2.84              2.09   1.60
80            4.36   3.03              2.23   1.70
85            4.64   3.22              2.37   1.81
90            4.91   3.41              2.50   1.92
95            5.18   3.60              2.64   2.02
100           5.46   3.79             2.78   2.13
105                    3.98             2.92   2.24
110                    4.17             3.06   2.34
115                    4.36             3.20   2.45
120                    4.55             3.34   2.56
125                    4.74             3.48   2.66
130                    4.93             3.62   2.77
135                    5.12             3.76   2.88
140                    5.31             3.90   2.98
145                                       4.04   3.09
150                                       4.17   3.20
155                                       4.31   3.30
160                                       4.45   3.41
165                                       4.59   3.52
170                                       4.73   3.62
175                                       4.87   3.73
180                                       5.01   3.84
185                                       5.15   3.94
190                                       5.29   4.05
195                                                4.16
200                                                4.26

[bgf]

I think I may be the guilty party for the formula:
http://americanlongrifles.org/forum/index.php?topic=10693.0

Not a lot of enthusiasm for the formula back then, but it is useful to me.  I still use that powder measure for woodswalks, no pride at all, I reckon .

[Canute Rex]

Well, BGF, if it makes the ball hit the target, no shame at all.

Actually, I don't think I got the 248 from that thread. If I had known such a thing had already been posted I wouldn't have posted it again. I think I put the calipers to a couple of commercial measures I have and derived the same number.

But really, I don't think the exact number of grains (accuracy) matters as much as getting the same number of grains each time (precision). You could make up a measure with no idea of grains at all and adjust it till your rifle shoots consistently good groups. That's probably what most gun makers and shooters did back in the day.

[bgf]

CR,
I was actually excited thinking someone had made use of it.  Whatever gr/in^3 number I used was as close as I could find, but probably also had a safety factor built in.  I don't think I had time to do much experimentation, so your 239 number based on experiment is good also, I expect, for whatever powder you were using, so you added something on your own.  As you say, it is good for getting close to the volume you need, and people are more likely to use a "spreadsheet" than a formula!  I think I also have a spreadsheet somewhere that I made up to figure out the minimum powder charge in my .40's "patent" breech, to see how much I should drill out the hole without requiring a huge "minimum" charge to seat the ball properly.

[cmac]

Not sure I understand?? Why not just check the measure by dumping the charge into an adjustable to find out the charge of the fixed measure, and adjust from there?

[Canute Rex]

Cmac: It's not for checking an existing measure as much as it's for designing a new one. For example, if you want to make an antler measure you can use the chart to pick out a piece the right diameter and length. It will also save time - you'll know exactly how deep to drill with what size bit, rather than using trial and error.

[T.C.Albert]

True, you can accurately drill a hole of predetermined diameter to a specific depth in an antler tip and it will measure the charge you want. So I hate to even go here, but most of the old time antler measures I've seen don't look simply "drilled", but rather have been carefully uniformly hollowed out tapering down to towards the tip. I wonder how those were made too.
tca

[bgf]

True, you can accurately drill a hole of predetermined diameter to a specific depth in an antler tip and it will measure the charge you want. So I hate to even go here, but most of the old time antler measures I've seen don't look simply "drilled", but rather have been carefully uniformly hollowed out tapering down to towards the tip. I wonder how those were made too.
tca

Uniform enough to be a tapered reamer?  I suppose it would be easy enough to make one for antler, or use on on hand for something else.  Interesting point, though, that we aren't always getting the same results as the old-timers because we aren't using the same tools. 

[Habu]

So I hate to even go here, but most of the old time antler measures I've seen don't look simply "drilled", but rather have been carefully uniformly hollowed out tapering down to towards the tip. I wonder how those were made too.

That's because most of the old ones weren't drilled, or at least not left as drilled.  I've got notes on over 500 originals, and less than 3% were drilled and left that way. 

Years ago, I picked up an antler measure like that with the intent of destroying it to see how it was made.  A quick trip to Mr. Bandsaw to rip it down the middle, and I could see the tool marks inside.  About 30 minutes later I had my own "uniformly hollowed out tapering down to towards the tip" antler powder measure (and most of that time was spent finding a good piece of antler). 

Cut the antler to length, bore a hole in it the approximate length you want, and dunk the antler in boiling water for a few minutes.  Then you just sort of scrape the "stuff" out with a long thin knife blade (yet another reason I prefer a "California" or "Turkish" clip blade on my pocket knife).  This results in the same appearance and tool marks as I found on the undated original I destroyed, and on may others since then. 

A couple of caveats: 1) It works better on fresher antler; with older antler, sometimes by the time the internal "stuff" is softened, the outside will absorb enough water that it will crack.  2) Try to hold it in the water so that the hole you bored is on top, and the antler is fully submerged; this seems to soften it up a bit more quickly.  3) Hollow it out before carving/shaping/etc the outside. 

If you start running into stuff that isn't softened, just dunk it again. 

Using fresh antler, I've never had one crack.   Using "sheds" gathered in the spring, I typically get 1-2 cracking and unusable for every 10 I make.

[pathfinder]

I haven't "wetted" any I've made,and there are a lot,and the only time I had any crack,was when I rushed the drilling.

I get the gun grouped in using an adjustable measure that that throw's close to the weight indicated on the plunger,then make a fixed charger. This chart will be taped on the wall by my tap and drill chart. Might help. but

I do have to agree with an earlier post,you CAN over complicate thing's. But,on the other hand, people in this hobby have a tendency to be either extremely analytical,or use the "bubba" methods!

[Shootrj2003]

 I look very carefully at the measure ,eyeball the material for thickness and stress capability,select a drill bit based on the results of a careful comparison of the three,and then drill it to a depth, also juggling the three values,and go to "jest short of the right depth"then try it out using a load from the adj. measure,if it's not enough I go "a bit mo' "if it's "too fer" fill it with beeswax or epoxy. Or,just hit her close but,in the end ,I mark  the actual measurement in grains with ink and clear coat it.soundds complicated but It takes about 10 -20 minutes with a cordless.