A Little Math Problem

[Duce]

I hunt deer with a 1894 Marlin in .44 Magnum. I use Winchester white box 240 gr. JSP. The advertized velocity from a 7" barrel is 1180 FPS. My Marlin has a 20" barrel. I did some math to come up with a ball park velocity, out of a 20" barrel. I figured if the Marlin barrel is considered 100%, 7" is 35% of 20", making the rifle barrel 65% longer. Would it be correct to assume taking 65% of 1180, then adding it too 1180, give me a ballpark figure for the velocity increase?.............<><Duce

 

[ryan3030]

I don't think velocity increases linearly, as you assumed when you began calculating a % increase based on barrel length. Rather, it increases on a curve that is determined by a few factors: barrel length, projectile weight, and powder type. (There are probably other smaller factors but we won't go into those)

Let's take this ammo, for example: Hornady Manufacturing Company :: Ammunition :: Handgun :: Choose by Caliber :: 44 Mag :: 44 Mag 225 gr FTX® LEVERevolution®

7.5" bbl: 1,410 f/s
20" bbl: 1,870 f/s

Again taking your example, 7.5 is 37.5% of 20. A 37.5% increase in velocity from 1,410 f/s would be roughly 1,938 f/s, not 1,870 f/s. It seems that this particular load, with your method, would indeed give you a rough ballpark of velocity increase, but I wouldn't rely on it to be very accurate.

The amount of increase you get in velocity will vary from powder to powder, as some burn faster and others burn slower.

Disclaimer: This post is entirely uneducated speculation on my part.

 

[HoughMade]

There are too many variables to use simple math to figure this out. If a powder is designed to fully burn in a 7" to 8" barrel, comparatively little velocity will be gained with a much longer barrel. Conversely, if the load is spitting unburned powder out of a shorter barrel, a proportionately larger velocity increase could be realized. So- you have to ask- what was the powder used, how fast does it burn and what barrel was it designed to fully burn in?

I'm afraid it would be a lot easier to find a buddy with a chrono.

 

[PGRChaplain]

And how much drag is introduced in the extra 12" of rifled barrel. Like Hough ^ stated friend with a Chrono.

 

[ol' poke]

Math makes my head hurt.

Andrew at Profire Ammo will rent you a chronograph.

ol' poke.

 

[JettaKnight]

Another way of thinking about your proposed equation is that given a long enough barrel*, it would be possible to make the bullet go faster than the speed of light!




* By my calculations, almost 2 miles.

EDIT:
I found this little gem:
http://www.ballisticsbytheinch.com/44mag.html
It basically shows that at about 10" (barrel) the velocity increase drops off to the point where velocity starts to decrease.

 

[youngda9]

2 miles long...OC or CC ?

 

[GoBoilers!]

I love math, but I don't have a definite answer for you. The bullet speed in relation to barrel lenght is definitly not a linear relationship, though, so your original calculations won't work.

I recall reading an article a few years ago that logged bullet speed out of barrels of different lengths (using same load) and I recall the speed reached max somewhere around the 20 to 24 inch length, if I recall correctly. Beyond that, friction actually started to slow if down.

Okay, I actually just went to my book shelf (old fashioned, I know...) and found the article. It was in the "NRA Firearms Fact Book (Third Edition)" They tested a .22 caliber, and the velocity peaked in the 18" barrel. It was about 40 fps slower in a 27 inch barrel.

They did say it will vary with load, and using faster powders will reach maximum speed in a shorter distance. So the answer.... It depends. You might be able to find some examples where similar tests were done on ammo, or as was suggested, use a chrono and test it yourself.