Shooting Math.....

Calibres, cartridges, ballistics tables and ammunition information.

Re: Shooting Math.....

Post by Baronvonrort » 28 Sep 2014, 12:28 pm

Yes please do recoil in various calibers and projectiles for those calibers.
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Re: Shooting Math.....

Post by 1290 » 29 Sep 2014, 10:39 am

Baronvonrort wrote:Yes please do recoil in various calibers and projectiles for those calibers.


Like this?

Image

These are ADI loads, except the rimfire which is Winchester....rifle mass are all the same to allow direct comparison of recoil, even the Browning (most likely would be 3 or 4 times that mass in reality) In a 30 pound rifle the Browning free recoil would be about 160J(120Ftlbf)...

I will later post a description of the workings for recoil and recoil velocity....
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Re: Shooting Math.....

Post by loopal » 29 Sep 2014, 11:25 am

1290 wrote:#if you don't like numbers units and calculations, turn away now#


Backing away slowly... :lol:
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Re: Shooting Math.....

Post by cavok » 29 Sep 2014, 1:17 pm

Great topic, and we also when shooting calculate and factor in the Coriolis Effect, So much to remember, no longer able to just load and shoot. Back to the drawing board. Lol. Need to me inserted a smiley face.
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Re: Shooting Math.....

Post by Baronvonrort » 29 Sep 2014, 1:53 pm

Nah not like that 1290, we want to see you do the maths....lol
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Re: Shooting Math.....

Post by 1290 » 29 Sep 2014, 2:10 pm

Baronvonrort wrote:Nah not like that 1290, we want to see you do the maths....lol


What, like a youtube video or just text of the workings :D
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Re: Shooting Math.....

Post by Baronvonrort » 29 Sep 2014, 3:15 pm

1290 wrote:
Baronvonrort wrote:Nah not like that 1290, we want to see you do the maths....lol


What, like a youtube video or just text of the workings :D


We have to see the texts showing how you worked it out...lol.

It's all cool, that pic gave all the info, someone else has done all the hard work.

The ballistics calculators have taken the work out of projectile motion, life is much easier these days.
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Re: Shooting Math.....

Post by RealNick » 30 Sep 2014, 10:57 am

JBM ballistics is a life saver :D
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Re: Shooting Math.....

Post by 1290 » 01 Oct 2014, 11:08 am

OK, here's the behind the numbers part,

Recoil energy

The recoil energy is referred to as the 'free' recoil and is the opposite reaction to the discharge of the firearm, it is not dependent on the shape of the stock, the way you hold it... its the absolute energy you will 'feel' when you discharge the firearm neglecting all other countering actions such as friction... so if the rifle is on roller bearings you would feel the whole of this effect.

The energy is derived from the projectile as well as the burning propellant, which is assigned a fixed velocity of 1585m/s representing the deflagration velocity, which is the velocity of the flame front or shockwave of the burning powder.

E(J) = [ (mp.vp + mc.vc) / 1000 ]2 / 2mr

Mass projectile (g) x Velocity (m/s) + Mass powder (g) x Velocity powder (m/s)

divide answer by 1000 (to convert to kg, SI units!)

Square answer (multiply by itself)

Divide answer by 2

Divide answer by rifle mass (kg)

There you will have it, free recoil energy in Joule (J)!

Example;

Projectile mass: 19.44g (300gr)
Projectile velocity: 914.4m/s (3000fps)
Propellant mass: 6.48g (100gr)
Propellant velocity: 1585m/s (5200fps)
Rifle Mass 4.08kg (9lb)

Do the math;

( 19.44 g x 914.4 m/s ) + ( 6.48 g x 1585 m/s ) = 28047

28047 / 1000 = 28.047

28.047 squared = 786.62

786.62 / 2 = 393.31

393.31/4.08 = 96.4

Free recoil energy = 96.4 J for the above example.


Now, many aficionados will be having conniptions about now due to the lack of feet and pounds, so;

IMPERIAL UNITS (foot-pound-force)

Imperially speaking, the calculation is similar to the above, the only differences are the 5200fps charge velocity and the use of the gravitational constant not required with the metric method; 32.174. The unit is a force.

We (Americanized shooters) prefer to input grain units, so pound conversion has to be considered along with the grav constant as well as the 2 divisor so we can clump those constants together to get the following simplest form;

F(ftlb.f) = ( mp.vp + mc.vc )2 / ( mr x 7000 x 2 x G )

[ Mass projectile (gr) x Velocity (fps) + Mass powder (gr) x Velocity powder (fps) ] squared

All divided by

[Rifle mass (lb) x 7000(grains per pound)squared x 2 x 32.174 (grav const.)]

divisor simplified to;
[Rifle mass (lb) x 7000(squared) x 64.348]

inserting the values from the previous example;

(300x3000 + 100x5200 ) / (9 x 7000x7000x64.348)
= 71.1ftlbf

There you will have it, free recoil force in the old units....!

((I'm sure someone will let me know if there are any errors up there^^))
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Re: Shooting Math.....

Post by riggee » 01 Oct 2014, 1:45 pm

I'm sure everyone appreciates the effort... Who's gunna double check all that though :lol:

Maybe it's just me and my little brain. Best firearm I could come up with is probably a slingshot :D
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