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Thread: recoil math

  1. #1
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    Default recoil math

    I am one of those nerdy guys who enjoy the physics behind the smoke and powder and thought there might be one or two other blackpowder geeks who want to know how much damage they are doing to them self and the object at the recieving end of the process. Here goes:
    Recoil: Example #1
    (muzzle velocity X bullet Grain weight) plus (velocity charge constant X powder charge in grains) divide by constant of 225400 = A

    (A X gravitational constant) divided by gun weight in pounds= A1

    (A1 X A1 Xgun weight in pounds) divided by constant of 64.32= Foot lb recoil.

    Lets use a 30-06 since most of us have shot one and have a general idea of how the recoil feels.
    (2,700(muzzle velocity) X 180(bullet grain)) + (4700 (constant) X 55(grains poowder))= 744,500. divide by 225400(constant)= 3.3

    3.3 X 32.2(gravity constant)= 106.26.

    106.26 divided by weight of gun 8 lbs= 13.2

    13.2 X 13.2 X 8(gun weight)=1394

    1394 divided by 64.32(constant)= 21.6 foot pounds of recoil.

    example #2. A 50 caliber muzzlelaoder shooting 385 grain bullet, with 100 grains powder, a muzzle velocity of 1375, and a gun weight of 7.5 pounds.

    (1375 mv X 385 bullet) plus (4700 X 100 gr.powder)=999375
    999375 divided by 225400 Constant= 4.43
    4.43 X 32.2 grav C=142.76
    142.76 divided by 7.5 gun wt in lbs= 19.03
    19.03 X 19.03 x 7.5 gn wt= 2716.87
    2716.87 divided by 64.32 constant= 42.2 foot lbs recoil.

    Now for the recieving end regarding foot lb energy delivered by the projectile.
    Bullet velocity squared divide by 7000,Divide by 64.32 (constant) then multiply by bullet wt. in grains.
    Example: 385 grain bullet traveling 1000 fps at 100 yards.
    (1000 X 1000)=1000000.
    1000000 divided by 7000 (gr/lb).=142.8
    142.8 divided by 64.32 (constant) = 2.22
    2.22 X 385 (bullet weight)= 855 foot pound energy at 100 yards.

    Ain't math great!

  2. #2

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    I'm not sure I want to know the answer for my light 54 cal carbine, but here goes:

    Gun wt- 6 pounds
    Charge- 120 grains FF
    Bullet weight- 450 grains
    Velocity- 1450 fps.

    If I've done my math right, that turns up 78.235 foot pounds of recoil.

    Now I know why I can't hold on to the forend when I light that booger off. Sure handy to carry, though.

  3. #3
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    Default math

    Your math is correct.
    Now If you use a 5 pound soft velcrow ankle weight around the butt stock when you sight in at the bench your 6 lb rifle will now weigh 11 pounds. The cool thing about recoil physics is the recoil will not just be reduced by 5 pounds from 78 fpr to 73 fpr. In actuality when you run the numbers the recoil will be reduced from 78 fpr to 42 fpr. Nice thing to know for bench work.

  4. #4

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    The heck with the ankle weight! I use a 25# bag of shot on the bench.

    Shooting that load offhand doesn't hurt too bad, but you can't keep the forend in your hand unless you wrap your fingers up over the barrel.

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    HAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHAAAAAAAAAAAAAAAA AAAAA HHHHHHHHHHHHAAAAAAAAAAAAAAA

    " but you can't keep the forend in your hand unless you wrap your fingers up over the barrel."

    HOLY COW!! I've got to get one of those. I like the ankle weight idea. I will put that to good use for sure.
    Thanks, Joel

  6. #6

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    So that explains the scope cut I got the first time I shot my 50 cal. Omega with a 245 gr Spitfire and 150 gr. of 777. I learned very quickly to keep my cheek firmly planted on the stock and to pull down on the forend when it was in the shooting sticks. The Omega with 325 Spitfires and 100 gr. of 777 seems to recoil more than my 54 Hawken with a 425 Great Plains and 100 gr or 777. There's something to be said for heavier rifles and big bullets.

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    Quote Originally Posted by BrownBear View Post
    I'm not sure I want to know the answer for my light 54 cal carbine, but here goes:

    Gun wt- 6 pounds
    Charge- 120 grains FF
    Bullet weight- 450 grains
    Velocity- 1450 fps.

    If I've done my math right, that turns up 78.235 foot pounds of recoil.

    Now I know why I can't hold on to the forend when I light that booger off. Sure handy to carry, though.
    BB,
    Your math is right but the charge constant of 4700 fps isn't valid for black powder. So that saves the shoulder a little. It will vary from 1600-2200 fps depending on barrel length and bore diameter. (expansion ratio)
    Is there nothing so sacred on this earth that you aren't willing to kill or die for?



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    Brown bear, the last reply indicates that the 4700 constant should be replaced ith 1600-2200. now lets do the math.
    We will use take 2000 as our new consant and apply it to the short barreled moster you stuff with a 120 grain charge and a 450 grain lead rock. Using this new addition to the existing formulae we arrive at 41 pounds of recoil. My 12 year old daugter wouldn't be happy touching this off, but I would bet the front end wouldn't get away from her.(maybe I should order her a 54 caliber 21 inch carbine.) Apply the 2000 constant to a standard 90 grain charge for a 50 caliber muzzleloader shooting a 177 grain round ball out of an 8 pound rifle, you now have 10 pounds of recoil. Crunch the numbers for a .243 kids deer rifle and you get a little bit more recoil than 10 pounds. I guess it may be apples and orages, but based on the black eyes and shoulder bruises I have personally enjoyed durring my personal research, I have concluded that a constant of 4700 is in actuality more representative of the impacts of modern rifles (without muzzle breaks) as well as the retinal jarring impacts of real rifles which are loaded from the muzzle. Just my personal opinion.
    As I am currently on a roll,if anyone would like to know
    why I prefer a 54 caliber round ball rifle and a 45 caliber 1-20 twist volenteer rifle for maxi balls over the standard 50 caliber please reply and lets let the debate commence.

  9. #9

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    Interesting change in the results with the change in constants, but it doesn't bear up in the "felt recoil" department. I'm well acquainted with the differences that can occur between calculated and felt recoil due to stock configuration, sight layout etc, but that light 54 is making me ponder it all. I've shot lots of large caliber CF's including some 500's. Those weren't as bad as the Ruger #1 a friend had rechambered to 460 Wby, by any means. He left the 460 with me for two years of load development and general horseplay. Gotta say that it was the worst kicker I've ever shot, but the 54 is very close behind it. A calculated 41 fp of recoil doesn't even come close to the sensation of shooting it.

    BTW- Running the #'s for my friend's 460 using Ruger's posted weight for the orginal Tropical 458 (8.5 pounds) and launching a 500 grain Hornady on top of 120 grains of IMR-4350 for 2600 chrono'ed fps, you get a spanking 129.7 foot pounds of recoil.

    Guess that goes to show the true nature of "felt" recoil versus statistical recoil.

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    brown bear take me to bed or loose me foreever.
    just kidding.
    Back eyes and bruised shoullders gotta love the math. I admit that the 1600-2200 is correct. However you know as well as I that when the barrel travels upawards and away, the force of 2000 is probalbly closer to 4700 fpr as determined for standard recoil. Lets put one of those .458 lion hunters on the end of the carbine you shoot and see if he can hold the barrel stable without wrapping his hand over the top..
    mmiler5.

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    Does this only apply to muzzleloaders? Would the constants be somewhat different with a centerfire or is the equation the same?
    Life's journey is not to arrive at the grave safely in a well preserved body but rather to skid in sideways, totally worn out, shouting "HOLY **** WHAT A RIDE!!!"

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    This is my fromula for recoil, it seems easier for me to calculate with this one. The powder velocity constant was given to me several years ago by an engineer at H.P. White. he said it would vary (with smokelss powder) at 1.4-1.7 * muzzle velocity. With black powder, I turned up somewhere a number of 1.2-1.5 * muzzle velocity. I have no way to measure this but have seen the constant expressed in several books from 4400-5200 fps for modern smokeless cartridges. It does make sense that it follow bullet muzzle velocity in some manner. Or another way to look at it would be consider peak chamber pressure and the rate of decay of the pressure curve. If exit pressure is lower, exit velocity would also be lower. Black powder pressure peaks are around 20-24 kpsi, right?

    I am curious and still learning about how this effect applies to BP shooting.



    Recoil is calculated in three aspects.

    Recoil Impulse (RI), Recoil velocity (RV) and Recoil Energy (RE. For best results, in that order.


    RI=(Bw*Bv) + (Pw*4400)/225190 = lbs/sec

    RV=RI*32.17/Gw = ft/sec

    RE=Gw*RV(squared)/64.34 = ft lbs

    Bw=Bullet weight in grains.
    Bv= Bullet velocity in ft/sec.
    Pw=Powder weight in grains
    Gw=Gun weight in pounds

    4400 is the constant which represents the exit velocity of the powder gasses. (a major part of recoil, I call it the Bill Lear effect)

    225190 is the acceleration of gravity (g) 32.17 ft/sec*7000(the number of grains in a pound) This constant gets it back to common units.

    g=32.17 ft/sec

    g2=64.34 ft/sec

    This will provide a close approximation of recoil. We are generally interested in Recoil Energy and Recoil velocity.
    Last edited by Murphy; 10-05-2009 at 14:10.
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    Quote Originally Posted by mmiller5 View Post
    INow for the recieving end regarding foot lb energy delivered by the projectile.

    Bullet velocity squared divide by 7000,Divide by 64.32 (constant) then multiply by bullet wt. in grains.
    Example: 385 grain bullet traveling 1000 fps at 100 yards.
    (1000 X 1000)=1000000.
    1000000 divided by 7000 (gr/lb).=142.8
    142.8 divided by 64.32 (constant) = 2.22
    2.22 X 385 (bullet weight)= 855 foot pound energy at 100 yards.

    Ain't math great!
    This is correct but seems like a long way around the barn.

    energy = m/2*V*V

    Half the mass times velocity squared. Mass is the weight in pounds divided by the gravitational constant 32.17. 385/7000/32.17/2*v*v=854.83.

    Is this easier or just my twisted view?
    Last edited by Murphy; 07-18-2007 at 00:15.
    Is there nothing so sacred on this earth that you aren't willing to kill or die for?



  14. #14

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    My old Lyman BP manual lists a max of 15 k for pre-inline sidelocks and such, but that's LUP rather than CUP. I don't recall the conversion, or if there is one. Pressures for inlines with the various synthetic black powder substitutes are quite a bit higher as I recall, but my references aren't close at hand.

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    Default recoil math

    It is interesting reading guys, but one reason traditional muzzleloaders seem to kick worse than equivalent modern rifles is the buttplate. Put a narrow crescent brass or steel buttplate on that 243 and the perceived recoil will increase dramaticaly,especially if you shoot it off your shoulder and not your upper bicep. I like to put a good broad ,flat plate on my heavy kickers, .58 and up, and with a good stock fit felt recoil seems less than the equivalent mathamatical recoil of centerfire rifles, even though most centerfires have a rubber recoil pad. Anyways my point is stock design contributes mightily to perceived recoil but can't be taken into account with mathamatical models. Kyle

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