## Examples to Try

224 Valkyrie MSR: 6.5 lbs, 90 gr bullet, 29
gr powder, 2828 fps, 0% muzzle brake

6.5 Creedmoor AR10 Rifle: 7.5 lbs, 147 gr bullet, 41 gr powder, 2650 fps, 0%
muzzle brake

Barret Model 82A1
50BMG Rifle: 32.7 lbs, 655 gr bullet, 248 gr powder, 3029 fps,
90% muzzle brake

US Army M4 5.56 Rifle & M193 ball ammo: 6.5 lbs, 56gr bullet, 27.5 gr
powder, 3250 fps, 10% muzzle brake (flash hider)

22LR rifle: 6 lbs, 40 gr bullet, 2.5 gr powder, 1185 fps (0% muzzle
brake)

S&W Model 340 PD Airlight 357 Mag revolver: 0.74 lb, 158 gr bullet, 13 gr powder,
1115 fps ,0% muzzle brake

S&W Model 686 Plus 357 Mag revolver: 2.3 lbs, 158 2gr bullet, 13 gr powder,
1115 fps (same load as the Airlight above)

S&W Model 500 8 inch 50S&W revolver: 4.46 lbs, 700 gr bullet, 27.5 gr powder,
1300 fps, 40% muzzle brake

Same S&W 500 with 275 gr bullet
with 40 gr powder, 1804 fps

308 Win is the default gun, just refresh your browser to load the
.308 rifle numbers

When I began researching
recoil I was surprised to find most of the mathematical theory was from the
early 1900's. The formulas from these early texts are still in
common use today but they do not jive with current muzzle brake research.
Classic recoil
formulas greatly underestimate the recoil generated by the exit
gas from the muzzle or the "jet effect".
Like uncorking Champaign, when a bullet clears the muzzle, gas
accelerates and shoots past the bullet. This acceleration of gas out of
the muzzle is called the "jet effect" and accounts for approximately 30
to 55% of total recoil energy.

PrecisionRifleBlog.com did an excellent series of articles on muzzle brake
effectiveness. The graphs below from these articles show how much force is
generated by the jet effect.

*The top blue
graph line is recoil force without a
muzzle brake. ***Notice how recoil levels off at 420 pounds when the bullet
exits the muzzle. After bullet exit the
force jumps to 655 pounds as exit gas blows out of the muzzle**. This shows
that for the 6XC cartridge in this gun, approximately 36% of recoil force is from the exit gas jet effect [(655-420) / 655 = .36]. A
muzzle brake's additional weight will also reduce recoil force, that's
why the graph shows these muzzle brakes reduce recoil while the bullet is still in
the barrel. This chart is from the
PrecisionRifleBlog.com muzzle brake test article with annotations added by
me.

*All recoil reduction that occurs while the bullet is still
in the barrel is due solely to the added weight of the muzzle brake.*

*The reduction in recoil highlighted in magenta above is due to a
combination of the muzzle brake weight and muzzle brake exit gas redirection.*

#### The best performing muzzle brake in the graph above, the Alamo
Four Star, reduces peak force by 305 lbs but 180 lbs of that is due to it's
additional weight. That's right, 60% of its recoil energy reduction is simply
due to adding the muzzle brake's weight to the rifle!

*Arms and Explosives*
(1909) used a constant velocity of 3200 feet per
second for gas muzzle exit velocity (*Arms and Explosives* page 20). I
believe this "constant" is wholly antiquated when used with today's high
efficiency smokeless gun powder. Instead of using a constant I have found a more
accurate estimate of muzzle gas velocity is bullet muzzle velocity * 2.4. Adding
this to the classic formula brings calculated recoil much closer to modern
recoil measurements and muzzle brake tests. I use 2.4 because it
matches up to muzzle brake
research and super slow motion film shows gas shooting past the bullet exiting
the muzzle at over 2.4 times the velocity of the bullet.

## Super Slow Motion Bullet Muzzle Exit

*Note how much faster the gasses exiting the muzzle are
compared to the bullet. I was surprised by how much gas gets around the bullet
and exits before the bullet.*

**Gun recoil momentum and energy are generated in three ways:**

**1. The acceleration
of the bullet in the barrel**.

Bullet Momentum is equal to: Bullet Weight *
Muzzle Velocity

Bullet energy is equal to: Bullet Weight *
Muzzle Velocity squared / 2g [g
is the acceleration of gravity feet-per-second per-second and is equal to
32.17405 fps]

An equal and opposite reaction to the bullet's acceleration is transferred to
the gun.

**2. The acceleration
of the powder burn gasses inside the barrel**.

Gas Momentum is equal to: Powder Weight *
Muzzle Velocity
/ 2

An equal and opposite reaction to the gas's acceleration is transferred to the
gun.

We use the powder weight because the gas created when the powder burns is equal
to the powder weight.

We divide the muzzle velocity by 2
because as the bullet moves from breech to muzzle, the powder's center of gravity only
moves from the breech to the center of the barrel.

** 3. The "jet
effect" of the powder burn gasses exiting the muzzle.**

Jet Effect Momentum is equal to: Powder
Weight * Gas Exit Velocity

When a muzzle brake is used Jet Effect Momentum = Powder Weight * Gas Exit
Velocity * (1 – Muzzle Brake Efficiency)^(1/e^.5)

Gas exit velocity is estimated at: 2.4 * bullet muzzle velocity

An equal and opposite reaction to the jet effect is transferred to the gun.

When a bullet clears the muzzle gas
accelerates and shoots past the bullet. This force is the only thing a muzzle brake can act against.
A brake's
additional weight will also reduce recoil energy (but the additional weight does
not affect gun recoil *momentum*).

##
My Jet Effect Momentum Formula

*GasExitVelocity = MuzzleVelocity * 2.4*

**The momentum of the bullet + gas acceleration + jet effect is
equal to the gun's recoil momentum.**

*Also*

##

## Gun Recoil Impulse Formula

*g = acceleration of gravity feet-per-second per-second = 32.17405*

##
Gun Recoil Velocity Formulas

*Gas Exit Velocity = Muzzle Velocity * 2.4*

## Gun Recoil Energy Formula

*g = acceleration of gravity feet-per-second per-second = 32.17405*

The above equations assume all powder is burned inside the barrel. A slow burning powder that
doesn't completely burn inside the barrel can greatly
reduce bullet velocity and recoil from short barreled rifles and pistols because
unburned powder imparts no energy to the bullet and has no jet effect. I use
QuickLOAD, an internal ballistics program, to select
powders that will burn completely in a given barrel length.

## Gun Recoil Calculation Spreadsheet

*A light 6.2 pound 308 rifle firing a 168 grain bullet at
2700 fps generates 33.23 foot-pounds of recoil energy. Download the ***
Gun Recoil Calculation
Spreadsheet.**

## Recoil Basics

All other things being equal, **a lighter gun will have more recoil velocity
and more recoil
energy**. The Smith & Wesson Model 340 PD 357 Mag revolver with a 2 inch
barrel and made of Scandium and Titanium is extremely light at 0.74 lb. It kicks
like a mule when firing heavy 357 Mag bullets. Plug in these numbers in the
recoil calculator above: 158 gr bullet, 13 gr of powder, 0.74 lb gun weight and
1115 fps (this velocity was measured from a 2" barrel), use 0% for
muzzle brake since it doesn't have one. **That gives us a very stout 20.5 ft-lbs of recoil energy from this "Airlight" pistol. Fire the same
exact load from the S&W Model 686 Plus which weighs 2.3 lbs and the recoil
energy drops to a very manageable 6.6 ft-lbs, a 67% reduction in recoil energy
due solely to the extra pistol weight!**

**S&W's 357 Magnum Airlight pistols are so light their recoil energy
noticeably increases as you empty the gun**. Four 158gr 357 Magnum cartridges
weigh approximately 0.12 lbs (the 340 PD holds five rounds but one is being
fired in this example). **For the first shot the pistol + 4 cartridges weigh
0.74 + 0.12 = 0.86 lb which gives us 17.6 ft-lbs of recoil energy compared to
the last shot at 20.5 ft-lbs for a 17% increase in recoil energy!**

The 8 inch barreled S&W 500 50 caliber pistol weighs in at 4.46 lbs and fires
a 700 gr bullet at 1300 fps using 27.5 gr of powder. I estimate its barrel ports
at 40% efficient as a muzzle brake. Plug those numbers into the
calculator above and we get an amazing 70 ft-lbs of recoil energy! The same
exact pistol firing a 275 gr bullet with 40 gr of powder will give you 1804 fps
of muzzle velocity with a recoil energy of "just 31" ft-lbs.

The US Army's M4 rifle using M193 ball ammunition comes in at 6.5
lbs, 56 gr bullet at 3050 fps using 27.5 gr of power and a 10% efficient
muzzle brake (flash hider) with a paltry 9 ft-lbs of recoil energy.

**A 6 lb .22 rifle using a 22LR cartridge: 40 gr bullet, 2.5 gr
powder at 1185 fps, no muzzle brake, hits you with 0.17 lb of recoil
energy!**

**When I fire my 20 lb Serbu BFG-50 50BMG rifle with a typical 50
cal round, 655 gr bullet, 248 gr powder at 3029 fps, with the muzzle
brake removed it generates a whooping 275 ft-lbs of recoil energy.
That's why it has a big muzzle brake. Assuming the muzzle brake weighs 2
lbs and is 90% efficient, the recoil energy drops to 113.5 ft-lbs (59%
less recoil) which is still a serious kick in the shoulder.**

All other things being equal, **a faster burning powder will generate a "sharper"
or "snappier" recoil with a higher ***peak energy*. This can be caused by two
factors: more of the powder is burned in the barrel generating more energy and
the quicker we accelerate the bullet in the barrel the shorter the recoil energy
impulse.

**Peak recoil energy plays a major part in our perception of recoil**. The more
secure a gun is when it is fired, the higher the peak recoil energy. A gun
mounted in a vise will show a much higher peak energy compared to the same gun
fired from the shoulder when standing because the shoulder will move and spread
the recoil over a longer time period. The same recoil energy is absorbed by the
vice and shoulder but the time in which it is absorbed affects the energy
peak.

All other things being equal, **heavier pistol bullets strike
high due to more recoil & more muzzle jump**.

**A shorter barrel can result in higher muzzle pressure and therefore more
jet effect. A shorter barrel also reduces weight which adds to gun recoil velocity and
recoil energy**.

**Jet effect recoil becomes more prominent with the use of high
velocity lightweight bullets**. Lightweight bullets generate less
recoil but the jet effect is the same so it becomes a higher percentage
of total recoil energy.

**A note about momentum versus energy:** Momentum is calculated by
simply multiplying weight x velocity whereas energy is velocity
squared x weight / 2g [g is the acceleration of gravity feet-per-second
per-second and 2g is equal to 64.3481 fps]. This means energy is more affected
by velocity--the relationship between energy and velocity is nonlinear so it's
not quite as intuitive as momentum. If you double the velocity you don't double
the energy, it is quadrupled.

A 100 grain bullet with a muzzle velocity of **1000 fps** has a
momentum of **14.3 and 222 ft-lbs** of energy

A 100 grain bullet with a muzzle velocity of **2000 fps** has a
momentum of **28.6 and 888 ft-lbs** of energy

With
double the velocity the momentum doubles but the energy quadruples.
This is why lightweight but high velocity bullets do so much damage and
one of the reasons the US Army adopted the 5.56 cartridge for the M16.

## Muzzle Brakes

Muzzle brakes primarily reduce recoil force by redirecting exit gas and
minimizing the jet effect but their additional weight also reduces recoil
energy. Adding a one pound muzzle brake to a 6.2 pound 308 rifle reduces
its recoil energy by 13.9% due
solely
to the added weight.

All other things being equal, **the lighter the gun, the higher the recoil
energy and the more effective a muzzle brake becomes**.

Typically, **the more powerful the gun, the more effective a muzzle brake
becomes**. This is why all 50BMG rifles have large muzzle brakes.

“*The Johnson muzzle brake. This reduces recoil from forty to fifty percent by
actual test*”, Hatcher’s Notebook p269.
PrecisionRifleBlog.com muzzle brake tests
show a similar maximum recoil momentum reduction of 44%. Since recoil momentum
is not affected by weight we know all 44% of this recoil reduction is from
redirected exit gas.

*The top blue
graph line is recoil force without a
muzzle brake. ***Notice how recoil levels off at 420 pounds when the bullet
exits the muzzle. After bullet exit the
force jumps to 655 pounds as exit gas blows out of the muzzle**. In this graph
36% of recoil energy is caused by the jet effect. This graph is from the
PrecisionRifleBlog.com muzzle brake test article with annotations added by
me.

Even with a perfectly designed muzzle brake there will be exit gas that will
escape through the brake's bore hole. Even so,
theoretically a muzzle brake can be more than 100% efficient if it can send
enough exit gas rearward to make up for the gas that escapes through the bore
hole. Any exit gas that turns more than 90 degrees from the bore axis (rearward) will actually
produce force opposite the recoil.

A good suppressor or "silencer" can reduce recoil momentum by approximately 25% by slowing gas exit velocity.
The added weight of a suppressor will also reduce gun recoil energy.