Bullet weight vs. speed vs. felt recoil

I'm trying to understand the relationship between bullet weight, bullet speed, the gun that is being used, and felt recoil.

For example, I used to shoot 115gr ammo in my Taurus PT9 "stock" handgun, and while I can't say the gun had a lot of recoil, what it did have was annoying.  User 'mustachio' suggested I try the heavier 147 gr ammo, which I found easier to shoot.  Less "felt recoil.

I know there's the mathematical equation of combining weight and speed.  All other things being equal, the heavier round should create more recoil.
I know the bullet speed is part of this, with the 115gr round being supersonic, while the heavier load is sub-sonic.

Since I'm referring to "felt recoil", there probably isn't any way to actually calculate that....??


My question.  Is it possible, using the data that can be found in reloading charts, to compare the expected recoil between two different rounds?

(.....and for a test, does this show the decrease in felt recoil in my 9mm gun, when switching from 115gr ammo to 147gr? )

If I'm being 100% honest I don't entirely understand it either. I see my own experience but seems like all calibers aren't the same.

With 45 loads I'm finding the lighter bullets have less felt recoil, I'm currently using 160 grain bullets. That's even considering I've got a tight pistol made by Jon and with a heavy 9000SC, so I've gotta heat up the load to 800+ for function with a 10 pound spring. It has noticibly less recoil than 185 bullets I've tried.

Then the 9mm crowd seem to favor heavier 147 grain bullets over smaller 115 grain bullets regarding recoil. So if they're presumably running the same energy to ensure function (not necessarily the same speed) to ensure pistol function the heavier slow bullet recoils more mildly, perhaps it's recoil velocity, more below.

Every pistol takes a specific amount of energy to reliably cycle. The energy can be increased by increasing powder charge thus increasing FPS and pressure, increasing bullet weight, increasing bullet diamerer or hardness. I think where we perceive some amount of felt recoil is through recoil velocity or now fast the recoil energy is expended. So a quick recoil velocity would be perceived as "snappy" versus a mild "push" recoil even though they expend the same energy.

But I still don't know why lightweight 160 grain .45 loads feel mild but light 115 grain 9mm loads are perceived as snappy. Assuming you're running right over the threshold of pistol function.

If only I didn't have to go to my day job I could so scientific recoil testing and analysis.

Here you go Mike. Have fun.

http://www.shooterscalculator.com/recoil-calculator.php

Below is the Dillon calculator that will give you the power factor generated by different pistol loads.  Bullet weight and fps are all that's needed.  A light high speed round delivering the same power factor as a heavier low speed round will have a sharper felt recoil.
 
There is a difference on felt recoil between some powders shooting the same weight bullet and fps (power factor).  Many competitors like Bullseye powder for sustained fire because they like the recoil impulse.
How the gun is set up will have an impact on FELT recoil.
Recoil and Main spring combos; example for the exact same light load shooter A might run a 10lb Recoil and a 19lb Main spring while shooter B could be running an 11lb Recoil and a 17lb Main spring. The Firing Pin Stop radius also impacts felt recoil.
Barrel fit/lockup, I've heard it does and it kind of makes sense but I'm not sure.
- Dave
https://www.dillonprecision.com/power-factor-calculator.html

Newton got it right, and the calculation is pretty straightforward.  The bullet, powder and velocities on one end equal the masses and velocities on the other.

Predicting perceived recoil, however, is very difficult and personal, depending on a myriad of factors.  For the purpose of this site, improving our shooting, the best thing to do, if you are really interested, is to try different guns, bullets and velocities, and determine which combinations give you better scores and raise your classification.  There is no substitute for trigger time.

The rub in all of this is the recoil action of the moving parts is the main absorber of the recoil energy. In a typical all steel pistol this is about half the weight. Couple that with the phenomenon that 9mm light bullets seem to shoot better at near max loads, and recoil “feels snappy”.

Another rub is the secondary movement and energy imparted by the slide hitting the frame at the rear.

"I'm trying to understand the relationship between bullet weight, bullet speed, the gun that is being used, and felt recoil."

I think, biggest confusion comes from the fact that given we have two rounds of the same caliber, loaded with same powder charge, having same OAL, same primers, but one that has lighter bullet will have lower velocity. And the opposite is true, - in order to have same velocity with lighter bullet as heavier bullet in the same caliber, - powder charge have to be higher. It sounds paradoxical. The answer is relatively simple, - we need to introduce and remember of another parameter, and in particular the pressure developed by particular round. Pressure (ENERGY) is what actually propels projectile through the barrel, and this is how Newton's formula E=mc² should be applied. Given same velocity (c - parameter) heavier bullet will produce more energy, and translate into HIGHER recoil impulse then lighter bullet. However with lower velocity (subsonic speed) heavier bullet will produce less energy then lighter bullet with higher velocity (supersonic), subsequently translating into LOWER recoil impulse. The next question to be answered comes from the misconception that same powder charge should produce same pressure (ENERGY) regardless of the bullet weight. It is ain't so!!! Bullet weight translates into geometrical dimensions, and lighter bullet is usually shorter, hence case capacity is larger (mind OAL parameter here), hence pressure developing would be lower in comparison with heavier bullet. One can argue that crimp can mitigate such, or ammo with lighter bullets usually have shorter OAL, etc., - it is all true. This is where theory meets practice. When we load our ammo, we take to account all these factors without much of theorizing.

AP

I thought that E=mc squared was attributed to that Einstein guy and had more to do with the Manhattan project.

STEVE SAMELAK wrote:I thought that E=mc squared was attributed to that Einstein guy and had more to do with the Manhattan project.

Yeah.... you get that from firing your gun and neither you nor anyone in the vicinity of Port Clinton will perceive any recoil!  .

STEVE SAMELAK wrote:I thought that E=mc squared was attributed to that Einstein guy and had more to do with the Manhattan project.

True.  I forgot my physics, at least partially!  Thank you for the correction, Steve.
However formula is universal, and establishes relationship between mass of the subject, the speed it travels and resulting energy such subject will generate.  That is exactly what Mr. Myers is after.
AP

LenV has kindly provided a calculator where you can use published data to determine recoil force. The only missing element in published data is the gunpowder weight, which contributes to recoil force as well.  The gunpowder weight thing is explained here: 
 https://en.wikipedia.org/wiki/Recoil#Including_the_ejected_gas


And some more explanation and real-world examples here: 
 https://www.shootingtimes.com/editorial/gunpowder-contribution-to-recoil/328788


Here is an article on recoil when different bullets weights are loaded to the same power factor, and it might answer a few questions;   https://www.shootingtimes.com/editorial/power-factor-recoil-bullet-weight-gives-edge/99399


Here is an article that includes information and data on the effect of using different gunpowders on recoil. https://www.shootingtimes.com/editorial/measure-relative-handgun-recoil/99442

"Felt" recoil and energy absorbed could be considered two sides of the same coin.
Shout a cheap blow back 380 and it usually stings my hand while a 45 with a slow burning powder charge gives a nice push.
Is the recoil pulse a short spike or a long curve?
Spreading the pulse makes all the difference....are you getting 90 ft/lbs RIGHT NOW or 120 spread out?  I'll take the spread.

STEVE SAMELAK wrote:"Felt" recoil and energy absorbed could be considered two sides of the same coin.
Shout a cheap blow back 380 and it usually stings my hand while a 45 with a slow burning powder charge gives a nice push.
Is the recoil pulse a short spike or a long curve?
Spreading the pulse makes all the difference....are you getting 90 ft/lbs RIGHT NOW or 120 spread out?  I'll take the spread.

90 ft-lbs of free recoil in your hand....

A 9mm is closer to about 6 ft -lbs.

Just talking round numbers

You get X input in this manner it feels one way
You get the same X input differently it will feel differently
You are absorbing the same total energy in both cases but with many variable added to the mix, all of which alter "FELT" recoil as opposed to the fixed number which is the load fired.

PhotoEscape wrote:

STEVE SAMELAK wrote:I thought that E=mc squared was attributed to that Einstein guy and had more to do with the Manhattan project.

True.  I forgot my physics, at least partially!  Thank you for the correction, Steve.
However formula is universal, and establishes relationship between mass of the subject, the speed it travels and resulting energy such subject will generate.  That is exactly what Mr. Myers is after.
AP

Sorry, that's not quite true  The Enstein's formula establishes relationship between matter and energy, basically stating that an amount of mass can be converted to a pure energy and the amount of that energy can be precisely calculated. So it is not applicable to shooting, unless we are talking nuclear explosions  
The formula we need here is indeed Newton's formula, it's F=mv^2 / 2, where m is a mass of an object (for example, mass of an 185gr bullet would be approximately 0.012 kg) times velocity squared (for example, as ASYM Ammo states on their page, their 185gr NM load is 775 fps, which is approx 236 m/s, squared, gives us 55696) and divided by 2 results in ~ 668.35 Newtons - that's the force which a fired round applies to the slide. Since the third Newton's law postulates that every action has an equal reaction, if we remove the recoil spring from the gun and measure the mass of the slide, knowing the force and mass we can calculate the velocity of the slide during the recoil (ignoring all other factors, e.g. friction, air resistance, etc). Then we can add recoil spring force to the equation, but that's a different story. You would need to apply a Hooke's law which is F = -kx, where x is a length of compression and k is a spring stiffness constant.

What he said.  

Standard load 46ft/lbs. It is kinda scary and not for the weak at heart. Or just weak.

500 S&W or another bear cartridge?

Another. 460S&W Mag. Harry Reeves.....Any CF Revolver   Also legal for .45 matches.

LenV wrote:Another. 460S&W Mag. Harry Reeves.....Any CF Revolver   Also legal for .45 matches.

I'm sitting back and watching rapid fire!!!!

dronning wrote:.......A light high speed round delivering the same power factor as a heavier low speed round will have a sharper felt recoil........

I need to sit down with a lot of free time, and review all those responses.   In the meantime, the above line describes what I'm "feeling".  

"Sharper felt recoil".....      and when I followed mustachio's suggestion, switching from 115 grain 9mm to 147 grain, it "felt" like less recoil force.  For all I know it might have been more force, spread out over a longer time, but the key word here is FELT.  

I'll check out my reloading books when I get home; I couldn't find the comparative data in a ten year old copy of the Lyman Pistol & Revolver Handbook.

Which is lighter felt recoil or which has less muzzle energy, should only be considered with at least one three other factors?

(1) Must the energy level or power be similar. I.E. is there a mathematical requirement such as Power Factor, or do you need to knock down a steel target?

(2) How important is accuracy, and to what distance?

(3) Does one load negatively effect the functioning of the gun?

Consider the following.

Power Factor is simply bullet weight times velocity.  Used as a simply measure or bar to be set in certain shooting sports.

Muzzle Energy in pound feet.

A bullet weight of 185 gr @ 811 fps has a PF of about 150,000 and ME of 270 lb/ft
A bullet weight of 200 gr @ 750 fps has a PF of about 150,000 and ME of 250 lb/ft
A bullet weight of 230 gr @ 652 fps has a PF of about 150,000 and ME of 217 lb/ft

To get the 230 gr to have 270 lb/ft of ME the velocity would need to be about 729 fps. The 230 gr bullet at 729 fps would have a PF of 167,670.

So in the above example and in just about any similar example, with a similar load "power" a heavier bullet moving slower generates less energy than a lighter bullet moving faster. This equates to less felt recoil in non-compensated guns. The feeling is even more evident in non-reciprocating guns such as revolvers or single shots. 

I think in general, it comes down to what load the gun likes for accuracy and functionality and what the feeling of the recoil is to the shooter. Does the gun have a scope? Is it slide mounted or frame mounted. Powder selection is another thing to consider. A given bullet weight at same velocity may feel different depending on what powder was chosen to propel the bullet to the same velocity as another. In conducting such tests, wear double plugs. It is easy to permit blast or sound to have an incorrect influence on felt recoil. But I suppose the blast or concussion can be part of felt recoil too, since we feel it as well.

Allgoodhits, I don't think comparing muzzle energy is the right approach. 

There are specific formulas for calculating recoil force, and trying to use muzzle energy in the mix is not useful because it's not the same as recoil force. Muzzle energy produces numbers that can misrepresent recoil. If you want to know if there is a difference in recoil, measure recoil.  

The formula for calculating recoil force is given at the SAAMI website:   https://saami.org/wp-content/uploads/2018/07/Gun-Recoil-Formulae-2018-07-9-1.pdf

If you want to know the recoil of different bullet weights at the same power factor, it is discussed and measured at this link:   https://www.shootingtimes.com/editorial/power-factor-recoil-bullet-weight-gives-edge/99399

S148 wrote:Allgoodhits, I don't think comparing muzzle energy is the right approach. 

There are specific formulas for calculating recoil force, and trying to use muzzle energy in the mix is not useful because it's not the same as recoil force. Muzzle energy produces numbers that can misrepresent recoil. If you want to know if there is a difference in recoil, measure recoil.  

The formula for calculating recoil force is given at the SAAMI website:   https://saami.org/wp-content/uploads/2018/07/Gun-Recoil-Formulae-2018-07-9-1.pdf

If you want to know the recoil of different bullet weights at the same power factor, it is discussed and measured at this link:   https://www.shootingtimes.com/editorial/power-factor-recoil-bullet-weight-gives-edge/99399

Roger that. However, how something "feels" to a shooter's hand(s) and what the overall experience of the shot going off is what matters most to the shooter. Some compensated guns recoil very little, but some do not shoot them well because of the noise. That and of course does the load perform as it is required to do. It is all quite interesting.

Some comments above correctly (and incorrectly) describe how to calculate energy and recoil.  I will go out on a limb here and say that "felt recoil", a basic question in the original post, can't be calculated, due to many variables.  For example, to mention a few,  I haven't seen any mention in posts above or shooting sites, that discusses rotational energy of the bullet.  Ask any novice shooting a ballgun with spec ammo if it feels like it wants to twist out of his or her hand. Revolver? - different leverage and geometry. The shooter is a variable part of the mass of the recoiling system.  I can change perceived recoil from tolerable to intolerable simply by changing my grip, strength, or stance, offset or recoiling straight back.  One or two hands?  All relate to felt or perceived recoil.

Sure, heavier and faster bullets impart more energy on the gun and shooter- that is easy to calculate and why so many try to find the lightest load that will find the X-ring, function the gun and not bounce off of the cardboard.

Remember- recoil is only in your head, and certainly felt long after the bullet has left the barrel  .  Find empirically what works for you and train with it.

How it “feels” is somewhat ( maybe significantly) subjective.

However, these concepts may help.

Recoil is a momentum exercise. The momentum of the gun has to match the momentum of the bullet. So MgVg = MbVb

So a 147 grain bullet at 920 fps has the same momentum as a 115 at 1175 fps. Those are about max loads in a 9mm. Both will impart the same recoil velocity to the gun. The recoil energy is the same. The difference is the time. The bullet is accelerated from rest to muzzle velocity in the same distance, the same peak pressure is reached. But the overall acceleration has to be different. The 147 grain bullet takes .00045 seconds to leave the muzzle. The 115 takes .00035 seconds. So the MEAN force to accelerate the pistol to the end velocity has to be higher. This means the mean force is about 30% higher for the 115 load. That will be perceptible.