Actual ballistic formulae for determining muzzle velocities

Keru627 · Rookie Member Joined: Jul 15, 2020 Posts: 2

Good Day everyone!

I am looking for the actual formulae for calculating muzzle velocities based on the type of powder and the amount of powder loaded into the shell casing of a known caliber. I ask this because I am questioning the Lyman reloading manual for the .40 caliber S&W bullet. From what I am loading into the shell casing, and what I get on the range, I am off by 2-3 inches in vertical drop at 30-40 ft. It would be nice to see what the formulae are for calculating the speed of the projectile and the drop at certain distances. without buying a chronograph. If anybody knows a site that would help me, please reply. Thank you.

Pumpkinslinger

I'm not 100% sure what you're asking for. Are you saying that you zeroed the gun with one load and your handloads don't have the same point of impact? If so, what were the loads?

Loke · Member Joined: May 13, 2013 Posts: 207

There is no formula that fits every load possible. The publishers of the loading manuals use very precise equipment to monitor the pressures of the loads that they develop. When they reach what they consider to be the safe maximum pressures of the firearm, powder, bullet, case, and primer combination that they are using they measure the velocities and put them into their books. You can compare your loads to other published data from reliable sources, but that still won't tell you what velocities you are actually getting from YOUR gun. Only a chronograph will do that.

Keru627 · Rookie Member Joined: Jul 15, 2020 Posts: 2

Pumpkinslinger wrote:

I'm not 100% sure what you're asking for. Are you saying that you zeroed the gun with one load and your handloads don't have the same point of impact? If so, what were the loads?

Mike,
Glad to meet you. Here is my dilemma. I am using the Sierra software to establish bullet trajectories for my .40 cal. S&W M&P. I use a 155 TFN bullet with a powder charge of 6.0 grains of Unique powder. I fired 50 rounds and the spread looked like an oval spread with a wider spread from 9 o'clock to 3 o'clock and the 6 o'clock to 12o'clock spread a little narrower. At a distance of 30 ft. I went a week later and fired 50 rounds of 165 grain Hornady hollow points at a distance of 40 ft. All bullets dropped below the center of the target by 2-3 inches, but were central to the target center. I noticed in all reloading manuals I have looked through that there really is no formulae for muzzle velocity(barrel to distance downrange). I know that you must take into consideration powder type, burn rate, bullet weight, weather conditions, etc. No where have I found an exact formula for bullet velocity. I once saw a formula that seemed to be a calculus derivation in and old set of Encyclopedia Britannica my parents bought for me when I was a kid of about 10(I am 70 now). That is what I am looking for. The Lyman catalog says that at anywhere from 5.4 grains to 6.5 grains I should have muzzle velocities from 847 fps to 1041 fps. If I load 6.0 grains of Unique, then I should have roughly 961 fps. I am not sure why my bullets are dropping that much at40 ft. Do you know what I mean, now?

DallanC · Site Admin Joined: Jan 18, 2005 Posts: 3572 Location: Utah

The most accurate "internal ballistics" software is Quickload. It does mostly what you want, however it will never give you exact results because every barrel has unique tolerances and imperfections that affect friction and therefore velocity.

You could model multiple loads, then load actual loads, cronograph and compute if your specific gun is "faster" or "slower" than the computed loads by a certain percentage... then use that value to adjust other computed loads.

-DallanC

DallanC · Site Admin Joined: Jan 18, 2005 Posts: 3572 Location: Utah

Keru627 wrote:

I fired 50 rounds and the spread looked like an oval spread with a wider spread from 9 o'clock to 3 o'clock and the 6 o'clock to 12o'clock spread a little narrower.

Sounds like a precession problem where the bullet is upset and yawing around the center of axis. If you drew the bullets path in 3d space, it would resemble a corkscrew as it went down range. These types of problems will actually stabilize as spin and wind resistance pushes the bullet into a straight orientation.

-DallanC

Pumpkinslinger

Keru, nice to meet you too! What they said! Different loads are going to shoot to different points of impact. Even the same load will shoot to a different point of impact for different shooters, due to differences in grip, etc.

The "Quickload" software that Dallan mentioned would get you in the ball park but you'd still have to test the loads to see what they do in your gun. For the cost of the software you can make a lot of test loads.

For external ballistics "PointBlank" would be hard to beat.

gelandangan

+1 I use quickload to predict the muzzle velocity of my loads, there are a bit of discrepancy but you can tune it to match pretty close.

Vince

Welcome aboard Hunting Nut Keru627. Grab a beer and pull a stump up to the fire mate. Feel free to jump in with your knowledge and experience (at 70 I’m sure you have heaps mate) and share with other members as will they as you have already seen.

Now maybe I’m reading your request wrong, but I am thinking that what you are looking for is a formula to calculate the velocity and trajectory from a give powder charge. The guys in here are very knowledgeable and will help where they can, but from my limited experience the only way you can measure velocity is with a chronograph of some sort. Now, trajectory is a whole different ball game and how that is actually calculated is beyond my knowledge. No doubt there is a formula of some sort for this, but where I can’t help.

As the guys have said, every firearm barrel is different. Tiny imperfections, throat wear, barrel wear, crown condition, headspace all play a part. Then there are other physical factors like case condition, primer, tiny differences in charge weight (a few granules different), projectile condition and minor variations in weight. Then there is the biggest factor of all...the human factor, the Nut behind the butt. All of these things will play a part which is why I use the “book data” as a close guide, but still, only a guide.

I don’t know if this is any help, but it is something I found in one of my obscure searches...

Bullet Trajectory calculations

It will be interesting to see what this post finally brings out.

Elvis

also.....even the gun gurus CANT accurately predict velocity from projectile drops...it was discussed in detal in Matt n Bruce Grants classic book "the sharpshooter" times have come a long way since then but principles still apply....it would be far easier NOW with great programmes like pointblank...because you can keep changing velocity till curve "fits"what paper is telling you...but...you talking handgun so things are not so clearcut as drops wont be large enough.
now correct me if Im wrong but I believe handguns do funny things with recoil and a heavier projectile will impact diferently to a lighter one when load is similar due to where muzzle is lifted to during recoil of firing???

Loke · Member Joined: May 13, 2013 Posts: 207

There is a lot of information missing that we need to make an informed guess as to your dilemma.
First of all, how were you shooting? Did you have a stable rest, or were you shooting freehand?
What experience do you have with precision handgun shooting? Are you a bona fide expert like Jerry Miculek, or a mere mortal like the rest of us?
How precise is your firearm? Is it stock from the factory or have you improved the trigger?

It looks like you have sighted your gun with one load and are expecting another to shoot the same. I don't believe that this is a logical expectation. The point of impact should be expected to change with different loads. The only way to know is to shoot them and make a note of the difference in point of impact.

slimjim

I appreciate your quest. However, you will not find your "pot of gold". As Elvis points out, barrels "react" during the firing impulse, pistol and rifle. I've had a lighter rifle bullet, high velocity load shoot 6" lower at 100 yards than a slower velocity, heavier bullet load. A rifle barrel is like a tuning fork and the muzzle is moving as the bullet travels down the bore. The barrel's bore can be "pointed" in different directions when bullets exit the bore. That is why we tune/develop loads specific for our firearms. Also, one can't always take the same powder load and expect the same results - powders vary lot to lot. I've been shooting Win 760 and way out. The new batch shoots 75 fps lower than the prior batch. I've had to restart my load development. One of my buddies called today and said his newer powder lot shoots 40 fps faster than the lot he just used up. Then there are differences in freebore that varies from barrel to barrel. The shorter freebore will have higher chamber pressure and velocity than a barrel of the same caliber with a longer freebore. The list goes on ...

But we HuntingNuts have fun talking about subjects like this.

Aloysius

Loke wrote:

There is a lot of information missing that we need to make an informed guess as to your dilemma.
First of all, how were you shooting? Did you have a stable rest, or were you shooting freehand?
What experience do you have with precision handgun shooting? Are you a bona fide expert like Jerry Miculek, or a mere mortal like the rest of us?
How precise is your firearm? Is it stock from the factory or have you improved the trigger?

It looks like you have sighted your gun with one load and are expecting another to shoot the same. I don't believe that this is a logical expectation. The point of impact should be expected to change with different loads. The only way to know is to shoot them and make a note of the difference in point of impact.

if this is what you want, I can only give 1 advice: the .375 H&H Magnum is said to give almost the same POI for different bullets... so take your distance from gun to target short enough and the requirements about your groupsize big enough and you will be happy... and the old .375 H&H will help you to become happy

PaulS

Keru,
First, let me welcome you to the nut.
If you fire a load at several different distances you can roughly get the velocity of the bullet by matching its trajectory by changing velocities until you get a good match. You will have to fire enough of the same round at each distance to establish an average trajectory. That will take a minimum of 10 to twenty rounds at each distance. find the average location of impact and move on to the next range. Your load seems to be below the trans-sonic threshold so we can forget about the gyrations that occur there. Once you have an average trajectory then you can enter the information on your load into the software and start changing the velocity to find the average velocity.
There are some "yea-but"s and some "gotchya"s that you may have to remind yourself of in getting results from this exercise.
1. ballistic coefficients vary due to temperature, humidity, pressure and a few other things.
2. garbage in = garbage out. You need to be very careful that your trajectory reflects the actual flight of your bullet. Flat field, targets in line with each other or at least at the same height, a good rest, trigger control, and breathing. Getting tired will obviously skew the results and the first few shots are just for warm up.
3. Each day the weather conditions will change but you WILL get tired shooting 60 to 120 rounds in one sitting.
4. Ideally you would set the targets up at ten yard increments from 20 to 75 yards and align them with a laser and position your firing point exactly in line so that each shot went through all the targets. If you could do that you would only have to fire one shot to get a good trajectory.

If you lived close I would gladly let you use my chronograph to shoot 10 or 20 rounds through to get a good average velocity. I am I the SE corner of Washington state in the Walla Walla valley and shoot at the East End Rod and Gun Club just east of Milton-Freewater Oregon. If you are not close maybe you can find someone who will help you locally. They might not want you to shoot over their chronograph but they might be willing to do the shooting for you. Shooters are generally helpful and great folks. Ask around. If you are close send me a PM and we will set up a meeting.
Paul

Gil Martin

Welcome to the Forum. Glad to see you here and hope that you post often. These folks have given good advice. Take care. All the best...
Gil