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Old July 31, 2012, 10:08 AM   #1
ThisIsMySig
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Calculating Velocity

The velocity numbers in my manual are stated only for the min and max loads. Does anyone know the formula for figuring velocity for loads in between? I imagine it would be a relatively complex formula.
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Old July 31, 2012, 10:45 AM   #2
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buy a chronograph
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Old July 31, 2012, 10:55 AM   #3
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Velocities are semi-sort of-kindof-linear in a normal load work up. Generically speaking, your mileage may vary, there are exceptions, it's not perfect even when it's not an exception.

Besides which, your gun WON'T match the published velocity. Almost guaranteed. Almost, again, there are exceptions.

So, yeah, buy a chronograph.
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Old July 31, 2012, 10:57 AM   #4
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For a reasonable approximation, draw a graph in "MS Excel".

low load & low velocity at one corner high load & high velocity at the other.
Join the points with a line & mark off the increments you want.
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Old July 31, 2012, 12:08 PM   #5
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The velocities in factory ballistics charts and our loading manuals are often so far off reality that any efforts to 'calculate' a speed has nothing to start from.
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Old July 31, 2012, 12:37 PM   #6
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As Brian said, there is no linear relationship between powder charge and velocity, but as long as you are staying between published min and max loads you can get a close approximation, AKA, a wag. But don't do this outside the min/max realm. Pressure spikes and so forth can really ruin your day.
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Old July 31, 2012, 08:55 PM   #7
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Linear is the best you are going to get without your own chronograph

While the relationship between minimum and maximum charge weights to velocity at those weights is not linear there are two things that make it necessary to assume that it is.

1) The load manuals are in a pressure range where the pressure curves are fairly well-behaved. While the curve may not be linear, the velocity goes up as the charge weight goes up BETWEEN the minimum and maximum.

2) Linear is the best guess for the first approximation.

Besides, you are "shooting in the dark" anyway.

3) Without a chronograph to tell you what you are actually getting (even at the published end points) your linear guess is no more unreliable than using the manuals' publishers' velocities and a linear assumption.

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Old July 31, 2012, 10:29 PM   #8
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Thanks very much for all your responses. They all make sense. Using the min and max velocities/loads, I can see that an Excel type graph would tell me what I want to know.

But like several have pointed out, a chronograph is really the only way to go.
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Old July 31, 2012, 11:50 PM   #9
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Also pay close attention to the barrel lengths used for the published velocities, especially in handgun cartridges. Usually 7-1/2" to 8-1/4" pressure barrels are used, so there is no barrel/cylinder gap or semi-auto action to bleed off pressure and velocity. It's not unusual for 4" to 5-1/2" revolvers to give more than 100 fps less than published velocities when actually chronographed.
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Old August 1, 2012, 05:31 AM   #10
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Linear will work fine, especially if you just need a number for a ballistic calculator.
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Old August 1, 2012, 05:58 AM   #11
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I think you'll get a better match if you do a linear calculation not on velocity but on bullet energy. Take the kinetic energy of the minimum and maximum loads and draw a straigh line between the two to find the kinetic energy of the between load and then calculate velocity based on that kinetic energy.

I have found that this works very well when someone posts results of several powder charges.
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Old August 1, 2012, 07:25 AM   #12
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There's no reason why you can't combine the Excel graph & the chronograph. Shoot a maximum minimum*, a median* & a minumium maximum* & draw a line through the three points with Excel. This is how I create a load ladder with new components.

This is one I made years ago matching a possible load to a trajectory compensating scope' choice for cams. I ran different powders & bullets to see what would be the closest match to the calculated cam in the range turret & tested the best calculated answer.


This was drawn manually but the "scatter graph" in Excel is excellent for this type of work where you have several sets of data points in different series & you want to get a real world projection of the likley outcome.

*Explaination of these terms.
Maximum minimum = The highest "starting load" from several reloading manuals.

Minimum maximum = The lowest "maximum load" (back off 10% if you feel the need for safety reasons)

Median = 1/2 way between the high & the low.
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Old August 2, 2012, 11:13 AM   #13
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You'll find the fps/grain between two points is actually quite linear provided the maximum load is not compressed and the charge doesn't cross a pressure where case expansion differences affect linearity (usually for loads that peak around the 30,000 fps range). It's actually more linear than KE is, though both are pretty linear. Once you start compressing charges, though, the air space in the case between grains is changed, and that can cause non-linear changes in pressure.

For load data and commercial ammo stated velocities, these are, as mentioned, taken from standard pressure and velocity barrels. Under SAAMI standards the lengths of these are 24" for the majority of rifles (with a few exceptions, like .30 Carbine at 18"), and for handgun rounds they vary a good bit more, sometimes having two standard lengths for a single round. The SAAMI standards are available on line, and pressure and velocity test barrel specifications are in the second halves of each of these documents:

Rifle
Handgun
Rimfire
Shotgun
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Old August 2, 2012, 11:29 AM   #14
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You could also do it the old fashioned way with a pencil(and calculator if you're numerically challenged). You'll still only get an estimate.
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Old August 4, 2012, 04:30 PM   #15
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Thre are too many of you guys who stayed awake in math class. Cheaters!
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Old August 4, 2012, 06:25 PM   #16
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I see the listed velocities as only a ruff guide line and 'starting' loads as just that, a place to start.

I have found that too many outside influences come into play with both the internal and external ballistics for me to be able to do more than give an educated guess. And I willingly will tell you that my guesses aren't very good.

Below are the numbers I got working up a loading. The round is the .223/5.56, mixed military brass, CCI SR primers, the bullets 62 grain SS109 (not pulls) and Varget powder. All brass was full length sized, trimmed to the same length and loaded to the same overall length. The only difference was the amount of powder and I was very picky about getting that right. All fired from the same 16 inch 1 in 8 twist SS barrel.
Velocities are an average of 5 shots each, with my Master Chrony Beta Model at 10 feet. All shot one after the other on the same day. All velocities are rounded to the nearest whole number. I did not have any wild velocity pop up on any of these strings.

24.5 – 2595
24.7 – 2654
25.0 – 2653
25.2 – 2689
25.4 – 2697
25.5 – 2676
25.7 – 2785
25.8 – 2750
25.9 – 2758
26.1 – 2815
26.2 – 2818
26.3 – 2842
26.4 – 2811
26.5 – 2832

Why did some velocities decrease with the addition of more powder? I don't have a clue (that counts). I did make a second run of one of the sets and yes, the velocities dropped. No, I didn't get them out of order. That was 14 baggies with the loading on a note and rounds sealed in each.

Be safe,

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Old August 5, 2012, 03:02 AM   #17
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Ballistic Latter

What caliber are you talking about,what powder,and what bullet?
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Old August 5, 2012, 03:57 AM   #18
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Quote:
Why did some velocities decrease with the addition of more powder?
My opinion:
If you had tested 100 rounds of ammo with a given powder charge, bullet weight, primer, etc, you would have a normal distribution of velocities, with 68% of them falling within 3 standard deviations, and the remaining 32% as outliers in the tails of the normal distribution curve. What you are seeing in your 5-hot samples when you see a decrease in velocity for adding powder is outliers affecting the velocity average. You also have some relatively large increases in velocity for somewhat minor increases in powder charge, and they are just as relevant as the decrease for a minor increase in powder charge.
* Even though you trimmed and sized the brass, were they all the same lots of brass to begin with? All brass is not created equal.
* Your charge increase is also very small, and could be less than the discretion of your equipment. How accurate is your reloading equipment?
*Plot the sample measurements and get a straight-line fit and you will see what your predicted velocity should have been. You are obviously intrigued by the velocity increases with small charge increases, but they may be the ones that are off the line.
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Old August 5, 2012, 11:32 AM   #19
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" Scorch
My opinion:
If you had tested 100 rounds of ammo with a given powder charge, bullet weight, primer, etc, you would have a normal distribution of velocities, with 68% of them falling within 3 standard deviations, and the remaining 32% as outliers in the tails of the normal distribution curve. What you are seeing in your 5-hot samples when you see a decrease in velocity for adding powder is outliers affecting the velocity average. You also have some relatively large increases in velocity for somewhat minor increases in powder charge, and they are just as relevant as the decrease for a minor increase in powder charge.
* Even though you trimmed and sized the brass, were they all the same lots of brass to begin with? All brass is not created equal.
* Your charge increase is also very small, and could be less than the discretion of your equipment. How accurate is your reloading equipment?
*Plot the sample measurements and get a straight-line fit and you will see what your predicted velocity should have been. You are obviously intrigued by the velocity increases with small charge increases, but they may be the ones that are off the line."


Very well said.

My point that I was trying to make is that each weapon is a mystery and must be studied and worked with to get the desired results.
The data in the example was not a study in velocities but in search of the more accurate loading with given components out of a single weapon. Just for info, I picked the 26.1 grain area for further investigation. But alas, I don't like those bullets and have given up with them.

Another testing I have done was to compare three very similar 1911A1 type weapons with the same ammunition. Statistics can and will rip my findings but I gather what I wanted to know from them.
The loads are new Star brass, 5.6gr of 231 (dumped from one of my powder measures), CCI standard LP Primers, cast 204gr SWC lead bullets (.452 and 4 grains heavy, all weighed to match). All round mixed during the process and carried to my table in a zip lock bag. Test firing: temp start - 81 deg., end - 85 deg., bright sun, 39% humidity, 30.19 MB pressure. Master Chrony Beta at 10 feet, new battery.
6 rounds (only) fired in order.
Weapon #1 (H) - 5 inch 1911A1. Average - 867.2 FPS
Weapon #2 (T) - 5 inch 1911A1. Average - 894.45 FPS
Weapon #3 (M) - 5 inch 1911A1. Average - 869.02 FPS

What does this prove? Simple, every weapon is different.
The only unexpected results were the same loads fired out of my S&W 1917 (It has went thought the War to End All Wars and the Argentinean Military and had been beat up a lot.) with it's 5 1/2 inch barrel and varying cylinder gap, the crain is not straight, gave an average of 879.62 FPS (with the greatest deviation, cylinder gap). And an unexpected increase in velocity (previous tests did not give this great of increase) when moving to my 16 1/2 inch Marlin, upped to 1045.5 FPS.

This all tells me the same thing. Some book lists a loading with velocities and some with pressures. They are only good for use as a guide. To give a starting point. Ever component variable will make a change, the method of putting those components together will make changes and every weapon introduces it's own mess of variables. Add temperature, pressures and humidity into the mix and I find it a wonder that I can hit anything

Results:
Find a safe 'starting' point and slowly and deliberately work from there.
Grabbing a book or some data from the net and taking it as fact is irresponsible and most likely not going to produce the same results out of your weapon.

Be safe and enjoy.

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Old August 5, 2012, 03:29 PM   #20
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There's something to both sides of the argument. I put the rifle data in Excel and got:



You'll notice that velocity increase with charge weight is pretty monotonic. Using the straight line least squares fit to predict what the velocities should be based on the average trend, then finding the deviations from the prediction I got a standard deviation of 23 fps. 68% of a popluation are within 1 standard deviation, 95% within 2 standard deviations, and 99.3% are within 3 standard deviations, so only one in 300 would be expected to be more than 69 fps off the prediction made by the line. Pretty typical of a rifle.

Just one problem.

The datapoints are 5 shot averages so we would expect the standard deviations to be 5 times smaller than typical of a rifle. So 23 fps for 5 shot groups is like having 115 fps standard deviation for single shots. Not so likely, though the mixing of brass and pulled bullets probably account for some of it. Unfortunately it's tough to catch all the variables. Changing light could account for some shift in chronograph readings, as could changing temperatures (both ambient and barrel), not to mention changing fouling in the bore. But I wasn't there so I don't know what did or didn't happen with all that. It's sometimes a messy business.
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Old August 5, 2012, 05:46 PM   #21
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Unclenick,
You do good work.
Working with better source data would give much better results data. As I remember something near or above fifteen samplings will reduce the random error to much more acceptable levels.
However, my experiment was only a quick view in search of a starting point for more in depth testing in my search for accuracy. I started by finding a bottom loading that fully functioned the weapon, followed by finding my top loading that I felt was safe. With these two limits, I did the listed .223/5.56 test. I shoot off of sand bags to paper at 100 yards and across my Chrony. The Chrony is only to verify that I don't have an odd load in the mix. It doesn't cost me anything to stop and wright down the readings and I want to have some cool down time anyway. Further tests are more extensive and if anything worth wile comes about, the range get extended. I found the bullets in use were too inconsistent for that use. I did like the search for the breaking point in causing instability with the 62 grain bullets out of 1 in 12 and 1 in 14 twist barrels.

The original post was asking for a formula to determine median velocities from a loading book. I don't think the results of the mathematical process would have much validity.
I feel this has been beaten to death and I have nothing more of value, if I ever did, to add to the discussion.

Thanks guys.

Enjoy,

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Old August 5, 2012, 07:48 PM   #22
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As the guys stated, velocity can vary from gun to gun so nothing is exact. Velocity can also vary by temperature, barometric pressure and humidity.

I take the max load, and divide it into my charge to get a percentage of max load. We'll say 94% of max charge weight. I multiply that 94% by the max load velocity. That's what I use for my personal records.

That method is NOT scientific and NOT reliable but it gets me in the ballpark. I own a chronograph so if I was that concerned, I'd actually test the rounds.

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Old August 5, 2012, 10:21 PM   #23
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Not for nothing but, you guys have an incredible wealth of knowledge.
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Old August 6, 2012, 01:55 AM   #24
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I have yet to have a factory round fired from my rifle to meet the advertised fps. Same can be said of the posted fps in reload manuals. Each rifle is an individual and the only way to really know is to get a chronograph. Why guess when you can know.
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Old August 6, 2012, 07:44 PM   #25
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Finally bought a Chrono a few weeks ago.

For a couple of calibers, my estimated MV based on linear interpolation of the charge/published velocity was pretty damn close.

Others, waaay off.

But, I kinda knew that before buying the chrono. After zeroing at one or two hundred yards, the come-ups required at 600 either verified- or shot down- the estimated velocities. As mentioned, it's the "real world" results downrange that matter.
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