Positive Compensation

[!Peter!]

Hi All,
So I’ve been thinking about positive compensation and ran some numbers to get a better understanding of positive compensation over various ranges which I thought I’d share.

Using BFX excel addin from http://www.bfxyz.nl/ I created a drop table with the following inputs:
Muzzle Velocity 2900 ft/s
Muzzle Velocity Variation +/- 20 ft/s
G7 BC 0.236
15 degC
101.325 kPa
0% humidity



I subtracted the muzzle velocity drop from the fast and slow velocity drops to give the difference in impact heights. In other words if I’m perfectly zeroed at a given distance with the muzzle velocity, how high or low would the fast or slow shot hit.


I graphed this data in two ways. First I looked at the impact change with velocity change for each distance.


Second I looked at the impact change with distance for the fastest and slowest velocity


What I see from these two graphs is that as distance increases the positive compensation rate required also increases.

So then I looked at if perfect compensation was set up for a given distance what would the impact height be at the other distances. I constructed the table below for the fastest muzzle velocity.


The green cells are where perfect positive compensation occurs and the yellow cells are where the impact height is less than or equal to 0.2 moa. I chose 0.2 moa as it is a little less than half the radius of the smallest ICFRA TR V-Bull.

From this table you can optimise the distances to tune for positive compensation. You can also use this table to setup positive compensation for a difference distance (i.e. test at 200m to see if you've got enough positive compensation for 900m).

I know the conclusions from these numbers and graphs aren't necessarily a revelation, but when I ran the numbers and built the graphs it made what needed to be achieved much clearer for me! So I thought I'd share

If you’d like a copy of the spreadsheet to play with just PM me with your email address. You will need to install the BFX Excel addin.

Now the big question, how do I get my rifle to have the needed positive compensation.......

Enjoy!

Peter

PS - I've got thoughts on the big question, but they're still developing

[AlanF]

...Now the big question, how do I get my rifle to have the needed positive compensation.....

Buy a second hand barrel that gives bad vertical, and index it 180 degrees different in your action .

[pjifl]

The yellow cell band indicates what tolerance may be acceptable at different distances to have some useful compensation.
It clearly shows a reduced tolerance at the very long distances.

At one time I experimented with a 22 rimfire by adding muzzle weights vertically off centre to induce a larger movement vertically. It certainly did that. But along with that was more variability.

I think that the same would be true using a large centrefire. Only one way to find out.

A series of experiments varying barrel weight vertical position shot deliberately at different velocities should show how much the impact point varied. If a graph of such results indicated that enough compensation was possible at 1000y you could then go further. I was always intending to try this but my access to 1000y is very limited and you need good conditions for such testing.
If there was wind shift, one would need to correct by subtracting any AJ.

In the past, we usually related powder weight to impact height but now better V measurements are possible which is probably more relevant. Probably best to measure and graph both V and Powder weight against impact height.

Peter Smith.

[williada]

Peter,

Your tables are an excellent presentation.

From the last table, you have clearly demonstrated the range of tolerance (spread) in more detail that I spoke about relating to a diagram about understanding your barrel if you want to achieve a compensation tune.

Let’s assume you have a compensating barrel i.e. slow shots are tossed up above fast shots then your table is a handy way to analyse from test results at say 500 yards what your barrel is likely to do at different distances in a broad sense. This is a great starting point for many.

Peter S has mentioned the reduced tolerance at the long ranges. From many practical tests at 1000 yards in the 1980’s with many different barrel profiles and in the early 2000’s from a machine rest it became very clear to me that you needed a specialist tune for the long distance. Given the tools of the age, comparisons of data were made on big data sets to see relative differences to eliminate noise. It would seem that better tools like “Labradar” could reduce the uncertainty and you could get away with smaller data sets. Peter’s advice is a sound way of doing things and indicates that wind effects have to be discounted from the data.

When it comes to the business end, there are many trade-offs to be made and a few variables you have to rank in importance to get the desired result which essentially comes down to barrel stiffness v natural harmonics; reflected vibrations v third point of inertia muzzle chatter; and torque as well as the fulcrum point of the unit for the degree of fundamental lift of the muzzle. The latter raises issues relating to stock design and a few armouring tricks. Barrel steel, hardness and composition also play a part.
As such, it’s hard to make a silk purse out of a sow’s ear but at least you can see what you have got and where you can apply it.

I will pm you Peter. David.

[!Peter!]

The yellow cell band indicates what tolerance may be acceptable at different distances to have some useful compensation.

Peter, That's a good way to explain it. I have a target accuracy requirement that I want myself and my hardware to meet. Once I’ve achieved that I stop!

williada, when I was going through the information on this site, your posts were a treasure trove of information from which I drew to build the tables and graphs.

Given the tools of the age, comparisons of data were made on big data sets to see relative differences to eliminate noise. It would seem that better tools like “Labradar” could reduce the uncertainty and you could get away with smaller data sets.

Indeed, lately there have been rapid advancements in technology which can now give the data to help unravel a lot of what in the past could only be speculated.

A while ago I had the opportunity to do some indoor smallbore shooting with a SCATT MX-02 and the additional data on the recoil of my shot was revealing.

When it comes to the business end, there are many trade-offs to be made and a few variables you have to rank in importance to get the desired result which essentially comes down to barrel stiffness v natural harmonics; reflected vibrations v third point of inertia muzzle chatter; and torque as well as the fulcrum point of the unit for the degree of fundamental lift of the muzzle. The latter raises issues relating to stock design and a few armouring tricks. Barrel steel, hardness and composition also play a part.

Absolutely. I think VarmintAl has the most representative analysis but it’s taken me a while to see the deeper fundamentals to start looking at what variables to play with to achieve the degree of compensation needed.
Incidentally, I’ve got colleagues who use the software that VarmintAl used in his analysis to analyse the dynamic behaviour of structures in heavy industry. Unfortunately, I can’t get them to do some special analysis for me.

For me the first graph is the most enlightening as it shows exactly the muzzle angle rate of change needed.

[!Peter!]

Hi All,
Looking more into positive compensation, I found a lot more information including published papers. One paper was published in 1901!

Anyway, I found that Dr Geoffrey Klobe (founder of border barrels) has developed a model for traverse barrel vibrations http://www.geoffrey-kolbe.com/articles/ ... ations.htm . Traverse vibrations are what allows positive compensation to occur. Klobe’s model is simplified but still agrees with the more advanced model of VarmintAl.

Below is a screen shot of the barrel response of a medium palma barrel.


To see when the bullet would exit I work out the bullet exit times by assuming constant acceleration and a 30 inch barrel. Assuming constant acceleration over estimates the exit time when compared with QuickLoad calculations.

Muzzle Velocity (fps) Exit Time (ms)
2880 1.736
2885 1.733
2890 1.730
2895 1.727
2900 1.724
2905 1.721
2910 1.718
2915 1.715
2920 1.712

Comparing the medium palma barrel to a light palma and heavy palma barrel, the light palma barrel’s response has higher amplitude and the peaks occur later. While the heavy palma barrel’s response has lower amplitude and the peaks occur earlier.

Light Palma


Heavy Palma

[DannyS]

Very interesting post Peter, great reading. Regarding centre of gravity, I could be wrong but I think Wiliada has previously made some very interesting comments re this.

We are so lucky to have such knowledgeable members on this forum.

Cheers
Danny

[williada]

Yes Danny, I have banged on about it for a few times in the past. Peter's modelling could well determine closer outcomes and is on the right track. Mine was by trial and error observations. Have not got time at the moment to do a lot at the keyboard.

Peter, I will reply to your email soon, just busy at the moment. You might be interested I revisited the BFXyz.nl site for an update of the Excel add on for the ballistics program that a few have used and a message came across the screen that I have bee reported to Dutch cyber crime on trying to download the update. Interested if anyone else has had the same rubbish as I know a few shooters have used BFX in the past particularly in South Australia. David.

[!Peter!]

I should caution people that the modelling presented isn’t exact. It should only used to understand the relationships between the model parameters and their effects. A common error I find is people assume that because a number is presented to the 10th decimal place it is accurate.

The biggest insight I gained is what causes the traverse wave in the barrel.

VarmintAl’s animation below shows the movements of the rifle from ignition to bullet exit. The movements have increased 1000x.


The animation moves a bit quick to see what is going on so I broke the animation into frames. Below are some of the key frames:
Frame 5 rifle starts moving back


Frame 16 chamber start expanding


Frame 21 action start rotating


Frame 37 bullet half way out. In this frame you can see the action rotated and the start of the barrel bent but the muzzle angle has not changed.


Frame 51 bullet exits


From this sequence it looks as though it is the action rotating about the center of gravity that is the major cause of traverse waves on the barrel. If this is the case then it explains the affect that rifle center of gravity and stock/ action dynamics has on positive compensation.

!Peter!

[DaveMc]

We have been playing with compensation for a while now and the idea and theory has been around for a very long time. There is no doubt it exists and throughout our trials we have observed very good positive compensation from 300-500 yards. Many shorter range load development regimes are based on it. (science by large amounts of anecdotal evidence).

However from what we were doing we saw very little influence of this compensation on the 1000 yard elevations due to the gradual overpowering effect of velocity influences (it is there but insignificant compared to velocity effects). This does not mean it cannot be achieved as our observations were based on heavy barrels and heavy varmints along with a few heavy and medium palma 308s in a few slightly different configurations with high and low cog and other influences (barrel time, weights etc). Of course this same short range compensation direction "helps a little" at the longer distances as it is in the correct direction. but the amplitude we have observed is either generally too small or the wavelength too short to help enough at 1000. I made a challenge a few years back based on these types of calculations you have done Peter. What is required for positive compensation at 1000 yards? (As this is what interests me the most) but have come to the conclusion for myself that it is better to concentrate on short range accuracy and tight velocity spreads to carry accuracy all the way out. If you intend to shoot ultra long range then velocity spread is the king - BUT I still have a great interest in anyone trying variations that may work.

Williada and a few others may have taken this further over the last few years and I stopped pursuing but am still extremely interested to see if someone can crack the nut.

Lets discuss:
So - you need to generate an upwards impulse of the barrel (as the slower bullets that leave later need to be launched at a higher angle) of significant amplitude and/or higher frequency (shorter wavelength) to make it work over what we have observed.

We came up with similar figures to you above Peter and in a recent post extrapolated out some of the variations for various bullets and posted a few graphs in the ES SD group viewtopic.php?f=5&t=7912&start=30

Originally we thought the answer may lie in some of the 308 FTR loads with slower bullets and lighter (whippier) barrels hitting the muzzle later with a larger upward impulse (the old 303's reported compensation regularly) but as it turns out you NEED more compensation for those bullets.

So - you need to generate an upward impulse with and angular magnitude of 1 moa per 40 odd fps (slightly different for variations of bullet and speed). To make this useable it needs to be maintained over a wide range or you risk the chance of falling out the top or bottom and having disastrous effects on elevation (double the negative effect of velocity alone).

So the compensation challenge - Show us your short range (Williada suggest 140 yards - I did a lot at 110m (just so happened to be the distance across a pond into the bank on other side)) groups where you have this range of movement. In my mind it needs to be 2moa over 80 fps to be usable in the real world.
With the development of powerful (accurate) velocity measurements being easily achieved with tools such as the LABRADAR then we should be able to determine the effect more accurately.

Dave

[Norm]

Interesting subject with some great input.

A 2 moa variation in point of impact at 110 yards sounds like it would be hard to achieve with a thick barrel.
Most of my 1.250" cylinder barrels move well under 1 moa with a 80fps change in average velocity.
How much benefit would 1/2 moa give in terms of compensation over the same change in average velocity?

[williada]

I have always maintained that if a rifle is not broke don't fix it. The use of top draw ammunition is paramount. Understanding the concepts behind different reasons why a rifle performs well can explain why it does not perform well at different distances. Yes the heavy barrels do compensate at 500 yards and there are interactions with OCW concepts and Nodal tunes. Unless the velocity is maintained they have a weakness with distance. Hence the importance of even weighing primers for 1000 yards.

The 140 yard testing is the minimum distance to test a rifle due to coning effects which otherwise may distort your data given given that there are so many variables to tease out. It would seem to me that information gathered on distances less than 140 yards is not as scientific as it could be.

The 140 yard testing was developed to run in a new barrel with a minimum of shots to preserve its accuracy life. Those barrels which may be considered top draw are few and far between, maybe 20%. Another key purpose of the 140 yards is to ensure you do not pick a trend on a barrel that maybe displaying an OCW tune where the muzzle distortion is minimised but the general slope of the barrel profile is negative. So the charge test process helps sort out those barrels with potential early . It also means when you are analysing groups at further distance you can discount the variables to determine true group size just as you would for aerodynamic jump, light effects etc. Hopefully I have demonstrated on previous posts with actual target plots that the group shape tends to hold with distance even if it is enlarged. I use knowledge of other factors to explain why a shot was outside the general group shape. These processes are merely conceptual tools and a way of determining what you have got.

Many people do not have the luxury of being able to utilise lots of barrels, but they sure want to know how to make the best of what they have got. Its not all about positive compensation because barrels have their own personality but if you find your barrel has that positive characteristic you can use that close to a node for insurance. Or would you prefer a negative compensating profile? The charge test is then followed up with a seating depth test to refine the consistency of the load and group size.

Of course further testing at long range takes place to determine an appropriate velocity for the distance.

There is no substitute for doing the work.

[DaveMc]

To be honest David I would choose a load that showed good short range or angular accuracy with a velocity sd of 3-5 and negatively compensating (in the order of what I have observed) OVER a positively compensating one with sd of 10-12 - but fortunately I don't have to and neither do the readers. I do like to see neutral or slightly positive compensation - It is just not my PRIMARY concern in load development. Accurate grouping and low velocity spread works for me.

There are many ways to skin the fish regarding load development and they can all get you to a decent endpoint. I am not saying one is better than the other but my approach is to find a load that exhibits low velocity variation and tight short range groups over a wide forgiving node. There are some well known formulas that do this for us in varying calibers and cartridges and it is generally where the primer/powder/projectile combination suits the volume of the case and barrel friction profiles to give the best (most consistent) burn curve. If you follow this type of approach and put effort into loading for tight velocity spread you will have an accurate rifle all the way through and well past 1000 yards.

So lets discuss the reality of the above figures (Peter our observations and calculations agree generally with your tables and graphs).

Norm - my figures for the barrels I have tested show more like 0.25 moa drop over 80-100 fps at 110m which equates to a pretty flat line at 300 for a straight 1.25. and maybe a slight rise at 500. I am keen to see others....? this is great when shooting 300-700 yards as you can get away with a bit of variation in velocity and stay in the x. The rifles will also tend to shoot well in this range. so an sd of 10 which sees 1 in 20 shots approximately varying by +/- 20fps (like Peters graph above) can hold fantastically flat groups but the same load even with a bit of positive compensation will drop out of the 6 at 1000 quite regularly. To hold x ring at 1000 you need to have the right load combo and great control of the variables. a quarter minute compensation over 80 fps will be swamped by 2-2.5 moa due to velocity.

A rifle holding 0.25moa at 100-110m can hold <0.5moa all the way to 1000 with this approach.

David I am not saying it is wrong and I have a great amount of respect for your work I would just like all those reading this forum to understand clearly that there are other areas too that need to be concentrated on. choosing the right powder and primer that works in your barrel (low or high friction coefficient), controlling the variables including but not limited to case volume, neck tension, etc etc. (if you feel a difference in neck tension or have too much runout these are areas you can quickly improve on).

By all means it is a terribly interesting exercise to map the group patterns at shorter ranges and see if there is any significant compensation going on (be careful not to make sampling errors from small group sizes) and also I would dearly love to see a lot of them posted.

[!Peter!]

Thanks for your replies.

DaveMc, unfortunately I won’t be able to do any testing for few months. When I do get a chance I’ll post my targets.

I suspect I’m getting positive compensation at 800m. Shooting on electronic targets earlier this year I noticed that I had shots which were registering a slower velocity on the target that were hitting higher than they should. I can’t say for sure as I can’t confirm the accuracy of the electronic target.
From what I’m seeing in the modelling that has been done is that the stock design has at least as big an impact on positive compensation as barrel profile.

I’m surprised about the need for a wide window as the 40fps in my numbers above only has an exit time difference of 0.024 ms which is about 1/10 of the grid on the graphs. The first major upswing goes from about 0.7 to 1 ms and second upswing from about 1.5 to 2 ms on the medium palma graph.

However, I’m guessing the center of the upswings (i.e. about 0.9 and 1.8 ms on the medium palma graph) when the moa per fps is at a maximum is not the best time for bullet exit as the muzzle’s velocity will be at a maximum which will increase the group’s size due to the disturbance on the bullet.


Williada, I agree with your philosophy of getting the best out a particular barrel.

You are also correct about OBT/OCW being another aspect. However, I would expect that the optimal barrel time can be adjusted by a bloop tube length.

Unfortunately, the target plots in your previous posts are no longer there.


On a related matter, has anyone played with purdy’s tuning method?

Thanks again for your replies.

!Peter!

[williada]

Peter, unfortunately I get labelled with "Positive Compensation" by some. Its just a tool to understand what your barrel is doing so you can discount all factors like aerodynamic jump or conditions to see the potential of the rifle I put it out there so people understood the concept. I take a holistic approach to tuning which does include armouring, stock design and load development. A few Queens winners across different disciplines current using my methods would agree even in recent times and the past. It just happens I have kept a low profile and liked to keep it that way. Most of us can't afford to keep swapping barrels to meet a specification, so we have to trick them up in other ways.

Yes, I have explored the Purdy methods and we used to do that by trial and error in the past. A bloke by the name of Percy Pavey not Purdy, who I used to take to the range regulary taught me all about the appropriate barrel length. Now Purdy produces it with harmonic in mind. Beware of the tradeoffs between harmonics and barrel stiffness, in tuning and muzzle distortion because things are not strictly harmonic. Yes I have mentioned the bloop and backbore but just put it out there rather than scare people with theory. If you are going to try Purdy use calculations for .308 based on a diameter of .866" as a minimum to determine the length of the bloop tube because this diameter deals with flack which can upset the bullet. The other thing I would say, is that tuners for full bore based on the 7 th harmonic would be better served by the 19th , 21st and 23rd due to the velocity and barrel length we use. Then its suck it and see by cutting back from the longest length and seeing how it interacts with the other variables. If you run with a variable thimble on top of the bloop tube and change the weight if you have to, to marry with muzzle amplitude on a compensation profile you desire if possible which you could calculate you can get around some issues. The bloop tube or variable tuner can be of sufficient weight to counter torque too. If you run with a backbore, you could also run with a muzzle weight like the great Cam Mc did. All components have to be balanced with bag handling.

Have fun. David.