Changing My Thinking About Slugs

[mackeral5]

You may find that the stability suffers at higher speeds, specially over 1050 ft/sec.

Thank you for weighing in.

[Scotchmo]

I’d like to revive this topic.

In this thread, Bob made the case that a 1000fps slug velocity could be preferred over slower velocities when looking for minimum horizontal dispersion (wind drift). Now I’m going to make a case for velocities in the 1050 to 1100fps range. Vertical dispersion is another component that we seek to minimize. Velocity spread is a primary contributor, especially for ELR. There is a phenomenon that some are unaware of that should be considered. Sonic velocity “trimming”. Bryan Litz recently referred to it as “Mach trimming”, not to be confused with the same terminology used for aircraft control surfaces.

There is a fairly steep rise in drag as velocity is raised into the transonic range. If we push too far past that inflection point, we are just wasting energy as that hard earned velocity is quickly shed. However, there can be a benefit from encroaching into this range, at least a little. When we are operating in that range, and we have a high ES, the down range velocity spread will be significantly less than if we were operating below that range. The extra drag tends to dampen out the higher velocity shots back to the inflection point, while those below the inflection point are less affected. The BC(RA4) delays the drag rise a little longer but then climbs even steeper. Maybe that’s why we see the 1050-1100fps range as a preferred velocity for the most accurate 22lr rounds. Standard velocity 22lr can have a fairly high ES while still having decent accuracy.

An example using my 7mm BBT projectile and an extreme spread of 10fps:

500m target distance

870-880fps
Vertical dispersion  = 17.2”

1070-1080fps
Vertical dispersion = 7.4”

If we have a projectile that will remain stable enough, and we are willing to waste some air, we might push it even faster:

1170-1180fps
Vertical dispersion = 4.6”

The farther the target, the more likely that it’s worth the trade offs. To explore this area, we need high BC projectiles with sufficient stability at close to sonic velocities, and a platform that that can push them that fast. I’m currently building a new ELR airgun that will let me explore this area a little more. Hopefully ready before year’s end.

[rsterne]

Interesting point, Scott.... I'm not so sure pushing beyond Mach 1 is a great idea, but I can see the advantage to using the steeper slope on the drag coefficient to push the downrange velocities into a tighter range, that makes sense.... I assume the numbers you gave for vertical dispersion are calculated, not measured?.... Please correct me if I am mistaken.... The farther the target, the higher the ideal muzzle velocity for minimum wind drift as well, within limits, and assuming the crosswind component is a constant all the way along the trajectory.... Otherwise, the part of the travel with the greatest wind velocity will have the greatest affect on the drift, especially if that is near the muzzle, when the velocities are further into the high drag zone....

Tuning with a movable (threaded) muzzle weight when shooting at constant range can change the release angle of the slug such that the faster slugs are shot on a slightly lower trajectory due to barrel harmonics.... A small change in the position of the weight can tighten groups significantly.... I understand this is used quite a bit by .22LR competitors.... You tune so that the slowest rounds are released just before the barrel reaches the top of its oscillation, and of course for optimum results the barrel must be indexed to oscillate as close to the vertical plane as possible....



The example I made (but have not tested) uses 28 TPI threads, which gives 0.003" movement per "hour" on the index marks (0.036" per turn).... The setscrew in the brass weight presses a Delrin ball against the threads to prevent it from "self-adjusting".... It threads onto the muzzle with standard 1/2"-20 threads, against a shoulder (actually the end of the CF outer tube)....

Bob

[Scotchmo]

Bob,

Yes. The vertical dispersion listed was calculated with Strelok.

Harmonic tuning can reduce vertical dispersion for a specific distance, but it can actually then make it a little worse at some other distances, so not a great solution when shooting at multiple distances.

[rsterne]

Correct.... but if you do a lot of shooting at a few known distances, you can dial it in at each and have a log book.... I know Rimfire shooters frequently use them.... If you don't change the load (slug and velocity), and hence have a set time from chamber to muzzle, the tuning should still work for sending faster slugs on a lower trajectory, but it might overcompensate (or maybe not)....

Bob

[ballisticboy]

The problem with modelling the effects of changes in muzzle velocity with programs like Strelok is that you are only looking at one isolated effect. You have not considered the reasons why the muzzle velocity changed. One common reason is the projectile weight, which will not only change the muzzle velocity but also the rate of loss in velocity throughout the trajectory.

I carried out a very basic modelling exercise once many years ago where I took a springer model and a PCP model and looked at the effects on muzzle velocity of small incremental pellet weights and in turn the effects at the target, which also took into account the change in weight. The most interesting aspect was that the PCP performed much better than the springer. However, the target spread was also much reduced when the pellet weight change was combined with the change in muzzle velocity.

The only way you can do that with something like Strelok would be to change the BC for each shot, but you will not know how much of the velocity change being modelled is due to change in projectile mass as opposed to other factors.

[rsterne]

I agree that changes in projectile weight make little difference in the vertical dispersion.... The heavier ones have a better BC, which helps to compensate for the originally (theoretical) flatter trajectory of lighter ones.... The vertical dispersion downrange will be less than calculated if you use constant BC, PROVIDED that the difference in velocity is predominately due to the weight difference.... Of course some of the difference in muzzle velocity is due to other factors, such as hammer strike, bore friction, and probably many others....

Bob

[Scotchmo]

I said the example was for my 7mm BC, but it was for my .308 which will have a higher BC. The 7mm slug has a lower BC, so even more dramatic difference in dispersion.

[Scotchmo]

The problem with modelling the effects of changes in muzzle velocity with programs like Strelok is that you are only looking at one isolated effect. You have not considered the reasons why the muzzle velocity changed. One common reason is the projectile weight, which will not only change the muzzle velocity but also the rate of loss in velocity throughout the trajectory.

…

Actually, I have considered the change in projectile weight, and yes, it could change BC. I sort slugs based on weight. So most of that effect can be eliminated and I don’t worry about it after that. The vertical dispersion reduction in this theoretical case is being looked at strictly from sonic trimming. That is the phenomenon that supports using a higher velocity than we might otherwise.

The correlation between BC and weight, and how it affects down range dispersion could be another good topic for discussion. Interesting that at some point down range, any reduction in BC will be just enough to compensate for the higher velocity, and there might be no change in vertical for the POI. But farther out, things will get progressively worse.

I like the sonic trimming idea since it acts to even out the velocity right after the projectile leaves the muzzle. And that has a beneficial affect for all down range distances that we might shoot.

[ballisticboy]

As many probably know, artillery systems use multiple charges to cover the range of muzzle velocities from about 250m/s up to around 850m/s. One of the first things which was drummed into me when I started working in the external ballistics section at RARDE was don't have a charge which propels a shell at speeds just under Mach 1. The reason is simple, stability dips down at speeds between Mach 0.95 and 1.0, particularly on boat tailed projectiles, which leads to large dispersions at the target.

Now, shells are normally designed with a Sg of around 1.2-1.3, so there is not much stability you can lose before you have problems. Small arms tend to have higher Sg values, though 1.5 is usually considered the optimum for maximum BC, so a bullet may be able to give up a bit more Sg and still give an acceptable performance, but you could easily find your reduction in muzzle velocity error at the target is reversed because of the poorer BC due to bullet yaw. Hence, you may find your reduced vertical spread due to muzzle velocity variability is more than offset by a reduction in BC and an increase in group size due to increased yaw.

It is not possible to model the total effect without a full six degree of freedom model. No point mass or modified point mass model can show the total effect. For target shooters, Mach trimming may work if they have minimal yaw or yaw rates to start with, or higher than desired Sg values where a reduction in Sg may give improved group sizes by itself. It is not possible to predict the outcome without a complex model and, at the ranges talked about, it may be difficult to test under the appropriate conditions.

[Spacebus]

I’d like to revive this topic.

In this thread, Bob made the case that a 1000fps slug velocity could be preferred over slower velocities when looking for minimum horizontal dispersion (wind drift). Now I’m going to make a case for velocities in the 1050 to 1100fps range. Vertical dispersion is another component that we seek to minimize. Velocity spread is a primary contributor, especially for ELR. There is a phenomenon that some are unaware of that should be considered. Sonic velocity “trimming”. Bryan Litz recently referred to it as “Mach trimming”, not to be confused with the same terminology used for aircraft control surfaces.

There is a fairly steep rise in drag as velocity is raised into the transonic range. If we push too far past that inflection point, we are just wasting energy as that hard earned velocity is quickly shed. However, there can be a benefit from encroaching into this range, at least a little. When we are operating in that range, and we have a high ES, the down range velocity spread will be significantly less than if we were operating below that range. The extra drag tends to dampen out the higher velocity shots back to the inflection point, while those below the inflection point are less affected. The BC(RA4) delays the drag rise a little longer but then climbs even steeper. Maybe that’s why we see the 1050-1100fps range as a preferred velocity for the most accurate 22lr rounds. Standard velocity 22lr can have a fairly high ES while still having decent accuracy.

An example using my 7mm BBT projectile and an extreme spread of 10fps:

500m target distance

870-880fps
Vertical dispersion  = 17.2”

1070-1080fps
Vertical dispersion = 7.4”

If we have a projectile that will remain stable enough, and we are willing to waste some air, we might push it even faster:

1170-1180fps
Vertical dispersion = 4.6”

The farther the target, the more likely that it’s worth the trade offs. To explore this area, we need high BC projectiles with sufficient stability at close to sonic velocities, and a platform that that can push them that fast. I’m currently building a new ELR airgun that will let me explore this area a little more. Hopefully ready before year’s end.

I'm glad you mentioned this! I recently watched an interview Bryan from Shot Show 2024. I was very surprised at his findings regarding Mach Trimming. I look forward to seeing how your new platform performs at ELR.

[Scotchmo]

This is somewhat related to this discussion, and I’d like to see about getting some feedback from Bob and Miles.

In order to have a good stability factor (at least 1.5), the maximum twist rate required occurs when shooting subsonic, but close to sonic velocity. Down range, as the velocity falls off faster than bullet spin rate, the stability factor increases, possibly to the point of being over-stabilized. At what point (over-stabilized at extreme distance), does the bullet lose enough tractability to cause it to have an angle of attack where the drag coefficient rises along with a lift coefficient appearing?

I’ve had good success with modeling that matches actual results when shooting subsonic airgun slugs at distances past 200yds. But there has always been issues in the 200yd to 500yd range where POI starts to rise slightly higher than predicted before falling back on point around 500yds, and then lower than predicted after that. It’s small but it’s there. No amount of juggling with BC or multiBC will make the predicted trajectory line up with actual results for the entire trajectory. My guess/theory is that the projectile has started to nose-up, experiencing increased drag and a slight lift. The actual trajectory is falling less than expected. At some point (around 500yds), the increased drag causes it to fall more vs distance, and the actual trajectory crosses back over the predicted trajectory, but from then on, the low POI just gets worse. It’s also possible that the bullets are 100% tractable, and I’ve got something wrong somewhere in the inputs. I have not had the opportunity yet to test much past that distance but hope to in the future. What are other’s thoughts on this?

[rsterne]

My quick reaction is that the drag model being used is not a good match for the projectile.... Field target shooters experienced the trajectory you are seeing using the GA model, but in the opposite direction.... flatter in the middle than expected.... Using multi-BCs is a band-aid for a poor drag model match....

Miles may be able to comment on the possibility that the bullet is not tracking along the trajectory, flying in a nose-up attitude which becomes worse with range.... However, I think the correcting force to the yaw should produce sideways drift, again Miles is the guy to ask....

I guess nothing beats good old fashioned range cards, mapping the drop (and drift) vs distance to target for your slug and velocity....

Bob

[ballisticboy]

It maybe that what you are seeing is the effect of vertical yaw of repose, though it is normally very small for direct fire as opposed to indirect fire at higher angles. There is a problem with point mass trajectory models, such as the ones used in just about all trajectory software available for shooters, in that it does not model the full effects of spin. There is a thing called the modified point mass model, which was developed specifically for long range artillery fire control, which takes the vertical yaw of repose into account. You will only see any difference when shooting at long ranges.

So what is the vertical yaw of repose? Every one is familiar with spin drift, caused by the spin induced side yaw of repose. However, there is also a very small gyroscopic reaction to the side yaw of repose which causes the bullet to have a very slight nose up attitude, called the vertical yaw of repose. Its effect is to produce a very small vertical lift force which modifies the trajectory, particularly as the range increases. Both the side yaw angle and the vertical one will increase as the gyroscopic stability factor increases.

Of course, it may not be that at all, it may just be a drag error. If it is the vertical yaw angle, I am quite surprised it is giving a noticeable error.

It is almost certainly not an over stability problem, if it is the vertical lift it is a model problem.

[Scotchmo]

Thanks Miles,

“vertical yaw of repose”, “vertical yaw angle”, “nose-up”, that is what I’m talking about.

“You only see any differences when shooting at long ranges.”

“It’s affect is to produce a very small vertical lift force which modifies the trajectory, particularly as the range increases.”

That’s what I’m seeing. I first noticed something off from the Strelok predictions in the 300m to 400m distances. It was not noticeable for an individual shot. But five shot group centers were slightly, but consistently high (a small amount, probably under one MOA), but then the group was suddenly hitting slightly low by 500m, like the projectiles were stalling out slightly, after a flare.

“There is a problem with point mass trajectory models, such as the ones used in just about all trajectory software available for shooters…”

I think that is it. I already know that even Strelok does not model as accurately as possible in all instances. For instance, Strelok calculates to meters, and when you want results in yards, it takes the value to the nearest higher meter, which can throw in some small (but easy to spot) errors in the predictions. The vertical yaw of repose effects are likely considered to be too small to worry about in most instances.

I’ve got two new .308 slug molds (150gr and 170gr) arriving today. The plan is to do some more testing at those long distances in the coming months.

[JungleShooter]

Scott,thank you for pushing the envelope!!
And Miles and others, for assisting!

I am not really in the position to do this at this time (and might never) — but at least I get to travel on the trail the people like you are blazing.

It is all very exciting to me to be able to reach and touch   
▪ such extreme distances,   
▪ with air,   
▪ without a gun license, 

▪ outside any officially sanctioned shooting range,   

▪ and at very low noise levels.     

Great times to be an airgunner! 😊

Matthias

[subscriber]

Scott,

This sounds like a good opportunity to get an even faster twist barrel and compare it to what you have.  Perhaps a .308 caliber barrel intended to .300 Blackout would make a good "overspun" test barrel?   

.300 Blackout uses 1:8 twist barrels to shoot 220 grain bullets at 1000 FPS.  You may not be shooting them that heavy, but you will be shooting them subsonic.  The same barrel is used to shoot .300 Blackout bullets as light as 90 grains at 2550 FPS.  One could argue that 125 grainers are the default supersonic bullet, with the 220 grainers are for less noisy purposes.

Perhaps .300 Blackout users have noticed odd trajectories from overspun bullets...

[Scotchmo]

Scott,

This sounds like a good opportunity to get an even faster twist barrel and compare it to what you have.  Perhaps a .308 caliber barrel intended to .300 Blackout would make a good "overspun" test barrel?   

.300 Blackout uses 1:8 twist barrels to shoot 220 grain bullets at 1000 FPS.  You may not be shooting them that heavy, but you will be shooting them subsonic.  The same barrel is used to shoot .300 Blackout bullets as light as 90 grains at 2550 FPS.  One could argue that 125 grainers are the default supersonic bullet, with the 220 grainers are for less noisy purposes.

Perhaps .300 Blackout users have noticed odd trajectories from overspun bullets...

I’m assuming that 220gr 300 Blackout bullet is copper jacketed. The lower density means a longer projectile, which needs a faster twist rate. A shorter cast lead projectile of 220 grains could probably get by with less twist. I have 150gr and 170gr molds. If I can launch the 170gr at 1100fps, and it beats out the 150gr for long range accuracy, I’ll be looking into getting a mold for 200gr slugs. It might work in my 1:10 twist.

For faster twist rates, I also need to consider barrel availability. 1:10 twist is the fastest .308 that TJ offers in their standard selection. And I’m not aware of any other manufacturer that can/will make barrels long enough for the velocities I’m trying to achieve.

[subscriber]

Scott,

Would I be correct that you are looking for a 32" long .308 barrel with 1:8 twist, if you can get it?  If not, please correct me.

[subscriber]

Scott,

I am sure that cost is a factor, but here are two 32" long 1:9 twist .308 barrels:

https://www.lothar-walther.com/gun-barrel-blanks/rifle-barrels/standard-usa/1479/barrel-blank-stainless-twist-9.30-od-1.26-l-32.01?c=35
https://www.lothar-walther.com/gun-barrel-blanks/rifle-barrels/standard-usa/1208/barrel-blank-stainless-twist-9.30-od-1.50-l-32.09?c=35

https://www.307lrp.com/product/bartlein-30-1-250-striat-1-9-twist-31-or-less-finished/
https://www.307lrp.com/product/bartlein-30-1-250-striat-1-9-twist-32-or-less-finished/

I also took the liberty of contacting a few US barrel makers under my own name via email, asking for the max barrel blank length they could sell in .308 with a 1:8 twist.  This includes Shilen, Black Collar Arms, Bartlein and Hart.  If they contact me back with barrels of suitable length (32"?), I will pass on the info to you.  Else, you might consider phoning them.