Why Use Multi BC's when modelling trajectories of highly efficient Lead Free Bullets

[Yew Tree Fieldsports]

I have been asked on many occasions why I use a multi BC solution for my TLR bullets for modelling trajectories and wind deflection, so thought it might be interesting (to some) to write a short note to illustrate the reason, including a real world examples.

As many will already know the G1 BC of a bullet, particularly a highly efficient lead free bullet varies considerably with its velocity. So how does this affect trajectories and wind deflection in the real world?

By using a multi BC solution you are essentially splitting a trajectory into much smaller sections and then 'stitching' them together. The upshot of this methodology is that the error in the predicted performance of the bullet (over the defined testing range) is so small that it is indistinguishable from the real world trajectory.

A simple initial example would be as follows:

My testing for the 6.5mm 114 TLR that I produce was done using a 6.5x47 rifle producing a muzzle velocity of 2,920 fps and a 6.5 PRC with a muzzle velocity of 3,240 fps. The multi bc solution resolved from that is as shown below:

BC​	Velocity (fps)​	​
G1​	Single Point​	Band ​
0.71​	3000​	2950 plus​
0.665​	2825​	2950-2680​
0.47​	2585​	2679-2490​
0.41​	2381​	2489-2272​
0.39​	2170​	2272-2050​
​	​	​

If you were to test the 6.5x47 in isolation at 500 yards (distance at which the bullet has slowed to 2,000 fps from the 6.5x47) looking for a single G1 BC you would confirm a G1 BC of 0.49. (Essentially you measure your MV and your impact velocity and extrapolate the result.)

When compared to the multi BC solution at the test muzzle velocity of 2,920 fps the results from the single BC are pretty close. Wind speed is 10mph and direction 90 degrees in this example. Spindrift has been ignored as its magnitude would be the same for either example.

​	​	Multi BC​	​	​	Single BC​	​	​	Difference​	​
Distance (yards)​	​	Elevation (MOA)​	Wind (MOA)​	​	Elevation (MOA)​	Wind (MOA)​	​	Elevation (MOA)​	Wind (MOA)​
0​	​	​	​	​	​	​	​	​	​
100​	​	0​	0.4​	​	0​	0.61​	​	0​	-0.21​
200​	​	1.3​	0.9​	​	1.4​	1.25​	​	-0.1​	-0.35​
300​	​	3.3​	1.5​	​	3.59​	1.94​	​	-0.29​	-0.44​
400​	​	5.7​	2.2​	​	6.17​	2.68​	​	-0.47​	-0.48​
500​	​	8.6​	3​	​	9.11​	3.48​	​	-0.51​	-0.48​
​	​	​	​	​	​	​	​	​	​

The problem arises when you try to apply that single BC to the bullet when it is fired at a significantly different muzzle velocity. In the real world example, a 6.5 PRC with an MV of 3,240fps. When you do this, the differences between the multi BC solution and the single BC become significant. In this case the table goes to 700 yards because that is the point at which the bullet velocity gets down to 2,000 fps.

​	​	Multi BC​	​	​	Single BC​	​	​	Difference​	​
Distance (yards)​	​	Elevation (MOA)​	Wind (MOA)​	​	Elevation (MOA)​	Wind (MOA)​	​	Elevation (MOA)​	Wind (MOA)​
0​	​	​	​	​	​	​	​	​	​
100​	​	0​	0.4​	​	0​	0.53​	​	0​	-0.13​
200​	​	0.9​	0.7​	​	0.97​	1.09​	​	-0.07​	-0.39​
300​	​	2.4​	1.1​	​	2.68​	1.69​	​	-0.28​	-0.59​
400​	​	4.2​	1.5​	​	4.73​	2.33​	​	-0.53​	-0.83​
500​	​	6.2​	1.9​	​	7.06​	3.01​	​	-0.86​	-1.11​
600​	​	8.5​	2.5​	​	9.67​	3.74​	​	-1.17​	-1.24​
700​	​	11​	3.2​	​	12.6​	4.52​	​	-1.6​	-1.32​
​	​	​	​	​	​	​	​	​	​

As is now evident the single BC elevation and wind deflection are significantly different to the multi BC solution. In real world absolute terms approximately 11 inches in elevation and 9 inches in windage. Real world testing of the multi BC solution through many rifles at many different MV's has proved it to be a very accurate reflection of trajectory and wind deflection.

As a bullet manufacturer I have to provide a ballistic solution that works at all sensible/practical muzzle velocities for a given calibre and this is the only way to do it in my view.

Conclusion

If you are shooting a lead free (efficient) bullet at the same or similar MV to that at which it was tested to produce the published single BC the predicted trajectory will be close to the actual trajectory and useable out to significant practical hunting ranges. If you are not and there is a significant difference between your MV and the test MV the error in a single BC solution becomes significant.

I hope some will find this useful
cheers
Rich

 

[jcampbellsmith]

Interesting, any plans to give your BC data to Igor so that he can update Strelok Pro?
Regards
JCS

 

[Yew Tree Fieldsports]

Interesting, any plans to give your BC data to Igor so that he can update Strelok Pro?
Regards
JCS

The bc data is freely available and published. I use strelok pro myself and just input the data. Quite happy to send whomever whatever data they need.
Cheers
R

 

[jcampbellsmith]

The bc data is freely available and published. I use strelok pro myself and just input the data. Quite happy to send whomever whatever data they need.
Cheers
R

Richard
I don't like keying in data, it's just asking for data entry errors. I much prefer to select the bullet data from the bullet database in Strelok Pro. I suggest that you contact Igor.borisov@strelokpro.online and send him your BC data as it becomes available. As you refine your data, send Igor the updates.
Thanks
JCS

 

[Yew Tree Fieldsports]

Richard
I don't like keying in data, it's just asking for data entry errors. I much prefer to select the bullet data from the bullet database in Strelok Pro. I suggest that you contact Igor.borisov@strelokpro.online and send him your BC data as it becomes available. As you refine your data, send Igor the updates.
Thanks
JCS

I’ll send him an email and see what he needs

 

[jcampbellsmith]

I’ll send him an email and see what he needs

Richard
An excellent plan.
Thanks
JCS

 

[Sharpie]

​

If you were to test the 6.5x47 in isolation at 500 yards (distance at which the bullet has slowed to 2,000 fps from the 6.5x47) looking for a single G1 BC you would confirm a G1 BC of 0.49. (Essentially you measure your MV and your impact velocity and extrapolate the result.)

This is very interesting to me, it seems like a more refined way of doing things than say just applying a single BC, for a particular velocity/distance range.

As explained by Hornady Ballistic Coefficient - Hornady Manufacturing, Inc simplifying it to "800 yard" and "200 yard" numbers. Or Mach 2.25 and Mach 1.75 velocities.

I am interested to know what equipment you use to measure the impact velocity of your bullets, out to as far as 700 yards. I understand that some electronic target systems can provide this information.

It sounds like a good approach to characterising your bullets in a practical way, without the sort of doppler radar equipment that Applied Ballistics and Hornady use to generate drag models for their solvers, for the specific bullets that they have measured.

Integration with Strelok Pro would be ideal.

 

[NigelM]

I gave Richard a bit of help testing the BC's on the 7mmTLR. It's a great system that measures velocity at target. We shot at 0/100/200/300/400 and 500m measuring velocity at each range over 3 shots. The consistency was surprisingly good with an ES of under 15fps at each distance which made his calculations pretty accurate.

This is as close to we get to the custom BC's produced by the likes of Bryan Litz. If stretching the range a bit it can make a couple of inches difference over a single number, both in drop and drift. It's also good to see a bullet maker taking the time to produce highly accurate BC's that are not exaggerated as is the case with some.

 

[Yew Tree Fieldsports]

This is very interesting to me, it seems like a more refined way of doing things than say just applying a single BC, for a particular velocity/distance range.

As explained by Hornady Ballistic Coefficient - Hornady Manufacturing, Inc simplifying it to "800 yard" and "200 yard" numbers. Or Mach 2.25 and Mach 1.75 velocities.

I am interested to know what equipment you use to measure the impact velocity of your bullets, out to as far as 700 yards. I understand that some electronic target systems can provide this information.

It sounds like a good approach to characterising your bullets in a practical way, without the sort of doppler radar equipment that Applied Ballistics and Hornady use to generate drag models for their solvers, for the specific bullets that they have measured.

Integration with Strelok Pro would be ideal.

The system I use is the Shotmarker system which was developed by a chap called Adam MacDonald who's based in Canada. In terms of testing all I'm really interested in is what the bullet velocities are doing over given distances. So in terms of 700 yards I don't normally need to go that far to get what I need. Indeed the reason why @NigelM was helpful in the 7mm testing was that he has a 7-08, which is pretty slow as a 7mm in MV terms. This meant I could measure what the velocities were doing at various distances and could get down to 2,000fps within 500 yards. Testing with straight 284 and 7 SAUM improved took care of the upper end of the speed ranges.

 

[Sharpie]

The system I use is the Shotmarker system which was developed by a chap called Adam MacDonald who's based in Canada. In terms of testing all I'm really interested in is what the bullet velocities are doing over given distances. So in terms of 700 yards I don't normally need to go that far to get what I need. Indeed the reason why @NigelM was helpful in the 7mm testing was that he has a 7-08, which is pretty slow as a 7mm in MV terms. This meant I could measure what the velocities were doing at various distances and could get down to 2,000fps within 500 yards. Testing with straight 284 and 7 SAUM improved took care of the upper end of the speed ranges.

The Shotmarker system looks good, and well packaged. I didn't realise that it could give precise chrono measurements as well. £725 it seems. I am impressed that it can derive such precise velocity measurements from it's planar array of three or four microphones, perpendicular to the bullet path, which I think must be a secondary function to it's use as a target. But @NigelM has found it to be consistent, which in itself suggests the results are useful.

I understand that is in use at Bisley. They give basic instructions here:: https://nra.org.uk/wp-content/uploads/Shotmarker-User-Guide-Website-Version.pdf

I have also glanced at the Steinert TrueZeroTarget® Electronic Target System, LOMAH, which appears to do something similar, claiming velocity precision to be within 1%, not exactly specified. However prices start at 3500 Euros, plus vat.

Steinert also do a pure acoustic chronograph, to be set up linear to the bullet path, but that seems not to have been developed with long range communication back to the firing point. Nor a larger distance between the two microphones for more precision.

I suppose there is limited call for such a thing for most civilian applications. Nor something with a wider array of multiple microphones that could operate in reverse, i.e. determining the bullet's origination point and vector, rather than the impact point. As well as velocity as it passes over the sensors of course.

 

[1894]

Interesting and thank you.
Do you have any plans to publish the BCs for the hollow points?

 

[Yew Tree Fieldsports]

Interesting and thank you.
Do you have any plans to publish the BCs for the hollow points?

I don’t to be honest as there’s no real point. They’re nowhere near as efficient as the TLR’s and provided the Mv they’re going out at is halfway sensible they follow the the 2 minute rule like pretty much every other bullet. Ie from a 100 yard zero a minute to 200 a further minute to 250. If you’re shooting passed that at quarry on a regular basis perhaps the TLR is a better option.

 

[borbal]

Richard, why do you stick with using ballistic coefficients for the G1 standard projectile when it has become widespread practice to use coefficients for the much more suitable G7 standard projectile? It would also be interesting to see the actual measured results rather than your modelled results...

 

[Stalker62]

Do you have any plans to publish the BCs for the hollow points?

I don’t to be honest as there’s no real point.

Beautiful.

 

[One on top of two]

I use my LabRadar , track my bullets from 0-100m .
Knowing those two MV’s it’s very easy to work out your BC , once I have all my data I will true my drops out too 500- 1000m ( depending on what I’m using )

Whole process start to finish just under an hour

 

[Yew Tree Fieldsports]

Beautiful.

I wish that was deliberate

 

[Utectok]

Interesting, any plans to give your BC data to Igor so that he can update Strelok Pro?
Regards
JCS

Great idea

 

[Yew Tree Fieldsports]

Richard, why do you stick with using ballistic coefficients for the G1 standard projectile when it has become widespread practice to use coefficients for the much more suitable G7 standard projectile? It would also be interesting to see the actual measured results rather than your modelled results...

I use them because over the speeds I’m testing there wouldn’t be any massive difference in the resolved results if the tests are done properly. I am happy that the resulting multi Bc solutions work very well over the relevant velocitiy ranges.
Over all the testing I’ve done I’m confident in saying that the bullets don’t subscribe to either a single G1 or G7 very well (when firing at varying MV’s) so you’d have to use multi bc’s whatever you do so that you can provide a useful model for people irrespective of their Mv. I suppose all the multi bc solutions I’ve seen use G1 so this was just the way I chose to do it. At some point I will try and sit down and look at the concept of a ‘G(Cu)’ for want of a better name and see if something specific can be done.

 

[Utectok]

Well done @Yew Tree Fieldsports great bullets and thoughtful and open about design and approaches. Not that it’s relevant to me but how is the journey to loaded ammunition going. People keep asking when can they buy them (estates ect who can’t reload).

 

[Yew Tree Fieldsports]

Well done @Yew Tree Fieldsports great bullets and thoughtful and open about design and approaches. Not that it’s relevant to me but how is the journey to loaded ammunition going. People keep asking when can they buy them (estates ect who can’t reload).

That journey has got bogged down in the mire of supply chain issues as far as I’m aware. Those that had got a fair way down the road to factory ammo now can't get the consumables in sufficient quantity.
It’s not something I was planning to do at any point soon as I simply don’t have the time.