Fun with Lab Radar Data - Initial findings on variability of BC as shot

[AlanMcD]

I picked up a used Lab Radar unit off the classifieds as an upgrade over my old Chrony (which still works well) with a goal of using it to study something that rarely gets discussed here - the variability of BC in the pellets as we shoot them, even though they are the same pellets out of the tin.

This is something that I have been curious about for years, ever since I first used average Chrony velocity data collected at two different distances (from two separate shot strings as I only have the one Chrony) and noticed that I was always getting a higher ES at distance vs at the muzzle – logic would say that since the pellets had lost a lot of speed, all else being equal the ES should be smaller. So all else is clearly not equal, and the big unknown to me was the BC on the different shots.

I am in the early stages of this, but even on my initial “proof of concept” trial I am seeing a lot of variation. I’ll have to do this again with more shots and better understanding of the humidity and barometric pressure, but I took 5 shots and got good trace data to use, so I did my test case on this data. It was shot from my .22 Huben K1, and was using JTS 18.1 grain pellets.

I took each individual shot file and truncated it for the S/N ratio data that I trusted – it was strange in that I was shooting at a steel spinner that was about 43 yards out, and it gave me velocity data for distances beyond that. But the S/N data clearly shows that this “extra” data is not good.

I then performed a quadratic polynomial regression analysis on each shot’s data, after having verified that the results proved to be an excellent fit. All five traces had R Squared values over .999, so the fit is excellent.

I then calculated the velocities for each shot at 0 and 50 yards from the equations and put each shot’s data in the JBM online BC calculator. While average of the five shots was a BC of 0.033 (approximate, as I was not precise on the atmospheric conditions – I’ll do better in the future), the five shots varied from a low of 0.030 to 0.035. While that might not sound like a lot, that represents a 15% swing in the BC of the individual shots. To me, that seems like a significant factor in long range accuracy . . .

More to come in the future as I continue to work on this . . . Here is what the data looks like.

Distance	Shot 1	Shot 2	Shot 3	Shot 4	Shot 5
0​	927.3	925.8	940.3	940.9	936.6
10​	889.8	885.6	897.3	897.0	894.1
20​	852.5	848.4	859.1	857.7	855.9
30​	815.6	814.4	825.7	822.9	821.8
40​	778.9	783.5	797.1	792.7	792.0
50​	742.5	755.7	773.3	767.1	766.4
R Squared	0.9997	0.9991	0.9995	0.9997	0.9997
G1 BC	0.030​	0.033​	0.035​	0.033​	0.034​		ES =	0.005​
							ES (%) =	15.4%​

 

[JimD]

Did you measure weight or head size on the pellets you used in the test? I have no idea why that would matter but it may be something to include until you can rule those differences out.

I've seen an interesting discussion of the need to spin pellets to look for differences in their weight distribution to address accuracy. That seems more likely to affect bc to me but I have no idea how you could do a meaningful check of a pellets weight distribution. It seems like the highest bc would be from a pellet spinning smoothly around it's geometric axis.

 

[Vetmx]

I could be missing something but I’m just going to look at your last three shots because those shots have an ES we like to see. Therefore things look quite normal. But please keep posting because it’s about time we start seeing interesting topics and not how to fix a FX Impact.

 

[AlanMcD]

Did you measure weight or head size on the pellets you used in the test? I have no idea why that would matter but it may be something to include until you can rule those differences out.

I've seen an interesting discussion of the need to spin pellets to look for differences in their weight distribution to address accuracy. That seems more likely to affect bc to me but I have no idea how you could do a meaningful check of a pellets weight distribution. It seems like the highest bc would be from a pellet spinning smoothly around it's geometric axis.

These were just shot straight from the tin, unsorted in any way.

In the past, I have messed around with all kinds of sorting, and I did find a bit better accuracy with pellets that were both weight sorted and head size sorted as well. I've tried sorting head sizes with both the Pellet Gage (the one with the precision head size holes in it), and by roll sorting. I found the best results from roll sorting, but to get those best results it took a lot of work. I'd have to flare the skirt a bit, then size it down in a Beeman pellet die at 5.57mm (to get the skirts all the same, leaving the head untouched) so that the same size heads would all roll to the same spot.

I always felt that the improvement in accuaracy from this was partly from reducing the variability in BC between pellets - after all BC is a function of shape and mass, and if the mass was closer and the shape was closer (via common headsize) the the BC should be closer.

It is something that I will eventually play around with. This was all just sort of proof of concept.

 

[AlanMcD]

I could be missing something but I’m just going to look at your last three shots because those shots have an ES we like to see. Therefore things look quite normal. But please keep posting because it’s about time we start seeing interesting topics and not how to fix a FX Impact.

The first two shots were clearly slower - I think I need to tune up my regulator a bit, as it might be creeping - and yes, the last three are closer in speed. But it should not matter to the point of the discussion, as each shot had it's own BC calculation performed on it. And the ES was only 15 fps /1.6% which is really not that bad - clearly it could be (and has been) better but it is well under 2%, let alone something like 4%.

And logically, since BC tends to "get worse" for wasp waisted pellets as the speed goes up over about 850 fps, the the slower speed shots should have a higher BC - but that is not the case here, so something else is clearly in play. Lots to study and learn . . . .

 

[GeneT]

The degree that the projectile precesses ( https://en.wikipedia.org/wiki/Precession ) will enlarge the effective frontal surface and increase drag. This is tough to do much about with pellets, other than sorting for head size and determining which size is optimal for your barrel, and then chambering as accurately as possible. A slug should be easier to align concentrically to the bore, but there will always be some precession.

GsT

 

[Ballisticboy]

The degree that the projectile precesses ( https://en.wikipedia.org/wiki/Precession ) will enlarge the effective frontal surface and increase drag. This is tough to do much about with pellets, other than sorting for head size and determining which size is optimal for your barrel, and then chambering as accurately as possible. A slug should be easier to align concentrically to the bore, but there will always be some precession.

GsT

Pellet yaw angles have to be very small, less than one degree, otherwise group sizes grow to be enormous. Since yaw induced drag is a function of the square of the yaw angle, small yaw angles produce minute increases in drag. I produced a thread on this subject, but never posted it on here. I will put it on.

Thread posted. https://www.airgunnation.com/threads/yaw-induced-bc-changes.1321557/

 

[DesertSilver]

Pellet yaw angles have to be very small, less than one degree, otherwise group sizes grow to be enormous. Since yaw induced drag is a function of the square of the yaw angle, small yaw angles produce minute increases in drag. I produced a thread on this subject, but never posted it on here. I will put it on.

Thread posted. https://www.airgunnation.com/threads/yaw-induced-bc-changes.1321557/

Shouldn't he be using GA instead of G1 BB?

 

[Franklink]

Shouldn't he be using GA instead of G1 BB?

Won't change much for what he's shooting (distance and particular pellet).

 

[Franklink]

I've seen a direct correlation to the best long range accuracy coming from barrel/projectile/speed combinations that also have the tightest ES @ distance.

IE, the long range accuracy stand-outs, also have much tighter ES at long range than the projectiles with ho hum long range accuracy.

 

[Ballisticboy]

Shouldn't he be using GA instead of G1 BB?

For pellets, yes you should not use G1, particularly at higher speeds, but the comparisons from shot to shot will be much the same unless the muzzle velocities are varying a lot. Chairgun will give you the GA BC, whereas MERO will allow you to choose GA, or GA2 with its modified high speed values.

 

[Stubbers]

Pellet yaw angles have to be very small, less than one degree, otherwise group sizes grow to be enormous. Since yaw induced drag is a function of the square of the yaw angle, small yaw angles produce minute increases in drag. I produced a thread on this subject, but never posted it on here. I will put it on.

Thread posted. https://www.airgunnation.com/threads/yaw-induced-bc-changes.1321557/

Does AoA also effect drag, and possibly how a labradar would report BC?

At longer ranges or inclined shots particularly.

-Matt

 

[Ballisticboy]

Does AoA also effect drag, and possibly how a labradar would report BC?

At longer ranges or inclined shots particularly.

-Matt

Since the radar can only detect out to fairly short ranges, the trajectory curvature is minimal, so the angles of the trajectory are very small and likely to make minimal contribution to the pellet deceleration. Similarly, the angles between the trajectory and the radar beam should also be very small, but this is not a Doppler tracking radar and so cannot take into account any angles between the trajectory and the beam.

If the target is higher or lower than the rifle, then there could be some contribution from gravity to the deceleration of the pellet, which will not be apparent from the Doppler speeds.

 

[AlanMcD]

So I reassessed the shot data using Chairgun to get a GA value for BC, and it gave me slightly higher values for all five, but the absolute variability stayed the same (a spread of 0.005 in BC across the 5 shots, for a ~14% potential swing).

The new values for the 5 shots are 0.031, 0.0338, 0.036, 0.0342, and 0.0346 in order. So GA was about 2.5% higher than G1 for these specific shots.

To Ballisticboy's point/ observation above, these shots were all slightly downhill - maybe 5 or 10 degrees downhill. I don't think that would impact the variation, but I'll be sure a future test is more horizontal to get a more representive BC value as thse might be slightly overstated due to gravity.

Interestingly, I put the two extreme BC values of the five shots into Chairgun and looked at the difference in drop and wind drift at 50 yards, and it is noteworthy. With everything else held constant between two shots (exact same muzzle velocity at the start etc.):
- There would be a 0.6" difference in drop
- There would be a 0.3" difference in wind drift, for a 5 mph 90 degree breeze (of course 0 difference if there is no wind)

That is a possibility of over 1 MOA just from variation in BC. Of course in the real world, some things add and some things cancel, but it is clearly a significant potential source of variation. It will be interesting to see if sorting can make a difference on this front . . .

I'm not sure when I 'll find the time to test it out, but I hope to do so before too long.

 

[Zesty]

Excellent work sir! Looking forward to your future findings!!!

 

[Smitty911]

I picked up a used Lab Radar unit off the classifieds as an upgrade over my old Chrony (which still works well) with a goal of using it to study something that rarely gets discussed here - the variability of BC in the pellets as we shoot them, even though they are the same pellets out of the tin.

This is something that I have been curious about for years, ever since I first used average Chrony velocity data collected at two different distances (from two separate shot strings as I only have the one Chrony) and noticed that I was always getting a higher ES at distance vs at the muzzle – logic would say that since the pellets had lost a lot of speed, all else being equal the ES should be smaller. So all else is clearly not equal, and the big unknown to me was the BC on the different shots.

I am in the early stages of this, but even on my initial “proof of concept” trial I am seeing a lot of variation. I’ll have to do this again with more shots and better understanding of the humidity and barometric pressure, but I took 5 shots and got good trace data to use, so I did my test case on this data. It was shot from my .22 Huben K1, and was using JTS 18.1 grain pellets.

I took each individual shot file and truncated it for the S/N ratio data that I trusted – it was strange in that I was shooting at a steel spinner that was about 43 yards out, and it gave me velocity data for distances beyond that. But the S/N data clearly shows that this “extra” data is not good.

I then performed a quadratic polynomial regression analysis on each shot’s data, after having verified that the results proved to be an excellent fit. All five traces had R Squared values over .999, so the fit is excellent.

I then calculated the velocities for each shot at 0 and 50 yards from the equations and put each shot’s data in the JBM online BC calculator. While average of the five shots was a BC of 0.033 (approximate, as I was not precise on the atmospheric conditions – I’ll do better in the future), the five shots varied from a low of 0.030 to 0.035. While that might not sound like a lot, that represents a 15% swing in the BC of the individual shots. To me, that seems like a significant factor in long range accuracy . . .

More to come in the future as I continue to work on this . . . Here is what the data looks like.

Distance	Shot 1	Shot 2	Shot 3	Shot 4	Shot 5
0​	927.3	925.8	940.3	940.9	936.6
10​	889.8	885.6	897.3	897.0	894.1
20​	852.5	848.4	859.1	857.7	855.9
30​	815.6	814.4	825.7	822.9	821.8
40​	778.9	783.5	797.1	792.7	792.0
50​	742.5	755.7	773.3	767.1	766.4
R Squared	0.9997	0.9991	0.9995	0.9997	0.9997
G1 BC	0.030​	0.033​	0.035​	0.033​	0.034​		ES =	0.005​
							ES (%) =	15.4%​

I need to get mine out and shoot more.

Simple question - What the hell is a

quadratic polynomial regression analysis???
Smitty

 

[Franklink]

So I reassessed the shot data using Chairgun to get a GA value for BC, and it gave me slightly higher values for all five, but the absolute variability stayed the same (a spread of 0.005 in BC across the 5 shots, for a ~14% potential swing).

The new values for the 5 shots are 0.031, 0.0338, 0.036, 0.0342, and 0.0346 in order. So GA was about 2.5% higher than G1 for these specific shots.

Yep. In my field, a difference of 5% or greater is recognized as statistically significant.

GA versus G1, for typical diabolo shaped pellets will always supply a BC of statistical INsignificance.

Yeah, GA is the "correct" drag model for a projectile for a typical pellet shape, but it just doesn't matter when the rubber meets the road.

Going the other way (using GA for a slug) is a bit more problematic.

 

[AlanMcD]

Simple question - What the hell is a quadratic polynomial regression analysis???

Most people are familiar with a "linear regression", which is looking to find the linear function that best fits a given set of data plotted on an X and Y axis. It can be done for the speed of a projectile vs. distance, but it is just an approximation - when doing one of these analyses, unless there is a true linear function involved all we get is an approximation. And that is all it is for projectile velocity too, as I'll explain.

We know that when we shoot a projectile, after the projectile leaves the muzzle it will decrease in speed as a function of the air resistance on it - and we know that the air resistance increases with the square of the speed, so the equation for it must include that term in it. This makes the equation "non-linear" because it will have terms that speak to both the distance (the variable in the equation) and the distance squared. So this clearly is not something that can be accurately understood with a linear regression . . .

Rather than a simple linear regression, I found the best fit using a quadratic regression (an equation with three terms, not two, with the added one working with the square of the distance). This proved to be incredibly accurate when I tested it against the raw data from the lab radar file, for all the points of data that I used in the analysis - the average data point from the Lab Radar trace was within 0.07%, and even the most extreme error in terms of fit to the equation was off by only 0.5%.

This lets me use the equation as an excellent "smoothed" function to forecast the best projectile speed to use for the BC calculation using the velocities at two distances, taking out any individual error in any one Lab Radar data point. I also find this equation to give "better" data than the Lab Radar does for the summary report on the speed at the different set point distances - I don't have access to their algorithm, but it is clear that they use the data points around the given value to calculate it, and this seems to be "noisier" to me than fitting an equation to the known good data and using that instead, but that is a whole separate discussion . . . .

 

[Arzrover]

Nice post
When @Franklink and I were collaborating on some barrel and ammo testing, I was the one with the LabRadar where he used 2 chronos. It took me a while to get to or near the point in understanding that you are at because I didn't analyze the base data at all for a while. I DID see the far velocities jumping around more than expected, as well. As you mentioned, checking the return signal can eliminate a few.
What ended up being most significant was the wind. It is QUITE variable here, even if light. Having flags out clearly showed a correlation between wind direction and far velocity drop. I know this is basic, but without flags, I may never have seen it...
You can plot the far velocity drop on the ballistic apps at 12 and 6 o'clock directions to see what I mean.
Bob

 

[BlackICE]

Does anyone know how to calculate BC in GA units giving V1 D1 and V2 D2? It's a PITA to enter numbers into Chairgun, it would be much easier to import the labradar data into a speadsheet and to just add a formula to the data.