How does velocity retention as measured by BC determine windage?

[RScott]

I'm evaluating pellets for AAFTA Hunter Division field target.  I figure 55 yard shot success will depend a lot on pellet choice, in particular the pellet's precision at that distance and minimizing the impact of wind.  Accuracy/precision have been easy to assess via shooting in near-calm conditions.  For windage adjustments, I'd like to rely on Strelok Pro or Chairgun, and so I determined BC for 55 yard shots in calm conditions using my chronograph and plugged the results into Airgun Depot's ballistic calculator (which I assume gives GA model BC's).

But conceptually I don't understand how velocity retention drives windage adjustments.  It would seem that BC as determined by velocity retention provides guidance on how efficiently the front of the pellet moves through air coming at it straight on.  But if there is a crosswind, the pellet is showing a different profile to the air flow than "head on".  (BTW, the first chart in the attached file shows the BCs I got from this exercise.)
 
How is it that a pellet that slices efficiently through a head wind is equally good with crosswinds?  Or should I consider checking BC in various crosswind conditions as well?

P.S.  I won't be using the 16.2 because it gave poor precision (low CTC and low mean radius), and very large drop, compared to the 10.3 grain pellets.  Among those pellets the AA seemed to outperform the JSB, but I didn't shoot enough pellets for statistically significant differences.

P.P.S.  I also determined BCs for 15, 28, and 42 yards, and for many other pellets and power levels.  I got different shapes to my BCs than Bob Sterne's typical charts show.  Mine are graphed in the second chart in the attachment.  Maybe I've done something wrong?

[rsterne]

The key to understanding how wind drift occurs is to realize that the pellet turns into the "relative / apparent" wind and therefore does not have a "side profile".... It is the downwind component of the drag that pulls the pellet off course.... Read Reply #35 in this thread and you should understand what is happening....

https://www.gatewaytoairguns.org/GTA/index.php?topic=169459.35

The greater the drag, the slower the pellet is going when it reaches the target, and the longer it takes to get there, starting from a given velocity.... This causes greater drift....

Bob

[RScott]

Thank you Mr. Sterne.
Reply #35 was very helpful.  I now realize that the side of the pellet does not "feel" the wind, i.e., the pellet is always facing the relative wind direction.

When I first read Reply #35, I thought that maybe the JSB 16.2's lower velocity - and thus more time exposed to the wind - would cause it to drift a lot.  But I think Reply #35 is saying that while that is true, the relatively low drag coefficient of that pellet causes it to have a direction more in line with the relative wind direction, i.e., the pellet tries to go towards the oncoming wind -- i.e., upwind -- which offsets the impact of the lower velocity.  In fact, Strelok Pro predicts the windage of the low velocity 16.2 grain pellet will be less than the low BC  but much faster 10.3 pellets. (And I interpret from Reply #35 that in the extreme case of a zero drag pellet, the POI on the target would actually be upwind). 

May I also ask if my other BC charts look reasonable or fishy to you?

Regards, and thank you for all your contributions to my and the airgun community's understanding of the science of our sport.

[rsterne]

Looking at your chart of BC's, most of them seem to peak around 800-850 fps.... I can't access the Airgun Depot BC Calculator for some reason, but some of the online calculators use an antiquated Constant Drag model.... Over a decade ago I made a similar chart to yours, showing the BC varying like crazy with velocity, and then I found out later that the constant drag model (which is what ChairGun, and pretty much all airgun sites, used at the time) is severely flawed at higher velocities.... An example of this constant drag calculator is the Pyramyd Air BC Calculator, which you can find here....

https://www.pyramydair.com/air-gunsresources/widgets/convert.php?BCalc&u=17

If you pick two distances (eg. 0 and 30 yards), and pick a "far velocity" that is 10% less than your muzzle velocity, that calculator will always produce the same BC (in this case 0.036), which is NOT the case.... Using the GA model, for example, and a BC of 0.036, the velocity at 30 yards for various muzzle velocities is as follows (using ChairGun)....

1400 MV.... 1051 @ 30 yds. (25% loss)
1200 MV..... 963 @ 30 yds. (20% loss)
1000 MV.... 861 @ 30 yds. (14% loss)
800 MV.... 718 @ 30 yds. (10% loss)
600 MV.... 544 @ 30 yds. (~9% loss)
400 MV.... 360 @ 30 yds. (10% loss)

As you can see, the velocity loss for a BC of 0.036 is about 10% below 800 fps, but above that the loss increases rapidly.... That is because of the rapid increase in drag in the Transonic range (Mach 0.8-1.2), which is built into the GA, G1 and G7 models.... The simplified calculator used by Pyramyd Air (and I believe AirGun Depot is affiliated with them? ) gets worse the higher the muzzle velocity.... Here are the most common Drag Models, with a "constant drag model" shown in black.... It ignores the drag increase in the Transonic range which every projectile experiences.... 



If you had a drag model that was a perfect match for your pellet, then the BC would be constant, regardless of the velocity.... Unfortunately, the best we currently have for pellets is the GA model....

Note that the drawing in Reply #35 indicates only the DIRECTION the pellet is facing, not the path it is following.... It is facing into the apparent/relative wind, but it starts out travelling straight towards the POA, and the more the crosswind, the further it drifts downwind from its original path.... The downwind drag component is what causes this drift.... I know it's a bit confusing, but once you "get it", it all makes perfect sense.... Incidently, since the drift increases with the drag, that explains why when you exceed about 850 fps the drift increases, even though the pellet has a shorter flight time to target.... Have a look at this chart....



Note that as you increase the velocity above about 850 fps, the wind drift actually increases....

Bob

[RScott]

Is there a way to calculate the drag coefficient from shot data?  I thought Cd was basically the inverse of the BC.  But if the BC is constant with velocity in a "correct" model, then wouldn't Cd be constant with velocity too?

Which ballistics calculator do you recommend we use to estimate BCs (and/or Cd)?

Thanks again.

[rsterne]

No, as you can see from the graph, the Cd is nowhere near constant with velocity.... Look at the yellow line (GA), and you will see that it starts out at about 0.2, drops a bit, then back to 0.2 at about 800 fps.... From there, it increases to 0.3 at about 980 fps, 0.4 at about 1070 fps, 0.5 at about 1150 fps, and about 0.6 at 1270 fps, eventually peaking at about 0.67 around 1600 fps....

The BC is calculated by comparing the Cd of your pellet to the Cd of the GA model, at your velocity, and corrected for the Sectional Density of your pellet.... The formula is:

BC = SD / FF .... Where the Form Factor is the Cd of your pellet, at the velocity tested, divided by the Cd of the GA model at that same velocity.... If your pellet has less drag than the GA model, then the FF is lower (below 1.000), and hence the BC will be greater than the SD.... If your pellet has more drag than the GA model, the FF will be greater than 1.000, and your BC less than your SD.... I have found that for JSB Round Nose pellets (the Exact series), the FF is about 1.5, so their BC is about 2/3rds of their SD.... Wadcutter pellets have a lot more drag, so a higher FF, possibly around 3.0, so their BC is about 1/3rd of their SD....

Sectional Density, if you are not familiar with the term, is determined by dividing the weight by the frontal area.... For ballistics, this is simplified to the weight in lbs. over the bore squared.... There are 7000 grains per lb., so for the weight in grains, the formula is:

SD = (Weight / 7000) / (Caliber^2)....

For 18 grains in .22 cal, we have:  SD = (18 / 7000) / (0.22 x 0.22) = 0.00257 / 0.0484 = 0.053.... If the FF is 1.5, then the BC would be.... 0.053 / 1.5 = 0.035, which is just about exactly the BC for an 18 gr. JSB Exact in .22 cal....

Cd is very complex to calculate, and it only applies at one (average) velocity.... You need two accurate velocities and the exact distance between, and the atmospheric conditions at the time of the test.... plus the frontal area and weight of the projectile.... I made my own spreadsheet to do the calculations, using input from my LabRadar.... For simple BC estimates (and that is all they are, since we don't have a perfect drag model for every pellet) I use ChairGun, but that is discontinued.... You can also use the online JBM Ballistics calculator, which can be found at:

http://www.jbmballistics.com/cgi-bin/jbmbcv-5.1.cgi

However, it does not have the GA drag model, only the G1 (and other PB drag models).... I also use Strelok, which is an Ap for Android, and it now has the GA model added to the others.... There is one more, called "Easy BC", available as a download from:

https://gpc.fotosoft.co.uk/Home.html

It not only has the GA model, but also the GA2 (by Miles Morris) and his new model for airgun slugs as well.... That may be your best bet, but I haven't played around with it a lot as yet....

Bob