Ballistics Coefficients Discussion

[Setarip]

My apologies for the errant posts. I will do a much more thorough read of the subject.  Very fascinating stuff. I also mentioned the G7 as an example of a model specifically suited for a specific type of projectile, in no way did mean or think that for pellets the G7 was better than the G1. My approximation for the bc at 1100 was simply extending the curve in the jsb graph posted a bit earlier so it was in no way an accurate estimation, just an example for my post. I will say that I have learned quite a bit just from this thread and am anxious to send you some results for the drag model.

[rsterne]

The very first graph posted, based on data several years old, was calculated with an early version of ChairGun that used a linear drag function with a Cd = 0.20 for all velocities.... That is why the BC varies so drastically.... That is explained in a more recent post....

Today I am beginning to investigate what we need to do to establish a new Drag Model (Profile, or Function, all terms are used).... The first thing I thought I would investigate is what the G1 Profile looks like for various values of the Form Function.... To remind readers, the FF is how the drag of a projectile matches the drag model chosen.... If the FF is 1.0, then by definition the BC = the SD exactly.... The more drag the shape has, the higher the FF.... When the FF is 2.0, then the BC is 1/2 the SD, as given by the formula:

BC = SD / FF

For this graph, I took the G1 Function and multiplied the Cd by various FF's from 1 to 2, with the following results.... The current data on the JSB Exacts are shown as well for comparision....



If the pellet was a perfect match for the G1 profile, the FF would be a constant, and it's drag curve would lie along one of the G1 lines that matches that FF.... As you can see, the match is very poor, the FF varies from about 1.5 down to 1.2, back up to 1.8 and then back down to 1.6.... Now it will be impossible to achieve a new drag profile that is  a perfect match for even one pellet, let alone useful for many.... but at a minimum what we need to achieve is a steeper slope between the lowest FF (at around 850 fps for this pellet) and the highest FF (right around Mach 1).... What I am proposing, based on current data, and subject to change as we collect more, is to use the G1 profile up to about 700 fps, and a profile like the G1 but with a FF of around 1.5 - 1.6 above Mach 1, with a much steeper transition between those two velocities.... to more closely represent what happens with Diabolo pellets.... I will give some examples in a future post....

Bob

[Tomg]

The JSB Exact is the 15.9gr, correct?

Good work by the way!

[rsterne]

Yes, the Exact is the 15.9 gr.... Here is a graph showing some possible new Drag Function Profiles where the slope in the Transonic Region is steeper....



I used the G1 Profile up to Mach 0.75 (845 fps), and then three of the curves from the above graph, with Form Factors of 1.4, 1.6, and 1.8 at Mach 1 and above.... In between, the FF increased in a linear manner to blend a FF of 1.0 to the three upper curves.... IMO the curve blending into the FF = 1.6 curve above Mach 1 is the best match.... This is still subject to change as we collect more data, of course, but is one possible way to come up with a new Drag Function for Diabolo Pellets....

Bob

[HPAJunkie]

I was able to shoot some more and the distance between was 20 yds this time with .22 JSB diablo 18.13gr.
Humidity- 33%
Density- 30.03 inHg
36deg dew point
elevation 4590ft
All shots were 10 shot strings and these are the averages:
0 yd             20 yd               difference
855.77         801.82                 53.95
808              761                       47
753.82         713.97                  39.85
699.63         658.34                  41.29
I am not sure why the difference on the last string is higher than the difference on the second to last but I ran the numbers twice.

[rsterne]

It is not uncommon for the BC to decrease at lower velocities, you can see it above with the 15.9 gr. Exacts.... I have included the data, and it agrees well with what we have for the 18.1 gr. Heavies.... Oh, do you have the temperature?.... I do have one data point that should be redone to confirm it, however, and that is the one you did previously with MV = 912 and downrange at 858.... If you get a chance to check it again, that would be great....

Bob

[HPAJunkie]

Yesterday the temp was 55 degrees at the time of the test.  Last week when the first test was done I think the temp was in the upper 40's but I can check the upper velocity range again. I will try to get around 950 at the muzzle and also 900 at the muzzle.

[rsterne]

That would be great.... thanks....

Bob

[HPAJunkie]

Have there been any more updates on this topic? I have not been able to add more data yet, but knowing what we do about BC of diablo pellets how do we use this to make more accurate shots? I have not used chairgun much but what are the next steps to start using the data in chairgun?

[rsterne]

Once we agree on a new Drag Model, I will convert it into Cd data to be used to customize the Gx profile in ChairGun.... Once the model more closely matches what our pellets do, then you would just select that model and input the BC for your pellet the way you normally would, but it would match reality close over a wider range of velocities than by using the G1 or GA models....

If you are interested in just one pellet, you can do a custom Gx profile just for that one pellet, of course, and then it should be 100% accurate over the range of velocities you have measured.... You can store as many Gx profiles as you want in ChairGun and name the files, but you can only select one to use at a time.... so you would have to remember to change profiles to the one for that pellet.... That is the "best" way, but I'm hoping to come up with a Gx that is "good enough" to use for all diabolo pellets, and much better than the G1 and GA currently in ChairGun.... To optimize it for your gun, it would still be a good idea to measure the BC for your pellet at one velocity, and use that BC and the Gx profile from there....

Bob

[Scotchmo]

OK - So we know that forward velocity affects the BC. And BC determines how much affect a side wind has on a pellet.

I'm trying to reconcile some BC data that I collected yesterday while shooting in a 4-12mph side wind. I measured the BC by taking velocity readings at 1yard and 35 yard.

I have a related question but not sure if there is a connection:
Will a side wind change the measured BC of a pellet?

[rsterne]

I have no idea.... I suppose it's possible because there is now a very slight sideways "angle of attack" due to the crosswind, but by vector analysis, the angle will be very small.... If the wind is 10 mph (14.7 fps) and the pellet velocity is 800 fps, the angle of attack is a whisker over 1 degree.... Pellets aren't exactly long and skinny, closer to a sphere (which should have no change in drag) than an airfoil, so I can't imagine the Cd would be much larger (or smaller) with a 1* change in the angle of flow.... Certainly the shot to shot (and pellet to pellet) variation should reduce the cross angle to just "noise", I would think....

On the other hand, the "nose up" angle of the pellet at 50 yards.... ie the difference between the boreline and the flight direction.... is also just a bit over 1 degree (strange they just happen to be about the same).... Of course that angle of attack is increasing as the pellet goes downrange (assuming the pellet stays aligned with the bore), whereas the angle of attack due to the wind is a constant (assuming the wind is the same speed from muzzle to target).... IIRC, didn't you find a measureable reduction in BC at longer ranges compared to the BC at the same velocity close to the muzzle?....

There is no question, of course, that if you have a headwind or tailwind, your downrange velocities will be affected, giving incorrect BC calculations.... In this case the actual airspeed would be the (vector sum of) sum of the groundspeed and the windspeed.... I wonder if your previous change in BC with range was seeing such an effect?....

Bob

[Tomg]

Interesting topic, no doubt. It would be critical to know if there is a declining BC when there is sidewind for us that chase absolute accuracy.

[rsterne]

Note the comment I added above about headwinds/tailwinds and the vector sum affecting BC measurement.... Yet another source of error in the measurements.... A 10 mph headwind will decrease the calculated BC by about 5% and a tailwind increase it by about 5%.... assuming you don't correct for it (which we aren't)....

To quantify BC changes, a 10% change in BC (quite large) would change the drift about 10%.... A 10% change in windspeed (from 9 mph to 10) has the same effect....

Bob

[Scotchmo]

Our range is usually windy. I'll need to get a calm day when testing to make any sense of it. This gun is shooting with a very consistent muzzle velocity and is very accurate.

Initial velocity: 785fps, ES 11fps.
Down range (34 yard spread) velocity: 653fps, ES=49fps.

Wind meter readings during test: 4-12mph (measured at eye level)
Flight is approx  1' off the ground so wind gradient would come into play.
According to ChairGun data, a 3-9mph wind could account for the amount of drift. That's probably about right after accounting for the wind gradient.

Variation from expected POI (35 yards downrange):
Vertical: +.25" to -.3"
Horizontal: +.7" to +1.8"

BC calculated average was .021, with a likely range of .026-.017 for 10 shots.

That seems like a big spread.

I did see a lower BC than expected when checking down range velocity in earlier tests. I was guessing that it was the increased angle of attack. Now I'm thinking maybe it was wind. Or maybe it's a combination. A 1 degree x 1 degree vector gives a 1.44 degree vector. That's still not much.

I don't want to steer this discussion off track, just seeing if it was a phenomenon that others experience.

Data in the wind can be useful, but the problem is that the wind varies second to second.

[rsterne]

Yes, with the total of the two (slightly greater than) 1* vectors being only 1.50*, when you consider how short and blunt a shape we are dealing with, my guess is that compared to all the other variables, it is insignificant.... As you say, the range of possible BC values over 10 shots is pretty large, all we can do is play the averages.... Better yet, if we can graph all the data points and then smooth out the curve, using the smoothed curve instead of the points, we are likely to get even closer....

One of the ways this can be used for those who are really fussy, is to them to take their own mass of data, over a wide range of (useful) velocities and develop their own drag model for a given pellet in their gun.... That could be extremely accurate, likely better than the pellet to pellet variation.... Imagine filling out the blue line for the 15.8 gr. JSBs in post 83 above with the missing data points, and using that line for the model, and you would get the idea....

Bob

[Scotchmo]

Yes, with the total of the two (slightly greater than) 1* vectors being only 1.50*, when you consider how short and blunt a shape we are dealing with, my guess is that compared to all the other variables, it is insignificant.... As you say, the range of possible BC values over 10 shots is pretty large, all we can do is play the averages.... Better yet, if we can graph all the data points and then smooth out the curve, using the smoothed curve instead of the points, we are likely to get even closer....

One of the ways this can be used for those who are really fussy, is to them to take their own mass of data, over a wide range of (useful) velocities and develop their own drag model for a given pellet in their gun.... That could be extremely accurate, likely better than the pellet to pellet variation.... Imagine filling out the blue line for the 15.8 gr. JSBs in post 83 above with the missing data points, and using that line for the model, and you would get the idea....

Bob

I do use the averages. But:

I would like to account for all variation that I can.

That .017-.026 BC variation would account for about 1/2 of the of the vertical dispersion that I'm getting. The rest could be me or the guns inherent inaccuracy.

If that BC variation is correct, I want to look for ways to reduce it if possible. This was 8.44gr. I need to try some 7.87gr and 10.34gr, but it will be later. I could spend all my time testing for the optimum but this is already good enough for FT pistol competition. The farthest target in pistol matches is only 35 yards, so BC is not that critical.

[rsterne]

IMO the only way to quantify the variation in BC is to use two Chrony's and calculate the BC for each shot.... then examine the ES for the BCs themselves....

I have mixed feelings about using two Chrony's.... On one hand, you get the BC for each shot, but on the other hand, just a 0.5% difference in how they read will give an error in the BC of ~4%.... If you use just one Chrony and move it, at least in theory the velocity readings should be consistent, but then you have to deal with the shot to shot variation, which could easily be 1% ES or more.... However, by taking the average velocity at near and far ranges, I have a gut feeling that using a single Chrony and moving it is better.... unless you have two Chrony's that read identical to each other consistently....

Bob

[Tomg]

To your point Bob. A larger data set from multiple sources is a good way of aggregating a reasonably accurate result.
That same process works both in macro and micro. So moving a single chrony, and doing an average over say 10-20 shots for each location, gives enough data to diminish the effect of outliers. 
Infact, I would to some extent suggest anyone participating in this, to remove shots that are more than 5-10% outside the trend in a shot string in each location. Those being a result of variation in the gun delivering the expected fps, a bad pellet, hitting a mosquito on the way down range, etc.

[rsterne]

In fact I do this on my data.... If I am experiencing a 1% ES and I get a shot that is 1% from the average velocity and therefore well outside the dataset, I discard it and shoot another one, which is almost always within the dataset.... If that replacement shot is "just" outside the next slowest or fastest, I keep it.... I know, it's a subjective choice, but it's just the way I do it.... I agree it is often a damaged or renegade weight pellet....

Bob