I am making a genuine attempt to keep my answers to AZ’s questions simple but accurate and with relevant practical support material. AZ's questions are copied, in italics, from a post further down.
Please do me the honor of reading what I have spent time collating and of opening the video at the end. My answers are just that, mine. But I hope that you will get food for thought in the package and if some read it twice, I will feel justified.
Q “So optimal BC is measured in terms of what?
A. In terms of the best average BC over the particular range being shot. Example from my previously displayed reference http://www.network54.com/Forum/79537/thread/1265721221/Experiment-+BC+changes%2C++with+range+and-+or+time+of+flight+and-+or+velocity-+Long-
“0 to 50 yards : 0.0398 or corrected 0.0337
0 to 100 yards: 0.0430 or corrected 0.0364.
0 to 200 yards: 0.0451 or corrected 0.0383.
All pellets/bullets have some yaw exiting the barrel. If, and as, this settles the drag coefficient may improve (and so the BC). Then later down range it may get worse again if dynamic stability and tractability are lost. See drag coefficient changes in the actual shot graph down this page.
Q. “… how are we going to capitalize this optimal BC?”
A. Under the conditions that prevailed , if shooting to 50 yards I would have used a BC of 0.0398 ; or of 0.0430 if shooting at 100 yards etc. Elsewhere, at a different altitude or temperature etc., I would enter the corrected BC into Chairgun but would then enter the environmental conditions for correction to the appropriate temperature, pressure, altitude etc.
Q. “Is a “Better BC” desirable for flatter trajectory at the expense of accuracy, or vice versa? “
A. If different pellets are shot at the same MV, then yes, the better BC pellet will have a flatter trajectory regardless of pellet weight.
If pellets are shot at different MVs then the answer is more complicated. A lighter faster MV pellet may have a lesser BC but still fly flatter to some particular range/distance, then it may be overtaken by the slower MV, heavier, pellet.
As to the implications regarding flatter trajectory and accuracy ? You are asking for an answer of thesis proportions.
Firstly accuracy does not necessarily derive from flatter trajectory. It may or may not depending on many variables. Just one major issue regards accurate ranging of the target. This should not be a problem in BR or similar competition target shooting but it is in Field Target and in hunting. If one's ranging ability is mediocre or poor, then the flatter shooting pellet may have an advantage PROVIDING it is equally tight at grouping from that rifle. If ranging ability is excellent (or irrelevant as in 25 m BR) then there is no advantage in flatter trajectory PROVIDING the slower pellet is equally accurate.
HOWEVER, if the pellet with the better BC has a shorter “delay”/”lag” time, then there is an advantage in the fact that it has a lesser wind deflection regardless of whether or not it is slower to the target, or has a higher trajectory curve. To save lengthy script here I will presume you understand “delay”/ “lag” time as compared to actual time of flight. If not, then ask and I will explain that at some future time.
If we are now on the same page, the rest is simple enough.
Q. “Aren’t we all after the most accuracy combined with the flattest trajectory. “
A. Yes, and not necessarily. Yes to accuracy, but it is not necessarily found in the pellet with the flattest trajectory. If they are together available, then OK. But to presume they always come together is to disregard what has been written thus far.
Q. “? Lots of questions don’t you think? How and why is this happening?”
A. Yes lots of questions, the reason being that some seem to want simple answers that are also accurate answers , and what seem simple questions are generally not. Example: What is the world made of?
Q. “? Is it that BC’s are really not really that important for accuracy or is it there something else that we need to discover?” (Quote as written).
A. How much importance a shooter gives to BC or drag coefficient is up to him. At the range one shoots, if the fine print of vertical and horizontal dispersion are not relevant to him, then why worry. A coffee can at 20 yards won’t know the difference; neither will a shooter with a flinch.
It is important to me.
Points of reference:
An accurate shot, or sequence of shots, depends upon coincidence of “intended” aim and point of impact.
Failure results if there is either vertical or horizontal error, or both.
Aside from simple aiming errors and lack of shooting skills, vertical
errors result from range misjudgement, or error in matching range to true pellet trajectory. Knowing true pellet trajectory relies upon anticipating the pellet’s flight path. Drag coefficient – the % loss of velocity per unit of range – is the key to determining trajectory; and a derived ballistic coefficient, as related to some standard projectile, allows for some prediction.
If the drag coefficient route is chosen, then some testing and maths is required . This can involve drop tests at various ranges with a one-range zero - then a graph with eyeballed line of best fit, least squares maths, or use of a fitted polynomial and its equation for future use. ( I used the last to good effect from the 80’s until the advent of Dave’s Chairgun and Steve Woodward’s calculator).
My Sheridan click chart from 21 years ago:
It was good enough to produce this 100 yards group in 1994; and to cleanly kill a rabbit at 92 yards using the relevant number of clicks.
Be honest; who thought a group like that could be shot with a pump Sheridan 21 years ago?
Ballistic coefficients are no longer much used outside of the air rifle scene but if meticulous data is collected and entered into a matching ballistics program then excellent results can result.
Graphs: Drag coefficient of one .25 cal JSB King shot to 90 yards and tracked by Doppler radar. Each dot is a velocity data point:
Cd to velocity feet/sec down range. This shot pellet reached its lowest drag/ best BC between 725 and 700 fps, between Mach 0.65 and 0.63, and 53 to 65 yards down range.
Cd to velocity in Mach number down range
Cd to range in yards
Plenty more questions to ponder on that. But I have other pellets that perform very differently. So yes AZ, there are other things in the equation to still be "discovered" and put into perspective by those willing and motivated to do so.
Horizontal dispersion errors ("x" error) due to wind, can be minimized by using a pellet with a high BC and reduced "lag" time. Those who shoot 24 m BR or FT or hunt should consider this BC phenomenon in the equation.
I took this video last month and it startlingly demonstrates how drag coefficient and derived BC may affect lateral dispersion or at least, wind deflection combined with other factors..
The 5 shots were taken at 100 yards with my .177 cal target rifle in a blustery 3 o'clock wind, note the mirage flow. Shots 1,3,4 were with a proven world class pellet which won titles at the recent World BR Championships @ 25 m but which lost stability late in the flight over 100 yards in that wind, spiraled to the left and either clipped or missed the 18" disc. They were shot at 930 fps. Shots 2 and 5 were experimental pellets which dropped straight down through the middle of the disc to land close together and with seemingly little wind deflection. They were shot at 686 fps and have a BC roughly 4 times higher.
http://vidmg.photobucket.com/albums/v392/Kyogle/PD%20pellet%20research%20Nov%202015_zpsybmmnoha.mp4
Which would you choose to shoot in that wind for accuracy and wind bucking, the fast, initially flat shooting pellet "A", or the slow incredibly high BC pellet "B"?
Play it full screen and watch for #s 1,3, and 4 coming down the left half of the disc from 11:00 to 8:30 o'clock; and #s 2 and 5 dropping down 12:00 to 6:00 o'clock.
And so, from the explanations above, it should be obvious that just one derived BC may not fit all ranges, BUT it will still be close enough for the vast majority of shooting done over the "normal" AR ranges to 50 yards. The incurred errors may well be hidden by the plethora of other negative factors relating to aiming, holding, trigger and follow-through skills.
With Christmas over, I am headed back to the farm to finish our lavender harvest.
I hope some appreciate this effort shoehorned into a busy "retirement" schedule.
Best regards to all and best wishes for the New Year ahead. .... Harry, Downunder.
Please do me the honor of reading what I have spent time collating and of opening the video at the end. My answers are just that, mine. But I hope that you will get food for thought in the package and if some read it twice, I will feel justified.
Q “So optimal BC is measured in terms of what?
A. In terms of the best average BC over the particular range being shot. Example from my previously displayed reference http://www.network54.com/Forum/79537/thread/1265721221/Experiment-+BC+changes%2C++with+range+and-+or+time+of+flight+and-+or+velocity-+Long-
“0 to 50 yards : 0.0398 or corrected 0.0337
0 to 100 yards: 0.0430 or corrected 0.0364.
0 to 200 yards: 0.0451 or corrected 0.0383.
All pellets/bullets have some yaw exiting the barrel. If, and as, this settles the drag coefficient may improve (and so the BC). Then later down range it may get worse again if dynamic stability and tractability are lost. See drag coefficient changes in the actual shot graph down this page.
Q. “… how are we going to capitalize this optimal BC?”
A. Under the conditions that prevailed , if shooting to 50 yards I would have used a BC of 0.0398 ; or of 0.0430 if shooting at 100 yards etc. Elsewhere, at a different altitude or temperature etc., I would enter the corrected BC into Chairgun but would then enter the environmental conditions for correction to the appropriate temperature, pressure, altitude etc.
Q. “Is a “Better BC” desirable for flatter trajectory at the expense of accuracy, or vice versa? “
A. If different pellets are shot at the same MV, then yes, the better BC pellet will have a flatter trajectory regardless of pellet weight.
If pellets are shot at different MVs then the answer is more complicated. A lighter faster MV pellet may have a lesser BC but still fly flatter to some particular range/distance, then it may be overtaken by the slower MV, heavier, pellet.
As to the implications regarding flatter trajectory and accuracy ? You are asking for an answer of thesis proportions.
Firstly accuracy does not necessarily derive from flatter trajectory. It may or may not depending on many variables. Just one major issue regards accurate ranging of the target. This should not be a problem in BR or similar competition target shooting but it is in Field Target and in hunting. If one's ranging ability is mediocre or poor, then the flatter shooting pellet may have an advantage PROVIDING it is equally tight at grouping from that rifle. If ranging ability is excellent (or irrelevant as in 25 m BR) then there is no advantage in flatter trajectory PROVIDING the slower pellet is equally accurate.
HOWEVER, if the pellet with the better BC has a shorter “delay”/”lag” time, then there is an advantage in the fact that it has a lesser wind deflection regardless of whether or not it is slower to the target, or has a higher trajectory curve. To save lengthy script here I will presume you understand “delay”/ “lag” time as compared to actual time of flight. If not, then ask and I will explain that at some future time.
If we are now on the same page, the rest is simple enough.
Q. “Aren’t we all after the most accuracy combined with the flattest trajectory. “
A. Yes, and not necessarily. Yes to accuracy, but it is not necessarily found in the pellet with the flattest trajectory. If they are together available, then OK. But to presume they always come together is to disregard what has been written thus far.
Q. “? Lots of questions don’t you think? How and why is this happening?”
A. Yes lots of questions, the reason being that some seem to want simple answers that are also accurate answers , and what seem simple questions are generally not. Example: What is the world made of?
Q. “? Is it that BC’s are really not really that important for accuracy or is it there something else that we need to discover?” (Quote as written).
A. How much importance a shooter gives to BC or drag coefficient is up to him. At the range one shoots, if the fine print of vertical and horizontal dispersion are not relevant to him, then why worry. A coffee can at 20 yards won’t know the difference; neither will a shooter with a flinch.
It is important to me.
Points of reference:
An accurate shot, or sequence of shots, depends upon coincidence of “intended” aim and point of impact.
Failure results if there is either vertical or horizontal error, or both.
Aside from simple aiming errors and lack of shooting skills, vertical
errors result from range misjudgement, or error in matching range to true pellet trajectory. Knowing true pellet trajectory relies upon anticipating the pellet’s flight path. Drag coefficient – the % loss of velocity per unit of range – is the key to determining trajectory; and a derived ballistic coefficient, as related to some standard projectile, allows for some prediction.If the drag coefficient route is chosen, then some testing and maths is required . This can involve drop tests at various ranges with a one-range zero - then a graph with eyeballed line of best fit, least squares maths, or use of a fitted polynomial and its equation for future use. ( I used the last to good effect from the 80’s until the advent of Dave’s Chairgun and Steve Woodward’s calculator).
My Sheridan click chart from 21 years ago:
It was good enough to produce this 100 yards group in 1994; and to cleanly kill a rabbit at 92 yards using the relevant number of clicks.
Be honest; who thought a group like that could be shot with a pump Sheridan 21 years ago?
Ballistic coefficients are no longer much used outside of the air rifle scene but if meticulous data is collected and entered into a matching ballistics program then excellent results can result.
Graphs: Drag coefficient of one .25 cal JSB King shot to 90 yards and tracked by Doppler radar. Each dot is a velocity data point:
Cd to velocity feet/sec down range. This shot pellet reached its lowest drag/ best BC between 725 and 700 fps, between Mach 0.65 and 0.63, and 53 to 65 yards down range.
Cd to velocity in Mach number down range
Cd to range in yards
Plenty more questions to ponder on that. But I have other pellets that perform very differently. So yes AZ, there are other things in the equation to still be "discovered" and put into perspective by those willing and motivated to do so.
Horizontal dispersion errors ("x" error) due to wind, can be minimized by using a pellet with a high BC and reduced "lag" time. Those who shoot 24 m BR or FT or hunt should consider this BC phenomenon in the equation.
I took this video last month and it startlingly demonstrates how drag coefficient and derived BC may affect lateral dispersion or at least, wind deflection combined with other factors..
The 5 shots were taken at 100 yards with my .177 cal target rifle in a blustery 3 o'clock wind, note the mirage flow. Shots 1,3,4 were with a proven world class pellet which won titles at the recent World BR Championships @ 25 m but which lost stability late in the flight over 100 yards in that wind, spiraled to the left and either clipped or missed the 18" disc. They were shot at 930 fps. Shots 2 and 5 were experimental pellets which dropped straight down through the middle of the disc to land close together and with seemingly little wind deflection. They were shot at 686 fps and have a BC roughly 4 times higher.
http://vidmg.photobucket.com/albums/v392/Kyogle/PD%20pellet%20research%20Nov%202015_zpsybmmnoha.mp4
Which would you choose to shoot in that wind for accuracy and wind bucking, the fast, initially flat shooting pellet "A", or the slow incredibly high BC pellet "B"?
Play it full screen and watch for #s 1,3, and 4 coming down the left half of the disc from 11:00 to 8:30 o'clock; and #s 2 and 5 dropping down 12:00 to 6:00 o'clock.
And so, from the explanations above, it should be obvious that just one derived BC may not fit all ranges, BUT it will still be close enough for the vast majority of shooting done over the "normal" AR ranges to 50 yards. The incurred errors may well be hidden by the plethora of other negative factors relating to aiming, holding, trigger and follow-through skills.
With Christmas over, I am headed back to the farm to finish our lavender harvest.
I hope some appreciate this effort shoehorned into a busy "retirement" schedule.
Best regards to all and best wishes for the New Year ahead. .... Harry, Downunder.
