Retained energy - .22 vs .177

[GPConway]

I have found his values to be near what is stated in Chirgun but I find the Chiargun values closer to the POIs that I get with my rifles.Although I must say that ambient temperature does make a lot of difference.

A.G

... and the ambient pressure even more so since air density is proportional to absolute pressure/absolute temperature.
The average altitude in the UK is 531 Ft and in the USA: 2493 Ft. according to Wikipedia.
If the ambient pressure isn't measured explicitly at the time of testing then those average altitudes correspond to average errors in measured BC of ~2% and ~9% respectively before the effects of ambient temperature, relative humidity and equipment accuracy/repeatability are considered. Do these tests on a hot summer day in Colorado (or a mid-winter day in Norwich) without all of the necessary compensations and the calculated BC values could easily be 25% or more in error.

George

[GPConway]

We're not seeing his experimental data (velocities at ranges). Instead, the graph is depicting the results of some method that takes his raw data and outputs a BC value. In this case, the method is based on an invalid assumption (constant Cd) resulting in an incorrect and therefore variable BC value.
If it's still not obvious, then I'll reverse engineer his graph - best I can - to show how it should have been interpreted.

George

Just for giggles - and since I had nothing better to do - I had a go at this last night.
For the sake of my sanity, I've only considered his curve for the 0.22 JSB Exact 15.9 Grain since we know that the particular drag law for this pellet (GA) is well matched.

First the excuses ...
1) I don't have access to the original velocity/range data so interpolation of the BC v. velocity graph is necessary. Obviously not an ideal scenario.
2) The said BC v. Velocity curve has been 'smoothed' by the original author but he doesn't mention how this was accomplished. i.e., by guesstimate or by polynomial regression, although I suspect the former as he seems to have a point to prove.
3) No atmospheric data is available and it's not clear if all of the original data was collected under similar atmospheric conditions.

The closed-form expression used to generate the graph assumes a constant Cd = 0.204 regardless of velocity so the BCs must the same at the velocities where the GA and constant Cd curves intersect.
That intersection can be seen at ~335 Ft/s and ~800 Ft/s so, by inspection and at 800 Ft/s, BC = ~0.036 from the graph.
To expand this a little, the underlying equation is:

BC1/Cdc = BC2/Cdv or, rearranging BC2 = BC1 * Cdv/Cdc
where BC2 = Ballistic Coefficient (GA drag law)
BC1 = Ballistic Coefficient (from graph)
Cdc = assumed constant drag coefficient at all velocities = 0.204.
Cdv = reference GA drag coefficient at any particular velocity.

So at v = 800 Ft/s, BC2 = BC1 * 0.204/0.204 = BC1 = 0.036 as above.

Applying this to values interpolated from the graph (BC1) with appropriate GA Cd values gives:
v = 1000 Ft/s, BC1 = 0.022, BC2 = 0.032
v = 900 Ft/s, BC1 = 0.029, BC2 = 0.035
v = 800 Ft/s, BC1 = 0.036, BC2 = 0.036
v = 725 Ft/s, BC1 = 0.038, BC2 = 0.035
v = 700 Ft/s, BC1 = 0.037, BC2 = 0.030
v = 600 Ft/s, BC1 = 0.030, BC2 = 0.031

So, according to the above, the average BC value amounts to 0.033 (GA) with max = 0.036 and min = 0.030 against the normally accepted value of 0.031.
The dispersion is about what you'd expect (see excuses #1 and #2 above) and the average BC value is surprisingly close considering the unknowns of excuses #2 and #3.

Evidence enough that, given the correct drag law, the Ballistic Coefficient can be considered constant and doesn't vary with velocity.
If a significant BC variation is to be seen, then the wrong (or at least an inappropriate) calculation method has been used.

George

[krisko]

honestly i have no clue how to calculate a BC "accurately", for it to be correct in value. I don't care since calculations like that always base on some mathematical model with all kind of fancy constants to make it right.

personally i would just take the chrony MEASURED velocity at your range lets say 25yards and divide it by the chrony MEASURED muzzle velocity, to get the idea about the loss of speed over the distance at certain speed for a certain barrel/pellet combo.
It is a shame i cant do the experiment for JSBs here legally. But if you look at tables in my second link, he does list his chrony results for various pellets for both low power PAL versus 25fpe+, and indeed the ratio between the speed at 25yards versus muzzle: IS interestingly better for high power for JSB diabolo! so there is a sweetspot in speed.

RWS hobby on the other hand is better at lower energies, at medium and high speed it looses way too much speed way too fast.

i am sure when he was drawing his curves based on his experimental data he just connected the dots like kids do, hence the smoothing.

[GPConway]

This has wandered way off topic but ...

honestly i have no clue how to calculate a BC "accurately", for it to be correct in value.

The point of all this is that the Ballistic Coefficient for any projectile is constant. i.e, independent of velocity.
Further, given the appropriate reference drag law, we can actually put a constant value on it.

By definition:
BC = SD/FF
where:
SD = Sectional Density = Weight (Lb) / (Diameter in Inches)² , and
FF = Form Factor = Cd.proj/Cd.ref
where:
Cd.proj = Drag Coefficient of the projectile at any particular velocity, and
Cd.ref = Drag Coefficient of the reference projectile at the same velocity

Note that:
a) If the correct drag law is chosen then FF is constant at any velocity.
b) SD must be constant too since the projectile weight and its diameter (hopefully) don't change in flight.
c) Since SD is constant and FF is constant at any velocity then BC must be constant at any velocity too.

If we see curves like the ones under discussion where BC varies dramatically with velocity we can see that - since SD is necessarily constant - it must be the FF value is varying with velocity ... but FF is defined as being constant so the only plausible explanation is that the calculating method's in error. QED.

In the case of the graphs in your links, a closed-form expression ...

BC = (R1-R0)/(ln(V0/V1) * 8000) *** Don't use this at home! ***
where BC = Ballistic Coefficient
R0 = near range (Yards)
R1 = far range (Yards)
V0 = velocity measured at R0 (Ft/s)
V1 = velocity measured at R1 (Ft/s)

... has been used and implies a constant Cd.ref = ~0.204. Trust me on this (although I can offer evidence if provoked). The problem is that the actual GA Cd.ref curve is anything but flat/constant between V0 and V1 so the Form Factor varies with velocity and the calculated BC value varies in sync.
This is why it's such a simple job to apply a correction for each BC/velocity couplet to get real BC values from these erroneous ones as I've shown in my previous post. i.e., we know the graph's implications are wrong but, knowing the real GA Cd values and the use of a constant Cd = ~0.204, it can be corrected in the manner previously shown. What we don't know about are the environmental conditions at the time of test. While these have no effect on the BC value (constant, remember?) they may have on it's calculation since the measured down-range velocity will be affected and this effectively changes the magnitude of the real BC value.
There's another problem with the above expression too. i.e., Since the BC apparently varies with velocity, do we attribute the calculated BC to V0 or V1 or an average velocity ((V0+V1)/2) or some other velocity? So many questions, so much time wasted ...

So how are BCs calculated "accurately"?
Unfortunately there's no "accurate" closed solution (as far as I'm aware) so the result has to be arrived at analytically. Unless you're really into days of calculator pounding (been there, done that) or are able to write suitable software, a computer program is required. If the projectile is a round-nosed JSB Exact (or close lookalike) you'll need the GA drag law resident in Hawke's Chairgun or X-ACT or maybe one of HL's other dedicated apps.
If you're using JSB Exacts (or clones) and are not especially bothered about accuracy, then you could use the G1 drag law with any of the numerous on-line or stand-alone apps.

I don't care since calculations like that always based on some mathematical model with all kind of fancy constants to make it right.

I'm not sure what you mean by 'fancy' constants but that sounds like something of an assumption to me. The only constants (if it's my explanation to which you refer) are the Cd values at various velocities in the GA drag law and those have been shown to be accurate enough in practice. Not really that fancy at all (not to demean the vast amount of effort and time that must have gone into its construction and validation).
If instead you're referring to the various methods used to calculate BC values from raw data, then I can think of only one additional pertinent constant - gravitational acceleration. The methods are published and can all be derived from the basic physics and fluid dynamics but, because of the variability of Cd values with velocity and the vast number of applicable drag laws, I can't see a universal closed solution being possible. But then, I know nothing.

personally i would just take the chrony MEASURED velocity at your range lets say 25yards and divide it by the chrony MEASURED muzzle velocity, to get the idea about the loss of speed over the distance at certain speed for a certain barrel/pellet combo.
It is a shame i cant do the experiment for JSBs here legally. But if you look at tables in my second link, he does list his chrony results for various pellets for both low power PAL versus 25fpe+, and indeed the ratio between the speed at 25yards versus muzzle: IS interestingly better for high power for JSB diabolo! so there is a sweetspot in speed.

All well and good but the V1/V0 ratio doesn't - in itself - yield a BC value nor is it useful for other aspects (eg., calculating wind drift).
I did see the other table but I'm dubious about the results, especially the low-velocity ones. I know from experience that the accurate measurement of velocities below 500 Ft/s is difficult because the differences over 25 Yards are very small and get overwhelmed by other systematic/equipment errors. He might have got better results at 50 or 75 Yards. Or maybe not. Using the log expression above, the results would still be wrong/misleading though.

RWS hobby on the other hand is better at lower energies, at medium and high speed it looses way too much speed way too fast.

I'm not sure what you mean by 'better' but its performance is poor at all points/energies because of it's excruciatingly low BC value!
Note that the GA curve is not suitable for wadcutters. Chairgun's GC drag law might be a better bet.

i am sure when he was drawing his curves based on his experimental data he just connected the dots like kids do, hence the smoothing.

Maybe or maybe not. We'll maybe never know.
Either way, I'd have liked to see the raw data or at least see the BC/velocity points through which the curves were drawn. How many BC/velocity points were plotted? If it was drawn through 50 points it'd be much more believable than it were drawn through 5. Again, we don't know. In any event, a statistically-based smoothing solution may have produced less ambiguous results.

George

[Airsporter1st]

This has wandered way off topic but ...


The point of all this is that the Ballistic Coefficient for any projectile is constant. i.e, independent of velocity.
Further, given the appropriate reference drag law, we can actually put a constant value on it.

By definition:
BC = SD/FF
where:
SD = Sectional Density = Weight (Lb) / (Diameter in Inches)² , and
FF = Form Factor = Cd.proj/Cd.ref
where:
Cd.proj = Drag Coefficient of the projectile at any particular velocity, and
Cd.ref = Drag Coefficient of the reference projectile at the same velocity

Note that:
a) If the correct drag law is chosen then FF is constant at any velocity.
b) SD must be constant too since the projectile weight and its diameter (hopefully) don't change in flight.
c) Since SD is constant and FF is constant at any velocity then BC must be constant at any velocity too.

If we see curves like the ones under discussion where BC varies dramatically with velocity we can see that - since SD is necessarily constant - it must be the FF value is varying with velocity ... but FF is defined as being constant so the only plausible explanation is that the calculating method's in error. QED.

In the case of the graphs in your links, a closed-form expression ...

BC = (R1-R0)/(ln(V0/V1) * 8000) *** Don't use this at home! ***
where BC = Ballistic Coefficient
R0 = near range (Yards)
R1 = far range (Yards)
V0 = velocity measured at R0 (Ft/s)
V1 = velocity measured at R1 (Ft/s)

... has been used and implies a constant Cd.ref = ~0.204. Trust me on this (although I can offer evidence if provoked). The problem is that the actual GA Cd.ref curve is anything but flat/constant between V0 and V1 so the Form Factor varies with velocity and the calculated BC value varies in sync.
This is why it's such a simple job to apply a correction for each BC/velocity couplet to get real BC values from these erroneous ones as I've shown in my previous post. i.e., we know the graph's implications are wrong but, knowing the real GA Cd values and the use of a constant Cd = ~0.204, it can be corrected in the manner previously shown. What we don't know about are the environmental conditions at the time of test. While these have no effect on the BC value (constant, remember?) they may have on it's calculation since the measured down-range velocity will be affected and this effectively changes the magnitude of the real BC value.
There's another problem with the above expression too. i.e., Since the BC apparently varies with velocity, do we attribute the calculated BC to V0 or V1 or an average velocity ((V0+V1)/2) or some other velocity? So many questions, so much time wasted ...

So how are BCs calculated "accurately"?
Unfortunately there's no "accurate" closed solution (as far as I'm aware) so the result has to be arrived at analytically. Unless you're really into days of calculator pounding (been there, done that) or are able to write suitable software, a computer program is required. If the projectile is a round-nosed JSB Exact (or close lookalike) you'll need the GA drag law resident in Hawke's Chairgun or X-ACT or maybe one of HL's other dedicated apps.
If you're using JSB Exacts (or clones) and are not especially bothered about accuracy, then you could use the G1 drag law with any of the numerous on-line or stand-alone apps.


I'm not sure what you mean by 'fancy' constants but that sounds like something of an assumption to me. The only constants (if it's my explanation to which you refer) are the Cd values at various velocities in the GA drag law and those have been shown to be accurate enough in practice. Not really that fancy at all (not to demean the vast amount of effort and time that must have gone into its construction and validation).
If instead you're referring to the various methods used to calculate BC values from raw data, then I can think of only one additional pertinent constant - gravitational acceleration. The methods are published and can all be derived from the basic physics and fluid dynamics but, because of the variability of Cd values with velocity and the vast number of applicable drag laws, I can't see a universal closed solution being possible. But then, I know nothing.


All well and good but the V1/V0 ratio doesn't - in itself - yield a BC value nor is it useful for other aspects (eg., calculating wind drift).
I did see the other table but I'm dubious about the results, especially the low-velocity ones. I know from experience that the accurate measurement of velocities below 500 Ft/s is difficult because the differences over 25 Yards are very small and get overwhelmed by other systematic/equipment errors. He might have got better results at 50 or 75 Yards. Or maybe not. Using the log expression above, the results would still be wrong/misleading though.


I'm not sure what you mean by 'better' but its performance is poor at all points/energies because of it's excruciatingly low BC value!
Note that the GA curve is not suitable for wadcutters. Chairgun's GC drag law might be a better bet.


Maybe or maybe not. We'll maybe never know.
Either way, I'd have liked to see the raw data or at least see the BC/velocity points through which the curves were drawn. How many BC/velocity points were plotted? If it was drawn through 50 points it'd be much more believable than it were drawn through 5. Again, we don't know. In any event, a statistically-based smoothing solution may have produced less ambiguous results.

George

So which is better, 0.177 or 0.22?

[rhyslightnin]

so which is better, 0.177 or 0.22?

.20 :d

[Airsporter1st]

.20 :d

Eureka!!!!!!

[GPConway]

So which is better, 0.177 or 0.22?

Yes. Probably.

George