Retained energy - .22 vs .177

[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!!!!!!

[max headroom]

What was the point of me reading this thread. i shoot a rabbit or rat with a .177 or a .22 its dead. it cant be any deader in any calibre.

[GPConway]

So which is better, 0.177 or 0.22?

Yes. Probably.

George

[Airsporter1st]

What was the point of me reading this thread. i shoot a rabbit or rat with a .177 or a .22 its dead. it cant be any deader in any calibre.

No, but if it was an older rat or rabbit, it would probably prefer to be killed with a 0.22, because we all know they hit harder.

[max headroom]

No, but if it was an older rat or rabbit, it would probably prefer to be killed with a 0.22, because we all know they hit harder.

specially when you shoot at the ground under them. they dont like that concrete up them sir. Oh. for yanks thats cement. Thanks.

[krisko]

the answer is .25