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# Ballistic Coefficients based on G1 model?`

October 4 2009 at 11:11 AM
YF

QUESTION 1-- Are the ballistic coefficients which are tossed about for pellets based on the G1 model?

Looking at webpage "A Short Course in External Ballistics" at:
I noticed that the absolute drag curve for balls (GC curve on top of graph)) about 3/5 way down the page, is very non-linear above about 500fps.

QUESTION 2 - Are diabolo pellets really more like balls (very large drag) then G1 bullets?

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There was also a study by Miller on Round Balls which I have not been able to locate on the internet as of yet.
Ballistics tables for spheres 7.5 to 25 mm (0.3 to 1 in.) in diameter
by Miller, Donald Gabriel, 1927-
Livermore, Calif. : Dept. of Energy, Lawrence Livermore Laboratory ; [Springfield, Va. :b for sale by the National Technical Information Service], 1979. 1979.
Work performed by the UCLLL under contract no. W-7405-ENG-48 Jan. 31, 1979

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Steve in NC
AR&P

# No. The BC math used in many popular airgun ballistic calculators...

October 4 2009, 11:27 AM
 ...uses a constant Cd model, in which drag force is proportional to velocity squared. Despite its simplicity, the accuracy of this approximation for airgun pellets at subsonic speeds has been pretty well verified.Steve
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Herb1836
YF

# constant Cd model....Is BC a constant for 400-1000 fps??

October 4 2009, 12:35 PM
 Steve, thanks for the clarification that the BC's are no relative to G1. But is it really reasonable to assume that the BC is a constant between 400-1000 fps? Harry showed some data recently in which there was a large change in BC for a small drop in muzzle velocity. http://www.network54.com/Forum/79537/message/1253695252 Using two chronys maybe 15 yards apart, a PCP could be shot down to 400 fps or so would give enough data to play with. Of course if you determine a BC for your gun in using the muzzle velocity at which you'd shoot, and to the range interest, then the "average BC" would change. You of course need two chronys so that you can "pair" the readings. The BC would be based on the difference between the two. Thus as the muzzle velocity of the PCP drops, you still get good data. In part I'm have also looked at the data by pellet and gun at the Straight Shooters website. I've been trying to figure out if at least part of the discrepancy between the BCs for different guns for the same pellet is due to starting muzzle velocity.
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Steve in NC
AR&P

# Trajectories predicted by that model have been verified - by Harry - in actual shooting...

October 4 2009, 12:51 PM
 ...to beyond 700yds. So yes. I'd say its practical accuracy has been prettywell verified over a wide range of velocities.Steve
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Steve in NC
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# As for whether it's reasonable to assume Cd constant...

October 4 2009, 5:43 PM
 ...take a look at the interesting behavior of the Cd of a .177" diameter sphere over the range of airspeeds 100 to 300m/s. Here's the source of the plot: http://www.aerospaceweb.org/question/aerodynamics/q0215.shtmlSteve
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Herb1836
YF

# "Screening" round balls

October 4 2009, 6:07 PM

screening balls

Interesting that you referenced webapge with discussion of smooth spheres vs. golf balls. Tom Gaylord was asked about rounds balls, and golf balls. He replied that a process called "screening" had been used to roughen up round balls. Basically roll ball between two blocks of wood covered with metal windowscreen. It did improve group size and carry distance.

--------
Edit ...

thought I asked, it was actually someone else...

Gary Barnes evidently coined the name "screening"

http://www.pyramydair.com/blog/2008/10/air-transfer-port-part-2.html

 This message has been edited by Herb1836 on Oct 4, 2009 6:15 PM

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Steve in NC
AR&P

# But note that roughing the surface only helps to a point. If the sphere is large...

October 4 2009, 6:38 PM
 ...and/or fast enough to get into a high Reynold's number with a smooth surface, then dimpling only increases drag. For a .50 cal ball, the critical speed where smooth beats dimpled would be about 890 fps. Steve
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Herb1836
YF

# Wrong equation?

October 4 2009, 7:04 PM
 Steve, this seems like the wrong equation. It seems like drag is a function of the velocity not the velocity squared. Also if the velocity goes up, the drag goes down? I'd expect that as the velocity of a pellet increased towards the speed of sound that the drag would go up. I think that this formula is for relatively "slow" moving objects. A golf ball is a lot bigger in diameter, and relatively slow moving. I don't think that the Reynolds equation holds for "fast" moving pellets. The equation probably could be used to predict the terminal velocity of a small sphere.
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Steve in NC
AR&P

# No. Right equation. Note that the plot is of the drag coefficient: Cd. Not drag per-se.

October 4 2009, 7:14 PM

Drag is equal to 1/2 x Density x Cd x Area x V^2. Meanwhile the equation is neither drag nor even Cd, but Reynold's number, which is a predictor of turbulent vs laminar flow.

This aerodynamics thing can get tricky - can't it!

Steve

 This message has been edited by pneuguy on Oct 4, 2009 7:17 PM

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Herb1836
YF

# Agree with your equation, I didn't state my case well?

October 4 2009, 8:55 PM
 Steve, I agree with the equation you gave, and the fact that the equation you give in the graph calculates the Reynolds number. However, let's double the velocity of the pellet from 200 m/s to 400 m/s. Now the Reynolds number changes from 6.5E4 to about 1.2E5. Looking at the curve, the associated drag coefficient, C(D), also changes from about 0.5 to about 0.15. Since the overall drag force goes as velocity squared, if the C(D) stays constant then the overall drag force would quadruple when the velocity doubles. But with C(D) changing from 0.5 to 0.15, the overall drag force barely increases when teh velocity doubles. As you increase the velocity of the pellet from 200 m/s to the speed of sound which is about 350 m/s, then the drag force (you're right not drag coefficient) should go up shouldn't it? My point is exactly that the equation/graph aren't infinitely scalable. The duo doesn't correctly predict the association between the Reynolds number and C(D) for a small fast moving object. It works for a bigger slower moving object. In other words, the equation works for increasing I, the diameter of the object, better than it does for increasing V, the velocity of the object.
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Steve in NC
AR&P

# Good point - sort of. But first note the log scale of Re. Doubling the velocity...

October 4 2009, 9:30 PM

...from 200 to 400m/s - and therefore the Re from ~6.5e4 to 1.3e5, decreases Cd only slightly. Even Re = 2e5, requiring a V = ~615m/s, reduces Cd only to 0.4. To get all the way down to Cd = 0.15 would need more than a quadrupling of Re to ~3e5 and therefore a velocity of ~900m/s (~3000fps!).

So despite the ~70% drop in Cd, drag would in fact increase - by 0.3 x (900/200)^2 = ~6x.

Second, (and perhaps just as important) I agree the graph applies only to the subsonic regime. So for .177, the graph departs from reality at somewhere near Re = 1e5.

However, below that point, I think it's at least qualitatively valid and therefore pretty soundly refutes the theory that Harry's BC observations can be accounted for by a Cd-vs-velocity-variation explanation.

But despair not. I'm working on another.

Steve

 This message has been edited by pneuguy on Oct 4, 2009 9:48 PM

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Herb1836
YF

# Right - I misread graph...

October 4 2009, 10:09 PM

Steve, you're right I misread the horizontal part of the graph. For Reynolds number changing from 6.5E4 to about 1.2E5 the C(D) changes very little.

Thanks for keeping me honest.

!@#\$%^&* I should know better. I worked with log scales for years...

I'd agree that for velocity changes that the graph probably isn't good above 1e5. For diameter changes it would work above that. The relationship isn't really a two-dimensional curve, but a surface. There should really be a family of curves plotted for different velocities, or velocity plotted in another dimension to show the surface.

 This message has been edited by Herb1836 on Oct 4, 2009 10:10 PM

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Steve in NC
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# No shame - it's an easy mistake to make. Meanwhile, as for that alternative explanation...

October 4 2009, 10:43 PM
 ...of HarrYrraH's apparent inverse relationship between MV and BC, consider these facts. 1. Imagine two pellets that are identical in every geometric detail (shape, mass distribution, surface finish, etc.) but differ fractionally in weight. Then their BCs would differ by the same fraction. That is to say, all else being equal, BC is directly proportional sectional density and therefore to mass. 2. If those two pellets were fired from the same airgun, then, also due to its greater inertia, the heavier pellet would likely have a lower MV. That is to say, all else being equal, MV is inversely related to mass. Ergo, simply from manufacturing variations in pellet mass and the effect of those variations on MV and BC, one would expect to see an inverse relationship between velocity and BC even if Cd were perfectly invariant with and independent of MV. Qualitatively, it works. Getting it to work quantiatively, however, may (* ahem *) be another matter. Steve
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Herb1836
YF

# No, I used 10 high pellets and 10 low for Harry's data not just one.

October 4 2009, 11:10 PM

Steve,

I used ten pellets from start of string and ten from end when I calculated differences in BC. The pellets weren't sorted so I don't see how each of the first ten pellets could have all weighed less than each of the last ten pellets.

It isn't just Harry's data that is sort of whacky. A lot of the data from Straight Shooters seems to show "odd" (ie unexpected variations) in BC vs gun & velocity.

Harry's data was particularly good since all the other conditions were controlled. The only real variable was the muzzle velocity of the PCP as it went down the power curve.

I don't have a PCP, but it would be really interesting to gather more data along the lines of Harry's experiment. Shoot PCP down power curve from max, to 350 fps or so. Measure BC via paired data all the way down the power curve. Be really sweet if different PCPs could be used. Also different pellets. Eg one that groups well and one that doesn't.

I really think the "problem" is that the pellet is "coning" around its line of flight. I think the pellet is drag stabilized so the Gyroscopic stabilization which a bullet would undergo isn't important initially. The larger the "coning" angle, the greater the BC. A "good" match of pellet and rifle and power results in a small "coning" angle. As pellet's velocity slows, the spin rate doesn't, so gyroscopic stabilization might become important down range.

 This message has been edited by Herb1836 on Oct 4, 2009 11:11 PM

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Steve in NC
AR&P

# Herb, Harry's data were sorted by MV - not shot order. Did you miss that?

October 4 2009, 11:27 PM

Harry said it in a rather peculiar way...

"The right side column shows mean near range velocity, average Mach number and average BC for each ten shots according to their ranked number (not the order of shooting) and so are random in terms of possible environmental changes."

...so I don't blame you for missing it. But I'm pretty sure that's what he meant.

So if, as I'm suggesting, MV is a function of weight, then they were automatically also sorted by weight. See?

Steve

 This message has been edited by pneuguy on Oct 4, 2009 11:30 PM

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Herb1836
YF

# Yes, I missed the fact that he data had been sorted. GREAT CATCH!!

October 5 2009, 1:10 AM
 Steve, You are absolutely right. I missed the fact that the data had been sorted. Harry had later reported the shot order also and I totally missed the significance. By that time I had already done the statistics and the notion that the data was reported in shot order was fixed in my noggin. Great catch!
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Steve in NC
AR&P

# PS: As for the Straightshooters data, while I admire...

October 4 2009, 11:46 PM
 ...without reservation the fact that they take the time and trouble to accumulate and publish such results for the products they carry, until (much) more information is made available about exactly how their velocity data are collected, I counsel caution before using them as a basis for elaborate ballistic theories.Steve
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Herb1836
YF

# Point taken.

October 5 2009, 1:46 AM
 Steve, Certainly understand your point. I'm not sure about if my notions are "elaborate ballistic theories" or not. It seems to me that in general the discussions are centered around ballistics of bullets from firearms. It seems that exterior ballistics can and should be be simplified for pellets in a different way. I've also wondered if we are really using too much theory. What if you just used nominal mass of pellet, nominal muzzle velocity, and calibrated at two ranges? Two empirical coefficients and you're done. If you are truly anal, you could shoot 10 shots at each of the two ranges measuring x-y deflection of each shot. You could then use statistics to calculate error bars around other ranges. I've fit a lot of data, and the resulting equation lures one into a false feeling of knowledge. When you start to put error bars around predictions, then reality is illuminated. All of us budding ballisticians plug numbers in Chairgun, and oh... that will be 0.00234 inches low. Like our group of 5 shots with a group size of 0.3 inches to zero scope was totally irrelevant. I must confess through, I'm flabbergasted by how well some of the guys shoot. With my cheap equipment and shaky hands, I'm happen to get groups at 10 yards that a lot of the guys are shooting at 50 or more.
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Steve in NC
AR&P

# My comment about spinning "elaborate ballistic theories", Herb, was meant only...

October 5 2009, 9:48 AM
 ...to point out that the simplest possible theory - constant Cd - seems to work pretty well. Which is a good thing - because it's tough enough to collect even the few simple parameters needed to use and understand it!!Steve
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Herb1836
YF

# Raw Drag Data on 9/16 inch Spheres (added image...)

October 4 2009, 12:09 PM

The raw data on 9/16 (edit..) inch spheres can also be seen on page 136 of the following pdf file:

Aerodynamic Data for Spinning Projectiles

Image:

Looks like "y-axis" is 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.44(?)

The data evidently came from BRL Report 514, by Charters, A.C., and Thomas. R.N., "The Aerodynamic Performance of Small Spheres from Subsonic to High Supersonic Velocities"

 This message has been edited by Herb1836 on Oct 4, 2009 5:38 PM

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