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wind drift based on drag

 
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  #1  
Old 06-21-2012, 09:46 PM
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wind drift based on drag

I hope there are some ballistic geeks who can help me out. After reading Applied Ballistics for Long-Range Shooting by Bryan Litz, I came to the conclusion that necking down a cartridge while using a bullet with a similar form factor, and KE, produces less wind drift. Two reasons that i can think of are- #1 the lag time is reduced from compressesing the time flight through higher velocity, and #2 the Cd is lower at a higher velocity. After reveiwing alot of numbers, i realize there is more going on because the smaller bullet has a greater advantage than i assumed. There is no mention of this in the book. can someone enlighten me? ( to keep things simple let's assume a 230 gr .308 and a 140 gr. .264 with i7 of 1 and 3096 ft-lbs at the muzzle, the equivalent of a 155 gr. .308 @ 3000 fps. Sd and g7 bc are .287 and .346.)
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  #2  
Old 06-21-2012, 11:31 PM
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Re: wind drift based on drag

Quote:
Originally Posted by ajhardle View Post
I hope there are some ballistic geeks who can help me out. After reading Applied Ballistics for Long-Range Shooting by Bryan Litz, I came to the conclusion that necking down a cartridge while using a bullet with a similar form factor, and KE, produces less wind drift. Two reasons that i can think of are- #1 the lag time is reduced from compressesing the time flight through higher velocity, and #2 the Cd is lower at a higher velocity. After reveiwing alot of numbers, i realize there is more going on because the smaller bullet has a greater advantage than i assumed. There is no mention of this in the book. can someone enlighten me? ( to keep things simple let's assume a 230 gr .308 and a 140 gr. .264 with i7 of 1 and 3096 ft-lbs at the muzzle, the equivalent of a 155 gr. .308 @ 3000 fps. Sd and g7 bc are .287 and .346.)
The French mathematician Didion work this out and published in 1859. you mention "lag time" and that is the key. Lag time is the actual time it takes a bullet to fly a given distance minus the time that same bullet would take if it had no drag. That time is simply the distance the bullet has traveled divided by the muzzle velocity.
Stateds as an equation:
D = W(t- (X/Vm))
where D is the deflection at distance X
W is the crosswind velocity
t is the time of flight to distance X
X is the distance the bullet has traveled.
Vm is the muzzle velocity

This equation only requires consistent units, such as meters and seconds.
It does not caculate drag. Determing the actual time of flight to distance X is not
calucalted by this equation. That's what all the drag tables and BCs are about. But just about every ballistice computer program has this very simple equation in it to additionally calculate wind deflection given the calculated time of flight. The ONLY information required is the muzzle velocity and the real drag curve. errors introduced by the use of single value BCs (like G1 or G7) not only adds errors to the drop but similar (not equal) errors to the calculated wind deflection.

In Robert McCoys book "Modern Exterior Ballistics" he shows the mathimatical derivation of Didion's equation and also the related math of the effect of fore/aft winds which were not addressed by Didion. Didion's equation does not address the effect that a projectile does not instantaneously orient itself into the oncoming air stream (from the bullets perspective) and precesses in a (usually tight) damped spiral about the predicted trajectory. That error is generally small compared to the bulk effect and very difficult to model mathematically.
Robert McCoy's book addresses that math too and discusses it's futility for practical shooting.

Anyway, It is practical to use the results predicted by most available ballistics computer programs (based on Robert McCoy's work) to compare the wind deflection of different bullets at different velocities in different atmospheres. I don't know of any simple rule of thumb which can be used to compare the wind deflection of different bullets or even the same bullets at different ranges of velocity. That's not just the muzzle velocity but the velocity as it decreases over the trajectory. Even with two identical bullets you can't say that the faster one will have the lower wind deflection. That depends on the real drag function of each bullet over the velocity range of each shot. And of course the crosswind does not have to be uniform over the trajectory.

Last edited by LouBoyd; 06-22-2012 at 12:21 AM.
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  #3  
Old 06-22-2012, 12:55 AM
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Re: wind drift based on drag

Right. Reading Bryan's chapter on scaling bullets got my gears in my head rolling. He talks alot about the inherent advantage of scaling up, but neglects the pro's of scaling down. I spend to much time looking at charts and not enough time shooting.
One thing i noticed, if we scale a bullet down, maintaining form factor and energy ( like going from a .308 to a 6.5-08) the smaller diameter has less drift until the higher b.c. makes up the difference at a range where these bullets are ineffective.
I started looking into this when bryan states the b.c. advantage of heavy bullets. I thought, at first, the heavier the better, but quickly found out otherwise. the faster the better.
reveiwing the g7 drag curve, i believe shows why. If the 6.5 leaves the barrel at a velocity of 3156fps, the Cd is something like .26. The .308, with the same energy is slower 2462fps. Cd is close to .284. The difference between the two bullets increase downrange as the slower one reaches the spike in the drag curve. The .308 goes transonic, Cd=.4, and the 6.5 is still happy, close to .3.
I assumed if i modified the .308's form factor to match the 6.5's Cd at the muzzle, things would even out. Nope. I had to reduce the .308's form factor to .890 to even things at 1000 yards. Comparing form factors of .890 and 1 is no longer apples to apples, or apples to any fruit.
Am i correct for assuming there is no better way to reduce wind drift than to reduce bullet diameter? That, or get more powder behind it. Same result if my assumptions are correct.
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Old 06-22-2012, 11:57 AM
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Re: wind drift based on drag

Quote:
Originally Posted by ajhardle View Post
[...]( to keep things simple let's assume a 230 gr .308 and a 140 gr. .264 with i7 of 1 and 3096 ft-lbs at the muzzle, the equivalent of a 155 gr. .308 @ 3000 fps. Sd and g7 bc are .287 and .346.)
Is it reallistic for 230gr .308 and 140 gr .264 bullets to have an i7=1 with normal materials?

Or, is this a purely hypothetical... "what if pigs could fly?"

-- richard
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  #5  
Old 06-22-2012, 12:14 PM
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Re: wind drift based on drag

Never mind.
Stupid question on my part after re-reading.
-- richard
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  #6  
Old 06-22-2012, 12:59 PM
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Re: wind drift based on drag

Quote:
Originally Posted by ajhardle View Post
Right. Reading Bryan's chapter on scaling bullets got my gears in my head rolling. He talks alot about the inherent advantage of scaling up, but neglects the pro's of scaling down. I spend to much time looking at charts and not enough time shooting.
One thing i noticed, if we scale a bullet down, maintaining form factor and energy ( like going from a .308 to a 6.5-08) the smaller diameter has less drift until the higher b.c. makes up the difference at a range where these bullets are ineffective.
I started looking into this when bryan states the b.c. advantage of heavy bullets. I thought, at first, the heavier the better, but quickly found out otherwise. the faster the better.
reveiwing the g7 drag curve, i believe shows why. If the 6.5 leaves the barrel at a velocity of 3156fps, the Cd is something like .26. The .308, with the same energy is slower 2462fps. Cd is close to .284. The difference between the two bullets increase downrange as the slower one reaches the spike in the drag curve. The .308 goes transonic, Cd=.4, and the 6.5 is still happy, close to .3.
I assumed if i modified the .308's form factor to match the 6.5's Cd at the muzzle, things would even out. Nope. I had to reduce the .308's form factor to .890 to even things at 1000 yards. Comparing form factors of .890 and 1 is no longer apples to apples, or apples to any fruit.
Am i correct for assuming there is no better way to reduce wind drift than to reduce bullet diameter? That, or get more powder behind it. Same result if my assumptions are correct.
FWIW - Here's what I came up with using your hypothetical...

(better get someone that knows what they're doing to check it)

0.308 = Cal
230 = Wt
0.346 = SD
1 = i7
0.346 = G7
2461 = MV
3093 = Ft-Lbs
10 = Full Value Wind
1000 = Yds
74.1 = Drift

0.264 = Cal
140 = Wt
0.211 = SD
1 = i7
0.211 = G7
3155 = MV
3094 = Ft-Lbs
10 = Full Value Wind
1000 = Yds
99.8 = Drift

Conversely, you can imporve BC by holding caliber constant and increasing section density with heavier=longer projectile.

In any case, Bryan did a comparison between the 168gr and 180gr Berger 7mm bullets...
http://www.appliedballisticsllc.com/...mNumberOne.pdf
http://www.appliedballisticsllc.com/...mNumberTwo.pdf

The bottom line is that this is the reason we have lots of bullet choices. i.e. compromises and priorities for different cartridges, applications, shooters

-- richard
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  #7  
Old 06-22-2012, 01:18 PM
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Re: wind drift based on drag

To me there seems something missing in the time lag rule of thumb(as applied/described).
The T-Lag formula implies to me that drift takes affect ONLY during SLOWING of an object.
And slowing of the object in my understanding is purely due to drag.
Maybe if I could see an ACTUAL drag curve of a bullet, instead of a drag coefficient curve..

This is why a faster/lighter/lower BC bullet producing lower wind drift doesn't make sense to me:
Drag is not drag coefficient. Right?
That is, there is drag, which goes UP with any object considerably with velocity. And then there is an object specific aerodynamic adjustment applied to drag (it's coefficient).
I would think that regardless of the coefficient applied(which should be relatively small), actual/total drag would still continue to climb with velocity.
So,,
If drag does continue to climb with velocity, then at any given span in a bullet's flight, T-Lag would follow the bullet's slowing rate -due to drag within that span.
For example, when measuring a bullet's drop in velocity between 50yds and 100yds, I should get a higher rate of velocity loss than the same measure between 950yds and 1Kyds,, this because of different drag rates(slowing rates).
And with this, the T-Lag should be higher at 50-100, than at 950-1000.
So a 10mph wind applied to both equally should cause more drift/deviation(in moa) at the 50-100 span, even though there was less TOF there, than at the 950-1000 span.

Coefficients aside,,
Do lighter bullets cause less drag?
Do they cause less drag due to smaller diameter?
What if they are the same diameter, but lighter?
Does higher velocity of this lighter bullet mean higher total drag?
Does higher total drag mean greater slowing rate and therefore higher T-Lag?

Not trying to hijack the thread, but to lead into an understanding that might help.
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