wind drift based on drag

Discussion in 'Rifles, Bullets, Barrels & Ballistics' started by ajhardle, Jun 21, 2012.

  1. ajhardle

    ajhardle Well-Known Member

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    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.)
     

  2. LouBoyd

    LouBoyd Well-Known Member

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    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: Jun 22, 2012

  3. ajhardle

    ajhardle Well-Known Member

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    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.
     
  4. rscott5028

    rscott5028 Well-Known Member

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    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
     
  5. rscott5028

    rscott5028 Well-Known Member

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    Never mind.
    Stupid question on my part after re-reading.
    -- richard
     
  6. rscott5028

    rscott5028 Well-Known Member

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    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/index_files/7mmNumberOne.pdf
    http://www.appliedballisticsllc.com/index_files/7mmNumberTwo.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
     
  7. Mikecr

    Mikecr Well-Known Member

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    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.
     
  8. Mikecr

    Mikecr Well-Known Member

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    In Richards comparison the BCs were not completely normalized(as per intent -I believe).
    When you set form factor to 1, BC becomes SD.
    To then match the 30 & 26cal bullet sectional densities/BCs, the bullet weights would need to be 140gr-vs-191gr.
    And with this, either bullet driven faster would hold less wind drift(the part I still don't understand).
     
  9. rscott5028

    rscott5028 Well-Known Member

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    Yep. Since the weight was stated for each bullet, I didn't get where he wanted it normalized.

    I also wondered if the MV for the 140 gr .264 was at the high end for most cartridges and the 230 gr .308 might be at the low end. ...such that a big 30 cal would have an even better advantage with respect to drift at ELR.

    As to your comments about T-Lag being a bigger factor at higher velocities, (if I understood you correctly), I'm presently trying to setup my 300wm with the 230 gr OTM for a 2076 yd shot. In doing so, I was hoping to remain supersonic. My current mild load was only a few hundred fps shy. So, I added that to my MV and reran the numbers. Much to my surprise, +200 fps on the front end doesn't equal +200 fps at 2k yds. Perhaps that illustrates your point? Or, maybe I'm just delerious?

    -- richard
     
  10. Mikecr

    Mikecr Well-Known Member

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    While I realize the wind drift rule of thumb works, I struggle to understand it.
    It seems to work based on TOF rather than T-Lag. One contributing to the other but completely different in themselves.

    I picture a boat traversing a river with a 10mph current. If it's velocity is held constant, while pointed a bit upstream, it travels in a line straight across.
    If at any point it decelerates, its line of travel lags downstream. The greater the deceleration, the greater it drifts. This is how I take the T-Lag formula.

    The constant speed boat requires added energy to arrive straight across because it's pointed a bit upstream and traveling upstream as needed to overcome losing ground. So it actually travels further in doing so, taking longer than it would take with no current. TOF

    A 'bullet' boat launched from one side hard enough to reach the other side does not have added energy and decelerates the whole time.
    That deceleration is greatest on launch due to all the extra drag in it(extra initial speed).
    Based on the lag here, I would think MOST of the resultant drift as seen on arrival would have occurred back nearest the launch point.
    With this, launching the boat faster, even reducing the overall time to cross, should cause more drift.
    BUT;
    Since this is apparently not how it works, I'm left to think that wind applies equally to an object that is decelerating, regardless of it's decelerating rate.
    And since a bullet is decelerating(at any rate) the whole TOF, wind applies equally the whole TOF -or,, 'time of deceleration'.
    So T-LAG and TOF cannot be taken with iterations as a decelerating rate, but a 'Time(or period) of Deceleration' overall.


    I would think I just solved MY misunderstanding,, but if TOD = TOF then why isn't drift based on TOF? Why the term T-Lag? And why does it work?
     
  11. LouBoyd

    LouBoyd Well-Known Member

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    QUOTE=Mikecr;665677
    >Coefficients aside,,
    >Do lighter bullets cause less drag?
    No drag is a force from the projectile pushing air out of the way. It is independend of bullet weight, However a ligher bullet has less energy to lose so it decellerates quicker.
    > Do they cause less drag due to smaller diameter?
    Yes. The have a smaller volume of air to push out of the way .
    > What if they are the same diameter, but lighter?
    I thought that was your first question. Shape matters too. A streamlined bullet loses less energy pushing air out of the way than the same diameter blunt one.
    > Does higher velocity of this lighter bullet mean higher total drag?
    Drag increases roughly with the square of the velocity, though the complexities of air flow can modify that considerabley, particularly around the speed of sounnd.

    > Does higher total drag mean greater slowing rate and therefore higher T-Lag?

    Generally yes. however consider if the higher drag takes the bullet subsonic where the drag may then drop cosiderably. It's possible (though not likely) for the bullet with the higher initialy drag to have less total wind deflection. When it reaches the target. Don't assume that bullets always slow down with distance. High trajectory low drag bullets can decellerate going up and actually accelerate going down if the force of gravity is higher than the drag force over a range of velocities (usually subsonic) velocity.
    Though I believe I understand the math I'm not able to predcit just by looking at the BC's and muzzle velocities which of two bullets will have the greater wind deflection at a given distance. But I do trust the results given by ballistics computers. Few commercial ballistics computers however allow you to enter variable downrange wind vectors. If winds were constant over every path you coudn't miss if you had a Kestrel wind meter at the shooting positiong. Reality is far different.

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

    The math may be precise, but it's really not of much practical help to the shooter. What is of help is lots of practiece trying to judge downrange winds from the very subtle clues from moving mirage, blowing leaves/grass/trees, and blowing particles in the air.
    That combined with watching bullet point of impact in those condtions can give good results. There are electronic instruments which can predict wind deflection using methods similar to watching mirage. but I don't know of any that are available commercially.

    Sighter shots work well if you can see the point of impact. The path of the next bullet will be close to the same if conditions aren't changing too fast and the second shot is immediate. It's the best wind meter avaialble to a shooter.
     
  12. ajhardle

    ajhardle Well-Known Member

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    better check you math. 140/7000*(.264*.264)=.287
    wind drift is now 63.5"
     
  13. ajhardle

    ajhardle Well-Known Member

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    thanks for the great info. Louboyd, you briefly touched on what's boggling me. You said it depends on " the drag funcion of of the velocity range of each shot." Well let's look at the drag function. Faster means more drag because the the bullet covers more distance ina given amount of time( because more particals of air are encountered). correct? But the drag coefficient is lower based on the drag curve. So if we shoot the same bullet at different velocities, higher velocity has a lower coefficient of drag? Am i off beat on this one?
     
    Last edited: Jun 22, 2012
  14. LouBoyd

    LouBoyd Well-Known Member

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    A "coefficient of drag", like a BC is number which is used to fit an equation describing someone's drag theory to observed reality. Just about all theories are simplifications of what's happening in reality. To describe an aerodynamics problem perfectly you'd need to know continuous vector velcity of every gas molecule that interacts with the bullet, either by direct collison or collision with neighboring molecules. No one could set up the model exacly and no supercomputer could handle the task for a single trajectory. So researches come up with models which give a decent fit to observed reality. Such equations input known data like time and velocity and tempearature and speed of sound and molecualar weight etc but they are not acturally calulating the moleules bouncing around, so if the models work (at least for some ranges of velocity) they are useful even if they aren't modeling what's physically happening. Observed or calculated coefficents need to be applied to make the equations work. I can't answer your questioin above. If the theory were perfect the drag model should give the correct answer for both velocities, as velocity would certainly be one of the variable coefficients in the model.

    Wheneverr you reduce a comples funtion, such as the drag function of a sepecific bullet to a single number, such as a G1 or G7 BC, or "Coefficient of Drag" you are introducing errors unless the model is perfect for the range of all parameters what the equation is applied to. In my opinion BC should be thought of "Before Computers", not "Ballistic Coefficients." They were a handy tool in the days when rooms of mostly women were employed by the military to solve ballistic table (and other useful equations), but today even a high end eell phone has easily enough storage and computing power to handle complete numeric drag tables for each bullet model one shooter might use over the range of velocity they might shoot it and in small enough increments as not to introduce addtional error. That would less memory than a high resolution photo or video clip.

    There are good reasons whey bullet manufacturers stick with G1 and G7 BCs. One is that all of the present ballistics calculators use BCs, and a single numner is easy to print in a catalog and it's a known fact that many shooters will buy one bullet over another it it has a 0.01 higher BC. Forget the fact that most bullet manufactures don't even state what velocity that number was correct for or how large the deviations are over the bullets useful range. I love Brian Litz's book. It provides two very useful things. One is giving precise details about many of the currently availabe long range bullets. The other is in pointing out clearly how well G1 or G7 coefficients do (or don't) match currently available bullets. My favorite example is the 240 Grain 30 Cal Sierra, wich in spite of being a a boattail the G1 model is the better fit, probably because of it's relatively short ogive, but for the 220 grain Sierra boattail the G7 coefficient is the better fit. It's not obvious why from looking at the shape of the two bullets. The magnitude of the error is similar but reversed in the two examples

    Sierra is (or was) unique among bullet makers. Although they don't publish G7 numbers, they do publishe multiple G1 values vs velocity in typically 3 or four segments. That's generaly more accurate than one single valued coefficent, though it requires a ballistic program whcih can handle the multiple inputs. I believe Lapua is also offering multiple G1 values for some of their bullets. Having an actual correct drag table would also require modifiction of the available computer programs. No ballistic software I'm aware of on the market handles complete drag tables, though if they did they'd actually be simpler than the existing programs.

    Likewise no bullet makers I'm aware of publish complete drag tables, though some either calculate the tables with programs like McDrag or measure drag tables using millimeter radar. Then they condense those curves down to one or a few values thowing away potentially useful information, particulary around transoinic velocities.

    Are the existing methods good enough?. For most hunters, yes. For long range precision first shots, no. But then hunters don't have a method for measuring downrange wind vectors precisely so it doesn't really matter. Using spotter shots corrects for all meaurement errrors including air density , errrors in the difference of the G coefficients vs the actual drag curve, and the uncertanty of downrange wind measurements (actually estimates or guesses). Even using spotting shots doesn't correct for the fact that wind conditions are changing continuously. That's a problem with any instrument you might use to measure downrange wind unless it's built into the aiming device and does it's calculations in real time.

    A Kestrel 4500 with it's built in weather sensors and ATRAG software may do what measurements it takes accurate to two decimal places and do the calculation are executed to better than six decimal palces. But the G() table have built in errors limiting their accuracy to two decimal palces, and the mini wind meter doesn't have a clue what the wind is doing more than a few feet from the meter. There is no place for the shooter to enter downrange wind information manually even if the shooter can guess what the wind is doing between his location and the target. Shooter wind estimates rarely better than 5% errror even with wind flags on flat terrain. In mountainous terrain with clear air and not foliage close to the trajectory guessing wind speed closer than 20% errror takes an excpetionally experienced shooter if it's possbible at all.

    I'd suggest you simply believe the deflection estimates that your ballistic program gives you. They aren't perfect, but the available commercial ballistics programs don't have access to either the precise drag tables of each bullet or the downrange wind vectors to do a better job. Neither is the fault of the software. The people who wrote the software (most built on Robert McCoy's work) are aware of the limitations and don't bother to incude the calcualtions for the parts where data isn't likely to be availabe, particulary piecewise downrange wind vectors. They still do a far better job than anyone is likely to do by looking at two published BCs and their associated muzzle velocities and mentally calculate (or guess) which will have the lower lag time and thus the lower wind deflection.

    Rober McCoy published McTrag which calculate trajectory, McDrag which calcullates bullet drag from bulllet dimensions & mass, which calculates bullet rotational stability from bullet dimensions and internal mass distribution based on years of research at the Aberdeen Ballistic Reesearch Labs (BRL). That was several years before he published the book Modern Exterior Ballistics.

    In that book McCoy states that the US Army has mostly abandoned the used of G functions and works directly with measured drag tables for projectiles. BRL had not soved the problem of practical downrange wind vector measurements at the time of that publication.

    There was a DARPA request for proposals arouund 2004 to the industy for an integrated rifle scope which could do multiple functions including rangefinding, weather, and and measuring downrnage wind vectors in two (or optionally three) dimensions. A web search of "scintillation anemometer" gives some idea of how the 2D type can work. A search on "particle image velocimetry" gives some info on 3D techniques. The hardware can be nearly as simple as a laser rangefinder and a cell-phone camera though the software is considerably more complex.

    There was a writeup in VeryHighPower, the FCSA periodical of early experiments in Israel around 1994. At that time a simple version using one laser, two photodiodes, and a PC could give downrange horizontal crosswind estimation about as good as their skilled marksmen could estimate from mirage at ranges to over a kilometer. Measurement period was less for the instrument than it took the shooters to study and mentally estimate the bullet deflection. I've found no additional material from that source since. The technology has had 15 years to improve and be made more compact. While the DARPA request for proposal was not classified, resuts of the DARPA request are classified. I can only surmise what is currently available within the military.

    It's anyones guess if or when Burris or Leica will offer such a unit commercally. I'm not sure I'd want one. It would make LongRangeHunting rather boring. Fortunately nothing on the market today comes close.
     
    Last edited: Jun 23, 2012