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Rifles, Reloading, Optics, Equipment
Rifles, Bullets, Barrels & Ballistics
wind drift based on drag
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<blockquote data-quote="LouBoyd" data-source="post: 665502" data-attributes="member: 9253"><p>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. </p><p>Stateds as an equation:</p><p>D = W(t- (X/Vm)) </p><p>where D is the deflection at distance X</p><p>W is the crosswind velocity </p><p>t is the time of flight to distance X</p><p>X is the distance the bullet has traveled. </p><p>Vm is the muzzle velocity </p><p></p><p>This equation only requires consistent units, such as meters and seconds. </p><p>It does not caculate drag. Determing the actual time of flight to distance X is not </p><p>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. </p><p></p><p>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.</p><p>Robert McCoy's book addresses that math too and discusses it's futility for practical shooting.</p><p></p><p>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.</p></blockquote><p></p>
[QUOTE="LouBoyd, post: 665502, member: 9253"] 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. [/QUOTE]
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