Now, I've heard it all...

[alphasigmookie]

Gene, that formula is antiquated. The proper one is the one I listed above. You can find it in Bryan Litz's book, Applied Ballistics for Long Range Shooting, aka The Bible for long range shooters. It is explained in chapter 5. Toss the Speer manual in the garbage.

Actually I think they're both nearly the same (although possibly with different units...not sure about the origin of the constants in the equation). Basically the important part is the TOF-TOFv which is in both of these equations. This is the difference between the actual time it takes to reach the target vs. the theoretical amount of time it the bullet should take to hit the target if there were no drag or wind. Calculating the actual TOF would require more complex calculations (more than likely solving a differential equation, or at least plugging into the analytical solution to one) and depends upon the ballistics coefficient. Measuring the actual TOF would be the ideal, but I'm not sure how realistic that is either.

[Gene L]

You will note that BC is not a part of the formula for Drift. What makes you think the formula was cobbled together by Speer, whose business is bullets, etc. It's all physics.

In the same book I quoted above, are pages and pages of Ballistic Tables figuring in BC for bullet drop. They all give TOF at different ranges, so you can go from there and figure out what you need to figure out if figuring drift.

[Pegasus]

Peg, what you say sounds relatively logical, but I'm interested in the underlying physics of why exactly that occurs. Would the same impact be observed with a wadcutter bullet with no point? My initial intuition on why exactly this might occur is that in a conventional pointed bullet the wind acts more strongly on the rear of the bullet (greater cross sectional area) than the front of the bullet, but then the rotation of the bullet would be around the center of mass which would be further back so I'm not sure it quite works out that way. It may have more to do with the fact that the bullet as long as it remains stable will generally at be forced into the most aerodynamic position by the drag forces acting on it from multiple directions.

I think you are still thinking about the crosswind hitting the bullet and pushing more on the rear than the front. You need to take that imagery out of your mind. The crosswind does not "push" on the bullet, it's just another vector in the overall oncoming airstream. The bullet remains point-on into the airstream by virtue of its spin and its gyroscopic effect. The same effect would occur for a wadcutter because it is also spinning and gyroscopic forces will direct the axis of rotation (the "point") to go into the oncoming airstream.

BTW yes there is "acceleration" of the bullet, but not in the forward direction. The muzzle velocity of most firearms exceeds the terminal velocity of the bullet so the velocity will not increase from any of the natural forces acting upon it in that direction, however it will accelerate (or decelerate) in the direction of the primary forces acting upon it. It will decelerate in the forward direction due to drag. It will also accelerate in the direction the wind is moving until it achieves a velocity in that direction that is equivalent to the wind speed. Finally it is accelerating towards the ground due to the effect of gravity. This last point is why bullet drop is usually measured in inches at 100 or 200 yds, but can be measured in feet at 500 or 1000 yds. Not only is the bullet slowing down the longer it is in the air, but it's also falling at a faster rate with every moment that passes. The instant the bullet leaves the muzzle it is actually not falling yet. After 0.1 seconds the bullet is falling at a rate of 0.98 m/s. After 0.5 seconds it's falling at 4.9 m/s. After 2 seconds it's falling at 19.8 m/s. Obviously these numbers assume no drag in the direction of the gravitational force which isn't exactly true so the actual falling velocities will be slightly less when drag is accounted for.

http://www.grc.nasa.gov/WWW/k-12/airplane/mofall.html

Right, a negative acceleration.

[Pegasus]

You will note that BC is not a part of the formula for Drift. What makes you think the formula was cobbled together by Speer, whose business is bullets, etc. It's all physics.

In the same book I quoted above, are pages and pages of Ballistic Tables figuring in BC for bullet drop. They all give TOF at different ranges, so you can go from there and figure out what you need to figure out if figuring drift.

Gene, I can explain it to you, I cannot comprehend it for you. Formule evolve over time and we discard older ones.

[Pegasus]

Actually I think they're both nearly the same (although possibly with different units...not sure about the origin of the constants in the equation). Basically the important part is the TOF-TOFv which is in both of these equations. This is the difference between the actual time it takes to reach the target vs. the theoretical amount of time it the bullet should take to hit the target if there were no drag or wind. Calculating the actual TOF would require more complex calculations (more than likely solving a differential equation, or at least plugging into the analytical solution to one) and depends upon the ballistics coefficient. Measuring the actual TOF would be the ideal, but I'm not sure how realistic that is either.

You are right; they are nearly the same. But the difference has to do with the use of "lag time" versus simply "time of flight." Lag time takes into account the BC of the bullet and more closely predicts the behavior of today's high BC bullets.

[alphasigmookie]

You will note that BC is not a part of the formula for Drift. What makes you think the formula was cobbled together by Speer, whose business is bullets, etc. It's all physics.

In the same book I quoted above, are pages and pages of Ballistic Tables figuring in BC for bullet drop. They all give TOF at different ranges, so you can go from there and figure out what you need to figure out if figuring drift.

Gene, it's not directly in the equation as presented but it is embedded in the TOF as it directly impacts it (ie TOF is a function of BC). Either you will directly measure TOF, calculate it using an equation that takes into account the BC, or you will look it up in a table (where someone else has either measured or calculated it). However there is a lot of physics hidden in those TOF values.

[alphasigmookie]

You are right; they are nearly the same. But the difference has to do with the use of "lag time" versus simply "time of flight." Lag time takes into account the BC of the bullet and more closely predicts the behavior of today's high BC bullets.

Gene's equation also effectively considers lag time too although it dumbs it down a bit and doesn't call it that. His is includes TOF minus an estimation of time of flight in a vacuum which seems at least conceptually the same as your lag time, although I don't know for sure because you didn't spell out the equation for ToFv.

[Pegasus]

My bad: ToFv = D/V

Where D is distance in feet
and V is velocity in FPS.

So for a MV of 3000FPS and a distance of 1000 yards (3000 feet), the ToFv is 1 second; (3000Feet/3000FPS).


ETA: I'm not saying Speer's equation is bad, I am saying Litz's equation is more precise. And yes, both equations take BC into account, but Litz's equation details its influence better, as it should.

[alphasigmookie]

I think you are still thinking about the crosswind hitting the bullet and pushing more on the rear than the front. You need to take that imagery out of your mind. The crosswind does not "push" on the bullet, it's just another vector in the overall oncoming airstream. The bullet remains point-on into the airstream by virtue of its spin and its gyroscopic effect. The same effect would occur for a wadcutter because it is also spinning and gyroscopic forces will direct the axis of rotation (the "point") to go into the oncoming airstream.

I suspect you are correct on the gyroscopic effect being the primary driver of this. I still think thinking of the effects of wind and gravity as a separate force vectors pushing on the bullet in different directions is the correct way to conceptualize it, but the ultimate impact is a combined force vector resulted in a single, but constantly changing velocity vector that combines velocities in all three primary directions [forward (muzzle velocity), down (gravity) and left or right (wind)]

[Gene L]

Gene, I can explain it to you, I cannot comprehend it for you. Formule evolve over time and we discard older ones.

Peg, I already comprehend Speer's method, which works. I don't understand why you think Speer is using outdated formulas while your guy is not. Do you dismiss their TOF tables as well? What other mathematical formulas have been discarded since Newton's time?

[Ernie Bishop]

You are doing a good job there Peg!
Keep it up!!!
And he isn't even pulling your leg

[alphasigmookie]

Peg, I already comprehend Speer's method, which works. I don't understand why you think Speer is using outdated formulas while your guy is not. Do you dismiss their TOF tables as well? What other mathematical formulas have been discarded since Newton's time?

Gene, I think the issue is that all of these equations are approximations of a process that to be precisely calculated would require the simultaneous solving of multiple differential equations. Use of such approximation is quite common in engineering and physics. The equations usually work quite well within a certain range of parameters for which they were designed for, but diverge from reality more and more as you get beyond the range of cases where they were designed for. If I had to guess your equation works perfectly well for common hunting bullets within 300 yds, although might be less accurate say for a .50 cal at 1000 yds or a 155mm howitzer shell fired 5 miles.

[Big Chief]

You are doing a good job there Peg!
Keep it up!!!
And he isn't even pulling your leg

These two truly deserve to argue with each other.........

[farm boy]

I like beer.

[Spk]

You guys are arguing the same equation, only the Litz equation lets you plug in wind speed directly in MPH while Speer requires you to make any necessary conversions since it uses wind speed in feet per second. The difference is a matter of "easy-ness" and the 17.6 is a conversion factor that's done for you.

Speer Method:

Drift (feet) = Vwind(fps)[Tof-(R/Vm)]

Drift measured in feet
Velocity of Wind measured in feet per second
Tof is time of flight actual
R/Vm the Range divided by the Muzzle Velocity (equiv. to tof in a vacuum)

Rewriting the Speer equation then becomes

Drift (feet) = Vwind[Tof-Tofv] -- NRA Firearms Sourcebook p. 357 or p. 279 in the Rinker book.

Now lets say we know the wind speed in miles per hour instead, let's do a conversion:

20 mph = 105,600 feet per hour or 1760 feet per min or 29.33333 feet per sec. Recall there are 12 inches per foot, therefore, 29.33333x12 = 352 inches per second.

So 20 MPH = 29.3333 FPS = 352 Inches per second

Since I'm looking for a conversion factor between MPH and inches of drift I can simply divide 352/20 = 17.6 and now a have a constant that's easier to use when I know MPH of a crosswind.

So the final equation is Drift (in.) = 17.6 Vwind (mph) (Tof - Tofv)

The Speer equation isn't wrong it's just not as convenient or "user-friendly."

[Gene L]

That's what I've been saying all along. Same destination, different route. My wind gauge has a fps conversion on it, however, so I don't need to do the math.

[knitepoet]

These two truly deserve to argue with each other.........

[Pegasus]

These two truly deserve to argue with each other.........

You're probably right, Alphasigmookie is one of the more interesting denizens of this realm and I enjoy the back and forth with him.

[snake284-1]

I believe the M16A1 had a chromed chamber (maybe be not the bore) for the just exact reasons you specified. I'm sure the M82 needs a chrome lined bore and chamber and would not have it any other way, but it's not "in order to improve accuracy."

They chromed it to prevent jams. That was a problem in the tropical humidity of Vietnam. Maybe it improved accuracy when the guys shooting them saw they weren't going to jam at an inopportune moment and get them killed so they settled down and shot straighter. That's about the only way it would improve accuracy.