For you ballisticians.

[alinwa]

Earlier this evening, I posted this on the wrong thread

Let us introduce momentum into the discussion. It is a vector that decreases in length as a bullet decelerates. The vector that represents the force of the cross wind on the bullet remains constant (assuming a constant crosswind). increasing in influence as the down range vector decreases. The instantaneous direction of the bullet can be calculated as the sum of these vectors. Even though two bullets leave and arrive at the same time, the differences in their momentum as they proceed down range will cause a difference in their drift plots. This is exaggerated as drift is added to drift. A dropped bullet has an entirely different momentum profile, since it starts with zero downward momentum and is accelerated by gravity till it hits the ground or reaches a maximum value. There is a limit to the velocity that can be achieved by a falling object, and from that point on the downward momentum vector stays the same length which is entirely different from a fired bullet.

Another point worth noting is that as a tank of given proportions is increased in size, it has more volume per surface area. If we apply this to a solid shape, and hold density constant, larger solids of a given shape and proportion have less sail area per weight, giving the wind less influence per unit of weight, which is why it is easier to blow dust than boulders.

OK, so let me put it another way..... fuhgeddabout flying through the air. We'll remove momentum and acceleration/deceleration in the forward or downward direction...... The bullet is just SET there on a frictionless surface. It's pointed at a target but has no velocity, ONLY a 10mph crosswind...

How far does it blow over in 2 seconds?

al

 

[alinwa]

Yep, that's exactly what I'm saying. The bullet is not free to just drift along sideways on its own; it is encapsulated if you will, by the airmass through which it is flying, which in this case is not moving relative to the ground, so there can be no drift.

Gene Beggs

So you are saying that Glen Newick and others are wrong, that a push is a push is a push no matter WHERE it occurs in the flight path....... the displacement is NOT like balls on a pool table establishing new vectors......


(Glenn in his book "Ultimate in Rifle Accuracy" diagrams how giving a bullet a nudge near to the muzzle has a much larger effect than the same nudge near the target........ like a bowling ball which hooks early VS later down the lane.)


thanxall!!! this is fun....


al

 

[tobybradshaw]

Let us introduce momentum into the discussion. It is a vector that decreases in length as a bullet decelerates. The vector that represents the force of the cross wind on the bullet remains constant (assuming a constant crosswind). increasing in influence as the down range vector decreases. The instantaneous direction of the bullet can be calculated as the sum of these vectors. Even though two bullets leave and arrive at the same time, the differences in their momentum as they proceed down range will cause a difference in their drift plots.

Momentum = mass x velocity

So, since the bullet doesn't change in mass (apologies to Einstein) during its flight, any change in momentum is purely a change in velocity. What you have said is that wind deflection is proportional to the rate of change in velocity, so a fast-starting bullet that arrives at the target going much slower deflects more than a slower-starting bullet that arrives AT THE SAME TIME but which hasn't slowed down so much (which is the only way it could start slower and reach the target at the same time). That is correct, but it isn't a prediction of the "sail area" model. It is a prediction of the "nose-into-the-wind" model.

A dropped bullet has an entirely different momentum profile, since it starts with zero downward momentum and is accelerated by gravity till it hits the ground or reaches a maximum value. There is a limit to the velocity that can be achieved by a falling object, and from that point on the downward momentum vector stays the same length which is entirely different from a fired bullet.

Regardless, the nose of a spin-stabilized bullet will point into the relative wind. If you drop a spinning horizontal bullet, it will turn point down as it falls. If there is a wind (relative to the ground) it will hit the ground canted nose-into-the-surface-wind, at an angle of:

arctan(wind velocity parallel to the ground divided by the "vertical" velocity due to acceleration by gravity and deceleration by drag)

Drop an arrow and see. Of course, this does require that you subscribe to the notion that fin- and spin-stabilized projectiles behave similarly.

Another point worth noting is that as a tank of given proportions is increased in size, it has more volume per surface area. If we apply this to a solid shape, and hold density constant, larger solids of a given shape and proportion have less sail area per weight, giving the wind less influence per unit of weight, which is why it is easier to blow dust than boulders.

And this is why BC scales with both the coefficient of drag (dependent on shape but independent of size) and the sectional density of the bullet (mass/cross-sectional area). Sectional density describes the phenomenon you are talking about above.

And "nose-into-the-wind" is why we don't need a "side BC," which is how this thread started.

Toby Bradshaw
baywingdb@comcast.net

 

[Boyd Allen]

'Don't know, don't have a frictionless surface. Just remember if the bullet has to roll, we are back to rotational inertia issues. The problem with the pool comparison is that to be like the wind, you would have to be re striking the ball an infinite number of times to represent a wind that is constant throughout a bullet's flight. Unfortunately, a fired bullet in the wind is not a dropped bullet, rocket, boat, or airplane, but if you must, think of a boat that is given a shove across a stream that is flowing, with no other propulsion or guidance.

 

[tobybradshaw]

So you are saying that Glen Newick and others are wrong, that a push is a push is a push no matter WHERE it occurs in the flight path

He is right about the effect but wrong about the reason. Note that he prefaces the passage by saying it is "simplified." So, either he understands the real reason that wind near the muzzle has a bigger effect (because bullet deceleration is most rapid there), or he really does think that the bullet's flight angle is permanently altered by a gust of wind near the muzzle (not correct).

After seeing how long these two wind drift threads have been, maybe he was smart to stick with the "simplified" version.

Newick also says that wind near the muzzle has a bigger effect because the bullet has not yet gotten its nose into the wind, and drag is even higher because of it. This is right -- there is a "sail area" for a very brief interval until the bullet gets pointed into the relative wind.

Whether he understands what is going on or not, the wind flags and sighter target are all you need -- not a degree in aeronautical engineering.

Going back to the hated boat/airplane analogy, imagine a 1000yd course with a crossflow only at 500-600yd. If the boat/plane speeds up (accelerates) between 200-300yd, then slows back down to the starting speed for the rest of the trip, the only difference in outcome is that the boat/plane reaches the "target" a little sooner. If, on the other hand, the boat/plane accelerates between 500-600yd and slows back down to the starting speed after 600yd, it will miss the target -- BY GOING UP-FLOW (deflection OPPOSITE the flow vector). As Greg Culpeper pointed out a long time ago on the other thread, a little rocket-bullet that accelerated constantly would deflect UPWIND of the aim point.

So, the "where the push happens" DOES matter, because the angle of the push (the angle of the long axis of the bullet relative to the ground) determines which direction drag force is pushing.

Wind deflection is all about acceleration magnitude and direction, and the nature of aerodynamic stability.

....... the displacement is NOT like balls on a pool table establishing new vectors......

If there were a lot of drag on the pool balls in a direction opposite to their velocity, and they were aerodynamically stabilized, sure. Otherwise, no. Make some spin-stabilized velcro billiard balls and try it.

Toby Bradshaw
baywingdb@comcast.net

 

[Gene Beggs]

Good mornin' Al

So you are saying that Glen Newick and others are wrong, that a push is a push is a push no matter WHERE it occurs in the flight path....... the displacement is NOT like balls on a pool table establishing new vectors......

(Glenn in his book "Ultimate in Rifle Accuracy" diagrams how giving a bullet a nudge near to the muzzle has a much larger effect than the same nudge near the target........ like a bowling ball which hooks early VS later down the lane.)


thanxall!!! this is fun....


al

Al, I haven't read Glenn Newick's book so I can't comment on anything said there but I'll try to break your question down into segments that I can address. You stated,

"So you are saying that a push is a push is a push no matter WHERE it occurs in the flight path....... the displacement is NOT like balls on a pool table establishing new vectors......"

(GB) That is correct, the airmass through which a bullet is flying may not be smooth and consistent in direction and/or velocity. We have all seen wind blowing in different directions and speeds from one end of the range to the other. No,, displacement is definitely not like "balls on a pool table', establishing new vectors.

To address the second part of your question,

"giving a bullet a nudge near the muzzle having a much larger effect than the same nudge near the target....."

(GB) No, this is not true! I heard this theory early on in my benchrest career and like so many others, I accepted it as truth but in recent years, I have come to realize it is simply not true.

A bullet, in flight does not behave like a bowling ball. If a crosswind in the first twenty yards drifts a bullet .050 and it then encounters zero wind in the next 80 yards to the target, displacement at the target is only .050. Once the bullet departs the airmass that was moving laterally and enters stationary air, drift stops; it does not continue to accumulate throughout the flight to the target.

Al, I hope this helps. My writing skills are not even close to those of Toby Bradshaw and Keith (MKS) Listen to them carefully; they know of which they speak and have a knack for explaining it in ways that even a redneck, eyeball engineer like me can understand.

Gene Beggs

 

[Boyd Allen]

What is the point in making comparisons between self propelled devices and bullets? Their differences would seem to be significant, and ignoring them for the convenience of making an argument would only seem to muddy the waters.

It would seem to me that the question is what the source of the energy that deflects a bullet from its initial flight path, and how is that energy coupled to the bullet? And the real problem, how to describe what is happening using words.

To those that imply, or state that the subject is too complicated to be adequately treated in a forum such as this, you may be right. To those who imply that others cannot understand their point because of a lack of background or ability, that would seem to be blaming the reader for obtuse writing. Also, if the application of mathematics and physics is a sure route to a correct conclusion, why do experts disagree? I think that mathematics is a tool, that is similar to a hammer in that nails can be bent, and thumbs struck. This is not to discount the importance of tools, but just to point out that they may be used with varying amounts of skill.

My purpose in this discussion has been to ask questions that seemed to arise from the various arguments and explanations that have been presented, so that what seemed too me to be logically faulty, or simply unproven statements might be clarified or discarded. It has been interesting, but I doubt that we are any closer too the production of a good explanation than when we started. What we have had, that no book or article allows is a chance to have a dialogue, that I hope has been enjoyable.

 

[Gene Beggs]

Toby, you're amazing!

He is right about the effect but wrong about the reason. Note that he prefaces the passage by saying it is "simplified." So, either he understands the real reason that wind near the muzzle has a bigger effect (because bullet deceleration is most rapid there), or he really does think that the bullet's flight angle is permanently altered by a gust of wind near the muzzle (not correct).

After seeing how long these two wind drift threads have been, maybe he was smart to stick with the "simplified" version.

Newick also says that wind near the muzzle has a bigger effect because the bullet has not yet gotten its nose into the wind, and drag is even higher because of it. This is right -- there is a "sail area" for a very brief interval until the bullet gets pointed into the relative wind.

Whether he understands what is going on or not, the wind flags and sighter target are all you need -- not a degree in aeronautical engineering.

Going back to the hated boat/airplane analogy, imagine a 1000yd course with a crossflow only at 500-600yd. If the boat/plane speeds up (accelerates) between 200-300yd, then slows back down to the starting speed for the rest of the trip, the only difference in outcome is that the boat/plane reaches the "target" a little sooner. If, on the other hand, the boat/plane accelerates between 500-600yd and slows back down to the starting speed after 600yd, it will miss the target -- BY GOING UP-FLOW (deflection OPPOSITE the flow vector). As Greg Culpeper pointed out a long time ago on the other thread, a little rocket-bullet that accelerated constantly would deflect UPWIND of the aim point.

So, the "where the push happens" DOES matter, because the angle of the push (the angle of the long axis of the bullet relative to the ground) determines which direction drag force is pushing.

Wind deflection is all about acceleration magnitude and direction, and the nature of aerodynamic stability.


....... the displacement is NOT like balls on a pool table establishing new vectors......


If there were a lot of drag on the pool balls in a direction opposite to their velocity, and they were aerodynamically stabilized, sure. Otherwise, no. Make some spin-stabilized velcro billiard balls and try it.

Toby Bradshaw
baywingdb@comcast.net

Toby, you continue to amaze me!

I especially appreciate your comment,

"Whether you understand what is going on or not, the wind flags and sighter target are all you need -- not a degree in aeronautical engineering."

I love it!

Later,

Gene Beggs

 

[tobybradshaw]

What is the point in making comparisons between self propelled devices and bullets?

Because they are subject to the same aerodynamic forces. One of the problems with bullets is that they are always slowing down, which makes it seem like there are multiple explanations (theories) that give the same qualitative outcome (bullet moves downwind by some amount).

A theory that can simultaneously explain the outcome of experiments performed on objects that are either:

1) constantly decelerating, like a bullet;
2) move at constant speed, like a boat or airplane; or,
3) constantly accelerating, like a rocket

is a more powerful ("better") theory. "Nose-into-the-wind" accurately predicts the outcome of wind deflection in all these cases, whereas "sail area" only makes the right prediction for case 1) above (and even then is wrong quantitatively).

Their differences would seem to be significant, and ignoring them for the convenience of making an argument would only seem to muddy the waters.

I know that the differences seem significant to you, like the differences between spin-stabilized and fin-stabilized projectiles seem significant to you. I guess we are at the point in the discussion when you are going to have to specify the differences you think are important for the physics of flight, so we can talk about those.

If I may be permitted a small digression to poke fun at physics and physicists. A group of horse race bettors asked a physicist to help predict the outcome of horse races. The physicist went away and performed countless hours of calculations, and returned with the answer. The bettors were poised with their notepads, pencils, and racing forms. The physicist began, "Assume a horse is a sphere of uniform density ..."

So, Boyd, you are right to question analogies, models, etc. But the questions can't just be framed as "these are different from those." We can all see that the details are different. What matters is, are similarities, or the differences, more relevant for making predictions?

It would seem to me that the question is what the source of the energy that deflects a bullet from its initial flight path, and how is that energy coupled to the bullet?

I don't want to seem like a prick (too late for that, eh?), but words like "energy" when "force" is what is being discussed are part of the problem. I teach science for a living and one of the biggest hurdles that students have is understanding the difference in meaning between the scientific use of words like "fact", "theory", "truth", "proof", etc. and the way those same words are used in everyday English.

Newton's Firsrt Law of Motion: an object in motion remains in motion until acted upon by an outside force

Newton's Second Law of Motion: F=ma

And the real problem, how to describe what is happening using words.

Guilty.

To those that imply, or state that the subject is too complicated to be adequately treated in a forum such as this, you may be right. To those who imply that others cannot understand their point because of a lack of background or ability, that would seem to be blaming the reader for obtuse writing.

If you think that I have shown any disrespect, I apologize and assure you (and everyone else) that it wasn't intentional.

I have taught thousands of students, though, and it is NOT the case that the instructor bears all the responsibility for learning. [You can lead a horse to water, etc.] The fact that a few people have stuck with this thread and wrestled with the complexities of bullet flight tells me that we have among us the three most valuable qualities a human can have: curiosity about the way the world works, an open mind, and the willingness to accept evidence that conflicts with belief.

Also, if the application of mathematics and physics is a sure route to a correct conclusion, why do experts disagree? I think that mathematics is a tool, that is similar to a hammer in that nails can be bent, and thumbs struck. This is not to discount the importance of tools, but just to point out that they may be used with varying amounts of skill.

I guess I don't see where experts are disagreeing on this one. All the ballistics programs are using the same algorithms derived from "nose-into-the-wind" physics, and giving outputs that generally get us on paper.

I still think Greg Culpeper's and Gene's posts in the previous thread, along with Bryan's "linearized" description of the physics (#249 in that thread) make the clearest case for "nose-into-the-wind."

Toby Bradshaw
baywingdb@comcast.net

 

[Tony Shankle]

Tony, I've never read Rinker, but I do agree with Gene.

Throw a Nerf football past a fan and see for yourself. Or get Gene to take you for a plane ride.

A spin-stabilized bullet (like an airplane) can't be drifting sideways in the air mass and still have its nose pointed straight ahead, because the nose MUST point into the relative wind (the vector sum of the downrange and crossrange velocities).

The lateral momentum of the bullet is negated (quickly) by collisions with air molecules on the side of the bullet when the direction of the relative wind changes.

Toby Bradshaw
baywingdb@comcast.net

Toby, let's play football. So you drive 50mph and I will stand on the flatbed behind a shield. You drive past a tunnel entrance that is 90 degrees to our path of travel. That tunnel is 10 yards from the truck. I will drill that bad boy into the tunnel (while simultanously throwing out my arm). So you think that football will not continue it lateral deflection once it goes into the tunnel?

By the way, Al is in the passenger seat eating chips and watching for the "law" in this scenario and Gene has to be in the back with me holding on to my belt!

Back to bullets. So at 601 yards you and Gene think that the air molecules, airmass, drag will act upon the opposite side of a laterally moving bullet to stop the momentum created by a 10 mph wind in one precession? If that force is there, and if it is that great then why didn't it cancel out that wind in the first place? So an object in motion stays in motion until acted upon by an opposite force so why didn't this "opposite force" not cancel out the wind force or even the drag force since it had to start at zero?

 

[tobybradshaw]

Toby, let's play football.

Oooh!

So you drive 50mph and I will stand on the flatbed behind a shield. You drive past a tunnel entrance that is 90 degrees to our path of travel. That tunnel is 10 yards from the truck. I will drill that bad boy into the tunnel (while simultanously throwing out my arm). So you think that football will not continue it lateral deflection once it goes into the tunnel?

As soon as the ball gets out from behind the shield it will turn to point into the relative wind. If the tunnel is off the left side (driver's side, in the U.S.) of the flatbed, and you throw the ball perpendicular to the direction of the flatbed's travel, the ball's nose will turn to the right (clockwise, as seen from above). WAY to the right unless you are Brett Favre.

When the ball enters the tunnel, the ball's nose will turn back to the left (counterclockwise) to point into the new relative wind in the tunnel. It will, of course, continue to drift in the direction of the flatbed's travel for a very short time until the nose gets pointed into the relative wind, but once the nose is pointed straight down the tunnel the ball can only go straight, because the only force (other than gravity) acting on the spinning ball is drag, and that drag vector is pointed straight down the long axis of the ball -- the only direction that drag can act (for long) on a stabilized projectile.

Back to bullets. So at 601 yards you and Gene think that the air molecules, airmass, drag will act upon the oppisite side of a laterally moving bullet to stop the momentum created by a 10 mph wind in one precession?

I don't know how long it takes, but the drag force on the newly-exposed side of the bullet at multiple Mach numbers would be astonishingly high, so it wouldn't take long.

If that force is there, and if it is that great then why didn't it cancel out that wind in the first place?

It did "cancel out that wind" by turning into the relative wind (vector sum of downrange and crosswind velocity). When the bullet turned into the relative wind, it aligned its drag vector at an angle to the line of departure from the bore. This angled force (from the shooter's perspective -- from the bullet's perspective the drag is always straight along the line between its center of pressure and center of mass) pushes backwards on the bullet, but now "backwards" isn't straight back to the line of the bore, it is angled to the left in a right-to-left crosswind.

Toby Bradshaw
baywingdb@comcast.net

 

[Boyd Allen]

We will forgive their leading off with a grievous error but this link should take you to a page that proves that at least one well known source of ballistic software believes that bullets turn with, not into the wind.http://www.exteriorballistics.com/ebexplained/5th/43.cfm

As to my choice of words energy vs. force, admittedly a force is applied, but the movement of the bullet by action of the wind is defined as work, and that as the transfer of energy resulting in motion of the object that it is transferred to. What this whole discussion seems to have been about is how the energy is transferred from the wind to the bullet, specifically, the mechanism by which the energy is transferred.

One more point about common usage of words...who would object to my choice of words if I said that the balloon was blown across the field, or that his drive was blown into the rough? It is in this same sense that bullets are blown by the wind.

 

[tobybradshaw]

One more point about common usage of words...who would object to my choice of words if I said that the balloon was blown across the field, or that his drive was blown into the rough? It is in this same sense that bullets are blown by the wind.

The balloon is blown across the field, but the golf ball isn't blown, it is deflected. The difference? The balloon is not stabilized, but the golf ball is (if it is spinning fast enough).

The force required to spin the ball reduces the force available to accelerate the golf ball downrange, yet golf club designers go to a lot of trouble to make the ball spin. Counterintuitively, a spinning ball with lower velocity leaving the club head flies farther than a "faster" golf ball that doesn't spin.

The physicist who discovered the electron, J.J. Thomson, had quite a bit to say about the physics of golf ball flight, including the effect of "cross-wind".

http://www.nature.com/physics/looking-back/tait/index.html

Such as:

"This problem is in any case a very interesting one; it would be even more interesting if we could accept the explanations of the behaviour of the ball given by many contributors to the very voluminous literature which has collected round the game; if these were correct, I should have to bring before you this evening a new dynamics, and announce that matter, when made up into golf balls, obeys laws of an entirely different character from those governing its action when in any other condition."

" ... a golf ball, which is, in reality, the most prosaic of things, knowing while in the air only one rule of conduct, which it obeys with unintelligent conscientiousness, that of always following its nose."

Toby Bradshaw
baywingdb@comcast.net

 

[tobybradshaw]

We will forgive their leading off with a grievous error but this link should take you to a page that proves that at least one well known source of ballistic software believes that bullets turn with, not into the wind.http://www.exteriorballistics.com/ebexplained/5th/43.cfm

Boyd, my reading of this is that the torque moment is rightward in a left-to-right crosswind. That means that the center of mass of the bullet moves to the right. But, in a spin-stabilized projectile, the center of mass is BEHIND the center of pressure, which means that while the center of mass is moving right, the nose of the bullet must be moving left (nose into the wind).

I'll tell you what -- email Sierra and ask them whether the bullet's nose points into the relative wind. Print their answer in this thread. If they say "no," I'll send you a box of John Parrish's 6mm BT bullets and take my licks in public like a man.

Toby Bradshaw
baywingdb@comcast.net

 

[Boyd Allen]

Done. Now, the rest of you that are following this thread, click on the link that I posted above, read the material, and tell us what you think that it says about where a bullet points as the result of a cross wind. Inquiring mind wants to know.

On another related matter

I just got out my old Second Edition Sierra reloading manual, and looked up the formula for computing wind drift, in inches, at any given range. Are you ready? It is the cross wind, in inches per second (1 mph=17.60 inches per second) times lag time. That is it. It actually looks a little more imposing in print since lag time is expressed as distance to time of flight minus distance to target (in feet) divided by muzzle velocity (in feet per second). Now I admit that measuring or calculating time of flight is required before we can do anything about drift, but still, you have to admit that it is a pretty simple relationship.

 

[tobybradshaw]

Done. Now, the rest of you that are following this thread, click on the link that I posted above, read the material, and tell us what you think that it says about where a bullet points as the result of a cross wind. Inquiring mind wants to know.

While you're at Sierra's site, you all might as well read this, too (especially the last paragraph):

http://www.exteriorballistics.com/ebexplained/5th/32.cfm

Toby Bradshaw
baywingdb@comcast.net

 

[tobybradshaw]

It is the cross wind, in inches per second (1 mph=17.60 inches per second) times lag time. That is it. It actually looks a little more imposing in print since lag time is expressed as distance to time of flight minus distance to target (in feet) divided by muzzle velocity (in feet per second). Now I admit that measuring or calculating time of flight is required before we can do anything about drift, but still, you have to admit that it is a pretty simple relationship.

It is the Didion approximation with units that don't require conversion. And it is pretty simple, just not intuitive (for most people).

As far as I know, all the ballistics programs calculate the time of flight from the underlying physical principles and chronograph data at two distances, rather than measuring time of flight directly.

Toby Bradshaw
baywingdb@comcast.net

 

[Boyd Allen]

Unfortunately, their (and apparently your) definition of "blown" is much narrower than that of the common usage.

When I say that a thing has been blown by the wind, I mean that it has been moved by action of the wind. I specify nothing about the mechanics of how this is accomplished, since it it highly likely that person to whom I would be speaking would know exactly what I meant, and would probably be disinterested in hearing my rendition of the exact mechanism. It would be like telling some how to build a watch, in response to "What time do you have?". I find it common that specialists develop their own vocabulary. Unfortunately, they also have a habit of correcting the rest of us when we use the same words in the way that was common before their specialty, or for that matter science was even thought of. I think that it makes them feel clever.


Getting back to why I pointed out the Sierra material, I believe that their published position as to which way a bullet turns in response to a cross wing is that the point of the bullet is moved in a down wind direction, to the right, in a left to right wind. I pointed this out to make the point that experts disagree on this point, and to infer that if one's whole explanation of the mechanism of wind drift hinges on this point, that there may be a problem with someone's theory. Furthermore, if ballistic programs written by those with oppositions on this point are equal in their usefulness in giving accurate predictions, it may be that what has been made much of here, may in fact be inconsequential in any practical sense. Wouldn't that be funny?

 

[tobybradshaw]

Unfortunately, their (and apparently your) definition of "blown" is much narrower than that of the common usage.

I wish you hadn't involved Monica Lewinsky in this thread. I have been trying to forget her.

I find it common that specialists develop their own vocabulary. Unfortunately, they also have a habit of correcting the rest of us when we use the same words in the way that was common before their specialty, or for that matter science was even thought of. I think that it makes them feel clever.

Not clever. Precise. This is one reason that math is better than English for communicating much of physics, but since most people cringe at the sight of an equation, we do the best we can to be clear using (mostly) words.

We can't use Humpty Dumpty's word definitions if we want to stay on the same page.

If you don't mind a page of math, Peake goes from first principles to the Didion approximation. The first equation (just below the definitions) shows that the bullet points into the wind, if you recall from plane geometry that the length of the hypoteneuse of a right triangle is the square root of the sum of the squares of the two sides. In this case the sides of the right triangle are the downrange and crossrange velocity vectors.

http://saxtech.eu/Ballistik/Didion/Didion.htm

Bryan manages to do essentially the same job without the derivatives and integrals in post #249 of the other wind deflection thread. ("Deflection," not "drift," because aerodynamically-stable objects can "deflect" upwind or downwind depending on their acceleration, but it's pretty hard to "drift" or be "blown" upwind.)

Toby Bradshaw
baywingdb@comcast.net

 

[tobybradshaw]

When I say that a thing has been blown by the wind, I mean that it has been moved by action of the wind. I specify nothing about the mechanics of how this is accomplished, since it it highly likely that person to whom I would be speaking would know exactly what I meant, and would probably be disinterested in hearing my rendition of the exact mechanism. It would be like telling some how to build a watch, in response to "What time do you have?".

I would wager that anyone reading this thread DOES care about mechanism. They're not asking for the time, they're wondering how a watch works.

Toby Bradshaw
baywingdb@comcast.net