Question on Applied Ballistics App and Coriolis

[Pdvdh]

Also, I should probably spring for a better solver. I think the phone type, point solver apps that I use have their limitations. In my opinion they seem to over correct but again, maybe I have an inherent shooting technique that "corrects" for right drift by inducing a left error and I don't even know it.

This statement brings back the recollection of one member of this forum that used to post 1000yd targets time and again, showing bullet impacts directly on a vertical line drawn thru the bullseye. I swear he posted 15-20 different targets all showing consistently similar bullet strikes at 1000-1200yds. All in the effort to support his contention that spin drift and coriolis were a figment of the imagination. He was an older fella, dead set in his ways. So closed-minded I never even considered any serious effort to explain the science behind coriolis, or the empirical evidence/proof of spin drift. Still makes me smile. Now I'm sure I posted in some of those threads that the US military respects, and corrects for, coriolis, thinking that might persuade him. Nope. Not to be dissuaded. Just more photos of bullet impacts at 100yds, and then photos of bullet impacts at 1000+ yards.

If the photos were for real, then I'll give him this much credit - he consistently set up his rifle/scope, and/or positioned it at the time the trigger broke, such that he continually counteracted the combined effects of spin drift + coriolis. He wasn't shooting left twist barrels, and he was shooting in the northern hemisphere. He, with his equipment, consistently eliminated the need to dope for spin drift and coriolis. He hasn't been active on the forum for many years now. Dunno if he ever converted, or not. He was a fully committed, non-believer.

 

[Pdvdh]

Timber338,
I hear you. In fact I previously shared this same interest in understanding coriolis, to the extent I researched quite extensively. The coincidental consequence was I reached the conclusion that the coriolis algorithms in my ballistic software were flawed.

I forwarded the reference articles I'd read to the owner/programmer of my ballistics software. After we exchange several e-mails, he concurred with my perspective and corrected the coriolis function in the software. But this is the point I wanted to communicate. The owner/programmer told me the article I'd forwarded was the best reference article he'd ever read on the subject. Based on my research experience, and further based on that comment from the owner of Patagonia Ballistics, I think it's unlikely you'll find any articles on the worldwide web that completely satisfy your curiosity and/or satisfactorily complete your understanding.

Based on my research, I believe the primary (if not sole) affect that angle fire has on the magnitude of coriolis drift is due to the changed time of bullet flight. Time of bullet flight is a function of angle of fire. The earth rotates while the bullet is in flight. The longer the bullet is in flight over the surface of the earth, the greater the magnitude of the vertical and horizontal components of coriolis. Based on this belief, I tentatively conclude that angle of fire is pertinent only to the extent that it affects/changes the time of bullet flight. Your ballistic software most likely calculates time of flight as affected by angle of fire. If the coriolis calculation includes that corrected time of flight (corrected for angle of fire), then the software IS correcting coriolis based on differing angles of fire.

That's my story, and I'm sticking to it,... until Bryan Litz puts me to shame with a more authoritative explanation.

Mr. Litz, where art thou?

 

[Timber338]

Based on my research, I believe the primary (if not sole) affect that angle fire has on the magnitude of coriolis drift is due to the changed time of bullet flight. Time of bullet flight is a function of angle of fire. The earth rotates while the bullet is in flight. The longer the bullet is in flight over the surface of the earth, the greater the magnitude of the vertical and horizontal components of coriolis. Based on this belief, I tentatively conclude that angle of fire is pertinent only to the extent that it affects/changes the time of bullet flight. Your ballistic software most likely calculates time of flight as affected by angle of fire. If the coriolis calculation includes that corrected time of flight (corrected for angle of fire), then the software IS correcting coriolis based on differing angles of fire.

That's my story, and I'm sticking to it,... until Bryan Litz puts me to shame with a more authoritative explanation.

Mr. Litz, where art thou?

Ok, good stuff. Details on the physics. I could not agree with you more that the time of flight is ONE of TWO important parts of the equation. You need not only time of flight but the difference in speed of the shooter/bullet and the target. You must combine those two elements correctly to calculate coriolis. Let me try and explain.

The fundamental concept of horizontal coriolis, as it applies to shooting a bullet, is that the target you are shooting at is moving eastward at a different velocity than from where it was fired. that's it. it's that simple. when you shoot north at a target in the northern hemisphere, that target is moving slower, so your bullet impacts right. The bullet is not traveling on a curve, it is traveling straight (negating all other things like spin drift). It is the target that is traveling slower than the bullet.

Do we agree on that? If so, that in itself is the OTHER part of what makes horizontal coriolis. It is the speed difference between the shooter/bullet and the target AND the time it takes for the bullet to reach the target. Both must be accurate.

Ok, so what happens if you are shooting at a target that is moving at the same speed as the shooter/bullet? what happens then? based on physics, the target is going to perfectly keep up with the bullet, and the bullet will see no change in point of impact left/right.

So now we look at what creates the velocity of the target and shooter/bullet. That is also very simple. It is nothing more than the distance of the target and shooter/bullet from the spin axis of the earth.

That is the heart of the coriolis effect. the shooter/bullet and the target are at different distances from the spin axis of the earth. combine that with the time of flight of the bullet and that's all there is to it.

well, what if the shooter/bullet and the target are at the same distance away from the spin axis of the earth? well, that's also easy. that means they are traveling at the same speed.

How in the real world do we ever have the shooter/bullet and the target moving at the same speed? well, we are either shooting due east/west where two points separate from each other are the same distance from the spin axis of the earth and therefore, have the same velocity ...

OR ...

we are shooting north where our inclination of fire matches our latitude, where the shooter/bullet and the target are both the same distance away from the spin axis of the earth and therefore, have the same velocity....

I think that's the best I can explain it.... but toss that around in your head a bit.

And as you said, "Mr. Litz, where art though" ??

 

[KYpatriot]

Phorwath I think you're dead on about the angle of fire influence on the Coriolis correction being a result of time of flight. I was an aero engineering major but to be honest my recollection of the physics on this subject arent sharp enough to be of much help. Without question of course the main factor in coriolis is time of flight, and angle of fire does affect that.

I still think, based on my own experience, that the solvers over correct for it. But I havent used the "better" solvers out there only the apps. The apps so far have been sufficient for me to get actual dope for my rifles. Again, it could also be that something in my technique offsets those inputs. I think that is part of the problem. Anytime you try to get data in a low "signal to noise" environment it is difficult to do if you can't control all the variables with absolute precision. Errors stack, or cancel, and the whole thing is never exactly repeatable because each day is different, each shot is different, and can lead to faulty conclusions about what was primary when we miss. I can zero my rifle, hand it to you, and for you it probably wont be zeroed. That alone ought to tell us something right there.

It would be interesting to find a mine somewhere with a thousand yard shaft, turn off the ventilation for a few minutes and shoot a thousand yard group underground with zero wind from a machine rest and see if our solvers match real world, clean data on coriolis and spin drift.

In the end, hits on target are what matter. Solvers give us a solution to get us close, but real world data from a logbook compiled over time are the real answer to first and second round hits, because everything from zero error, scope click tolerance, shooter technique, and all the internal and external ballistic inputs are all rolled in because they are actual recorded shots. For whatever reason, that data tells me that I can and should ignore coriolis because my app calls too much correction...for my setup that is. For many reasons that can and probably will be different for everyone, and even for me if I do turn it on, I probably wouldnt notice except in the absolute best conditions.

I know one thing, if I could change anything about my shooting it would be better wind calls. The man who invents a device that Measures an averaged wind vector along a particular line of sight will have advanced the science of long range shooting as much as the first rifled barrel!

Are boundary layer effects accounted for when calculating coriolis? In other words is the solver taking into account that the bullet in flight is not flying through a vacuum completely free of earths influence as it rotates, but is in fact flying through an air mass getting drug around with the rotation, at least at the altitudes bullets are flying at...

 

[Timber338]

In the most simple form, the equation is simply D=RT, or, Distance = Rate * Time.

Distance being the Horizontal drift in inches.

Time being time of flight of the bullet. getting the tof is complicated ballistics that Bryan Litz is great at.

Rate is the difference in velocity that the target is traveling with respect to the shooter/bullet. That is calculated by knowing the velocity of the earth at the equator and then adjusting based on latitude.

When the velocity of the target and the bullet/shooter is the same the R value drops to zero and there is no D (distance), or drift.

 

[Timber338]

I should have done this from the beginning. I'll post up some equations that prove my point. Giving my kids a bath now. Will post up some equations later.

 

[Pdvdh]

How in the real world do we ever have the shooter/bullet and the target moving at the same speed? Well, we are either shooting due east/west where two points separate from each other are the same distance from the spin axis of the earth and therefore, have the same velocity ...

Your statement (above) leads me to conclude you believe that shooting due east or due west, across level ground, eliminates the horizontal component of coriolis.

If that's your current understanding, I contend that's incorrect. If your understanding is incorrect, it's unlikely your mathematical expression for horizontal coriolis could be correct. Don't take this wrong. Not trying to get you worked up into a dither.

My sermon from the pulpit: The magnitude of horizontal coriolis is constant over equal distances of fire, in every direction of fire. Fire your bullet one mile due north, due east, due south, or due west, and the magnitude of the horizontal component of coriolis is identical. Yes, it is a brain teaser. The magnitude of the horizontal component is only zero at the equator, and it's zero in every direction of fire at the equator. At all other latitudes, horizontal coriolis is present, and equal in magnitude, in every direction of fire. Where I live at 61* north latitude, horizontal coriolis is greater than in the 48 states. The horizontal component is the largest at 90* latitude, at both poles of planet earth.

I conceptually understand vertical coriolis for all directions of fire. I have a conceptual understanding of the horizontal component of coriolis for north / south directions of fire. Conceptualizing the horizontal component of coriolis in the east / west directions of fire is a brain drain. Mentally fatiguing. You'll find videos on the web that attempt to visually display horizontal coriolis. STILL a brain drain.

Bryan Litz may explain it clear as day in one of his books. I don't own them. He's sounded in on coriolis on this forum in the past, but I never saw him try to explain horizontal coriolis. And I don't think he will, because when all's said and done, most still wouldn't understand it. Certainly not well enough to explain it to anyone else.

 

[Timber338]

Your statement (above) leads me to conclude you believe that shooting due east or due west, across level ground, eliminates the horizontal component of coriolis.

If that's your current understanding, I contend that's incorrect. If your understanding is incorrect, it's unlikely your mathematical expression for horizontal coriolis could be correct. Don't take this wrong. Not trying to get you worked up into a dither.

Good lord, I believe you're right! I oversimplified the whole thing because North/South shooting is so simple to visualize. I'm not wrong for the very simple version of two targets that I had laid out in my simple head, but I think I am definitely wrong for how horizontal Coriolis really works. Well I'll be damned. It was too late to do any thinking after the kids got to bed, and its far to late to do any real thinking now. But I still want to figure this out, whether it's a brain drain or not. At the end of the day it's just physics, and the principals just take some research.

Thanks for sticking with me through this, and finally shedding some light into my brain. Just plugging numbers into an app don't cut it for me. I like to discuss them.

Well, the good news, is that 1500 yard shot at an elk where I hunt, at a steep 45 degrees, that I never would have attempted in the first place, would have been right on with my Shooter app.

 

[KYpatriot]

The horizontal component of coriolis in an east west line of sight happens in exactly the same way as it does north/south and is not any harder to explain...it is still due to rotation, and in my opinion even easier to visualize. I caught the snarky shooter reference, but the jokes on you because I understand exactly how coriolis behaves, though not how the various ballistic tools choose to address it. I think I can help though, as usual it is a matter of perspective...

I think it may seem harder to visualize because you are trying to imagine it from the same vantage point as the north south example which you understand. Start there: When you imagine a north/south shot, you probably assume the vantage point of looking at the globe from the "side", level with the equator with the north pole on top and south pole on bottom. It is very easy to see how a shot straight south from some northern latitude towards the equator would appear to bend right as the target rotates away from it. If you shoot north, it takes only a little more imagination to see that the bullet starts with more tangential velocity than more northern target, and again drifts right relative to the slower rotating target.

The problem with east/west shots is that you are likely trying to imagine the shot from the same vantage point you used for the north/south visualization. What you need to do is look at the east west example from the vantage point of hovering above the poles. For some reason people never seem to imagine that viewpoint, perhaps because we learn geography from two dimensional maps...people forget that it is shorter to go to russia over the pole...anyway I digress. Think of yourself looking down at the globe from over the north pole. Looking at the earth from over the north pole, the earth looks like a circle, the equator is the outer edge. From the north pole, the earth rotates counter clockwise. With the pole as the center of the circle, any point the same distance from the pole is on the same latitude. Illustrate it yourself, its easy. Draw a circle on a piece of paper, and pick two points the same distance from the center (the pole), make two dots the same distance out, one is the shooter position the other the target. If they are the same distance from the pole, they are the same latitude, and therefore directly east and west of each other. Lay your pencil across the two points, as if it were the path of the bullet, and Hold it still while you rotate the circle counterclockwise around the pole. Watch how the target rotates out from under the pencil to the left, which has the effect of causing the shot to miss right. Imagine the shot going the other direction...same thing, the target rotates left. For the southern hemisphere youd need to rotate the circle clockwise, which causes the target to rotate out to the right, making the shot appear to drift left.

Another way to visualize it is the east west shot is exactly like tossing a ball to someone on a merry go round who is the same distance from the center that you are. The north south shot is like throwing a ball from the edge to the center, or from the center to the edge.

I still dont think the discussion has much to do with hitting real world targets with small arms but it is fun to consider, and if I had confidence the solvers were giving me the correct magnitude and the interface was easy it might as well be done.

What if I told you that your bullet was not taking the shortest path to the target except on pure north/south shots....would that blow your mind???? On earth, the shortest distance between two points that are east/west of each other is NOT a straight line, but that is another discussion I suppose...

 

[Timber338]

The problem with east/west shots is that you are likely trying to imagine the shot from the same vantage point you used for the north/south visualization. What you need to do is look at the east west example from the vantage point of hovering above the poles. For some reason people never seem to imagine that viewpoint, perhaps because we learn geography from two dimensional maps...people forget that it is shorter to go to russia over the pole...anyway I digress. Think of yourself looking down at the globe from over the north pole. Looking at the earth from over the north pole, the earth looks like a circle, the equator is the outer edge. From the north pole, the earth rotates counter clockwise. With the pole as the center of the circle, any point the same distance from the pole is on the same latitude. Illustrate it yourself, its easy. Draw a circle on a piece of paper, and pick two points the same distance from the center (the pole), make two dots the same distance out, one is the shooter position the other the target. If they are the same distance from the pole, they are the same latitude, and therefore directly east and west of each other. Lay your pencil across the two points, as if it were the path of the bullet, and Hold it still while you rotate the circle counterclockwise around the pole. Watch how the target rotates out from under the pencil to the left, which has the effect of causing the shot to miss right. Imagine the shot going the other direction...same thing, the target rotates left. For the southern hemisphere youd need to rotate the circle clockwise, which causes the target to rotate out to the right, making the shot appear to drift left.

Another way to visualize it is the east west shot is exactly like tossing a ball to someone on a merry go round who is the same distance from the center that you are. The north south shot is like throwing a ball from the edge to the center, or from the center to the edge.

I still dont think the discussion has much to do with hitting real world targets with small arms but it is fun to consider, and if I had confidence the solvers were giving me the correct magnitude and the interface was easy it might as well be done.

KYPatriot - I appreciate the explanation, I think you and Phorwath were really able to explain why my logic was flawed. I was oversimplifying in my head by only visualizing a single/simple scenario. I was only thinking in 2 dimensions and that made the east/west shot appear to be flat. you've gotta think about it from the correct perspective as you point out, and your visualization from the north pole looking "down" really does an excellent job of showing the problem in 3 dimensions.

DocUSMC, I now disagree with you that I was overthinking... Of course I am making fun of myself right now, but I can see that was your way of being nice. I was very much underthinking. A common problem of mine.

I also agree that wind and spin drift dominate the real world application of this. Like you point out, artillery it does start to matter, but small arms are dominated by other external forces like spin drift but mostly wind. You discussed this earlier and I was more focused on the physics of it all, but you certainly have valid points. I personally think that even if the math is slightly wrong in the coriolis solvers, they get your solution more close to perfect by including them than by not including them. Phorwath's post about the guy who posted all the pictured of targets was pretty funny, and shows that all of this is mathematical at best for small arms. He didn't disprove coriolis, he just proved that it sure is hard to see when a guy is shooting a rifle.

But, let's jump back to the physics... I'll be honest, my simple brain did not put this all together this morning until I really visualized in 3 dimensions. And I hope you guys all get a kick out of this... I got my boys bouncy ball and started drawing on it. looking "down from the north" based on KYpatriots explanation. drawing two points and rotating the bouncy ball. It all clicked and showed that east/west shot has the target moving in both up/down and east/west. And then it gets funny. My 2 year old started throwing his diaper around the house. The dog started chasing it, and of course I had to do something. My 4 year old got ahold of the ball and followed my example of drawing on it.

I believe he did the best job of illustrating coriolis. DOC and Bryan Litz, I believe my 4 year old is on to something... and he just might have broke the space-time continuum... I think we've got a genius on our hands.

 

[Pdvdh]

The problem with east/west shots is that you are likely trying to imagine the shot from the same vantage point you used for the north/south visualization. What you need to do is look at the east west example from the vantage point of hovering above the poles. For some reason people never seem to imagine that viewpoint, perhaps because we learn geography from two dimensional maps...people forget that it is shorter to go to russia over the pole...anyway I digress. Think of yourself looking down at the globe from over the north pole. Looking at the earth from over the north pole, the earth looks like a circle, the equator is the outer edge. From the north pole, the earth rotates counter clockwise. With the pole as the center of the circle, any point the same distance from the pole is on the same latitude. Illustrate it yourself, its easy. Draw a circle on a piece of paper, and pick two points the same distance from the center (the pole), make two dots the same distance out, one is the shooter position the other the target. If they are the same distance from the pole, they are the same latitude, and therefore directly east and west of each other. Lay your pencil across the two points, as if it were the path of the bullet, and Hold it still while you rotate the circle counterclockwise around the pole. Watch how the target rotates out from under the pencil to the left, which has the effect of causing the shot to miss right. Imagine the shot going the other direction...same thing, the target rotates left. For the southern hemisphere you'd need to rotate the circle clockwise, which causes the target to rotate out to the right, making the shot appear to drift left.

Another way to visualize it is the east west shot is exactly like tossing a ball to someone on a merry go round who is the same distance from the center that you are. The north south shot is like throwing a ball from the edge to the center, or from the center to the edge.

Nice. Thanks for tagging/hanging in and providing this description/visualization. Where's a Globe when I need one? There used to be one in every classroom. Instead there's a computer (or multiple PCs) in every classroom. I haven't seen a Globe for a long time. And I'm too old, kids out on their own, to have any basketballs in the garage. Guess I can buy some balloons and blow them up.

I have a mental handicap visualizing the east / west concept of horizontal coriolis. I'm going to get my hands on a Globe and follow your instruction/prescription. Hopefully, the visualization will then set up like concrete and be permanently etched in my memory bank. The last time I worked at this was 7-8 years ago. It's starting to come back, just looking at Timber's photo above. I can begin to see how the target would move in a leftward arc, when looking down on the 3D image.

The visualizations I found on the internet weren't as good as your text description.

 

[Timber338]

Nice. Thanks for tagging/hanging in and providing this description/visualization. Where's a Globe when I need one?

Agree, thanks to both of you for hanging in there. The globe (bouncy ball) was the final key.

On a side note, I've got the first half of the equations worked out, and now need the time to include inclination. I think it will drop out once I get it all written out. But not really that important since I think I fundamentally can visualize all of this now. That was my goal from the beginning and happy enough with that. I want to get out and shoot more.

 

[Jordan Smith]

The horizontal component of coriolis in an east west line of sight happens in exactly the same way as it does north/south and is not any harder to explain...it is still due to rotation, and in my opinion even easier to visualize. I caught the snarky shooter reference, but the jokes on you because I understand exactly how coriolis behaves, though not how the various ballistic tools choose to address it. I think I can help though, as usual it is a matter of perspective...

I think it may seem harder to visualize because you are trying to imagine it from the same vantage point as the north south example which you understand. Start there: When you imagine a north/south shot, you probably assume the vantage point of looking at the globe from the "side", level with the equator with the north pole on top and south pole on bottom. It is very easy to see how a shot straight south from some northern latitude towards the equator would appear to bend right as the target rotates away from it. If you shoot north, it takes only a little more imagination to see that the bullet starts with more tangential velocity than more northern target, and again drifts right relative to the slower rotating target.

The problem with east/west shots is that you are likely trying to imagine the shot from the same vantage point you used for the north/south visualization. What you need to do is look at the east west example from the vantage point of hovering above the poles. For some reason people never seem to imagine that viewpoint, perhaps because we learn geography from two dimensional maps...people forget that it is shorter to go to russia over the pole...anyway I digress. Think of yourself looking down at the globe from over the north pole. Looking at the earth from over the north pole, the earth looks like a circle, the equator is the outer edge. From the north pole, the earth rotates counter clockwise. With the pole as the center of the circle, any point the same distance from the pole is on the same latitude. Illustrate it yourself, its easy. Draw a circle on a piece of paper, and pick two points the same distance from the center (the pole), make two dots the same distance out, one is the shooter position the other the target. If they are the same distance from the pole, they are the same latitude, and therefore directly east and west of each other. Lay your pencil across the two points, as if it were the path of the bullet, and Hold it still while you rotate the circle counterclockwise around the pole. Watch how the target rotates out from under the pencil to the left, which has the effect of causing the shot to miss right. Imagine the shot going the other direction...same thing, the target rotates left. For the southern hemisphere youd need to rotate the circle clockwise, which causes the target to rotate out to the right, making the shot appear to drift left.

Another way to visualize it is the east west shot is exactly like tossing a ball to someone on a merry go round who is the same distance from the center that you are. The north south shot is like throwing a ball from the edge to the center, or from the center to the edge.

I still dont think the discussion has much to do with hitting real world targets with small arms but it is fun to consider, and if I had confidence the solvers were giving me the correct magnitude and the interface was easy it might as well be done.

What if I told you that your bullet was not taking the shortest path to the target except on pure north/south shots....would that blow your mind???? On earth, the shortest distance between two points that are east/west of each other is NOT a straight line, but that is another discussion I suppose...

I was just about to weigh in with this exact "north pole" explanation, but I saw that you had already done so. Great post.

To add to this description just a little bit- I believe one reason for this effect, is that the shooter/bullet trajectory is perpendicular to the surface of the earth (parallel to the axis of gravity), regardless of geographical location, and the only place on earth that this perpendicular axis is completely parallel to the rotation axis of the earth, is shooting in an east/west direction, right at the equator. Here's a quick sketch that was drawn by my kid in grade 1 (cough), illustrating this point. At the equator when shooting E-W, there is no horizontal component of the earth's motion, relative to the trajectory of the bullet. When shooting the same direction further north, the axis' are no longer completely parallel, introducing a horizontal component to the earth's rotational motion, relative to the axis of the bullet trajectory (parallel to gravity's axis).

The circle is the earth, the black lines intersecting the earth's axis' represent the axis of the poles, and the equator. The red triangle and circle are the shooter's position, and the red arcs are the bullet's trajectory at two different geographical locations. I made the northern trajectory's E-W shooting direction exaggerated to more easily illustrate the point. The black line intersecting the northern shooter and the center of the earth is the axis of gravity.

 

[KYpatriot]

Your welcome. Unfortunately for me Im better at physics than shooting.

Ill try to upload some pics of what Im saying...Here is a snapshot from a North pole view, two points are drawn equidistant from the pole, therefore directly east /west of each other. Notice the card edge is parallel to the table edge.

[/URL][/IMG]

Ok next I have laid a straightedge along the two points, representing the path of a bullet. Notice that by chance it is at a slight angle to the table edge:

[/URL][/IMG]

Now, I will rotate the earth, counterclockwise for the Northern hemisphere, while holding the straight edge still. Notice the angle of the earth has changed, the earth rotated. The left dot has rotated away from the straightedge (bullet path), the right dot has as well and is now under the straightedge. The angle of the straightedge is unchanged.

[/URL][/IMG]

In a final snapshot, now the earth has rotated enough that even the shooter position is left of the line of sight of the shot.

[/URL][/IMG]