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Rifles, Reloading, Optics, Equipment
Rifles, Bullets, Barrels & Ballistics
Canting - the right answer
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<blockquote data-quote="JBM" data-source="post: 109722" data-attributes="member: 1969"><p>I found why I was off when I tried to verify my results again this morning -- I had the wrong coordinate system checked. I think that is also why we are have some disagreement as to what the right answer is.</p><p></p><p>If you note in my first post, I said I checked the box "Drop and Windage Relative to Target" in my online calculation. This provides drop and windage values in a target reference frame (e.g. relative to the target). My formula calculates the angles in that reference frame so the results of the trajectory are in the same reference frame. If you uncheck this box, you get much larger windage values. I had to think about this for a while and drew a picture so that I could see it. (You can see the picture at <a href="http://www.eskimo.com/~jbm/temp/cant.pdf" target="_blank">cant.pdf</a>). Both are correct, but in different reference frames.</p><p></p><p>You can play with these online calculators at my site, <a href="http://www.eskimo.com/~jbm" target="_blank">JBM</a>. Just click on "Calculations" at the top and then Trajectories. You can calculate in either reference frame and see the differences in drop/windage due to different cant angles and zero ranges.</p><p></p><p>If you look at the picture, there are two sets of axes. One is rotated by 10 degrees, this is the LOS, or canted reference frame. The other is the target reference frame. Also labeled on the target is the impact point. Look at the difference in windage in the two reference frames and you'll see why we got different answers. Also as the drop increases, the difference is more.</p><p></p><p>I'm still not convinced that the simple sin/cos formulas are correct, but they are in a different coordinate system. I still think mine is correct for the uncanted coordinate system. It's just that it tells you where on the target that the bullet is going to hit. If you are intentionally canting the firearm, my formulas will tell you where it will hit RELATIVE TO THE TARGET. The other case is that if you want to correct for a cant -- In this case you can correct relative to the target or line of sight (LOS), but since you are looking through the scope/sights, the LOS coordinate system is probably easier to do the correction in. In which case, my formulas don't do a lot of good.</p><p></p><p>Keep in mind that when you zero at a far range you have a much bigger elevation angle. If you look at my formulas, you'll see end up with much larger elevation and azimuth angle changes. This leads me to believe that to minimize the effects of cant, you zero close to minimize the elevation angle (angle between the line of sight and the bore axis). Granted this isn't always convenient, but would certainly minimize the errors due to canting.</p><p></p><p>Let me think about them some more, I should be able to come up with formulas in both coordinate systems.</p><p></p><p>JBM</p></blockquote><p></p>
[QUOTE="JBM, post: 109722, member: 1969"] I found why I was off when I tried to verify my results again this morning -- I had the wrong coordinate system checked. I think that is also why we are have some disagreement as to what the right answer is. If you note in my first post, I said I checked the box "Drop and Windage Relative to Target" in my online calculation. This provides drop and windage values in a target reference frame (e.g. relative to the target). My formula calculates the angles in that reference frame so the results of the trajectory are in the same reference frame. If you uncheck this box, you get much larger windage values. I had to think about this for a while and drew a picture so that I could see it. (You can see the picture at [url="http://www.eskimo.com/~jbm/temp/cant.pdf"]cant.pdf[/url]). Both are correct, but in different reference frames. You can play with these online calculators at my site, [url="http://www.eskimo.com/~jbm"]JBM[/url]. Just click on "Calculations" at the top and then Trajectories. You can calculate in either reference frame and see the differences in drop/windage due to different cant angles and zero ranges. If you look at the picture, there are two sets of axes. One is rotated by 10 degrees, this is the LOS, or canted reference frame. The other is the target reference frame. Also labeled on the target is the impact point. Look at the difference in windage in the two reference frames and you'll see why we got different answers. Also as the drop increases, the difference is more. I'm still not convinced that the simple sin/cos formulas are correct, but they are in a different coordinate system. I still think mine is correct for the uncanted coordinate system. It's just that it tells you where on the target that the bullet is going to hit. If you are intentionally canting the firearm, my formulas will tell you where it will hit RELATIVE TO THE TARGET. The other case is that if you want to correct for a cant -- In this case you can correct relative to the target or line of sight (LOS), but since you are looking through the scope/sights, the LOS coordinate system is probably easier to do the correction in. In which case, my formulas don't do a lot of good. Keep in mind that when you zero at a far range you have a much bigger elevation angle. If you look at my formulas, you'll see end up with much larger elevation and azimuth angle changes. This leads me to believe that to minimize the effects of cant, you zero close to minimize the elevation angle (angle between the line of sight and the bore axis). Granted this isn't always convenient, but would certainly minimize the errors due to canting. Let me think about them some more, I should be able to come up with formulas in both coordinate systems. JBM [/QUOTE]
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Canting - the right answer
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