Shooting Uphill or Downhill

[rsterne]

I see many questions about this topic on various Forums, so I though I would approach it from a practical point of view.... When you sight your gun in over level ground, most of you understand that the trajectory follows an arc, usually passing through the line of sight twice, and being slightly higher in between.... This allows you to have what is called a "point blank range" where you can hold "dead on", without allowing for distance, and know you are going to be within a narrow vertical range of where you are aiming, called the "kill zone".... Programs like ChairGun allow you to put in your velocity, scope height, and Ballistics Coefficient, and the size of your required kill zone (I usually use 0.50", which means 1/4" above and below my point of aim), and it will give you the optimum sighting distance for your rifle.... Here is what Chairgun predicts for a generic Airgun, shooting a pellet with a BC of 0.030 at 900 fps with a MilDot scope 1.5" above the bore....



The optimum sighting in range is 35 yards, producing a point blank range of 12.7 to 39 yards for this combination, which is typical of many airguns.... You can also print out a chart over longer ranges, showing how much "holdover" you need, like this....



The numbers given by ChairGun on the right axis, adjacent to the MilDot lines, are the ranges where the pellet crosses them.... in this case 53, 66, 78, 89, and 99 yards for 1 to 5 MilDots down.... This allows you to use the MilDots as aiming points for those ranges, and also to estimate in between.... pretty handy setup....

You may have heard that when shooting uphill or downhill, you can use the HORIZONTAL distance to your target instead of the direct (eg. lasered) distance, and for angles up to about 30 degrees, this is pretty good advice.... The red lines on the above graph are the horizontal distance to your target if it is a lasered 100 yards away at 20, 30, and 40* angles.... They work out to about 94, 87, and 77 yards.... Let's see how that compares to what ChairGun predicts for our airgun, at various angles....



The chart above is for 20 degrees.... At 100 yards, you should hold 4.7 MilDots high.... Using the horizontal distance rule gives 4.5 MilDots....



The chart above is for 30 degrees.... At 100 yards, you should hold 4.0 MilDots high.... Using the horizontal distance rule gives 3.8 MilDots....



The chart above is for 40 degrees.... At 100 yards, you should hold 3.2 MilDots high.... Using the horizontal distance rule gives 2.9 MilDots.... 

Now a MilDot at 100 yards is 3.6", so an error of 0.2 MilDots is less than 3/4", which is probably better than you can shoot at 100 yards, if you shoot like me.... That means that using the horizontal distance for angles less than 30* uphill or downhill is probably good enough.... Note it doesn't make any significant difference if you are shooting uphill or downhill, in both cases you have to hold as if the range was the HORIZONTAL distance to the target.... Incidently, many laser rangefinders, particularly those for archery, give the horizontal distance in addition to the actual distance, so you can just use that to determine your range for holdover.... In the next post I will work on steeper angles....

Bob

[rsterne]

OK, so what about steeper angles.... Well, then the horizontal distance rule breaks down, because the time of flight, and hence how much the pellet drops because of the longer path it takes, relative to the horizontal distance it travels, increases.... Before I get into that, however let's look at a chart I drew showing what various angles look like at different ranges, and the likelihood of you needing to compensate for them.... Horizontal Distance is from left to right, and Vertical Height is from bottom to top.... For 20 and 30 degrees, the lines are 100 yards long.... For steeper angles they are only 50 yards long....



There are three horizontal coloured lines on the chart.... The red line is at 30 feet up, and represents the height of a 3-story building, or perhaps a barn.... The green line is 60 ft. up, which is a pretty tall tree.... The blue line is 90 feet up, taller than most trees.... Note that at 40 degrees and steeper, we are very unlikely to be shooting further out than 50 yards, and in many cases 25 yards or less on really steep shots.... Based on that, I have produced more ChairGun charts, for the same gun as above, but only out to 50 yards.... The thick green vertical line represents the distance to the top of a 60 foot high tree.... On some charts I added a red line for 1/2 MilDot above the crosshairs as a handy reference point....



The chart above is for 20 degrees elevation.... Note that there is a small range from 22-33 yards where the pellet is slightly above the normal kill zone, but only by a whisker (less than 1/16").... so you can basically still hold dead on out to over 40 yards....



The chart above is for 30 degrees elevation.... Note that the top of a 60 foot high tree is now within your point blank range, so you never need to worry about holdover.... However, from 20 to 39 yards, the pellet is hitting above your kill zone if you don't allow for the angle.... At 27 yards out, it just reaches the 1/2 MilDot height, so you should use an aiming point just above the crosshairs (ie you are aiming low).... Using 1/4 MilDot should put you on target at anything in the tree, unless it's really close (less than your normal point blank range)....



The chart above is at 40 degrees elevation.... Now it starts to get significant.... but note that the top of that 60 foot tree is now only 31 yards away.... If you use an aim point 1/2 MilDot up (the crosshairs are 1/2 MilDot below where you want to hit), you should hit within your kill zone from 15 yards out....



The above chart is at 50 degrees elevation.... I would suggest that 1/2 MilDot is still what to use, unless the tree is very tall.... Note that the pellet never reaches the 1 MilDot line regardless of distance.... So for anything around 45 degrees, 1/2 MilDot above the crosshairs is the POA to use (aim 1/2 MilDot low)....



The above chart is at 60 degrees elevation.... The pellet now reaches the 1 MilDot line at the top of a 60 foot tall tree, which is now only 23 yards away.... Here is where it starts to get tricky.... If the target is halfway up that 60 ft. tree, it is only 11 yards from you, and a dead on hold will produce a hit at the bottom of your kill zone.... When the target is just 5 yards higher, the pellet would hit at the top of your kill zone if you don't hold low, about 1/2 MilDot would be perfect.... It is becoming critical that you judge accurately how high in the tree your target is.... You may have to use anything from dead on to 1 MilDot above the crosshairs for your aim point (aim up to 1 MilDot low)....



The above chart is at 70 degrees elevation.... Estimating how high in the tree your target is becomes increasingly important.... You may have to use anything from a dead hold to the first MilDot above the crosshairs as your POA (ie aim zero to 1 MilDot low)....



The above chart is at 75 degrees elevation.... I would have done 80 degrees, but ChairGun stops at 75.... The top of a 60 foot high tree is now only 21 yards away, and you will feel like you are shooting straight up.... Half way up the tree, your pellet will hit at the bottom of your kill zone with a dead on hold, but at the top of the tree, it will be hitting more than 1 MilDot high.... About 3/4 of the way up the tree, using 1/2 MilDot above the crosshairs for your POA would be perfect.... At these steep angles, estimating how far up in the tree your target is, is the most important thing.... By the time you are shooting straight up into the top of a 60 foot tall tree, your pellet will hit about 1.5 MilDots high.... Note where the boreline crosses the 20 yards range to see that (the pellet follows the boreline when fired straight up, with no drop)....

One other thing I should mention.... The references above to MilDots are to actual, correct MilDots, which are 3.6" at 100 yards.... For most scopes that will be at 10X, but your scope may be different.... If you have a variable scope, when you change the magnification, the MilDots will no longer be 3.6" at 100 yards (unless you have an FFP scope).... Often when shooting at close range, you may choose a lower power on your scope, so you would have to allow for the apparent change in MilDot separation if you do that.... I hope that the above will help you understand what happens when shooting uphill or downhill....

Bob


PS, I will unlock this topic so that you can ask questions and I will try and answer them to the best of my ability.... PLEASE STAY ON TOPIC or I will lock it to prevent clutter....