By Brian Samson
Angled shots (both up and down) have always been a popular tool in an HFT course setters arsenal, but the practice is becoming ever more popular in Field Target too, especially in mainland Europe. Fully adjustable hamsters are becoming a standard stock addition for international FT shooters and now that the practice of setting ‘anti-aircraft’ targets is seeping into UK competitions too, more and more UK competition shooters are interested in how the trajectory of a pellet changes when aiming either up or down at a steep angle.
Possibly one of the most misunderstood aspects of the change in trajectory for steep shots is that the effect is the same regardless of whether it’s a steep upward or downward angle.
Why is it the same for up and down angled shots?
If we consider the trajectory of a pellet when the target is at the same level as the firing position, the pellet leaves the barrel and gravity is acting on the trajectory of the pellet pulling it down toward the ground in a parabolic arc. To help understand the effects of angled shots, consider the two most extreme cases – shooting directly up or directly down at 90 degrees. In those cases, when the pellet leaves the barrel gravity is still pulling the pellet back towards earth, but the path of the pellet and the path of gravity are now coincident rather than at 90 degrees to each other. If we were to plot the path of a pellet fired directly up or down the trajectory would be a straight line up or down. So in those most extreme cases (up at 90 degrees or down at 90 degrees) the change in trajectory is the same – they both flatten from an arc for a level shot to a straight line for a totally vertical shot.
The plotted parabolic arc or trajectory we are all used to seeing in ballistics applications is usually displayed with the assumption that when the pellet leaves the barrel, gravity is acting at 90 degrees to the initial path of the pellet. When the rifle is pointed straight up or straight down, that angle changes from 90 degrees to 0 degrees (or 180 degrees, however you want to look at it). So we can say that at 90 degrees to the path, the effect of gravity causes the most pronounced curve and at 0 degrees there is no curve at all, it’s a straight line.
So what happens at 45 degrees?
If we accept that gravity has the most pronounced effect on the trajectory at 90 degrees to the pellet path and the least pronounced effect on the path at 0 degrees (up or down), it’s easier to appreciate that at 45 degrees (either up or down) the effect on the trajectory is half way in-between the two extremes.
The trajectory isn’t a straight line like it would be directly up or down, but it’s a flatter trajectory than it would be if the shot was taken on the level. Gravity has half the effect on the trajectory, as it would have done if the shot were taken on the level. The steeper the angle the flatter the trajectory – and it’s the same if shooting up or shooting down, the important factor is the angle.
So what does that mean in practical terms? Where should I aim?
Since shooting at any angle either up or down is going to have the effect of flattening the trajectory, angled shots will always result in the pellet hitting higher than it would have done if the shot was taken at the same distance on the level. A flatter trajectory means the pellet doesn’t drop as much and will hit higher. How much higher depends on the distance and angle.
The ‘Riflemans Rule’
Another area of confusion for airgun shooters is the ‘Riflemans Rule’, which essentially states that an approximate correction for angled shots is to shoot for the horizontal distance instead of the true distance to the target. So if the target is 30 yards away, but is placed at the top of a high tower 18 yards high – the distance to the base of the tower will be 24 yards (using Pythagoras’ theorem) and you should expect the same aim point on the 30 yard target as you would expect to see when shooting at a 24 yard target. Unfortunately, this rule often gives completely the wrong answer when using a scoped rifle shooting at close range – both very common conditions in air gunning.
So my advice is to ignore the riflemans rule completely and instead use a rule I’ve invented called the “Airgunners Rule of 15’s”.
The Airgunners rule of 15’s
If the target is closer than 15 yards OR the angle is less than 15 degrees. Simply ignore the fact that the target is at an angle and shoot it using the same aim point / clicks as you would do if the target wasn’t at an angle. So that’s 15 yards (no matter what the angle – including vertical!) OR 15 degrees (no matter what the distance).
If the target is further than 15 yards AND it’s steeper than 15 degrees (up or down) then you will need to adjust your aim and aim lower than you normally would for a target at that distance but on the level.
Before I go into detail about how much lower to aim, I’ll explain why the rule of 15’s works and what assumptions it makes.
Firstly, the rule is independent of scope height, but it assumes a .177 air rifle using reasonably efficient pellets (JSB Exact for example) and running at UK legal power levels. It also assumes that you are using the rule for either HFT or FT and the smallest kill zone size is 15mm. Fortunately, those assumptions are ideal for UKAHFT or BFTA/WFTF target shooters.
The rule works below 15 yards at any angle because the difference between a level shot and the worst-case scenario of a completely vertical shot is purely the difference that the effect of gravity has on the shot. At distances up to 15 yards the pellet reaches it’s target so quickly that gravity has hardly any effect on the trajectory. Even when shooting on the level the pellet doesn’t drop by more than a few millimetres, so even if we completely remove the effect of gravity on the trajectory, the most it can do is cause the pellet to strike a few millimetres higher than it would have done on the level.
When aiming at a 15mm kill zone, the difference isn’t big enough to cause a miss.
When shooting at an angle of 15 degrees or less (no matter the distance) the effect of gravity on the trajectory is reduced by 17% which again isn’t enough of a difference to cause a miss on any legal size of kill zone in use in either HFT or FT.
Beyond the Rule of 15’s
For a shot further than 15 yards at an angle greater than 15 degrees (these are still quite rare) you can use a rule of thumb of aiming between 1/2 MoA to 1 MoA lower than you would have aimed. In FT where you are allowed to adjust the elevation turret, that would mean taking between 4 and 8 clicks off of your usual settings (assuming a 1/8 MoA turret. The value would be half as much for a 1/4 turret)
For HFT using a true mildot scope, that would be aiming lower than normal by about 1/4 of a milliradian. If thinking in terms of MoA’s, clicks and mildots is confusing, another alternative is to just aim at the inside bottom of the kill zone. This will take the vast majority of targets down that are outside of the rule of 15’s.
If absolute accuracy floats your boat, you can print out and laminate the following table of allowances in millimetres, but you should bear in mind that estimating the actual angle is often much more difficult than estimating the range of a target and even if you know the range and the angle already, a further problem is being able to hold your rifle steady to actually take the shot.
Personally, I just remember the rule of 15’s and if the target is outside of that rule I either aim at the bottom inside of the kill zone or just below the kill zone for a very steep shot. That may not be enough to take down every possible target placement and angle, but the targets that fall outside of both of those methods are so few and far between, I don’t worry about them.