All About Scopes - IV

In our last post, we studied some details about the reticle inside a scope. In today's post, we will look into some more uses of reticles, namely rangefinding. We had actually dealt with this topic some time ago, when we talked about telescopic sights.

The key to rangefinding in most scopes is to compare an object of known height or width against a series of markings on the reticle, to determine how far away it is. We will see how this works with a few examples.

Reticle from a Russian PSO-1 Scope, as used by the SVD rifle. Click on the image to enlarge. Public domain image.

The above image shows the reticle from a PSO-1 scope, which was originally designed for use by the Soviet military Dragunov SVD sniper rifle. When this was originally introduced in 1964, it was the most advanced mass-produced scope available. This scope is a fixed power scope with 4x magnification. It has several markings on it. The top chevron (^) mark is used as the main aiming mark. The horizontal marks (10...10) are used for adjusting for windage and also allow to lead the target, in case it happens to be moving. The horizontal marks can also be used for rangefinding, if the width of the target is known beforehand. Each marking on the horizontal 10..10 marking is spaced at one milliradian interval, therefore the calculation for finding distance can be determined by the following formula:

D = S / mils * 1000

where
D = distance to target in meters
S = Known height or width of target in meters
mils = Number of markings wide that it appears when viewed through the scope

Say the user is viewing a Land Rover vehicle, which is known to measure about 4 meters long (i.e. 13.12 feet long). Let's say that when it is viewed through the scope, it measures up to 8 markings long. Then, we put S = 4, mils = 8 in the above formula and calculate D = 4/8 * 1000, which works out to 500 meters. Therefore, the Land Rover is approximately 500 meters away from the scope.

Also notice the curved line on the lower left quadrant with the numbers (10..2). This can also be used to measure distance to the target, in this case using a human for range finding. The markings assume that an average human is 1.7 meters (5 feet 8 inches) tall. The user simply aligns the scope so that the person's feet touch the bottom horizontal line and see which marking the person's head touches, as shown in the image below:

Public domain image

In this case, the person's head touches the 4 mark, which means that the person is about 400 meters away. Using this set of markings, the user can determine ranges from 200 to 1000 meters.

The PSO-1 scope has a bullet drop compensator (BDC) to adjust range in 50 meter increments from 100 meter to 1000 meter ranges. Therefore, once the range to the target is determined, the user can turn the knob and adjust the elevation to correspond to the appropriate range and then align the target with the top chevron mark (^).

Notice that the scope also has other chevron marks (^) below the first one. These are used to shoot at ranges beyond 1000 meters. The user sets the elevation to the maximum of 1000 meters, then uses the other chevrons to line up to 1100, 1200 and 1300 meters respectively.

Now we'll look at another reticle.

Reticle used by Schmidt and Bender scope. Public domain image.

The above reticle is used by scopes made by Schmidt & Bender. Note that the center of the scope has several dots in the horizontal and vertical lines. These are called mil-dots and each dot corresponds to 1 milliradian. Therefore, if the width or height of an object is known, the user can determine the range by counting the number of dots that it covers and then using the same distance formula that we saw above for the PSO scope. Therefore, if an average person, who is about 1.7 meters tall (or 5 feet 8 inches tall), covers 4 dots when viewed in the scope, we can take S = 1.7, mils = 4 and plug it into the formula D = 1.7/4 * 1000, which works out to 425 meters.

There is also another way to quickly compute the range with this reticle, without doing any arithmetic. Note that the bottom of the reticle, there is a long horizontal line and above it are a series of smaller horizontal lines in a step pattern. These lines can be used to quickly estimate the distance to a target, using a human as the scale. To estimate distances between 100 and 250 meters, the user simply frames the target's head between the lines as shown below:

Public domain image.

The average human head is around 0.25 meters high. The two lines that best frame the top of the helmet to the chin tell the distance to the target.

For longer ranges, the same horizontal lines can be used, except that the user frames the top of the target's head to the belt buckle between the two lines.

Public domain image

Using this, the user can measure distances between 400 and 1000 meters.

Note that in both these instances, the scopes are fixed power models. Therefore the user cannot adjust the magnification power and the rangefinding calculation is easier.

For scopes with variable power magnification, the method of rangefinding depends on whether the reticle is placed on the first focal plane (FFP) or second focal plane (SFP).

Recall in our last post, we mentioned that if the reticle is placed on the first focal plane, the size of the reticle resizes with the magnification, so if the user zooms into the target, the reticle also appears to enlarge in size correspondingly. So, if a target measures 4 mil dots at 3x zoom, it will still measure 4 mil dots at 10x zoom, when using a FFP reticle. Therefore, for a variable power scope using a FFP reticle, the range calculation formula is the same as that of the fixed power scope, D = S/mils * 1000.

We also mentioned in our last post, that in a reticle placed at SFP, the size of the reticle does not change with magnification power. Therefore, for a SFP scope, the mil-dot range estimation is calibrated accurately only at one particular magnification power, generally at the highest magnification power setting, or sometimes at the middle magnification power setting. Some SFP scopes have an index mark on the power ring, to show at which magnification power setting the mil dots are accurate (for instance, some manufacturers set it at 10x power, Bushnell generally sets theirs at 12x power). The formula for range estimation changes a bit in this case. Assume a SFP scope where the mil-dots are calibrated accurately at 10x magnification power. The distance formula for this scope is:

D = (S/mils) * (mag/10) * 1000

where
D = Distance to the target in meters
S = Width or height of the target in meters
mils = Number of markings covered by the target
mag = Magnification power of the scope.

As you can see, with a SFP scope, the range calculation is a bit harder to do because it depends on the magnification power setting on the scope. Therefore, some users usually set their scope at the power setting that it is calibrated at and leave it there, so that they don't have to do the extra math. For instance, in the above example, if the magnification power is set to 10x (i.e. the same magnification power that it was calibrated at), the formula simplifies to D = S/mils * 1000 (i.e.) the same formula as for a fixed power scope. Alternatively, if they change the magnification power, they change it to half or double of the calibration setting. For example, a Bushnell Elite 4200 6-24x40 variable power scope is calibrated at 12x magnification power, so if the user wants to change the magnification power, they usually select 6x or 24x, so that the range calculation can be modified by dividing or multiplying by 2. If the user chooses any other magnification power settings, the math becomes correspondingly harder.

This is why many military scopes use fixed power scopes, to reduce the amount of math calculations that the user has to do, and also avoid the chance that the user makes an incorrect calculation due to not paying attention to the magnification power setting of the scope.

All About Scopes - III

In our last couple of posts, we studied about different types of scopes and what they look like from the outside. In today's post, we will look at some of the stuff inside a scope. Specifically, we are going to study about a part called the reticle.

We actually dealt with reticles a little over four years ago, when we studied telescopic sights originally. A reticle is a device consisting of fine lines, which is embedded into a telescope and helps the user to line up a target precisely.

The classic image of a telescopic sight is a target centered around two crosshairs, such as the image above. This is usually what is shown in movies and TV shows. However, there are many different types of reticles, which we will study.

Different types of reticles. Public domain image.

Thanks to movies, most people are familiar with the Fine Crosshair type of reticle above. Fine crosshairs allow the user to see more of the target and do not block out much light. However, it is easier for the user to lose sight of the lines, especially in complex backgrounds. Thicker lines are more visible, but they block out more of the image and lose some precision. Therefore, modern telescopic sights use a mixture of both (i.e.) thicker lines on the outside and thinner lines closer to the middle. Examples of this would be the Duplex Crosshair, the Mil-Dot and the Modern Rangefinding reticle above. The thick lines allow the user to quickly figure out where the center of the reticle is and the thinner lines allow for precision aiming.

Back in the day, the crosshairs of reticles were made of  natural fibers, such as hair or spiderweb. Later on, they were made of thin wires (and many scopes still use wire crosshairs to this day, especially cheaper ones). The wires are mounted on the inside of the telescope tube. By flattening the wire in different places, the manufacturer can make Duplex Crosshairs or Target Dot type crosshairs. The nice thing about wire reticles is that they don't block out much light and are very durable.

Another technique to make the crosshair lines is to etch the lines onto a thin plate of glass, using a diamond cutter. The thin plate of glass is then mounted inside the scope. The etched lines allow for more complex crosshair shapes, including circles, lines that don't need to touch or have gaps in between. This allows them to have features such as estimating range and bullet drop (such as that seen in the Modern Rangefinding and the SVD type above). The etched lines block off a bit more light and the thin glass plate may reflect some of the light back instead of letting it through. Modern scopes usually coat the glass with special coatings designed to minimize the reflected light.

For aiming in low light conditions, many scopes have illuminated reticles. The illumination is usually provided by a few methods. The first is to use a bit of fiber optic cable to collect ambient light from the outside of the scope and deliver it inside to the reticle. Another technique is to use a battery powered LED to provide enough light to illuminate the reticle. While this method requires the user to carry a battery with the scope, it has the advantage that the user can usually adjust the brightness by turning a knob. The user may also be able to change the color of the backlight illumination, if the LED method is used. The third method, which is used in military scopes, such as the Trijicon ACOG, or the British SUSAT sight, is to use tritium, which is a mildly radioactive form of hydrogen, to provide illumination. The tritium slowly decays and emits light as it does so. The nice thing about this is that tritium glows for a long time and could last 11 years or more before the tritium tube needs to be replaced.

As you may have observed in movies, if the crosshairs are backlit, they are usually red, though some products use green or yellow. There is a good reason for this. Red happens to be the color that least interferes with the user's night vision.

Reticles may be mounted inside the telescope tubes in one of two spots: the first focal plane (FFP) or the second focal plane (SFP). For fixed power scopes, it doesn't make any difference which focal plane the reticle is mounted at, but it makes a difference for variable power scopes. If the reticle is mounted at the first focal plane, then the size of the reticle resizes with the target (i.e.) if the user adjusts the magnification to zoom into the target, the reticle also appears to enlarge in size and if the user adjusts the magnification to zoom out of the target, the reticle also appears in decrease in size correspondingly. If the reticle is mounted on the second focal plane (i.e. closer to the eyepiece), then the size of the reticle remains a constant, irrespective of the magnification power. Americans tend to prefer scopes with reticles mounted SFP and this is used in the majority of the scopes. Some high end European manufacturers make FFP scopes on request.

We will study more about the advantages and disadvantage of FFP and SFP scopes, when we study the topic of scopes and rangefinding tomorrow.