Joined: July 16 2005 Location: United States Posts: 25366
Posted: September 11 2010 at 4:14pm | IP Logged
The Slope Doper is an Angle Cosine Indicator tool for long range shooting that fits in your pocket or log book.
When hunting there will be times where you will be faced with shooting up or down hill and the old adage is to always hold low when shooting at high or low angles but the problem has always been how low you need to hold.
Chuck Hawks wrote a nice article on the problem called Shooting Uphill and Downhill. And I could not say it any better myself so Iíll quote him.
ďTrajectory, the bullet's flight path, depends on the horizontal (level) range to the plane of the target, not the line of sight range up or down hill. Your eye sees the line of sight (slant) range from your position to the target, which is longer than the horizontal range.
Remember that it is gravity working on the bullet during its flight time that causes it to drop. If you were to shoot straight down, say from a tethered balloon, the bullet would have no curved trajectory, it would travel toward the earth in a straight line, just as if you simply dropped it. Likewise, if you shoot straight up, the bullet travels up in a straight line until its momentum is expended. Again, there is no curved trajectory.
You can infer from this that the farther from the level position a rifle is held when a bullet is fired, the less the bullet's drop will be over any given line of sight distance, whether it is fired up or down. Since your sights are set to compensate for bullet drop, and there is less bullet drop when shooting at an up or down angle, you must hold lower than normal to maintain the desired point of impact. For example, if you are shooting up or down at a 40 degree angle and the line of sight range is 400 yards to the target, the horizontal range is only 335 yards. 335 yards is the distance for which you must hold.Ē
For years long range shooters and snipers would use a protractor and string to find the angle, and then use Trigonometric functions to find the cosine angle and multiply that by the range to the target so you have a corrected range based on the angle.
The cosine of an angle is defined as the sine of the complementary angle. The complementary angle equals the given angle subtracted from a right angle, 90į. For instance, if the angle is 30į, then its complement is 60į. Generally, for any angle t.
Then David Rolls invented the Slope Doper in 1998 while preparing for the Carlos N. Hathcock II Charity Sniper Competition and long range shooters, tactical shooters, snipers, and hunters have been using this simple device that takes all the voodoo out of getting the range and making the calculations in the field, and itís so simple even I can use it.
Now if I were to say R x SAF = Corrected R and thatís easier than the old way you would likely look at me funny. What that means is the Range to the target x the Slope Angle Factor = the corrected Range.
Now if thatís still fuzzy, letís introduce the tool. The Slope Doper is made of aircraft-grade aluminum plate, the Slope Doper is not affected by cold, heat, humidity, or impact and it does not need batteries.
It is carried either in your shirt pocket or your rifle logbook (we will be talking about the logbooks in an upcoming article). The slope doper is such a simple device, but thatís whatís great about it, itís not one of the hundred dollar Angle Cosine Indicatorís you mount on your rifle, but itís used in much the same way. The slope doper is a bit larger than a business card and itís well engraved with the slope angle, the Angle Cosine with a small metal arm. Now you can use this tool two ways. You point towards the target and place the tool on your barrel to find the angle, or you can sight along the top edge of the tool and then read the slope angle as well as the slope angle factor.
Itís the slope angle factor that takes all the work out of the calculations leaving you to only do the math for the corrected range. So letís try an example.
Your target is 500 yards away and you use the slope doper to find that the target is at a 30 degree angle. Right above the slope angle you will see another number which is .87
R x SAF = Corrected R
500 yards x .87 = 435 corrected yards
So rather than setting up your shot based on 500 yards and holding a little low and guessing, you know you have to reduce your range by 13% based on the 30 degree angle and to setup your shot for 435 yards and forget about holding low.
If you are trying to figure out the 13% itís simple take 100 Ė the slope angle factor of 87 and you get 13.
In fact you could say 500 yards x .87 = 435 corrected yards or you could say 500 Ė 13% = 435 (the first one is easier).
Donít let all the math talk get in the way of thinking this tool requires too much math. Actually this tool is a bit easier than the Angle Cosine Indicatorís you can attach to your rifle because this one reminds you of the formula while the others do not. The simple math is the same no matter which device you use.
Personally I like the Slope Doper, and itís less than a quarter the price you would pay to have one to attached to your rifle and itís easy enough, you use the tool to find the angle, and it provides the slope angle factor to multiply to get the corrected range. Now on the backside of the tool you will find the Mil Dot Ranging Formulas, so you can estimate the range to the target based on your scopes Mil Dots
For those who donít know what the Mil Dots are if you look into some scopes you will see the reticle as two lines in a cross with little dots on it. The Dots are the Mil Dots.
With a Mil-dot reticle-equipped scope the distance to an object can be estimated with a fair degree of accuracy by a trained user by determining how many angular mils an object of known size subtends. Once the distance is known, the drop of the bullet at that range (look into external ballistics), converted back into angular mils, can be used to adjust the aiming point. Generally Mil-dot scopes have both horizontal and vertical crosshairs marked; the horizontal and vertical marks are used for range estimation and the vertical marks for bullet drop compensation. Trained users, however, can also use the horizontal dots to compensate for bullet drift due to wind. Mil-dot reticle-equipped scopes are most suited for long shots under uncertain conditions, such as those encountered by military and law enforcement snipers, varmint hunters and other field shooters. These riflemen must be able to aim at varying targets at unknown sometimes long distances, so accurate compensation for bullet drop is required.
So in other words you can use the reticle in your scope to determine the range. You can also use another tool called The Mildot Master, but we currently donít have a product review on that tool and how it works to determine the range.
A lot of hunters these days will use a laser range finder to get the range, and then use the slope doper to correct the range based on the angle.
Now the Slope Doper typically sells for less than $20, so if you are a big game hunter or out after a big elk and you spend money on a guide, license, travel and you miss your target by 65 yards on a 500 yard shot because you figured you could guess the corrected range, well you are better off knowing the real corrected range and nail that elk with one shot because in the end you will save money.
As for Snipers and Zombie Hunters who are always shooting at angles where it be from trees, buildings, hills, mountains, or even helicopters, you want that first round to count because the last thing you want is a zombie eating your brains (snipers know better and use the right tools).
I personally have a slope doper and I keep it in my log book along with a few other shooting tools. I trust it and recommend it to other shooters and think that people who are tired of guessing how much to hold over to hit a target will like the Slope Doper and get a lot of use out of it.
The Slope Doper is also recommended by others such as www.snipercountry.com check around and read the reviews and I don't think you will find a single bad word about it.
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