In the lower left corner of the display it also tells you the angle at which your are ranging and the line of sight range from your position to the target.įor example, if I range the top of a tall fir tree some distance from my house the line of sight range is 151 yards and the angle is 19 degrees of elevation, while the horizontal range-the true ballistic range-is only 130 yards. Leupold calls this "true ballistic range" and you can set the RX-III's main readout to display the horizontal distance to the target, which is the distance you need to worry about in terms of trajectory. The Leupold RX-III rangefinder that I reviewed for Guns and Shooting Online includes among its many features a mode that automatically compensates for up and down angle shots. Illustration courtesy of Leupold & Stevens,Inc. Leupold RX-III TBR display for example above. 335 yards is the distance for which you must hold. With the angle measured, you can reference the corresponding cosine, multiply it by the distance in yards, and use the resulting number in yards as your actual shoot-to range. 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. 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. 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. Likewise, if you shoot straight up, the bullet travels up in a straight line until its momentum is expended. 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. Remember that it is gravity working on the bullet during its flight time that causes it to drop. Your eye sees the line of sight (slant) range from your position to the target, which is longer than the horizontal range. Trajectory, 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. This seems odd to many, and they insist on making the problem more difficult than it needs to be. (At gentle angles you can ignore the problem altogether over the maximum point blank ranges of hunting rifle cartridges.) The correct answer is to hold lower than normal when shooting steeply up or down hill at long range. It seems that many hunters understand that shooting at a steep angle changes the point of impact, but can't remember why or in which direction. I know you have to add X_c to L to find the total distance the block is moved by the spring, and I really don't understand why this is wrong.The hoary old question of where to aim when shooting up or down hill regularly rears its head. Use g for the magnitude of acceleration due to gravity.Įxpress the distance L in terms of mu, theta, g, x_c, m, and k.Ġ.5k(x_c)^2 = 0.5mv^2 + (mu)mg((x_c) + L)cos(theta)Ġ.5k(x_c)^2 = (mu)mg((x_c) + L)cos(theta) Also, assume that the uncompressed spring is just at the top of the gun (i.e., the block moves a distance x_c while inside of the gun). Ignore friction when the block is inside the gun. The block is released, exits the muzzle of the gun, and slides up an incline a total distance L.įind L, the distance traveled along the incline by the block after it exits the gun. The incline makes an angle theta with the horizontal and the coefficient of kinetic friction between the block and the incline is mu. A block of mass m is placed in a smooth-bored spring gun at the bottom of the incline so that it compresses the spring by an amount x_c.
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