Shooting at angles is not intuitive…
Pop quiz….there’s a squirrel at the top of a 60 ft tall tree. You must shoot upward. You are standing 30 ft away from the tree. What holdover distance do you use to hit the squirrel? 60 ft? 30 ft? More? Less?
How about a different problem? Say you’re at the top of a 60 ft tall cliff. Now you must shoot downward. There’s a rabbit standing 30 ft away from the base of the cliff. What holdover distance do you use to hit the rabbit? 60 ft? 30 ft? More? Less?
While it might not be intuitive, you would use the exact same holdover distance for either shot. The gravity created by the mass of our planet pulls objects towards it’s center at precisely the same rate. That rate is 9.8m/sec² towards the center of the Earth (at sea level). Force is a vector, and therefore has both a magnitude (9.8m/sec²) and a direction (towards the center of the Earth). This is a very important concept to grasp for the rest of the conversation.
Let’s set up a hypothetical thought experiment. We’ll take an airgun and adjust it so that the barrel is completely level over completely level ground. We load the airgun with a pellet, and also put one of the same pellets in our hand. Somehow, we time things so that the gun can be fired and the pellet in our hand can be dropped at exactly the same time. So now we’re in a situation where we can fire the gun and drop the pellet in our hand simultaneously….and we do so. Which pellet hits the ground first? The answer is that they both hit the ground simultaneously. As counter-intuitive as that may be, it’s the truth.
Because the gun was fired completely level with the ground, the force of gravity acts perpendicular to the horizontal motion of the projectile. This means gravity acts at “full value” to the projectile as well as the one we dropped from our hand. Consequently, the two objects are exposed to the same force, and will travel the same distance in the vertical direction at the same time. They will hit the ground simultaneously.
Gravity will never act at more than full value. This is also a pertinent point for our discussion. I hate to bring equations into this, but there is a simple one that I must use. F = mg cos Θ. It says that the force acting upon an object (F) equals the mass of the object (m) multiplied by the force of gravity (g) multiplied by the cosine of the angle from our origin (Θ). Θ is the Greek character Theta and represents our angle. The most important part for our discussion is the cosine.
I’ll spare you the trigonometry lesson, but the cosine of any angle (other than 0°) is always less than 1. It is a percent in a manner of speaking. By using cosine, we know that the force of gravity acting upon our projectile will be less than full value. It will be a certain percent of the full value, and that percentage depends soley on the angle of our shot. It does not matter if you’re shooting up or down. All that matters is the angle.
I hope I didn’t lose you with the mathy stuff, but here’s what it means in plain speak. When shooting at an angle, if you use the real distance to the target for your holdover…you will hit high. Again, it does not matter if you’re shooting up or down. You will hit high in either case if you use the real distance to the target.
So how do I know where to hold? Well, the first thing you need to know is the angle at which you are shooting. There are many angle/cosine indicators available on the market. I use only myself. I prefer the cosine indicator to the angle indicator because it saves me a step. If you know the angle, you still need to know the cosine of that angle. If you know the cosine, which will be a decimal value less than one, you simply multiply that cosine by the actual distance you’re shooting. That will give you the distance to the target so far as gravity is concerned, and it will be LESS than the actual distance to the target. That is the hold you should use.
I know some of this is rather boring to read, but I felt this blog was necessary. I feel this concept is rather misunderstood. I hope this information is helpful to you and serves to clear the air a bit. I have surely not covered the entirety of the phenomenon, but that was on purpose. My hope was to simplify things as much as possible. I’d be happy to discuss it further in the comments section, or hear anything you have to say. Thanks for reading!