How is arrow trajectory calculated?

How is arrow trajectory calculated?

If you've recently joined the ranks of archers and bowhunters in the world, you know it's fun. But as you become more serious about taking game, you start wondering how you'll know you'll put your arrow into your mark every time. That's why it's so important to understand how to calculate arrow trajectory. Knowing your arrow's trajectory will take a lot of guesswork out of hunting and will help you bring home that prized buck or bull every time.

Arrow trajectory

Understanding the Mathematics and Physics Behind Shooting

If you fell asleep in your high school geometry or physics classes, you might groan a bit when you hear that calculating trajectory has to do with both geometry and physics. Assuming the arrow travels in two dimensions -- horizontal or X and vertical or Y -- without accounting for drag, the equations look something like this: X = V initial t ( cos ( theta )) Y = V initial t (sin ( theta )) - 1/2 gt2 Where V is the velocity t is time Theta is the launch angle g is the gravity constant You then have to account for drag on the arrow to get the trajectory, making the mathematics fairly complex.

An Easier Way to Calculate Your Arrow Trajectory

An easier and better way to calculate the arrow trajectory (and one that won't hurt most people's brains) is to use the one of the myriad arrow trajectory calculators to determine what your arrow trajectory is. Math is math and it simply makes sense to use the tools available on the Internet rather than waste your time number crunching, when you'd rather be out in the field looking for that big buck or bull. So, let's look at a few of the trajectory calculators and see how they work.

Arrow Ballistics Calculator

The arrow ballistics calculator on is a handy, no frills calculator which gives you the arrow's ballistics in flight. You input the arrow weight, the velocity, the draw weight, and the zero distance, it crunches the numbers and gives you a handy table with the height of the arrow in relation to the zero drop point. It further calculates the arrow flight based on the arrow's weight in grains to draw weight, so you can see how your combination is performing compared to other combos.


Another nice calculator worth mentioning is ArcheryCalc from Backcountry Bowhunting. This calculator doesn't just calculate your arrow's trajectory, but actually gives you several calculators, including arrow speed, arrow weight, FOC, and shot angle/distance. The shot angle/distance is the one that will give you the pertinent information when it comes to the arrow's trajectory. You input the straight line distance to your target and the angle you're shooting from to get the angle you need to shoot your game. It will tell you how you should aim your bow as though you were shooting an animal at a straightline distance. They also have a handy chart enclosed so you can quickly guesstimate how you should aim on an angle. Very nice.

Pete Ward's Archery Ballistics Calculator

If you want to input some very precise measurements that will accurately calculate drag on the arrow, you should consider Pete Ward's Archery Ballistics Calculator. This calculator requires that you input fletching length and height, type of fletchings (plastic or feather), shaft diameter and length, arrow speed, and arrow weight. What you get in return are the vertical drops, energies, speeds, and momentums of the arrow shot at distances in increments of 10 yards. A nice calculator for determining what kind of arrows are best for your bow.

Best Crossbow Source Arrow Ballistics Calculator

Lastly, Best Crossbow Source has an excellent Arrow Ballistics Calculator that is easy to use and has nice graphics. You input the arrow speed and the arrow weight to get the ballistics. For a more accurate number, you need to add the fletching length, fletching height, and shaft length, otherwise use their standardized numbers. What you get in return are the vertical drops, kinetic energies, speeds, and momentums of the arrow shot at distances in increments of 10 yards.

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