Any archer who as shot 3D, Field archery, bowhunted or done any shooting at various distances has come up against the simple fact that gravity is alive and well. As arrows fly, they drop! Even though this may seem like an easy thing to understand there is often a lot of misunderstanding on what is really happening and why it happens.
The very instant an arrow leaves the bow it begins to accelerate towards the earth. This does not mean that the arrow is dropping towards the earth instantly, in fact it is usually rising away from the earth initially. Seem a little confusing? Let’s take this one step at a time.
Arrow flight basics
Archery is aptly named as all arrows fly in an “arch.” In nearly all cases (unless shooting at a target downhill) the arrow will begin its flight at an upward angle, peak at some point, then arch downwards until it hits the target. However, the archer is looking in a straight line at the intended target. Because of this, the arrow actually crosses the line of sight twice.
Upon the archer releasing the arrow, there is no longer any force keeping the arrow from beginning to fall due to gravity. The act of shooting the arrow may cause the arrow to have an initial upwards velocity, but it is also beginning to accelerate downwards. To understand this it is very important to understand the difference between velocity and acceleration.
Velocity: the change in position of an object over time, IE the arrow moves 300 feet in one second.
Acceleration: the change in velocity over time, IE gravity causes an object to fall towards the earth at 32.2 ft/sec^2
The old adage that a bullet that is dropped by hand will hit the ground at the very same instant a similar bullet is fired perfectly horizontal is true. If you doubt it, go watch the MythBusters episode where they proved this! The same applies with arrows and any other object. Gravity does not care about how fast an object is moving horizontally, it will always affect equal objects equally in the vertical direction regardless off the horizontal velocity.
An object that is dropped in a vacuum (area absent of air) will fall towards the earth, accelerating at a rate of 32.2 feet per second squared. In the real world where there is air involved, there is some resistance to falling due to the air. For example, a feather will fall at a slower rate than a lead ball because the ratio of it’s cross-sectional area to its weight is much greater; also it’s form “catches” air and resists falling. Another exception is airfoils (such as airplane wings) that create lift that counteracts gravity and pushes the wing upwards.
Now back to arrows: because an arrow is accelerating towards the earth from the moment it is shot, the longer it is in flight, the faster it falls towards the earth. A horizontally shot arrow at release is falling at 0.0 inches/sec towards the earth while after it has been in flight for 0.2 seconds is falling around 75 inches per second.
The following is a graph of how many inches a horizontally shot arrow has dropped over time. This is neglecting the air resistance of the arrow falling, which would be different for different shapes and weights of arrows. An actual arrow would show slightly less amounts of drop because of the air resistance, but the graph serves to show how quickly the acceleration towards the earth adds up.
There are two reasons that on bow sights that the pin gaps increase as distances get longer (assuming the pins are set to equal distances in between, IE 20, 30, 40, etc. yards.) The first is what we have just discussed; the longer an arrow is in flight, the faster it falls towards the earth. The second reason is that the arrow is slowing down in its forward motion. This deceleration is due to the air resistance of the arrow moving forward. More on this can be read in the Downrange Speed and Power Article.
Real world arrow drop over time and distance
To illustrate the above discussion with some real world numbers, I shot two arrows that are identical on the outside, but one was layered with additional weight on the inside. The two arrows are Victory VForce HV arrows, one weighing 326 grains and the other 580 grains. Both were shot from the same bow with the lighter arrow beginning at 316.4 fps and the heavier 243.1 fps.
I zeroed both arrows to hit dead-on at 20 yards. Then I dropped back to 30 yards, and using the 20 yard pin shot at a vertical line and measured how far the arrow dropped below the line. At 30 yards, the arrow traveling 316.4 fps dropped an average of 3.2″ and the 243.1 fps arrow dropped and average of 7.8″. That’s a fairly big difference!
Now for an even bigger difference: at 40 yards the faster arrow dropped 10.7″ and the slower arrow 23.7″! Because these arrows were identical on the outside they both experienced exactly the same initial air resistance in the vertical direction. However, because the heavier arrow is going slower, it had more time to accelerate towards the earth and additional time to drop significantly more.
There are other very important factors to consider when picking an arrow for the various types of target shooting including FOC (front of center), kinetic energy and momentum as well as how all these affect penetration when hunting. However, a basic understanding of how arrows fly and how gravity affects them is necessary to begin with.