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.
Arrow drop over time
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.
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{ 7 comments… read them below or add one }
Nice article, I especially like the “arch” in “archery”. Do you know if those two words are actually related or is it a coincidence?
I have one correction:
There are two reasons why the pin gap increases with distance, but the two reasons you gave should be combined into one: drag increases the amount of time the arrow is in flight, which causes the pin gap to increase roughly proportional to the drag. Without drag (and without the second reason below), the pin gap is constant because pins measure angles, and the linearly increasing angle (between a line parallel to the arrow, and the peep-pin line) with each pin multiplied by linearly increasing distance gives the quadratic increase in drop you’ve plotted.
The second reason for increasing pin gap is the peep and the pins are located several inches above the arrow and this causes a parallax effect. This effect is large at short distances and goes away at large distances. On my bow, shooting at 9 yards uses the 20 yard pin. That is, the pin gap for those two distances is zero, but the pin gap for 20 and 30 yards is big enough to need another pin!
I’m not positive on the origins of the word “archery” but I believe it has its roots in “arcus” which is Latin for “bow.” Not 100% sure, but something like that. Whatever the case, the “arch” is still there in name, shape of the bow and arrow flight!
Drag does have a small portion in pin gap determination; it is true that the longer an arrow is in flight, the more it will slow down in the direction it is shot and thus it will have more time to drop (IE the travel time between 0 and 10 yards is shorter than the travel time between 50 and 60 yards.) However, the fact that the arrow is accelerating towards the ground due to gravity is a much bigger factor. It’s just like dropping a marble; when first dropped, it’s velocity is zero, but as it continues to fall, it speeds up. Thus the first tenth of a second it falls it covers much less distance than the second tenth of a second. If you forget about drag completely (solely for arguments sake) and say that an arrow maintains all of it initial forward velocity, you would still get a gap in pins due to the acceleration of the arrow towards the earth.
Hi again Mike
Just writing to let you know I enjoy these articles and charts a lot…good work.
I am now starting to send chosen ones to our 75 club membership as general interest for all the areas and subjects you cover.
I would like you to consider adding a list of all previous articles (no matter how long ) to the base of each newsletter…we can scroll and get back to things easily as your links are now spread out over all the articles “somewhere”.
This would help newcomers viewing your articles to easily see all the previous ones.
Bob May
Montreal, Canada
Bob,
I’m glad you get some enjoyment and benefit from reading the articles!
As time has gone on, the article list keeps growing and I definitely need to organize it better. I’ve been thinking of getting it done, but keep procrastinating it because I’d rather work on new articles!
I like your idea and I’ll give some thought on how to accomplish it. It’s a tad complicated since the website software is run separate from the mailing list software, but I’m sure I can do something to make things easier to find!
Thanks,
Mike
Another great article.
It would be interesting to time arrows of various weights in flight. Yes, a lighter arrow drops less than a heavier arrow…aka MORE ARCH in archery… Regardless of the trajectory of the chosen arrow, knowing the target distance is critical. I would just be curious as to how much longer it takes a 580 grain arrow to reach 40 yards when compared to a 326 grain arrow. My guess is not much on a practical level.
I have been trying to figure a way of measuring the impact sound and calculating it backwards. Video, digital microphone?
Measuring in FPS seems simple mathematically until you consider that sound travels a greater distance if you measure the bow release and impact sound from the location of the release. My intended solution was to measure sound at the midpoint, settling on an average distance between the two emanating sounds of release and impact.
Any thoughts?
Too tempting to provoke this kind of test!
John
I shoot at 60, 80 and 100 yards normally with my bear compound 70# bow. I have the pins set at these distances. I found that if I shoot from 10 feet high at 60 yards my carbon arrows go quite high. I purchased some aluminum arrows which are heavier at Wal-Mart. At 60 yards with my 60 yard pin I can hold the pin dead on the target just like horizontal with the carbon arrow. I don’t have to change my aim point even though I am 10 feet higher than on the ground. (Also, once a year right before hunting season stock carbon and aluminum arrows at $3.00 a piece and they are great. I buy up to 100 arrows and milk them the rest of the year until Wal-Mart carries them again.
Gene, something seems a bit fishy here. Unless you are changing something in your for, shooting at those distances with only a 10 foot elevation change should have virtually no difference in impact position. Are you bending at the waist when shooting at a downward angle or just changing the angle of your bow arm?