The instant that an arrow leaves the string, it is at its maximum velocity and will immediately start to slow down. There is much talk about how much kinetic energy and momentum that an arrow has, but most of it centers around the initial velocity produced by the bow. However, what is much more important is how much speed, kinetic energy and momentum the arrow has at the point of impact, especially in bowhunting conditions where the arrow must effectively penetrate an animal. This article will be broken into three sections:
- Part I: a discussion of how arrow weight affects downrange velocity, kinetic energy and momentum
- Part II: mathematical look at the above discussion to better understand what is really happening
- Part III: real world results from experimental shooting
Most readers will benefit from Part I as I discuss in a verbal fashion what happens after the arrow leaves the string. Many people will not appreciate Part II as I delve into the math and physics, though many will enjoy it, and it won’t hurt my feeling if you skip that part! I’m a engineering and physics geek so bear with me. Part III will probably be the most interesting section as actual experimental numbers will be used to test out the theories and descriptions of the previous parts.
Part I: Heavy vs. Light Arrows, a Discussion of Arrow Deceleration
As the arrow leaves the string, there is no longer a force pushing and accelerating the arrow. Once the arrow is in flight, the only outside force acting on it is the air resistance slowing it down called the drag. The total amount of drag on the arrow is a factor of the shape of the arrow, the speed of the arrow and the density of air. Because there is no thrust or anything else to power the arrow’s flight after leaving the string, the drag alone will determine the arrow’s deceleration over the remainder of the flight.
Consider two identical arrows on the outside, same shaft diameter, fletchings, point and nock. One arrow is very light, and one much heavier. For the sake of keeping the argument simple, we’ll consider both arrows to have the same spine as well. When shooting both arrows out of the same bow, the lighter arrow will of course be faster at point blank range. However, the heavier arrow will leave the bow with more kinetic energy and momentum due to the bow being more efficient at delivering energy into the arrow (for more discussion on this, see the Arrow Kinetic Energy and Momentum article.)
To determine how much drag is experienced by an arrow in flight, the drag coefficient must be known. The drag coefficient is a dimensionless number (a number having no units such as inches, pounds, etc. associated with it) that describes how aerodynamic an object is. This number is determined by the shape of the body and can be found either experimentally or by looking it up in tables found in fluid mechanics texts or other places. In the case of our light and heavy arrows, this number is the same because on the outside they are dimensionally equivalent.
Once the drag coefficient and speed of the arrow are known, the drag force on the arrow in flight can be determined. As the speed of the arrow increases, so does the drag force on the arrow. The faster the arrow, the higher the force trying to slow it down. Thus the faster arrow is going to have more force slowing it down initially.
For this section, one equation (I promise, only one!) needs to be understood; Newton’s second law of motion: F=ma (force = mass times acceleration.) This simple law states that the higher the force placed on an object, the faster it will accelerate. Also, the higher the mass, the harder it is to accelerate. In the case of the flying arrow, the force is acting against the forward motion of the arrow and the arrow will experience deceleration. The force on the lighter, faster arrow will thus slow the arrow down at a faster rate than the heavier, slower arrow.
At typical archery distances, the lighter arrow will almost always maintain a higher speed than the heavier arrow. Even though the lighter arrow is slowing down faster, it started out much faster and the heavier arrow is also slowing down. Because the heavier arrow is decelerating at a slower rate, it will maintain a higher percentage of it’s original speed than the faster arrow. Also remember that the heavier arrow has more kinetic energy and momentum than the lighter arrow at launch already. This gap only grows larger as the arrows progress downrange.
This entire discussion would tend to favor the slower, heavier arrows for having more power at impact for multiple reasons. However, as always, there is a drawback. The lighter arrow is going to drop less over the full distance to the target and is thus less dependent on accurate yardage judging (notice I said less dependent; accurate yardage judgment is still extremely critical!) For more details on speed and drop over distance, head on over to the One Pin to Forty Yards article.
Hopefully this all makes some basic sense. Continue reading for the mathematical proof and a better understanding behind the physics of what is happening.
Part II: Mathematics and Physics of Heavy vs. Light Arrow Flight
Coming soon!
Part III: Experimental Data of Heavy vs. Light Arrow Flight
Coming soon!
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{ 9 comments… read them below or add one }
What I would love to know is, which arrow gets a tighter group and is more accurate, at let’s say 90 meters, like a victory v6 nano 400 or similar arrow, say one arrow with a 80 grains point, another with a 100 grain point and another with a 110 -120 grain point, all shot from a 58 pound compound like my Hoyt proelite.
Barry, that’s a great, though very tough question. Unfortunately you won’t find that answer in this particular article as it only deals with speed and power, not accuracy. Generally speaking, at known distances, the experience of most target shooters has been that arrows with a higher FOC tend to be more accurate as well as drift less in the wind. For your setup I would guess that the heavier points (as long as the spine stays within your limits) would give the best accuracy. However, it’s always best to experiment for yourself to find the best combination.
Thanks Mike for the tip
I may have missed something, so if I did, correct me, but rather than compare arrows of identical size and shape, but varing only in weight, shouldn’t you be comparing the arrow shot from the same bow? The bow is going to produce different numbers depending upon the arrows weight, and in my opinion should be the common factor. My findings have been different than those stated by you. I change the arrow weight, the speed increases with the lighter arrow as you stated, but the k.e. also increases. Because the speed is so much faster, the K.e. is higher at the bow than the heavier arrow as well as the speed. You stated the opposite results. I have checked this out to 50 yards (computer programs) and as you stated, the k.e. drops off slower with the heavier arrow, but at 50 yards, the comparison of the two arrows k.e. is so close, that it isn’t a consideration for me. I have been using T.A.P. for this comparison. I have been comparing a 350 grain arrow to a 400 grain arrow shot out of a 70 lb Elite GT 500 at a 30 inch draw. The numbers for both arrows far exceed the recommended minimum k.e. for big game hunting. So, from a hunting perspective, seems too much energy is being spent by individuals trying to get the optimum arrow weight when nearly any combination will work effectivly. Guess it is a great way for the manufacturers to get a sale by convincing the public that it is important. Dead is dead.
The argument seems to be that a heavier arrow will push through bone where a lighter arrow wil not. In my experience, when the speed increases, the rules of the game change. Consider the history behind bullet resistant vests over the years as they have progressed from silk to kevlar and why. When a fast moving object hits bone, it tends to explode the bone. When a slow moving heavy object contacts bone, it has to “push” through it. The results of the impact are different depending upon the projectile’s speed. I would love for you to do an indepth study of this and publish your findings. I had this discussion with a weapons engineer for the military. He had some real enlighting information he shared with me. In a nut shell, he said that cutting was a function of motion. This makes sense as to why you want to use a heavy arrow when using a cut on contact broadhead…. you need to keep the arrow moving so the broadhead will do its job. Fast doesn’t depend on cutting, it “punches” through objects so weight isn’t as much of a factor. That is why silk was dropped from the bullet resistant vests and kevlar is now used.
Bow Dude,
One extremely important factor to remember is that as the weight of the arrow goes up, the efficiency of the bow does as well. If you read the “Arrow Kinetic Energy and Momentum” article linked to above, you’ll see my actual data of this phenomena. Because the efficiency of the bow in converting the stored potential energy at full draw to the kinetic energy delivered to the arrow increases, all other things being equal, the heavier arrow will always have more kinetic energy and momentum than the lighter arrow. The lighter arrow will certainly have more speed, but less energy. Couple that with the fact that the heavier arrow maintains a higher percentage of the energy downrange and with respect to energy and momentum, the heavier arrow will always win.
That being said, speed is important as well when shooting at longer distances where small mistakes in judging yardage can have huge effects. I personally like a well balanced arrow and will be shooting a 470ish grain arrow at about 305-310 fps out of my Destroyer 350. Like you said, most setups will have more than enough energy at reasonable ranges for most game and the majority of this type of discussion is academic. But it’s also fun to do the math and play with the physics of arrow flight!
What I want to know is if you have a 350 grain arrow and a 425 grain arrow both leaving the bow at 315 fps, which one will have the flatter trajectory? The heavier arrow?
Tyler,
If they both leave the bow at the same speed and have the same outward dimensions and FOC, then the heavier arrow will have a flatter trajectory by a small amount. This is because it will retain a higher amount of it’s initial velocity and energy. Truth be told, most likely the difference will be very small at reasonable distances but it will be there.
does the light arrow go far or heavy arrow?
does it effect on angle that we shoting?
what is the maximum range it can reach by light and heavy arrow?
Zaki,
Before I can answer you questions fully I need a little more information. What do you mean by “going far”? Do you mean total distance or effective hunting range? Total distance is very hard to predict because the lighter arrow will be decelerating quicker, but it starts faster and vice-verse for the heavy arrow, so there is some give and take there. For effective killing range, the heavier arrow will start with and maintain more KE and momentum than the lighter arrow and therefor be more effective downrange. However, most light arrows are going to have enough killing power anyhow, assuming the shot placement is good.
The angle being shot is somewhat affected by the weight of the arrow. A lighter, faster arrow is going to have a flatter trajectory and therefor the angle at longer distance will be lower.
For you last question, I need to know what do you mean by “maximum range”? For hunting? Target? Also it’s important to know what are you calling a “light” arrow and a “heavy” arrow? What grain ranges are you looking at?