# Arrow drop calculator



## ChappyHOYT (Feb 26, 2009)

Anyone know of a good website that can calculate arrow drop based on speed, weight, etc. besides the Pinwheel software. Thanks.


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## Mac2118 (Dec 21, 2007)

something like this:

http://www.bestcrossbowsource.com/crossbow-arrow-ballistics-calculator

or this?

http://peteward.com/ballistic.calc.htm

http://backcountrybowhunting.com/calculator/


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## bstring (Jan 24, 2013)

Hey good stuff. Thanks


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## ChappyHOYT (Feb 26, 2009)

Wow! It's crazy my arrow drops so much at 30. Didn't think it'd be that much. Fun to plug other #s in and see too.


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## Bowen Aero (May 13, 2015)

ChappyHOYT said:


> Wow! It's crazy my arrow drops so much at 30. Didn't think it'd be that much. Fun to plug other #s in and see too.


An arrow starts to drop as soon as it leaves the string.

Sent from my RCT6773W22B using Tapatalk


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## ChappyHOYT (Feb 26, 2009)

Bowen Aero said:


> An arrow starts to drop as soon as it leaves the string.
> 
> Sent from my RCT6773W22B using Tapatalk


Actually, it rises a little.
http://archeryreport.com/2011/06/understanding-arrows-drop/


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## Luke Cool (Oct 16, 2015)

All arrows fall at the same rate "the acceleration due to gravity (9.8 m/s/s)", weight does not matter.
An arrow going twice as fast will go twice as far before dropping the same amount.



ChappyHOYT said:


> Actually, it rises a little.
> http://archeryreport.com/2011/06/un...rise makes no difference to the calculations.


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## ChappyHOYT (Feb 26, 2009)

Luke Cool said:


> All arrows fall at the same rate "the acceleration due to gravity (9.8 m/s/s)", weight does not matter.
> An arrow going twice as fast will go twice as far before dropping the same amount.
> 
> 
> ...


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.

Maybe we can all agree.


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## aread (Dec 25, 2009)

ChappyHOYT said:


> Actually, it rises a little.
> http://archeryreport.com/2011/06/understanding-arrows-drop/


An arrow or bullet or any projectile, fired on the horizontal, will immediately begin to fall a the same rate as an arrow that is simply from your hand. The rise that the article refers to is simply the arrow aimed above the horizontal. This is how we compensate for the drop that begins immediately upon firing.

Gravity is a law that we can't repeal.

Allen


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## rs_hh (Oct 2, 2016)

Arrows, at least in target archery, are usually not fired horizontically unless shooting very short distances. When shooting greater distances arrow trajectory will be upwards for some time/distance, the apex of the trajectory getting closer and closer to half the shooting distance as the latter increases. Accounting for air resistance the point of highest trajectory may even be a little farther than half the shooting distance, especially when using fatter arrows. From launch to highest point of trajectory gravity slows down the upward vector of arrow movement until the vertical velocity component gets to zero, from which arrow drop in the sense of arrow downward movement can be observed.


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## rs_hh (Oct 2, 2016)

By the way, arrow weight plays a role not in arrow drop as such but in arrow drop in relation to horizontal arrow travel. A heavy arrow will impact higher than a light one (with same diameter) shot with the same initial velocity. Why? Because when shooting identical diameter at identical initial velocity, the heavier arrow has more kinetic energy and thus is more resilient to ******ation due to air friction. Arrow drop as a function of time would be identical but the lighter arrow would take more time to the target, causing it to impact lower.


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## Luke Cool (Oct 16, 2015)

rs_hh said:


> By the way, arrow weight plays a role not in arrow drop as such but in arrow drop in relation to horizontal arrow travel. A heavy arrow will impact higher than a light one (with same diameter) shot with the same initial velocity. Why? Because when shooting identical diameter at identical initial velocity, the heavier arrow has more kinetic energy and thus is more resilient to ******ation due to air friction. Arrow drop as a function of time would be identical but the lighter arrow would take more time to the target, causing it to impact lower.


This is a true statement. But:
Weight makes no difference in the acceleration due to gravity calculations. 
And the difference it makes to the foreword velocity calculations is not significant at reasonable distances.
Friction is a function of size, aerodynamics, and air temperature pressure and humidity.
Weight is a function of momentum.


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## rs_hh (Oct 2, 2016)

Yeah, that is true. Arrow weight does not affect gravity drop, nor is air friction dependent on projectile weight. The only (minute) influence of arrow weight ist that, provided identical initial velocity and shaft diameter, the heavier arrow should retain horizontal speed a tad better. Of course, it is clear to me that, being shot out of the same bow with same DL, arrows of different weight will usually not have the same initial velocity. One would have to try if the lighter arrow, most likely taking off faster than the heavier one, thus would probably over-compensate its higher loss of kinetic energy due to air friction. BTW, I have some target arrows exactly matched to my DL (26") which are identical length- and weightwise, one set being made of X7 aluminum whereas the other set are (much thinner) Easton Apollo carbon arrows. Both leave my bow at almost identical speed and make no visible difference as to height of impact for distances up to 50 yards. Arrow shaft air friction truly not seems to play too an important role in arrow trajectory (for the record: even fletching half of those with 1.6" and half with 4" vanes made for no systematic difference whatsoever as to impact height under 50, haven't tested longer though).


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## Luke Cool (Oct 16, 2015)

We are speaking the same language. It sound like what I've experienced.


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## Bowen Aero (May 13, 2015)

ChappyHOYT said:


> Actually, it rises a little.
> http://archeryreport.com/2011/06/understanding-arrows-drop/


Actually, it doesn't.

It drops from the launch plane. It is irrelevant what angle it is launched as it immediately begins to drop.

You knew that.

Sent from my RCT6773W22B using Tapatalk


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## Bowen Aero (May 13, 2015)

rs_hh said:


> By the way, arrow weight plays a role not in arrow drop as such but in arrow drop in relation to horizontal arrow travel. A heavy arrow will impact higher than a light one (with same diameter) shot with the same initial velocity. Why? Because when shooting identical diameter at identical initial velocity, the heavier arrow has more kinetic energy and thus is more resilient to ******ation due to air friction. Arrow drop as a function of time would be identical but the lighter arrow would take more time to the target, causing it to impact lower.


Leonardo da Vinci disagrees. Why don't you take some weighted balls up into the Leaning Tower and disprove his theory?

Sent from my RCT6773W22B using Tapatalk


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## jonfinnell (Nov 26, 2008)

The theory of the heavier arrow getting further faster is based on the velocity being the same as the lighter arrow. But you would not be able to achieve this from shooting only one bow. The same bow shooting the heavier arrow would come out slower than the lighter arrow. 
And yes, also, they would absolutely still fall at the same gravity rate. 


Sent from my iPhone using Tapatalk


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## rs_hh (Oct 2, 2016)

Bowen Aero said:


> Actually, it doesn't.
> It drops from the launch plane. It is irrelevant what angle it is launched as it immediately begins to drop.


You're using dialectics. You stated the arrow drops as it leaves the string. Now you introduce the "launch plane" to salvage what ist left your erroneous theory. The "launch plane" may be directed vertically upwards assuming a vertical shot. The truth is that, in almost all target archery, the arrow actually gains height relative to ground level before it starts to drop (yeah, while hunting from a tree stand things will be different). An arrow that "drops as it leaves the string" would have to be shot horizontally or downward to do so. The fact that many of the online trajectory calculators assume a horizontal shot may be misleading in that respect.


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## nvcnvc (Jan 27, 2009)

That was Galilleo...



Bowen Aero said:


> Leonardo da Vinci disagrees. Why don't you take some weighted balls up into the Leaning Tower and disprove his theory?
> 
> Sent from my RCT6773W22B using Tapatalk


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## nvcnvc (Jan 27, 2009)

Luke Cool said:


> This is a true statement. But:
> Weight makes no difference in the acceleration due to gravity calculations.
> And the difference it makes to the foreword velocity calculations is not significant at reasonable distances.
> Friction is a function of size, aerodynamics, and air temperature pressure and humidity.
> Weight is a function of momentum.


With all due respect...
Weight is a function of mass and acceleration due to gravitational attraction, not momentum. An object that is stationary has weight but not momentum.


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## nvcnvc (Jan 27, 2009)

What he means by launch plane is that: If one shot an arrow at 10 degrees above the horizontal (launch angle=10 degrees), in the absence of gravity it would continue to travel at that angle forever. Because earth attracts every mass, an arrow launched at 10 degrees above the horizontal travels in a parabolic arc away from the straight line of 10 degrees. That happens immediately upon the arrow stops being in contact with the bow. That is the meaning of the phrase "the arrow starts dropping immediately due to gravity". It drops below the straight line that it would follow if gravity was not present. 



rs_hh said:


> You're using dialectics. You stated the arrow drops as it leaves the string. Now you introduce the "launch plane" to salvage what ist left your erroneous theory. The "launch plane" may be directed vertically upwards assuming a vertical shot. The truth is that, in almost all target archery, the arrow actually gains height relative to ground level before it starts to drop (yeah, while hunting from a tree stand things will be different). An arrow that "drops as it leaves the string" would have to be shot horizontally or downward to do so. The fact that many of the online trajectory calculators assume a horizontal shot may be misleading in that respect.


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## rs_hh (Oct 2, 2016)

Bowen Aero said:


> Leonardo da Vinci disagrees. Why don't you take some weighted balls up into the Leaning Tower and disprove his theory?


I was writing about two arrows leaving the bow with the same amount of kinetic energy. That ist the exact opposite of two balls of different weight being subject to free fall, during which the heavier ball picks up more KE than the light one (in fact, it also has more potential energy from being hauled up the tower than the lighter ball). In your example (which I repeat has nothing to do with what I wrote) the lighter ball, even if of the same density than the heavier, would impact later because its surface area to weight ratio, accounting for the amount of re_tard_ation (have to write it this way because the forum software will otherwise asterisk it out) due to air friction, is greater than that of the heavier ball.

How come that people with decades of experience in archery sometimes gladly throw the basic laws and relations of physics overboard when it involves their sport? I have heard the strangest statements from year-long archers as to arrow flight physics. Discussions would be more prolific if the scientific basics of the pastime we share were fully understood and accepted.


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## rs_hh (Oct 2, 2016)

Would he have mentioned the "launch plane" in his initial post as to arrow drop, I'd never have intervened. When making statements on physics without providing a reference system, the statement maker is to blame for inaccuracy and should not try others to. Especially when writing about "rise" and "drop" that normally are, beyond reasonable doubt, associated with earth surface level for reference unless stated otherwise.


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## rs_hh (Oct 2, 2016)

jonfinnell said:


> The theory of the heavier arrow getting further faster is based on the velocity being the same as the lighter arrow. But you would not be able to achieve this from shooting only one bow. The same bow shooting the heavier arrow would come out slower than the lighter arrow.


True, almost impossible to achieve using a real world bow shot normally (over-drawing with the heavier arrow might bring one close to it). The example of mine was just a constructed one to shed some light of the physical parameters in play when it comes to arrow flight.


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## rs_hh (Oct 2, 2016)

Oh, and before I forget, a small percentage of the KE at which the arrow leaves the bow is used up by the vanes/feathers (if attached to provide for arrow spin) when getting the arrow to rotate. Vanes with a strong offset or any other fletching aimed at significant arrow rotation will slow the arrow down relative to an arrow with straight fletching. Won't make a huge difference unless shooting large distances though.


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## rs_hh (Oct 2, 2016)

rs_hh said:


> I was writing about two arrows leaving the bow with the same amount of kinetic energy.


Sorry, that one was misleading. I was comparing arrows shot at the same initial velocity, same diameter but different in weight. Drop these down the leaning tower and the lighter arrow will most likely impact a tad later because the amount of KE absorbed by air friction over time is identical with both arrows but the heavier one retains (KE and) velocity better. However, the effect may be too tiny to observe. Galileo used balls of different weight AND different diameter which caused the lighter ball to have less air friction than the heavier, compensating for its lower KE. Had he used balls of the same diameter but different weight, the heavier one would have impacted somewhat earlier. Just imagine a match and a nail dropped from there at the same time and you get the picture. Or, reverting to horizontal travel, a baseball and a tennis ball pitched at the same velocity. Which one will pass the batter at higher speed and with a flatter trajectory? Transfer that to arrows and you see what I mean.


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## Bowen Aero (May 13, 2015)

rs_hh said:


> You're using dialectics. You stated the arrow drops as it leaves the string. Now you introduce the "launch plane" to salvage what ist left your erroneous theory. The "launch plane" may be directed vertically upwards assuming a vertical shot. The truth is that, in almost all target archery, the arrow actually gains height relative to ground level before it starts to drop (yeah, while hunting from a tree stand things will be different). An arrow that "drops as it leaves the string" would have to be shot horizontally or downward to do so. The fact that many of the online trajectory calculators assume a horizontal shot may be misleading in that respect.


I love you guys!

You will defend a flawed argument until the next ice age.

Still hurting from Hillary's loss?

Sent from my RCT6773W22B using Tapatalk


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## Bowen Aero (May 13, 2015)

nvcnvc said:


> With all due respect...
> Weight is a function of mass and acceleration due to gravitational attraction, not momentum. An object that is stationary has weight but not momentum.


Has mass.

Sent from my RCT6773W22B using Tapatalk


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## Luke Cool (Oct 16, 2015)

nvcnvc said:


> With all due respect...
> Weight is a function of mass and acceleration due to gravitational attraction, not momentum. An object that is stationary has weight but not momentum.


In the context of the discussion at hand, heavier arrows carry speed and kinetic energy with greater efficiency because of the momentum of a greater mass due to its increased resistance to friction. Momentum and friction are separate entities. 
For there to be "acceleration due to gravity", planetary gravitational attraction must act on a free falling mass. The weight of the mass is irrelevant. Without friction (in a vacuum), a feather falls just as fast as a ball bearing. 
The elements being discussed are an arrow's reaction to gravity and forward velocity. The only Stationary object in this scenario is the target.


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## rs_hh (Oct 2, 2016)

Bowen Aero said:


> You will defend a flawed argument until the next ice age.
> 
> Still hurting from Hillary's loss?


Yeah, I'd rather elaborate on and defend an argument I believe is right than using none at all and dragging things down to a personal level. YMMV.

Oh, and while I loved seeing Hillary lose, I'd rather see our Lady-in-chief resign. I'm from Germany and Mrs. Merkel has already done worse to my country than Hillary would ever have been capable of as to yours.


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## Luke Cool (Oct 16, 2015)




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## Luke Cool (Oct 16, 2015)

Bowen Aero said:


> I love you guys!
> You will defend a flawed argument until the next ice age.


No argument, this is reality.
Let's look at the rise before it falls thing.
Your looking at it from the wrong perspective, it is an ark, pure and simple.
If you have a laser screwed in where the arrow's tip should be. Where its light hits the target is the top of the ark.
Where the arrow hits the target when released is the bottom and the end of the ark. 
The difference between the two points is the arrow's acceleration due to gravity.

Now for the "heavier arrows carry speed and kinetic energy better" thing.
The comparisons I've seen published are a heavy and a light arrow being shot from the same bow.
There is one good reason for the larger difference shown in their test.
To see why, dive into water from the side of a pool, then do so from a 100 foot bridge.
From the pool side the water is soft. From the bridge, the water is like concrete.
Air is the same. At extremely high velocities, air friction can heat the skin of a jet to a few thousand degrees.
But like the water, air fiction is progressive; the faster the arrow, the greater the amount of air friction.
As you can now see, the difference in the published weight test is for two reasons:
Greater momentum for the heavier arrow, and more friction on the lighter faster arrow.
In rs_hh test comparing different weighted arrows shot at the same initial velocity, 
the difference would be so small, it would be hard to measure. But the difference can be mathematically proven.

And lastly, the acceleration due to gravity vector, at 30 yards, only falls a few inches.
This downward velocity is so slow, that friction will have a negligible effect at that speed.
Air friction however does play a fair size part in decelerating an arrow's forward velocity.


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## rs_hh (Oct 2, 2016)

Luke Cool said:


> And lastly, the acceleration due to gravity vector, at 30 yards, only falls a few inches.
> This downward velocity is so slow, that friction will have a negligible effect at that speed.
> Air friction however does play a fair size part in decelerating an arrow's forward velocity.


Exactly. I was thinking about going into details on dividing arrow speed in horizontal and vertical vectors (which helps a lot in this case because both can be calculated on independently) but I felt it to be pointless. Shot with identical initial velocity (which practically means, NOT out of the same bow) the heavy arrow will end up at higher speed than the lighter one. Thus its time of flight will be shorter, causing a little less gravity drop compared to the lighter arrow. This has NOTHING repeat NOTHING to do with both arrows reacting differently to gravity (which of course they don't) but with the lighter arrow being subject to gravity drop for fractions of a second longer than the heavier one.


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## EcoRover (4 mo ago)

Bowen Aero said:


> Leonardo da Vinci disagrees. Why don't you take some weighted balls up into the Leaning Tower and disprove his theory? Sent from my RCT6773W22B using Tapatalk


 Ah, that was Galileo, not DaVinci.


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## Tolbnd (Feb 11, 2020)

EcoRover said:


> Ah, that was Galileo, not DaVinci.


The da Vinci and Gallileo thing was corrected in this thread 6 years ago. Don't necro, please, to up your post count. Especially a discussion with a lot of incomplete and erroneous statements that have many times over been addressed on archerytalk.


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## EcoRover (4 mo ago)

Meow. Nice welcome to the forum dude.


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## huteson2us2 (Jun 22, 2005)

rs_hh said:


> By the way, arrow weight plays a role not in arrow drop as such but in arrow drop in relation to horizontal arrow travel. A heavy arrow will impact higher than a light one (with same diameter) shot with the same initial velocity. Why? Because when shooting identical diameter at identical initial velocity, the heavier arrow has more kinetic energy and thus is more resilient to ******ation due to air friction. Arrow drop as a function of time would be identical but the lighter arrow would take more time to the target, causing it to impact lower.


This reminds me of the lady cop who told me that the cute guy that crashed into me was going the speed limit until he hit his brakes. Then his car gained a lot of speed because cars speed up when the brakes are slammed. Having a degree in physics couldn't convince her and I had to get a judge to tell her how stupid she was.

Heavy arrows do not drop less than light arrows and arrows do not rise when first shot. The reason you use the 50 yard pin at 3 yards is because the sight is higher than the arrow and it takes about 7 yards before the arrow and the sight matches. Shoot a light arrow at 30 yards and then shoot a heavier arrow with the same diameter at 30 yards using the same pin and bow. If the heavier arrow hits higher than the light arrow, I recommend that you go back and practice more.


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## reddogjack (Dec 7, 2016)

Mac2118 said:


> something like this:
> 
> Arrow Ballistics Calculator - Kinetic Energy, Drop, Momentum
> 
> ...



Thanks


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## Uniquename (Oct 19, 2021)

If anyone gets a chance Chronograph your field tip then do broadheads.
Do a ten shot average and you can see the difference in speed loss.
Some broadheads loose more then others, and downrange you will see the difference, between the small field tip and bigger diameter broadheads.


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## EcoRover (4 mo ago)

huteson2us2 said:


> This reminds me of the lady cop who told me that the cute guy that crashed into me was going the speed limit until he hit his brakes. Then his car gained a lot of speed because cars speed up when the brakes are slammed. Having a degree in physics couldn't convince her and I had to get a judge to tell her how stupid she was.
> 
> Heavy arrows do not drop less than light arrows and arrows do not rise when first shot. The reason you use the 50 yard pin at 3 yards is because the sight is higher than the arrow and it takes about 7 yards before the arrow and the sight matches. Shoot a light arrow at 30 yards and then shoot a heavier arrow with the same diameter at 30 yards using the same pin and bow. If the heavier arrow hits higher than the light arrow, I recommend that you go back and practice more.


Spot on: This is why flight arrows and long distance target arrows are lightweight. Heavy arrows are good for hunting because they absorb more energy from the bow and penetrate more deeply--but they sure aren't faster than a light arrow.


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## Lee_Wells (Apr 9, 2021)

Uniquename said:


> If anyone gets a chance Chronograph your field tip then do broadheads.
> Do a ten shot average and you can see the difference in speed loss.
> Some broadheads loose more then others, and downrange you will see the difference, between the small field tip and bigger diameter broadheads.


I can see the difference in points and mechanical heads at 20 and 30 heads are a bit lower I’d say 3 to 5 FPS


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## Tbonecpa (5 mo ago)

1738.8 x Distance x(Pin - distance)/(Velocity x Velocity) You have to make adjustments at close range due to the arrow starting out 3-4" below the pins but I have verified it past 20 yds. or so.


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