Moultrie Products
Uphill/downhill
Equipment
Contributors to this thread:
Razorrick 22-Apr-20
Medicinemann 22-Apr-20
Glunt@work 22-Apr-20
Ermine 22-Apr-20
greg simon 22-Apr-20
>>>---WW----> 22-Apr-20
Will 22-Apr-20
Grey Ghost 22-Apr-20
bigdog21 22-Apr-20
WapitiBob 22-Apr-20
Old School 22-Apr-20
JohnMC 22-Apr-20
Glunt@work 22-Apr-20
JL 22-Apr-20
GF 22-Apr-20
ahunter76 22-Apr-20
x-man 22-Apr-20
JL 22-Apr-20
x-man 22-Apr-20
IdyllwildArcher 22-Apr-20
Mild Bill 22-Apr-20
x-man 23-Apr-20
Old School 23-Apr-20
JL 23-Apr-20
Bou'bound 23-Apr-20
Grey Ghost 23-Apr-20
Old School 23-Apr-20
JL 23-Apr-20
Grey Ghost 23-Apr-20
Old School 23-Apr-20
greenmountain 23-Apr-20
Matt 23-Apr-20
Medicinemann 23-Apr-20
x-man 24-Apr-20
APauls 24-Apr-20
Kurt 24-Apr-20
GF 24-Apr-20
APauls 24-Apr-20
Mild Bill 24-Apr-20
GF 24-Apr-20
Cheesehead Mike 25-Apr-20
x-man 25-Apr-20
Grey Ghost 25-Apr-20
WapitiBob 25-Apr-20
GF 25-Apr-20
Grey Ghost 25-Apr-20
GF 25-Apr-20
Ermine 25-Apr-20
GF 25-Apr-20
Pop-r 25-Apr-20
WapitiBob 25-Apr-20
GF 25-Apr-20
Mild Bill 25-Apr-20
Buffalo1 25-Apr-20
Mild Bill 25-Apr-20
GF 25-Apr-20
x-man 26-Apr-20
JL 26-Apr-20
Mild Bill 26-Apr-20
x-man 26-Apr-20
Mild Bill 29-Apr-20
x-man 29-Apr-20
wytex 29-Apr-20
GF 29-Apr-20
Mild Bill 03-May-20
GF 04-May-20
x-man 04-May-20
GF 04-May-20
x-man 04-May-20
Mild Bill 04-May-20
x-man 05-May-20
x-man 05-May-20
Mild Bill 05-May-20
x-man 06-May-20
From: Razorrick
22-Apr-20
If you can’t practice uphill or downhill shots, what general adjustments are made to what the rangefinder says. Is there a rule of thumb for yardage adjustments. Thanks

From: Medicinemann
22-Apr-20
on a 30 degree angle, multiply the rangefinder distance by 0.9.... on a 45 degree angle, multiply the rangefinder distance by 0.7.... on a 60 degree angle, multiply the rangefinder distance by 0.5

From: Glunt@work
22-Apr-20
That's spot on advise

From: Ermine
22-Apr-20
I use a good angle compensated rangefinder. But with that said I would practice the shot

From: greg simon
22-Apr-20
Use an angle compensating rangefinder and hold for ranged distance. Less math for me which is a good thing.

22-Apr-20
Do a google search for (cut chart) You can copy it off and tape it to your bow.

From: Will
22-Apr-20
Couldnt one just remember to aim low shooting down, etc? I'm thinking that's my tree stand eastern guy bias speaking with shots sub 20 most of the time. I imagine a 40-60yd shoot up a steep hill on the ground would be tougher to estimate...

From: Grey Ghost
22-Apr-20
In simple terms, up and downhill shots will always shoot shorter than the actual ranged distance. How much shorter depends on the angle. The best practice is practice.

Matt

From: bigdog21
22-Apr-20
old rule of thumb subtract 5yds from what you think it is has aways worked. if in timber just range the tree he is by. level with you and sub. 5yds

From: WapitiBob
22-Apr-20
Use cosine of the angle. Angle comp rangefinders can be good (cosine) or really bad (ballistics solution) depending on angle and distance.

From: Old School
22-Apr-20
If you’re shooting downhill and don’t have a angle compensating range finder - range the elk (say it’s 25 yards) then range a tree close by the elk - at 25 yards. Come up that tree to your elevation and range the tree - that’s how far away your elk is for shooting purposes.

From: JohnMC
22-Apr-20
I'll stick to my angle compensating rangefinder. I can't imagine trying to figure the angle, then distance, then do the math. I know a small angle is not near the difference you would think unless is a steep angle.

From: Glunt@work
22-Apr-20
Simple method is if it's a decent angle but not past 45, take 10% off. Shallow angles, just fudge a hair low and steep angles really need to be practiced.

From: JL
22-Apr-20
Pendulum sight??

From: GF
22-Apr-20
+1 for practice.

I never thought about it; just shoot.

From: ahunter76
22-Apr-20
Thank God for over 60 years of shooting 28 target field course's on every kind of terrain you can imagine. I have a range finder now but I guess all that up/down & around field courses has burned a high/low calibrator in my brain. That being said, my home ground shots are under 25 yds.. Nothing beats practice & knowing how your tackle performs.

From: x-man
22-Apr-20
"Pendulum sight??"

I put that in the same category as the cough suppressor, skunk scent cover scent and the deerview mirror.

From: JL
22-Apr-20
^Have you ever used one? I tried and didn't care for it. However I had some buds who swear by it.

From: x-man
22-Apr-20
It was invented by a guy who had poor form and dropped his arm rather than bending at the waist. The physics behind it doesn't work.

22-Apr-20
At 25 yards, it doesn't really matter. You really need to be getting out beyond 40 yards and a pretty steep angle to have it make enough of a difference to need to adjust your shot.

From: Mild Bill
22-Apr-20
It's the same as shooting from a tree stand: use the pin for the horizontal distance.

This said, the downhill shot will hit a tad higher than the uphill shot due to the effect of gravity, but shooting for the horizontal distance is a good rule of thumb.

From: x-man
23-Apr-20
Gravity is gravity. Doesn't matter uphill or downhill. The arrow will drop the exact same amount over the horizontal distance.

Unless you're hunting extreme angles in the mountains, it's a moot point. Form is much more important than the few yards of adjustment needed. Mountain shots have other variables to consider such as wind currents that affect the arrow as much or more.

From: Old School
23-Apr-20
My sons and I walked up on a spike a couple years ago while bowhunting. He was unaware of us but up above us on a pretty steep slope standing broadside in spotty timber. I ranged him at 70 yards and immediately thought “no shot, that’s too far”. Granted I practice out to 100 yards and am accurate at 80 putting arrows consistently in the kill zone. After a couple of minutes, he walked away and it was only then that I thought, with that steep angle, he was closer than 70 yards. I found a base of a tree 70 yards below me and ranged it at the same horizontal level I was at and the rangefinder read 50 yards. Angle compensating rangefinder would have fixed my issue or if I would’ve thought a little quicker. In my mind 60 was my max shot so when I saw 70 on the rangefinder I just didn’t even consider taking the shot.

From: JL
23-Apr-20
For folks like myself who need pictures to help understand a subject, this is a fantastic tutorial for shooting angles and how to figure the horizontal distance. Actual distance and horizontal distance are different unless you're shooting straight up/down. Horizontal distance will always be less than actual distance unless shooting straight up/down. The instructor is talking rifle shooting and touches on archery at the end but the math is the same. I treestand hunt and rarely, if ever, bow hunt from the ground. I do not have a consistent form when shooting. I might be standing or leaning or I might be sitting when I shoot or I have to turn around in the stand to shoot. You see alot of folks shoot over or spine a stationary animal because they sight in on the ground and didn't have the same form up in the stand for whatever reason. To resolve my lack of consistent form, I sight in and practice from the height I set my stands at....usually 21'. I put one foot markings on my stick ladder so I can hang my stand at or near the same height each time to get standardization between practice shots and actual shots. This solved my early problem of hitting high or shooting over the animal and I didn't have to worry about my form so much. Of course folks have different ways of doing things to solve problems...this was my way. If I were to do a western hunt or blind hunt, I would adjust and practice for that.

From: Bou'bound
23-Apr-20
Old school It was still 70 yard shot. That did not change. How you aimed for it changed but not the difficulty of placing an arrow where you wanted it to go after spending 70 yards in the air

From: Grey Ghost
23-Apr-20
Bou is correct, an angled 70 yard shot is still as difficult as a horizontal 70 yard shot, perhaps more difficult due to form issues, regardless of what pin you use.

Matt

From: Old School
23-Apr-20
No doubt he was 70 yards, that’s what the rangefinder indicated. With the steep angle, I would’ve been using my 50 yard pin though. That was my only point.

From: JL
23-Apr-20
If you watch the video, the instructor will easily explain what your horizontal distance was.....that is the distance you would have shot for instead of 70 yards at an angle. It's pretty easily actually. I believe some of the newer rangefinders will tell you what the horizontal distance is.

From: Grey Ghost
23-Apr-20
Old School, you said your self-imposed limit was 60 yards, and that you would have considered taking the shot if you had known you would've been using your 50 yard pin. Our point is, that angled 70 yard shot was still outside your limit, regardless of what pin you would have used. The target doesn't get any larger, just because it's at a steep angle. The margin for error is the same.

You made the right decision, IMO.

Matt

From: Old School
23-Apr-20
GG - you're right, I probably made the correct decision. Who knows though since I didn't take it. I was regularly placing hunting arrows in the kill zone at 80 at home - but that's a stationary target, hence my reason for my self imposed 60 yard limit on game. It does give me something to think about though - is it the true distance that should limit your shot or the angle compensated? If I was using an angle compensating range finder, it would have read 50 and I would have taken the shot without hesitation not even thinking about the whole "its still really 70 air yards".

This year it may be a moot point though. My son is talking about taking his Fedora recurve and I'll take my Treadway longbow. If that's the case, our self imposed limit will be significantly under 60 and steep angles will probably have little impact on a 30 yard or under shot.

-Mitch

23-Apr-20
Hello Old School : I have taken a few shots in my lifetime I wish I hadn't . I have had a few I passed on and probably would have made a clean kill . I can't think of any of them I regretted not taking. Funny the excitement is there even if you don't take a shot you wonder about.

From: Matt
23-Apr-20
"Gravity is gravity. Doesn't matter uphill or downhill. The arrow will drop the exact same amount over the horizontal distance."

Is that the case though? Wouldn't an uphill shot decelerate faster than a downhill shot due to gravity? I would only think that you would see that over longer distances, but still a thing.

From: Medicinemann
23-Apr-20
Matt, I used to wonder about that....and for a rifle, it may have merit.....but for archery gear, it is a moot point.

From: x-man
24-Apr-20
Yes Matt, that is the case. An object doesn't know or care if it is going at a 45 degree angle up or down. If it(hypothetical object) goes 100' after being shot at at parallel plane at a zero degree angle before hitting the ground from 5' off the ground,... then it would always fall 5' vertically after 100' traveled horizontally. (assuming no outside influences such as wind or pressure)

So,... The only exception would be a nearly straight up or straight down. If the velocity is suspended to a point below the terminal velocity of said object before this object travels 100' horizontally for example.

From: APauls
24-Apr-20
Imagine being a flatlander heading west with a single pin sight and non angle-compensating rf.

OH HERE COMES A BULL!! Where's he going to pop out? Oh about there, what's the angle of that hill? OK I'm gonna guess 45 degrees...range it, 42 yards, ok so do the math..carry the one...ok so it's like 39 yards ok, let me just move my slider up to 39 on the sight tape... ok done. Look up. Where did he go?

As opposed to an angle comp RF and multi-pin sight. Where's he gonna come out? Range. Shoot.

From: Kurt
24-Apr-20
Adam P gets it as per the angle compensation and the multi pin sight! But he screwed his math up in the excitement of even thinking about the shot at the bull....he should have held for 30 yds....39 would have sailed right over the top if he even would have had the time to shoot!

From: GF
24-Apr-20
“ is it the true distance that should limit your shot or the angle compensated?”

The angle has nothing to do with anything except vertical departure from line of sight..

Maybe this is less true for you compound guys/sight-shooters, but as a rule, groups tend to open up over distance due to form errors and windage. Form error over distance is linear; if you were off by 10 inches at 50 yards, most likely you’ll be off by 20 inches at 100. Windage, on the other hand… That goes up exponentially, because your projectile is accelerating laterally, So whatever the drift is at 100 yards will be more than 2X what you saw at 50; it’s not equal to the difference in drop between 50 and 100, but the same principle applies - it’s WAY more.

So using your 50 yard pin may put you spot on at 70 once the drop has been compensated for, but that arrow still has to travel 70 yards, which is 40% farther… Which makes a hell of a big big difference when you’re dealing with nerves, oxygen deprivation, crosswinds and most of all, of course, animals that move while the arrow is in transit.

The only way that I was ever able to get my thinking straight on the vertical drop thing is this: as soon as you stop holding your arrow up, it starts to fall, accelerating at 1G. So it doesn’t matter what direction you launch it; after X milliseconds in flight, it will have fallen off of the original trajectory by a certain amount. When the original trajectory is perfectly horizontal, it’s easiest to visualize it as a vector.

So it’s like a weight on a string out towards the end of a long pole; the length of the string is the vertical drop, and when the pole is horizontal, the weight is at its maximum distance from the pole.

When you raise or lower the end of the pole, though, the weight actually gets closer to the axis of the pole - it’s the same distance at the point where it’s tied on, but the absolute distance between the weight and the pole will continue to decrease as you change the angle of the pole; once the pole hits just about vertical, the weight will bang right into it.

If you launch an arrow vertically, it will never fall off of that initial line; it’ll just keep going Up until the string reaches the ground.

And FWIW... at 40 yards on a steep hillside, my arrow will be in the target before Adam can get his rangefinder out of his pocket.

From: APauls
24-Apr-20
Just I’m guessing you don’t need to carry the 1 either ;) I wasn’t actually doing any math, because I don’t believe in doing math at the time of a shot lol

GF if you’re going to get into a contest with what I wrote you’d realize I ranged a spot before the bull got out of the timber. Therefore we’d be side by side at full draw when the bull comes out of the timber, at which point we both release. Besides my instinctive range guessing abilities I’d also have an exact range to go off of, where you don’t. Now if I remember, according to the absurdity of a lot of your comments, that you are a trad shooter, unfortunately for you I’d be sticking that bull and he’d prob take a big lunge before your arrow even gets there getting deep penetration through the thin air he once inhabited ;) Especially 40 yards. That would be quite the arc you’d be lobbing.

I’m also curious as to how you think the average flat lander can acquire this wonderful instinctive angle adjusted range guessing ability that you have - seeing as that is what the OP was asking about. Without any hills near home.

From: Mild Bill
24-Apr-20
x-man and Matt: When shooting the same distance, the arrow falls more when shooting uphill than downhill. The reason is that arrow velocity is faster downhill with gravity acting along the arrow's path. When gravity acts against the arrow's path (uphill shots), the time of flight is longer and the drop is more.

From: GF
24-Apr-20
Thin skin much?

I’ve lived a lot of places; have yet to find one without any steep hills if you just get out and look. Not sheep-steep, necessarily, but bluff country isn't too bad.

Funny, though... you keep your shots within normal bowhunting ranges and most of this stuff goes away ;)

25-Apr-20
Mild Bill, I'm not sure if physics supports your theory...

From: x-man
25-Apr-20
I know physics doesn't support his theory... at least not in bow hunting situations.

Like I said earlier though, there is an angle steep enough that allows the velocity to decelerate below the terminal velocity of the arrow. At that point gravity will keep carrying the downhill arrow, and stop & turn around the uphill arrow. I seriously doubt anyone has ever attempted a shot that steep at an animal that was far enough away that the arrow slowed to that point before reaching the target. That would be a shot of at least 100-150 yards line of sight with a horizontal distance of less that 10.

From: Grey Ghost
25-Apr-20
The force of gravity will have the same affect on an arrows trajectory, regardless of whether it's uphill or downhill within the effective range of a bow.

It's an easy test to do with an angle compensating range finder. Just place a target on a steep hill. Physically measure and a mark a spot that is 30 yards uphill and 30 yards downhill from the target, then use your angle compensating range finder to tell you how far to shoot. You will find that the rangefinder will give you the same reading at both spots.

Matt

25-Apr-20
Horizontal and vertical motion have no relationship with respect to gravity, correct? The compensating range finders are quickly calculating horizontal distance via the angle and linear distance to Target. Only horizontal distance need be considered.

From: WapitiBob
25-Apr-20
When shooting a bow at little targets, the guys that win will tell you to use cosine for most shots, but at some point that quits working and depending on distance and slope, you need to add yardage back on. Also, horizontal distance doesn't work for close steep angle shots. For most hunting situations an angle comp rangefinder will work fine but it's not as simple as cosine or horizontal distance for all circumstances. Gillingham has talked about it on a podcast with snyder, noting you get schooled the first time shooting in Europe where everything is steep. A friend of mine who one a European event said the same thing.

From: GF
25-Apr-20
I guess I’ll switch to cosine for squirrels, then....

From: Grey Ghost
25-Apr-20
It's simple geometry, really. It's call the Pythagorean Theorem. A-squared + B-squared = C-squared. The angle compensating range finder does the math for you, and it's the same for uphill or downhill angles.

Matt

From: GF
25-Apr-20
Yup. It ain’t rocket surgery...

From: Ermine
25-Apr-20

Ermine's embedded Photo
Ermine's embedded Photo
Regardless. I would practice. You would be surprised how off “angle compensating rangefinders” can be. If also suggest shooting in your own cut chart. Real life Conditions and equipment can be different than brain storming on paper. Just my experience

From: GF
25-Apr-20
Now, that right there.... THAT is Sheep Steep!

You don’t make a shot like that without having to think about it unless you’ve had a chance to think about it....

From: Pop-r
25-Apr-20
It's apparent some people haven't a clue what their arrow is going to do.

From: WapitiBob
25-Apr-20
When experience comes from the back yard it’s to be expected.

From: GF
25-Apr-20
Kinda depends on the size of the back yard, I suppose....

I’ve been pretty blessed that way.

From: Mild Bill
25-Apr-20

Mild Bill's embedded Photo
Uphill Downhill Shots Calculations
Mild Bill's embedded Photo
Uphill Downhill Shots Calculations
Physics? Who needs physics?

Well, everyone. Along with math. This gives us insight into the real world. In our case, it makes us better hunters and archers.

I had calculated years ago the effect of gravity of shots from tree stands since this is my usual mode of hunting. I concluded that using the horizontal distance to the target was a good rule of thumb. Not exact to the third decimal point, but good enough in hunting situations.

I had never really calculated the effect of gravity on uphill shots, but had a sense (more than a theory after my tree stand calculations) that uphill shots would fall more than downhill shots of the same distance. This was the basis of my first post.

This thread caused me to add the uphill analysis to my downhill calculation. The results are attached.

Here’s a real-world example: 290 ft/sec initial arrow speed, 30 degree slope, 40 yard (120 ft) shot.

Putting these values into equation 4 for an uphill shot gives an arrow flight time of 0.435 seconds. (Sorry for the three decimal places; that’s how I am.)

Using equation 6 for a downhill shot yields a flight time of 0.396 seconds.

It’s interesting to note that a 40 yard shot on flat ground would take 0.414 seconds, falling between the above two values as it should.

So how much difference in impact point is expected with a time differential of 0.039 seconds between uphill and downhill shots? Well, if this time difference existed on a level ground shot, the impact point difference would be over 6 inches.

So physics has been used to help answer this uphill/downhill question. Now someone needs to fling some arrows up and down a slope using the same point of aim to determine how air resistance, etc. really affects where the arrow impacts.

Since my physics is better than my shooting, I’ll leave it to others to do the testing. But I’ll be very interested in the results.

Bill

From: Buffalo1
25-Apr-20
How many people have time to work out a calculation, when a split second shot is on the line. Use a rangefinder with a built-in angle compensator and shoot !

In golf, more club is required for an upward hill shot and less club downhill shot- its about gravity.

From: Mild Bill
25-Apr-20
Of course a rangefinder is the best way to go. However, if you only have a linear rangefinder like I do, it's helpful to know that downhill shots, like from a tree stand, can be approximated for hunting accuracy by shooting the horizontal distance.

By the way, needing more club for uphill shots in golf and less club for downhill shots is not about gravity. It's because the arc of the ball hits the hill sooner (less distance) for uphill shots and later (more distance) for downhill shots.

From: GF
25-Apr-20
I’m compulsively analytical myself.... just not that great with the math....

And when it comes to the Field..

But all we’re trying to do here is plunk a melon.

From: x-man
26-Apr-20
Bill, If I made up my own equations , I could reach any conclusion I want as well. The gravity is constant. It's the same equation for both uphill and downhill until the arrow slows below terminal velocity. I really don't want to repeat myself a third time so I won't.

From: JL
26-Apr-20
I suggest watching the video above. If you can judge the horizontal distance up hill, flat and down hill....you got it figured out.

From: Mild Bill
26-Apr-20
These are not made up equations, x-man. They have been known for ages. Check this out: https://physics.info/motion-equations/

If you really don't understand physics, it's okay to say so.

From: x-man
26-Apr-20
Bill, please go to that link and re-read the first paragraph. An arrow does not maintain constant velocity, let alone constant acceleration. Both uphill and downhill shots will fall the exact same amount until terminal velocity is reached during the deceleration process.

Let us all hope that no one is stupid enough to shoot at an animal that is far enough away so that the arrow slows to below terminal velocity before hitting the animal. No matter how short the horizontal distance may be.

From: Mild Bill
29-Apr-20
x-man, the equations of motion under constant acceleration hold when external forces like wind friction are assumed to be negligible. The equations are ideal case, but usually serve to get you in the ball park. Yes, the arrow slows in real life, but over the distances we'll be shooting let's assume it is constant. Otherwise an analytical solution becomes much more difficult. Beyond my capability, at least. The acceleration on the arrow, though, IS constant. This acceleration due to gravity. The acceleration always acts downward, no matter if the arrow is shot downhill or uphill. So, on an uphill shot, the acceleration on the arrow is downward, slowing it down. On the downhill shot, the acceleration increases the arrow speed. As you know, faster arrows drop less. This means that using the same pin for an equal distance shot, the downhill shot will hit higher than the uphill shot. In your example, terminal velocity would be reached by an arrow shot straight down and straight up in different ways. For the arrow shot straight down, gravity will accelerate it from the get-go and its speed will increase constantly until terminal velocity is reached. For the arrow shot straight up, gravity decelerates it initially until it reaches zero velocity. Then gravity will accelerate the arrow as it heads back toward the earth until it reaches terminal velocity, if it somehow can travel enough distance. I am pretty confident that the calculations that I posted are accurate and not "made up." If you see an error in them, please let me know. Someday, I plan to make a few uphill and downhill shots and prove, at least to myself, that what I posted is true. As I said before, my shooting ability may not be sufficient to be definitive. So if you (or anyone else) can do an experiment on, say, a 30 degree hill with 30 to 40 yard uphill and downhill shots, please post the results. If nothing else, it will give you good practice. Bill

From: x-man
29-Apr-20
A few corrections for you...

An arrow shot straight down will decelerate until it reaches terminal velocity, not accelerate. Most arrows have a terminal velocity of around 118 fps. The force of drag will slow every arrow immediately from the moment it leaves the string. It is not physically possible for it to "accelerate". An exception would be an arrow fired straight down from a kids toy bow that has a speed less than 118 fps.

Mythbusters did such an experiment about 10 years ago. Their results mirrored my suggestions. The test they did with ballistics in this manor were actually proven and published in the scientific journal as such. But, I can tell you won't believe it until you prove it yourself. Which is fine...

From: wytex
29-Apr-20
Wow, glad I shoot instinctive.

From: GF
29-Apr-20
“ On the downhill shot, the acceleration increases the arrow speed.”

Yeah, I got to go with X-Man on this one... looks like you mastered projectile motion, but never quite got around to Fluid Dynamics…

Your answer might well hold in a vacuum (if you could build one tall enough), but we mortals must shoot our arrows through this thick, goopy stuff called “air“. If you drop an arrow straight downward, gravity cannot accelerate it beyond its terminal velocity, and when coming right off of the string, it’s already going a hell of a lot faster than that. But we put these great big drag chutes on the backs of our shafts to make ‘em fly straight, and they (by causing boo-koo Drag) slam on the brakes immediately, and never more forcefully than when the arrow is moving the fastest.

So basically what you’re saying here is that we should ignore the effect of drag on the speed of an arrow as it is shot over level ground, but we should not ignore the effect of gravity on an arrow shot straight down even though the drag is exponentially higher (also pronounced greater force) at launch speed than it is at terminal velocity.... which, as you may recall, is the point at which the force of gravity (accelerating the arrow straight down) is in precise balance with the force of Drag, which had hitherto been accelerating the arrow straight back UP, and net acceleration on the arrow is reduced to zero.

But for all of that to make sense to you, you may have to review the definition of Acceleration.

From: Mild Bill
03-May-20
x-man and GF: Thanks for your input on terminal velocity. It never occurred to me that the arrow speed leaving the bow could be greater than terminal velocity.

I calculated the terminal velocity of a 465 grain, 0.31 inch diameter arrow, and an air density of 0.079 lbm/ft3. The velocity I got was 293 ft/sec. I am sure that it is happenstance that this is just above the 290 ft/sec initial arrow velocity used in my example. The result is dependent on the drag coefficient and air density, two variables that can sway the result either way. In any event, the initial arrow velocity and terminal velocity are very close. So an arrow could accelerate or decelerate to terminal velocity when shot straight down.

In other news, I went to an area that I hunt that has some pretty good hills. I hung my block target on trees about 37 yards apart, along the 25 degree slope. I took 5 shots down the hill and marked each shot. Then I moved the target to the uphill tree and did the same thing. The same arrow and the same point of aim was used for all shots.

As you can imagine, I expected to see a clear difference in the groupings with the downhill shots hitting higher. As it turned out, the uphill shots ended up an average of 0.4 inch higher.

Perplexed about this result, I searched the internet for information regarding uphill and downhill shots. Here’s a link for a 2009 Bowsite thread related to this subject. https://forums.bowsite.com/tf/bgforums/thread.cfm?threadid=366543&forum=2

Copied below are two posts from this 2009 thread. Déjà vu all over again.

From: Mild Bill 06-May-09

To those who asked the question about "Where did you get those figures?", the answer is particle physics. The equation for how far an object travels is:

d = (v x t) + (.5 x a x t x t)

where: d = distance, v = initial velocity, a = acceleration on the object, t = time This equation can be used to develop the following equation which I actually used in the example:

(v2 x v2) - (v1 x v1) = 2 x a x d

where: v2 = the velocity of the object after it travels a distance d, v1 = the initial velocity of the object, a = the acceleration acting on the object When shooting up hill and downhill, the acceleration is: a = g x sin(theta) where g is the acceleration due to gravity, 32.2 ft/sec/sec and theta is the angle of the shot. Note that "a" is negative for uphill shots and positive for downhill shots. So uphill shots slow down, downhill shots speed up. (How ironic!)

So this is how it's done. To those of you who questioned the numbers yesterday, congratulations. I made a math error. The corrected values for the velocity of the arrow after 30 yard shot from a 280 fps bow on a 20 degree incline are:

uphill: 277 fps downhill: 283 fps This is my answer and I'm sticking to it. Hunt high, stay late, Bill

From: x-man 06-May-09 "uphill: 277 fps downhill: 283 fps " That's more like it. :)

Another post in the old thread gave an interesting archery ballistics table: http://www.peteward.com/ The chart is under Balistic Calc near the bottom of the left-hand side. I entered the following parameters for my arrows: fletching length = 2”; fletching height = 0.5”; shaft dia. = 0.31”; shaft length = 28.5”; arrow speed (initial) = 290 fps; arrow weight = 465 grains.

The table generated from these input values displays information about the horizontally shot arrow. Assuming this data is accurate (because everything on the internet is accurate), the change in arrow velocity divided by the change in time can be used to approximate the arrow’s acceleration. Since the arrow is slowing down, it is actually deceleration.

For my arrow specs, the change in velocity was 3 fps or 2 fps for each 10 yard distance out to 100 yards. Using 3 fps gives the higher value of deceleration as 28.85 ft/sec2.

Using Newton’s Second Law, the 465 grain arrow at a deceleration of 28.85 ft/sec2 indicates that the drag force on the arrow due to air resistance is 0.06 lb. This was calculated for a horizontally shot arrow, but it also applies to arrows shot uphill/downhill through “thick, goopy stuff called air.” The retarding force due to air resistance always acts in the opposite direction that the arrow is traveling.

When I did the terminal velocity analysis mentioned at the beginning of this post, the equation: Fdrag = 0.5 x C x D x A x V x V was used. C is the drag coefficient, D is the air density, A is the arrow cross-sectional area, and V is the arrow velocity. The resulting drag force due to air resistance from this equation is 0.0649 lb. This is similar to the rough estimate of 0.06 lb extracted from the table. This probably only means that whoever made this table used the same drag force equation that I did. So we are either both wrong or both right.

So, here are my summary conclusions after all these calculations and my shooting experiment.

1. Downhill shots will hit slightly higher that uphill shots, but the difference is not appreciable over bowhunting distances. I am just not good enough of a shot to prove this. Also, I need some third axis adjustment. 2. The drag force on my arrows due to air friction is on the order of 0.06 to 0.07 lb. This drag force can be neglected on analyses such as uphill/downhill shooting since only the relative difference between the different directions is of interest. The drag force will be the same in either direction, so it can be neglected from consideration. Just don’t expect the final numerical answer to be dead nuts accurate. Also, GF would be happier if he got those “great big drag chutes” off the back of his arrows and used some 2” Blazers. “Boo-koo” less drag. 3. Bows are now pretty fast and some can be expected to shoot faster than terminal arrow velocity. Who knew. 4. I thoroughly understand the definition of acceleration. It is true that my projectile motion ability is greater than my fluid dynamic skills, but only because I have used projectile motion more. Sometimes I need a little help from my friends to apply and interpret the results correctly, but I’ll stick with it until the analytical and empirical results agree. 5. It felt good to be in the woods and to shoot a few arrows after 5 months. Looking forward to September. 6. wytex may be on the right track.

Bill

From: GF
04-May-20
I could shoot field points with 2”’ fletchings, I suppose; I shoot bare shafts often enough! But shooting off of my fingers and a leather side plate, I like more fletching than that. Especially with a good-sized broadhead up front.

Gotta be honest, though - I suffered mightily through Trig and a semester of Calc, and it just wasn’t pretty... So I’m going to have to take your word for it on the calculations....

From: x-man
04-May-20
One quick note Bill. Your terminal velocity number for your arrow is not correct. You'll have to account for the drag imparted by the fletching. A bare shaft will indeed travel around the speed you indicated. Adding feathers slows it down considerably to the speed I posted above.

I used to be part of a Physics online forum, not unlike this one only for physics nerds. We did testing for this back in the mid 2000's. The fletched arrow used by the guy who did the test(he was testing terminal velocity of hundreds of items). was 117.???? so for this forum I rounded that up to 118. A far cry from the 293 you posted. I can only assume you were calculating a bare shaft to achieve that number.

Go to www.physicsforums.com and search terminal velocity. You might be able to dig up that article from the mid 2000's.

From: GF
04-May-20
Good info, Rob...

I knew his number struck me as much too high and now I know why - I read your other post! (I have always a read a LOT and have pretty good comprehension/retention, but I’m terrible for recall of authors & titles...)

Sounds like you’re gonna have to re-crunch those numbers, Bill....

But do let us know what you find out... I’m still pondering the potential of a nock to snap a little spin onto a shaft as it slides off o’ the serving...

From: x-man
04-May-20
In my best Mr. T voice:... "I pity the fool who argue archery physics wit me"

From: Mild Bill
04-May-20
Well, I am now registered on physicsforums.com. However, I wasn’t able to find anything related to the drag force on arrows.

However, I did find this site that addresses the drag force on arrows: http://thewretchedlongbow.com/wordpress/estimating-the-drag-co-efficient-of-a-wooden-arrow/ This deals with wooden arrows, feathers, and found the drag coefficient in a wind “tube” at 100 fps, but, hey, it sounds like something GF can relate to.

I used a drag force coefficient of 1.2 in my previous calculations. I thought that this included some type of fletching since the peterward.com link required entries for fletching length, height, and type. As you’ll recall, the estimated drag force from peterward.com was 0.06 lb. The actual drag force used in my calculations was higher at 0.0649 lb, as generated using a drag coefficient of 1.2.

From the wretchedlongbow.com link, it is seen that a 29” long bare shaft has a drag coefficient of 1.204. So, perhaps the 1.2 value I used initially was for a bare shaft. So, let’s jack the drag coefficient up to 1.9, the value given for 4” feather fletching. The terminal velocity for this case is 233 ft/sec, well above the 118 ft/sec value you recall, x-man.

Conversely, what drag coefficient is needed to result in a terminal velocity of 118 ft/sec? This is calculated to be 7.4. A drag coefficient of 7.4 seems to be way too high, unless you are talking about a flu-flu with a trailing parachute.

I’d hate to get on the bad side of Mr. T, but if the drag coefficient for my hunting arrows is less than 2, ain’t no way its terminal velocity is 118 ft/sec.

Bill

From: x-man
05-May-20

x-man's Link
I googled "terminal velocity of an arrow" and this came up.

From: x-man
05-May-20
One other clarification Bill. The 118 number was measured as an actual speed, not a calculated speed using a formula. These guys actually clocked the arrow in free-fall. They also did a bullet. It took some trial and error but, they got a 38 bullet to land in a small circle after being fired straight up in the salt flats. Measurement was taken by using a high speed camera. He commented on how difficult the arrow was to "clock" in relation to every other object he tested for terminal velocity.

And obviously not every arrow is going to be the exact same. By changing the angle of the fletching, one can create more or less drag. For example: I used to bowhunt for pheasants with a 3" bird wire and Flu-Flu arrows. I could easily catch those arrow with my bare hands as they fell straight down at what I can only guess as less than 50 fps. My FITA arrows with 1.25" low profile Diamond Vanes probably don't slow much at all compared to a bare shaft.

From: Mild Bill
05-May-20
That’s an interesting link, x-man. The program as it stands does not reflect normal arrow parameters, though.

For instance, line 11 of the first program shows an arrow mass of 0.019 kg = 293 grains. The arrow diameter is 0.0053 m = 0.2087”. Pretty skinny, light arrow.

Line 17 has the drag coefficient set to 2.7. From what I’ve seen, this drag coefficient seems to be high. In any case, running the program with these parameters gives the terminal velocity (as calculated by line 29) as 72.9791 m/sec = 236.8 ft/sec. (He carries even more places past the decimal point than I do!) Note that the equation in line 29 is the same one that I’ve been using to calculate the drag force.

The nice thing about this program is that the input parameters can be adjusted. To agree with my previous calculations, I changed the arrow diameter to 0.31” and the mass to 465 grains (converting these parameters to the metric parameters used in the program) and the program delivered a terminal velocity of 200.8 ft/sec. This is with a drag coefficient of 2.7.

As far as I can tell, the key factor in all this is getting a drag coefficient, C, that is accurate for the arrow in question at about the eventual terminal velocity. From everything I’ve been able to find online, it seems that reasonable values of C will result in a terminal velocity significantly greater than 118 ft/sec.

Well, I think that this thread has diverged enough from the original question for me to leave it here. But it has been fun. Like catching falling arrows.

Bill

From: x-man
06-May-20
Right, very fun! These are the threads that keep me coming to Bowsite. I enjoy a good discussion more than most. All in good fun of course. Healthy debates are the root of all knowledge. :)

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