**Contributors to this thread:**

Matt

I never thought about it; just shoot.

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

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.

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.

Matt

You made the right decision, IMO.

Matt

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

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.

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.

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.

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.

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.

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 ;)

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.

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

Matt

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

I’ve been pretty blessed that way.

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

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

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.

And when it comes to the Field..

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

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

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.

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...

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.

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

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....

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.

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...

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

x-man's Link

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.

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