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Local conditions, drag and distance

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willie:
I am at a bit of a disadvantage from Steve and Alan, in that I can only participate in a somewhat theoretical discussion about arrow flight, and have not actually been on the ground at a flight shoot to observe arrows in flight from a down range perspective. I hope you guys don't think that I am trying to put you "on the spot" when asking so many questions, as I know it is not easy to put observations into words.
But... when I read    from...     http://www.primitivearcher.com/smf/index.php/topic,61455.msg863183.html#msg863183

--- Quote --- In other words it is descending a bit nose up, causing drag. This drag slows the descent, keeping it in the air longer and giving it more time to travel a little farther
--- End quote ---
OK, I think maybe Alan could also have said "lift" but chooses to describe it as "a type of drag that keeps it in the air longer". Not worth quibbling about, really. as drag and lift are sometimes two sides of the same coin. But now Steve seems to imply that there is an "ideal" air density. Not too thick to slow the arrow too much, but thick enough to somehow keep it in the air longer.  But it's not "glide". My mind is clocking in some over time to get a grasp of how that can be.

 Once again, I am not finding fault with the observations of others, but I wish to ask more about this aspect of "beneficial drag". Having drag in the right places, such as feathers, seems to me, to be a "necessary evil" to be managed. Is there also an existence of another "useful drag", (for other than control), Perhaps an accepted concept in flight community discussions? Can I read more about it somewhere else? What are it's different attributes? Is it controversial or even discussed much?

curious
willie

Marc St Louis:
I tend to stay out of arrow discussions as it seems to me that there are too many variables to take into account to make a definitive conclusion.  That said I would be inclined to think that heavy moist air would be detrimental to distance shooting

joachimM:
I always like a good discussion. Takes me out of my comfort zone, and forces me to dig deeper. In the end I always feel I’ve learned something.

Is drag additive relative to air density? Increase air density by 10% and drag will increase by 10%.

In a world without friction and drag, an arrow would should a symmetrical, parabolic curve. The only force countering movement is gravity. With drag, however, the horizontal distance during the downward path is shorter than the upward horizontal distance, because drag slows the arrow down from the moment it leaves the bow.

Since drag is quadratically related to velocity (arrow speed), this asymmetry becomes more and more exaggerated with faster and faster launch speeds. Arrows being shot very fast will fly further, but will also fall out of the sky in a more vertical manner (landing at much more than 45° relative to the ground) since drag reduced the initial velocity more. I’m sure the experienced flight shooters have witnessed this.
Under exceptional circumstances, Alan’s theory about beneficial drag in a mildly rotating arrow might be valid (with a change in drag behavior due to different arrow movement through the air beyond the apex), but I don’t think when I shoot it matters a lot ;-). In general, the less drag, the more the arrow follows the drag-less path, and the further it will shoot. Drag that slows the descent  also slows down the horizontal speed. With no horizontal speed, the object falls vertically.

How did I calculate the distances? I didn’t do complex calculus. I modified the spreadsheet presented in the technical archery page I linked to. Through the spreadsheet I track the vertical distance, Y (column AC). The horizontal distance is read at the moment the value in column AC reaches zero again.
I didn’t have input for drag coefficients (which differ for each arrow). For the calculations this wasn’t necessary either: I just needed to see how an increase in drag of 10, 15 and 23 % influenced a regular shot. Still, I used Steve’s rule of thumb’s relation between 10 gpp arrow speed and distance: 170 fps will yield c. 200 yards (183 m), 205 fps will yield c. 300 yards (274 m). From this, you can calculate the expected drag coefficient. If you know initial arrow speed (chronograph) and distance, you can calculate drag.
If you then increase the drag coefficient by 10% (effect of 5°C versus 25°C), 15% (effect of altitude) or both (23.5%) you can track the max distance in the spreadsheet. This teaches me that for a typical 200 m shot, the effect of altitude or temperature isn’t negligible at all.

joachimM:

--- Quote from: Marc St Louis on December 11, 2017, 10:44:47 am ---I tend to stay out of arrow discussions as it seems to me that there are too many variables to take into account to make a definitive conclusion.  That said I would be inclined to think that heavy moist air would be detrimental to distance shooting

--- End quote ---

Actually, moist air is beneficial, as it reduces drag. Counter-intuitive, but it's neatly explained here https://fogmountaintennis.wordpress.com/2014/06/05/atmospheric/ (under the heading "humidity")

willie:
Joachim, nice read about the tennis ball. It covers a lot of the factors in an easy to understand way.

--- Quote ---Is drag additive relative to air density? Increase air density by 10% and drag will increase by 10%.
--- End quote ---
yes, at least the coefficients commonly used to define form drag are linear by definition. But is density linear to elevation and temperature change? I asked earlier because the scales used in the nomographs are not linear, they vary slightly from end to end. Density effects lessen as temps get higher, but increase as elevations goes up.

Your question made me ask myself "what factors affecting drag are not near so linear?" And attitude appears to me to be the biggest non linear player. Out of attitude flight increases turbulence, where drag coefficients can increase rapidly.

One question that keeps coming to mind, is that when considering an arrows total flight down range, different drag factors may have different importance as velocities vary. it's not quite like the simple momentum vs time of a trajectory in a vacuum. I often think we might be better served if we split the flight into a few different components.

1. Launch...    where acceleration is obtained from the bow, velocities are high and attitude induced drag "makes or breaks" the shot.

2. The turn at the apex...    where gravity causes a substantial change in flight direction and attitude and velocities are low.
     Is this where the "less drag that keeps the arrow from falling out if the sky" examination needs to comes in?

3. Decent.....    acceleration due to gravity along a new course with a new attitude and starting from a much lower velocity.

A few different problems, each with their own criteria?

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