Local conditions, drag and distance

[joachimM]

I did quite some flight exercises lately, and was rather appaled by my results.
Bow-arrow combinations that gave me OK results last summer, yielded absolutely awful distances the past few days.

It has been awful weather, however. Lot of side wind, which increases drag quite a bit.
But still, I started to look for variables that could affect flight path, especially how local environmental conditions affect drag.

I knew altitude had and effect, but had no idea how large that effect was. The Bonneville range is at 1286 m asl. The air density at this altitude is about 15% lower than at sea level, which reduces drag by 15%. Say you shoot an arrow at the Bonneville flats and it flies 205 m (supposing a broadhead), it would fly some 8 m shorter at sea level.

Next, there is temperature: the higher the temperature, the less drag there is. At 25°C, there is c. 10% less drag than at 5°C (my current temperature).
Summer versus winter temperature alone would reduce my distance by c. 6 m.

Combining temperature and altitude, a flight shot of 205 m at the Bonneville range at 25°C versus at my place at 5°C would make a difference between 205 and 192 m. 

That's rather considerable. And it makes me more comfortable not closing in on the 300 yard mark in flight with flight arrows yet 


Sources:
https://fogmountaintennis.wordpress.com/2014/06/05/atmospheric/
https://sites.google.com/site/technicalarchery/technical-discussions-1/trajectory



 

[Badger]

  I don't think it is that simple. You have less drag going into the direction of the arrow but you also have less drag that keeps the arrow from falling out if the sky downward. Cooler moist air tend to give better results that hot dry air for instance.

[joachimM]

At high temperatures, moisture reduces drag, indeed. Bur at low temperatures the effect is much smaller and close to negligible. See attached graph, from the tennis paper.

[willie]

Joachim

I wonder if the combined effects are worse than you estimate?  Not all the corrections you cite are linear, (and I do not presume that your calculations/numbers are), but when combining factors to estimate drag, are the results simply additive?

https://www.faasafety.gov/files/events/NM/NM09/2013/NM0951144/Density_Altitude.pdf

the pdf has a nomograph that you might find interesting for comparision .

I realize not walking as far as hoped to get your arrow, can be disappointing, but not near as bad as failing to clear the tree at the end of the runway. 

but you also have less drag that keeps the arrow from falling out if the sky

Steve, are you saying arrows might "glide" better with higher air density?


Edit: it is not exactly clear in the FAA publication if the displayed nomograph is adjusted for engine performance reductions.
this interactive nomograph might be more fun to play with.       https://www.takeofflanding.com/

[Badger]

  Not necessarily glide but it seems to equal out advantages and disadvantages. Arrows are cutting through the air forward but also falling. Thin air is nice to cut through but it also doesn't give the good drag you want to keep the arrow from falling as fast.

[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

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

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]

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

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.

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

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?

[Badger]

   I notice that one of the problems we have is dealing with the lighter arrows around 200 grains or less. They come of the bow very fast but the slightest sideways motion kills the speed right out of the bow. Arrows around 300 grains from 50# bows can pretty regular hit the 300 mark but not good enough for records. I am moving my arrow weight up to about 250 or 260 this next year and see how it does.

[willie]

Steve,

what is the spine of the 200 and 300 you are comparing?

[Badger]

   I don't measure the spine on 200 rain arrows, I just test with my finger, with no point weight it doesn't take much, It would be cool to video tape in slow motion just to check it. On a tapered arrow I think the dynamic spine point is well behind center. If I were to guess I would say about 20# spine some as high as 35#

[willie]

  I don't measure the spine on 200 rain arrows, I just test with my finger

If the lighter arrows are having trouble, wouldn't you want to have an objective way to test stiffness? I realize that stiffness measured at the center of a tapered arrow doesn't tell the whole story, but it is always part of the story. What am I missing here?

[Badger]

  I measure on occasion. I feel like there are so many factors at work and so little available testing time or space, so many arrow style variations that I am better off just working intuitively basing everything on small samplings and then going in the right direction. I have had a steady improvement in arrows. I feel like if I could practice 1 time per month it would speed up my progress by dozens of years. 

    I am starting to think longer draws will pay off in primitive flight as well. Use the extra stored energy of a full 28" draw to beef up arrow weight.