Archer's paradox

[Dennis La Varenne]

To all,

Here are some YouTube links with slow motion videos showing the archer's paradox phenomenon.

http://www.youtube.com/watch?v=48R2ajWx ... re=related

http://www.youtube.com/watch?v=G1Kj6X_A ... re=related

http://www.youtube.com/watch?v=aNI9BG87 ... re=related

http://www.youtube.com/watch?v=WzWrcpzu ... re=related

[greybeard]

Hi Dennis,

I hope you don't mind me adding the following?

Archer’s Paradox.

The term archer's paradox refers to the flexing of an arrow shaft that occurs when it is shot from a non-centreshot bow. Coined by Robert P. Elmer in the 1930s, the archer's paradox centres around the idea that, in order to be accurate, an arrow must have the correct stiffness, or "spine", to flex and return back to the correct path as it leaves the bow.

The word paradox refers to the fact that in order to strike the center of the target, the arrow must be pointed slightly to its side.

Less powerful bows require arrows with more spine (literally, the ability of an arrow to curve - like a spine). Less powerful bows have less effect in deforming the arrow as it is accelerated from the bow and the arrow must be "easier" to flex around the riser of the bow before settling to its path.

Conversely, powerful bows need stiffer arrows, with less spine as the bow will have a much greater effect on the arrow as it is accelerated around the riser.

As the diagram shows, an arrow with too little spine for the bow will not flex and as the string comes closer to the bow stave, the arrow will be forced off to one side. Too much spine, or flexure, will result in the arrow deforming too much and being propelled off to the other side of the target.

In archery, compensation of the archer's paradox led to the invention of the Plunger button, also known as a pressure button or Berger button (after its inventor, Vic Berger).

Archers Paradox.jpg (25.79 KiB) Viewed 2168 times

Diagram of the archer's paradox, showing what happens when arrows are incorrectly spined.

http://en.wikipedia.org/wiki/Archer's_paradox

Daryl.

[Steven J]

Darryl, that's an interesting diagram. On my first interpretation, I always thought that the stiffer arrow would travel to the left of the target, and the more flexible arrow to the right of the target. On further analysis my error comes from referring to a stiffer arrow as having more spine and a more flexible arrow as having less spine, which is opposite to what you have written.

Thanks for the videos Dennis. I like the last one the best. I do wonder what we would see if a release aid was used. Is the paradox caused by the string rolling off the fingers? Would a timber arrow still paradox with a release aid due to to heterogeneous nature of the grain? I am pretty convinced that there is no paradox from a wooden crossbow bolt, but then it is easy on one's first introduction to archery to imagine an arrow from a bow flies as a straight shaft too.

Steve

[greybeard]

Steve,

The information/details came from Wikipedia.

Daryl.

[Dennis La Varenne]

Daryl writes -

I hope you don't mind me adding the following?

Go for it Daryl.

Steve writes -

On my first interpretation, I always thought that the stiffer arrow would travel to the left of the target, and the more flexible arrow to the right of the target.

I agree with Daryl's postulation re his pics. I have found that greatly underspined arrows in fact bounce off the arrowplate with a noticeable 'clack' and they bounce away from the arrowplate with a lot of visible wriggling. However, I haven't noticed the phenomenon of shooting so far around the bow using overspined arrows indicated with the right hand pic in my own shooting, possibly/probably because of my natural cant. My supposition is that I am shooting an arrow which is resting in a shallow 'V' rather than from a left facing 'L' (being right handed).

However, there may well be something of truth in the diagram. I was once told by John Clark (Ausbow) from his FITA days when he shot here in Victoria that it was known among FITA people that there was something in the region of 2kg lateral push from the arrow against the arrowplate at loose. If there is any truth in that, that may well explain the 'paradox' of the right-hand pic because the arrow at initial launch and before the rear of the arrow begins to flex to any degree actually pushes the bow away from the arrow somewhat so that the bow is actually pointing to the right by the time the arrow leaves the string.

This is pure speculation on my part of course.

Steve's referral to whether or not there is paradox in a crossbow bolt at loose may well have something to do with the way in which it lays on the stock when the crossbow is spanned. I may be completely wrong, but I once thought I could see a sort of 'lift' shortly after the bolt left my crossbow. I cannot prove anything, but it is something which I thought my eyes detected almost half-consciously, the way some shotgun shooters can see the semi-visible cloud of shot when they shoot.

If what I think I saw has any validity, then perhaps there is a 'paradox' effect resulting from the bolt bounces against and upwards from the stock in which the bolt then sort of porpoises away from the crossbow until it stabilises. It would be interesting to come across some high speed footage of a crossbow to see if their very short arrows are long enough to flex on launch.

Once again, if this crossbow effect is also true, that my explain why the lateral movement of arrows under paradox is far less obvious in a canted bow because of the way in which the arrow lies in a shallow 'V' to a greater or lesser degree depending upon the degree of cant.

In my early shooting days, I shot with a very heavy cant, and again, I thought that my arrows 'lifted' from the bow on loose. I thought that this is why I could always hold under the 'A' zone (6 o'clock hold - the only time I shot like this) on the long group 5 targets and hit them pretty regularly using a 50lb bow and 500+gn arrows from a 26 inch draw.

[GrahameA]

Morning Dennis.

I have found that greatly underspined arrows in fact bounce off the arrowplate with a noticeable 'clack'

The same effect will happen with stiff arrows. It not so much the arrows bouncing off the arrow plate but rather the tail of the arrow colliding with the riser as a result of the natural frequency being such that the tail of the shaft is not flexed away from the riser as it goes past it.

[Steven J]

My observations are similar re stiff and weak arrows. The difference I have is in the naming of the spines. Wikipedia names an arrow with a more spine a more flexible arrow, where as I always thought of more spine being a stiffer arrow. Time for a change in terminology?

In playing around looking for a well spinned arrow, I smeared lipstick on the sight window to look to see where the arrows were colliding. I was looking for a mark to be left on the arrow. It was only semi-successful. I then tried putting lipstick on the edge of the feather and seeing where the feathers touched the riser. A little tell tail smudge can be seen on the arrow shelf. The contact appeared to be no greater when shooting cock feather in or out.

Steve

[Dennis La Varenne]

Steven,

I am with you on the terminology thing. The Wiki interpretation is wrong, I am sure. More has always meant stiffer and I have never heard of more read of it being anything different. It seems to me that the writer seems to equate more spine with more flexing which is arsy-turvy.

I found out about the cock-feather in-vs-out thing many years ago when first informed that one 'had' to shoot with cock feather out because it would cause fish-tailing of the arrow in flight. Of course, being a newbie at the time, I accepted the handed down knowledge, but noticed that when I managed to drive the leading edge of a raised lower bow feather into the index finger of my bow-hand, that the distance from the scar to the arrow plate was 5/8 inch out from the arrow plate. I then deduced that even if the cock feather was inwards it would barely touch the arrow plate if at all.

Then, I simply went out to my backyard range and put a dozen arrows into my backquiver and shot them as they came to hand without looking at the orientation of the feathers as I nocked them. They shot into a nice group anyway. I then proceeded to shoot them deliberately with cock feather in and they still shot a nice tight group where I was looking. I repeated the sequence with cock feather out with the same result.

Conclusion: Cock feather orientation didn't matter a whit.

[Stickbow Hunter]

The Wiki interpretation is wrong, I am sure.

From my understanding that is not an unusual thing Dennis and I most certainly don't trust what Wiki has to say on many subjects as has also been pointed out by others.

Conclusion: Cock feather orientation didn't matter a whit.

In the context of what you are discussing here I would agree; however if shooting woods one should always keep in mind the direction of the rift and reed of the shaft. I have also found that some woods will give different spine readings when placed opposite on the spining jig so the arra will only shoot best when it is made taking that into account. In other words there is only one correct way to make a wood arra taking into account spine stiffness and the rift and reed and with that sorted you then fletch your arra with the cock feather in or out as you choose.

Jeff

[Steven J]

Jeff,

I agree on the grain issue in woods. One of the students in the school archery club had an arrow break as it was shot and drove it through his hand. Fortunately for me it happened out of school and thus I avoided the paperwork. It was a terrible injury. I am not sure if grain had anything to do with the lads injury, but if aligning the grain correctly can help to lessen or remove the possibility of similar injury that is advice well heeded.

Typically I find the grain run-out on cedar shafts to be inconsequential for safety, but the spine with the grain and perpendicular to the grain will always be different. The hardwood shafts I have used seemed to have more of a grain run-out problem.

Steve