What Factors Affect (DYNAMIC) Arrow Spine?
When an arrow spine is at rest, we refer to its stiffness characteristics as static spine.  But when that same arrow is in motion, its stiffness is a matter of dynamic spine. An arrow being shot from a bow is considered to be the “dynamic” spine of the arrow because several factors are affecting the spine. Unless your arrow shaft breaks or is altered, it's static spine remains the same.  But your arrow's dynamic spine can change dramatically.  The real arrow performance relies on the arrow's dynamic spine.  The dynamic spine is how the arrow actually bends when shot - and there are many factors which affect the dynamic spine.  The static spine of the shaft is only part of the equation.  When you shoot an arrow, the explosive force of the bow compresses the shaft and the shaft momentarily bends under the strain.  Unlike the unwavering characteristics of an arrow's static spine, the dynamic spine of two identical arrows, shot from two different bows of varying output, could be drastically different.  How is that possible?  If your arrow has a perfect amount of dynamic spine when shot from 70# bow - it's stiffness is just right - not too limber - not too stiff.  BUT, if you take that same arrow and shoot it out of your son's 40# youth bow, it will be dramatically too stiff.  The arrow will have too much dynamic spine.  Likewise, if you shot your son's arrows in your 70# bow, it's likely the arrows would be dramatically too limber - not enough dynamic spine.  Determining a proper dynamic spine is a bit complex and requires examination of several contributing factors. 

There are four main things that affect the arrow spine:

1. The stiffness of the actual shaft material (Static Spine)

2. The length of the shaft

3. The tip weight that will be used

4. The type of bow shooting the arrow
 
THE STIFFNESS –
Let's start with actual static spine of an arrow shaft.  If you support an arrow shaft at two points a given distance apart, then hang a weight in the middle of the arrow - the weight will cause the arrow shaft to sag.  The shaft's resistance to being bent this way is known as it's static spine.  The actual static spine of the arrow shaft is determined by the elasticity of the materials in the shaft and the geometry of the shaft. In multi-layered arrows (carbon/aluminum, etc.) the bonding materials also contribute to the static spine.  The inside diameter, the cross-section shape, and the thickness of the material all contribute to the static spine of the shaft material. A hanging weight doesn't really represent how forces are applied to arrows when they're actually shot, so static spine is really used as only a benchmark for predicting dynamic spine.

THE LENGTH -
An arrow shaft bends, not because it is being pulled down in the middle, but because it is being pushed inward from the ends.  It is being compressed when it's shot.  And the longer the shaft, the more easily a compressive force can bend it.  Imagine a brand new pencil.  If you put each end of the pencil between your palms and began compressing the pencil by squeezing your palms together, this would be similar to the forces that cause an arrow to bend when shot.  So, with your standard length pencil, could you push your hands together hard enough to make the pencil bend?  Probably not.  A short pencil is surprisingly stiff and resists bending this way.  But if that same pencil were 2 ft long, you could bend it easily by compressing it.  Under a compressive load, the longer pencil had less spine than the short one, even though the shaft material (the wooden pencil) remained the same - with the same static spine per given length.  Again, same concept applies for arrows.  Longer arrows have less spine (more limber), shorter arrows have more (more stiff).
 

THE TIP WEIGHT -
Every arrow should have a tip.  The tip is the business end of the arrow.  It could be a simple steel practice point, a razor sharp hunting broadhead, a small-game judo tip, or a number of other tips designed for a variety of purposes.  Each of these arrow tips is also designed to a specific grain weight.  The most popular weights are 75gr, 85gr, 90gr, 100gr, and 125gr.  However, some specialty tips can be much lighter or heavier.  

OK.  Now remember how a bow compresses the arrow shaft?  It's not hard to figure out what's pushing in one direction - the forward movement of the bow's string.  That's an easy one.  But what force pushes back the other direction?  You can't get that kind of compression if you don't have two opposing forces - one pushing on each end of the shaft, right? 

Right!  So what pushes on the other end?  Oddly enough, it's the arrow's TIP.  Of course, the tip doesn't actively do anything.  It's just a weight - hanging out at the end of the shaft.  But surely you must remember learning about Newton's Laws of Motion in school, eh?  Remember the one that says "An object at rest tends to stay at rest unless acted upon by a force"?  AH-HA!  Well think of it this way.  The arrow's tip is the "object at rest", and the forward movement of the string is the "force".  The stationary mass of the arrow resists the forward motion of the string, and since the heavy tip of the arrow is where most of the arrow's mass is concentrated, that's the area of the arrow that resists the most.  So the resistance of the heavy stationary tip and the forward motion of the string create opposing forces and.....Viola!....compression.

So, the greater the tip weight, the greater the compression (and flexing) of the the arrow shaft when shot.  The lighter the tip, the lesser the compression (and flexing) of the arrow shaft when shot.  See where we're going?  You guessed it.  A heavy tip DECREASES an arrow's dynamic spine (makes it act more limber).  A lighter tip INCREASES an arrow's dynamic spine (makes it act more stiff). 

THE TYPE OF BOW -
.If all this talk of spine is becoming a real pain in the neck, don't worry.  We have just a couple more details to cover, then we'll sum up the discussion on arrow spine.  
The physical features of the arrow (the shaft's static spine, the shaft length, and the arrow's tip weight) all play a part in giving the arrow it's spine characteristics.  But as we mentioned earlier, the arrows final dynamic spine (how much it will actually flex when shot) will also depend greatly on the output of the bow.  Your draw weight, draw length, cam-type, let-off percentage, and bow efficiency all contribute to the actual output of the bow.  And bows with more powerful outputs will require stiffer arrows to achieve the proper dynamic spine when shot.  Bows will less powerful output will require more limber shafts.

APPLYING SOME COMMON SENSE
Fortunately, the engineers have already crunched the numbers for us. You won't need to solve any equations or plot any graphs.  Most arrow manufacturers publish charts which take some, or all, of these bow output factors into account when recommending a particular arrow spine size. Some manufacturers have very complex charts that take many variables into account.  But other manufacturers offer a more simplified chart that just represents an average bow setup.  So you may have to apply a little common sense if your particular bow setup isn't exactly "average".  For example:  If you shoot a typical 300 fps compound bow, with normal 100gr tips, and 60-75% let-off, all you'll need to do is follow the chart.  If your bow is set for 60# and you use 29" arrows, you just follow the dots on the chart and choose the 200 spine.  Easy!

But what if you shoot a very aggressive low let-off speed-bow with an IBO speed over 330 fps.........say a Bowtech Black Knight or a Mathews Black Max.  In that case, your bow will have more output than an average 60# bow, so you would need to accommodate by choosing a little stiffer spine like the 300 shaft.  So be prepared to use your best judgment, should your bow setup have some special characteristic that needs extra consideration.  
 

FINAL THOUGHT ABOUT ARROW SPINE
You may have noticed that most arrows come in different sizes denoted by some kind of number system:  Gold Tip 5575's, Beman 400's, A/C/C 3-60's, Carbon Express 4560's, etc.  While each manufacturer's number system is often different, the important thing to note is that the number on the arrow specifies the spine (the stiffness) of that particular shaft, and doesn't necessarily denote the exact draw weight of the bow from which it should be shot.  For example, don't assume a Gold Tip 3555 will only work in bows ranging from 35# to 55# of draw weight.  That may or may not be the case.  The actual stiffness (static spine) of the shaft material is only one factor in determining the effective, or dynamic, spine of your finished arrow. 

And don't assume spine sizes transfer from one brand to the other.  In some brands, higher numbers represent the stiffest spine sizes.  In other brands, lower numbers represent the stiffest.  So don't assume if "300" is your spine size in one brand that it will be the same in the next brand.  Each manufacturer has their own system.  Be sure to check the individual manufacturer's charts (more on this in a moment) before you decide which spine size is right for you.

Remember that changing your bow's draw weight or draw length will change the energy output of your bow.  If you order arrows to match your 70# bow, then later decide to turn the bow down to 60#, your arrows will likely be too stiff.  Before you order your new custom arrows, make sure you're comfortable with your bow's current draw length and weight.  If you're a tinkerer, a growing youth archer, or you're "working up" to a heavier draw weight, you may need multiple arrow sets with more than one spine size to ensure you get the best arrow flight throughout your "transitional periods". 

Arrow Straightness:  by the Thousandths
Most carbon arrows are advertised to have a specific straightness tolerance (usually measured along a 28" section of the shaft) between .001" and .006".  The straighter the arrow, the more expensive they will typically be.  Most standard-grade carbon arrows have a straightness of around .006".  These basic shafts are usually called "Hunters", and for good reason.  For the purposes of close-quarters treestand hunting, most standard-grade shafts are more than adequate.  A typical human hair is about .004"-.006" in diameter.  So even a basic carbon shaft of .006" straightness is quite good, and straighter than you could possibly perceive without specialized equipment.  But most manufacturers also offer a mid-grade shaft which will have an advertised straightness of around .003", and finally a "Pro" shaft that will claim .001" or less.

Many hunters and recreational shooters report they can tell no difference in .006" arrows and.001" arrows, except for the size of the dent each respectively puts in their wallets.  Of course, we're not suggesting that arrow straightness is an insignificant attribute. Pro-level shooters often report the opposite, and choose the straightest arrow they can find for competition.  Of course, most pro shooters don't have to pay for their own arrows.  So choosing the best arrow in the line-up isn't really such a hard choice to make for these shooters.   

From a pure physics standpoint, arrow straightness certainly does matter.  When fired from a sophisticated shooting machine, the difference becomes more evident, as the straighter arrows fly and group measurably better, particularly at longer distances.  So theoretically, shooting good straight arrows can increase your “effective shooting” distance and provide better hits on the marginal shots.  But be advised, if your accuracy isn't as spectacular as you would like, it's most likely the result of tuning/clearance or shooting-form issues, rather than arrow straightness.  Nonetheless, arrow straightness is one variable you can tip in your favor for a few extra bucks.  If that extra advantage yields a few more points on the 3D range, or helps you to land the shot of a lifetime - then it's money well spent.  It certainly doesn't hurt to get the straightest arrow you can afford.  So.....good, better, or best?  The choice is up to you.

Regarding straightness, carbon arrows offer a distinct benefit over aluminums.  While a carbon arrow's advertised specs may be no straighter than a typical aluminum shaft, carbon arrows resist distorting and "bending out of shape" much better than aluminum arrows.  Though an aluminum shaft may BEGIN with a similar ±.003" straightness, it's straightness quickly deteriorates through normal use and handling.  So after a few months of use, your aluminum arrow set may contain a few arrows that are ±.003", a few at ±.012", and a few at ±.025".  Carbon arrows generally do not retain this kind of "memory" after being stressed.  So your carbon arrow set stays much more straight and uniform - even with heavy use.  Some archers even joke that there are only two states of a carbon arrow: straight or broken, but never bent.  While that's not entirely accurate, it does help to illustrate the point.