STATIC SPINE OF THE SHAFT MATERIAL
.
Let's start with static spine.  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.  However, arrows don't perform under static conditions - like a floor joist or a curtain-rod.  Arrows perform under dynamic conditions, with motion.  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.

DYNAMIC SPINE OF THE SHAFT
.
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 mean-n-potatoes of 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's that possible?  If your arrow has a perfect amount of dynamic spine when shot from your modern 70# hard-cam 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 more complex and requires examination of several contributing factors.  So hang in there.  We're almost through. 

SHAFT LENGTH AFFECTS ARROW SPINE
.
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 (stiffer).
.

TIP WEIGHT AFFECTS ARROW SPINE . 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).  This concept is a bit more abstract, so consider a dramatic example to illustrate the concept.  Imagine if you screwed a bowling ball on the end of an arrow and tried to shoot it.  Upon firing the bow, the arrow shaft would bend dramatically as it grudgingly inched forward, trying to get the heavy stationary mass of the bowling ball into motion.  The arrow would be highly compressed between the forward movement of the string and slowly accelerating mass of the bowling ball. MACHO "BIG-MAN" TIP WEIGHTS In sections #4-5, we'll discuss the topic of tip weight selection and explore it's effects on arrow mass, front-of-center balance, loss of shot trajectory, and kinetic energy in greater detail.  But for now, it's worth noting that many archers choose a ridiculously heavy tip weight for their hunting arrows.  There's often no logic behind the selection, other than the macho idea that bigger is better, and the often distorted and misunderstood notion that heavier tips "hit harder".  So don't get too puffed-up bragging about how you "always do better when shootin' them big XXX grain super-ultra-magnum broadheads".  With today's hot new compound bows often pumping out 50, 60, even 70+ ft-lbs of kinetic energy, much of the "old school" thinking about hefty arrow tip weight is no longer applicable.

.
BOW OUTPUT AFFECTS DYNAMIC ARROW SPINE
.
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.

Fortunately, the engineers have already crunched the numbers for us.  In just a few moments we'll take a look at a sample spine-size selection chart.  You won't need to solve any equations or plot any graphs today.  But before we go to the charts, you should understand which attributes affect the output of a bow and the spine requirements of the arrow.  Most arrow manufacturers publish charts which take some, or all, of these bow output factors into account when recommending a particular arrow spine size.
 

APPLYING SOME COMMON SENSE

As we said, some manufacturers have very complex charts that take many variables into account.  But other manufacturers offer a more simplified chart, like the one on the left, 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.  
.