If you've ever gone fishing, you probably already understand this concept. A fishing pole shouldn't be too limber or too stiff. You wouldn't take your heavyweight fishing-rod when you go Bluegill and Perch fishing? It's simply too stiff for the job and would perform poorly. A stiff rod doesn't cast light baits very well, and dragging in small pan fish on a heavyweight rod would be no fun anyway. On the other hand, you wouldn't dare take your ultra-lite fishing-rod for an afternoon of Florida Tarpon fishing. The ultra-lite rod wouldn't be stiff enough to fight such large fish, and it might even break if you hooked a good one. Right? For arrow selection, the concept is essentially the same - the arrow must have the appropriate strength and stiffness for the task - not too stiff - not too limber.
Before we go on, please note that the official term is "spine" - as in backbone. Not "spline" - as in gears and sprockets. Arrow spine refers to the arrow's degree of stiffness - how much the arrow resists being bent. Some arrows are very stiff, others are very limber. And if you ever intend to achieve serious accuracy with your compound bow, you'll need to choose an arrow that's just stiff enough - but not too stiff for your particular bow setup.
Most people think an arrow flies just like it looks when at rest - perfectly straight. But nothing could be further from the truth. Once fired from a bow, an arrow immediately begins flexing and oscillating. That's not a defect. Each arrow bends and flexes in a particular cycle as it leaves the bow (archer's paradox). If the timing of the cycle is correct, the tail of the arrow clears the bow without making contact with the arrow rest, riser, or cables. If the timing of the cycle is not correct due to improper arrow spine, the over- or under-oscillation of the arrow results in serious fletching contact and/or paper-tune tears which cannot be corrected. So we have to get this one right.
Determining Factors which Affect Arrow Spine
There are three main ingredients which determine an arrow shaft's general spine characteristics:
(1) the stiffness of the actual shaft material
(2) the length of the shaft
(3) the tip weight that will be used
But it's not quite as simple as 1-2-3. How stiff an arrow is when it's sitting still on the workbench, and when it's busy accelerating from 0-180 mph as it's fired from the bow, are totally different issues. When the arrow is at rest, we refer to it's stiffness characteristics as static spine. But when that same arrow is in motion, its stiffness is a matter of dynamic spine - which adds more ingredients into our consideration pot. So pay attention. This gets a little tricky.
Static Arrow 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. How much the shaft resists this type of bending would be a function of the arrow'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 Arrow Spine
Unless your arrow shaft breaks or is altered, its static spine remains the same throughout its life. But your arrow's dynamic spine can change dramatically depending on how it's used. 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. As you fire the arrow, the explosive force of the bow compresses the shaft and it momentarily bends under the strain. The more powerful the bow, the more the arrow bends. So the dynamic spine of two identical arrows, shot from two different bows of varying output, could be drastically different. If your arrow has the proper amount of dynamic spine when shot from your modern 70# hard-cam bow - its 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 shoot your son's arrows in your 70# bow, it's likely the arrows will 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.
Shaft Length Affects Dynamic Arrow Spine
When an arrow is fired it bends because it is effectively being compressed. The arrow is momentarily trapped between the forward motion of the string and the static load of the arrow's tip. And the longer the shaft is, the more easily this 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.
If you had two pencils, one standard length and one that was 2 ft. long, you would get very different results when you tried the compress them. A short pencil is surprisingly stiff and resists bending this way. But the long pencil would bend easily under the compressive load between your palms.
So although the shaft material (wood & pencil lead) would be the same for each of your tests, the shorter pencil would exhibit more spine stiffness - it would act stiffer. The longer pencil would exhibit less spine stiffness - it would act more limber. This is similar to how arrow length affects dynamic arrow spine. The shorter an arrow shaft is, the more dynamic spine stiffness it will exhibit under acceleration. The longer the arrow shaft, the less dynamic spine stiffness it exhibits under acceleration.
So if you change your arrow length, you must consider how that affects your arrow spine requirements.