​To most archers the number that describes arrow spine is just a number, you understand that a smaller number means a stiffer arrow but perhaps that’s all. In fact, the process used to give a spine measurement is incredibly simple. The most common method is the ASTM (American Society for Testing and Materials) method, used by all major arrow manufacturers of carbon and aluminium shafts.

​This method involves fixing an arrow shaft at two points, 28 inches apart. Directly in between the two supports a weight of 880 grams is hung. Naturally, the arrow will bend (deflect), and it is the size of the deflection that determines the spine number. The deflection is measured in thousandths of an inch, so if the arrow deflects half an inch, that’s 0.5”, then the spine number is 500.

Let’s imagine a very simple set up. When you release the string it accelerates. Suppose that the string accelerates to full speed instantaneously. Then the nock must also go through the same acceleration. If the arrow was perfectly stiff, that is had a spine rating of 0, then the point would also go through the same acceleration. Of course, our arrows are not perfectly stiff. Instead, the shaft of the arrow absorbs some of that force applied upon release. So, the force must travel down the shaft of the arrow, called an impulse. That delay in the force reaching the point of the arrow means that, just for a brief moment, the nock is moving at full speed while the point of the arrow is still stationary. The distance between nock and point is therefore less than the length of the arrow so the arrow shaft must bend.

​We made some strong assumptions about the acceleration of the arrow. For a lot of modern bows, particularly compounds with cams that are not circular, the acceleration of the nock is purposefully increased over a period of time, from initial release all the way until the nock loses contact with the string. This allows bows to launch arrows at a much greater speed, but it also has a large impact on how much force is being applied and how long it takes for that force to travel from nock to point. Where the force is increased throughout the cam motion the size of the impulse travelling down the arrow is greater and so the arrow will bend more, and later in the bow window. A cam that allows for faster arrow flight will require a stiffer arrow shaft.

We can already see that the speed at which the bow shoots an arrow, as well as how smoothly it accelerates the arrow, affects how stiff we need our arrow spine to be.

​For those using release aids there is no horizontal movement (or at least there shouldn’t be) upon release and so the arrow doesn’t have this guidance of where to bend. Instead, a vertical force needs to be introduced. This is so that the arrow, particularly the vanes, have good clearance above the arrow rest. To ensure this some compound bows are set up so that the nock travel is not perfectly straight, rather it moves the nock upward slightly, others require their nocking points be positioned marginally above centre. Either way this introduces a very slight vertical force and so the arrow is encouraged to bend vertically. Simply put, the arrow will bend in the direction it finds the easiest, so consistently placing a small force upward or sideways ensures the bend occurs in the direction it is needed.

​Now, what about where along the arrow the bend occurs? When you simply have a shaft with no components on it and you just hang a weight from the centre the arrow will of course bend where the weight is, in mathematics we would say we are modelling the arrow as a light uniform rod. But we aren’t in this perfect world where chickens are all spherical. Instead, the force is being applied not at the centre of the shaft but at a slight angle at one end of the shaft. Moreover, the arrow is not uniform because its centre of mass is not in the centre, it is closer to the point of the arrow because the components all add weight. How does this affect the arrow bend?
To get to the answer we first need to understand the oscillation of the arrow. Of course, as the arrow flies the arrow as a whole is moving toward a point on the target. However, most of the points on the arrow, certainly early in the arrow flight, are not travelling directly there. They are wobbling up and down or left and right. The reason the arrow continues towards this one point is that for every point of the arrow applying a force in one direction there is another point of the arrow applying the equal force in the other direction.
Even amongst all this wobbling there are two points on the arrow, called nodes, that don’t wobble, they travel exactly along the flight path of the arrow. Consider a rope, if you’ve not done it yourself you’ve probably seen the popular exercise that involves moving a rope up and down to force it to make waves. Those waves are oscillations. The vertical force you’re applying at one end of the rope is similar to the force your bow applies to the nock. As you settle into a rhythm different parts of the rope move up and down, some parts of the rope move more than others, and there are at least two points along the rope that don’t move at all.

​The same thing happens with your arrow. The nock is moved slightly off the flight path causing an oscillation. No further force is applied once the nock leaves the string, so the oscillation is fixed. That means, like in any oscillating system, there must be some nodes, some points that don’t wobble. The amplitude of the oscillation is how much the arrow bends at it’s most. That spot of maximum bend will be halfway between the nodes; however, the nodes will not be evenly spaced from each end of the arrow. Because the arrow carries more weight at the front because of the arrow point, the nodes will be closer to the front of the arrow, and so the position at which the arrow is bending the most is nearer the front as well.

If you could watch your arrow flight accurately you would find that the nodes of the arrow were the points of the arrow that followed the arrow’s flight path to the target, not the point itself as is often thought.

So, the bend of your arrow is changed by how the arrow is set up. It is also changed by the length of the arrow. Even in the controlled conditions used to test the arrow bend, if the test were done by pinching the arrow at 30” rather than 28” you would get more deflection, similarly you get less deflection if you pinch it closer together. In our arrow flight the same thing is happening with respect to the nodes of the oscillation rather than a place you pinch the arrow.
If the nodes are far apart the arrow will be able to bend more, signifying a weaker arrow. If the nodes are closer together the arrow will bend less, signifying a stiffer arrow. So, a stiffer arrow spine will always have nodes that are closer together than a weaker arrow spine, but the stiffness of the spine isn’t the only thing that affects how far apart the nodes are.
​​By making the arrow longer we move the nodes further apart, so an archer with a longer draw length will have arrows that bend more and so will need to use a stiffer spine arrow than an archer with a shorter draw length, and vice versa. We can also use a heavier point in an arrow as this moves the node nearest the point closer to the end of the arrow, that means the nodes move further apart and the arrow can bend more. So, a heavier point effectively weakens the arrow, while a lighter point will stiffen the arrow.

​The two main factors I use to quantify the appropriateness of an arrow to my set up are grouping and forgiveness. There are a lot of factors you can control when choosing your arrow set up, but these two factors are the things you’re want to achieve. A stiffer arrow will group better as the arrow flight is straighter, thus generally more consistently, all the way until the arrow reaches the point of too stiff to avoid contact, when the grouping rapidly declines. However, forgiveness is much more difficult to attain. It depends on the location of the nodes in respect to the arrow rest, but also where the arrow rest can be placed in relation to the throat of the grip. It also generally needs a heavier point up to a threshold of easily reaching the distance. Moreover, a slower arrow is more forgiving but won’t group as well at distance due to atmospheric conditions, not just wind, so fletching offset or helically can help or hinder.

​There are two mathematical principles that affect the quality of the flight of an arrow: impulse – how much force is applied to the arrow, at what direction, and for how long, and oscillation – the location of the nodes of the arrow.
The style of the bow, the cam shape (if a compound), the limb materials, the string material, the string thickness, the poundage, amongst others, can all affect the impulse. The arrow spine, length, components and the placement of those components can all affect the oscillation. So, if you ever think matching your arrows correctly is difficult, you’re right, but it needn’t be a mystery.

You need a completely neutral posture to test your draw length. To do this takes time and you’ll probably need someone watching you to be able to tell you when you get it and when you don’t. A neutral position consists of the following:

• A vertical spine that has little to no bend in it,
• Bow arm elbow only slightly bent to align the bones in the arm,
• Flat and level shoulders at resting height, again to align the bones,
• Release arm elbow directly in line with the arrow.

 
The first is achieved with tension in your abdominals, making sure your sternum is dropped and your bum is tucked in so that your spine straightens. You also need to balance the weight on your feet to ensure you’re vertical, not leaning backwards.

The elbow positioning is straightforward to achieve because you should be able to tell when your arm bones are lined up, as your muscles can actually relax without your arm pulling toward you. Do this against a wall to start, or with an exercise band, to find the position and then have someone tell you when you match that position with your bow. Similarly, your release arm elbow position is controlled by the tension in your rear rhomboid, so you can alter when in the draw cycle your rhomboid activates in order that your elbow is pulled around the correct amount.