Paper Tuning is a method of bow tuning popular with compound archers. The method is to shoot arrows through a sheet of paper placed in front of the bow and adjusting the bow until the tear pattern is a 'bullet hole' i.e. the fletchings pass through the same hole as the arrow pile. The arrow is therefore leaving the bow straight with no vertical or horizontal rotation.

For recurve archers, using the paper tuning approach has limitations because of the Archers Paradox effect. The effect of the finger release results in the arrow leaving the bow with significant vibration in the horizontal plane. The following diagram indicate the problem:-

Because the arrow is flexing, even with a perfectly tuned setup you will probably get a horizontal tear in the paper because of vibration of the arrow as it passes through the paper. (illustrated by the green line).

If the arrow is of length 'L' and speed 'V' then the time for arrow to pass through the paper is L/V.

If the arrow is vibrating at frequency 'F' then the time to go through a complete bending cycle is 1/F.

E.g. if L = 80 cm, V = 55 meters/sec and F = 60 cycles/second then the time for the arrow to go through the paper is 80/5500 = 0.015 seconds and the time per vibrational cycle is 1/60 = .017 seconds. The number of bending cycles that the arrow goes through when passing through the paper is 0.015/0.017 = 0.9 cycles. In general we can expect the arrow to go through multiple bends while passing through the paper which will result in a horizontal tear varying from zero (the arrow snakes through a single hole - unlikely but possible) to the amount the arrow flexes sideways (which depends on the arrow - anything up to 2 inches say).

You can use paper tuning in principle for three purposes, arrow dynamic spine assessment, nocking point adjustment and pressure button adjustment.

Spine Assessment

If the arrow comes out of the bow with a large amount of rotation (very weak/stiff arrow) then you will get a very wide horizontal tear in the paper, the combination of the arrow vibration and its rotation. If this tear is too big its unlikely that any amount of bow tinkering or tuning will produce a good flying arrow and the arrow needs to be changed or replaced. Rick Stonebraker's tuning guide puts the maximum allowable horizontal tear at 3 inches. Any larger then this then a weaker/stiffer arrow as appropriate is required.

Nocking Point Adjustment

There is a negligible amount of Archers Paradox effect in the vertical plane so any vertical tears in the paper result from arrow rotation. You can therefore adjust the bow (usually the nocking point) towards having zero vertical tear implying the arrow is leaving the bow with no rotation in the vertical plane. As any vertical rotation will result in the arrow porpoisng it is important that the 'zero tear' is obtained over a range of distances. At very short distances the amount the the arrow will have rotated will be small - low tuning sensitivity. At longer distances the arrow may have rolled over to the horizontal or even be aligned in the other direction - possibility of false interpretation. The tuning 'distance range' will depend on the arrow (say 2-10 metres)

Pressure Button Adjustment

In the horizontal plane the paper tear is essentially going to be a random combination of the arrow vibration and any arrow rotation in the horizontal plane. Even a perfectly tuned bow is going to give an unpredictable horizontal tear depending on how the arrow 'snakes' through the paper. For pressure button adjustment therefore paper tuning is not a method that can be recommended

If an archer tries to get a bullet hole tear by adjusting the pressure button what effectively is happening is that the arrow rotation (miss-tune) is being used to offset the arrow vibration effect as far as the paper tear is concerned. As the arrow rotation tear effect depends on the bow to paper distance if at a specific distance you get a bullet hole tear then by moving forward or backwards the tear magically reappears again.

Approaches to tuning inevitably comes down to archers preference (some swear by, some swear at). In my own ranked list of ways of bow tuning paper tuning resides at the bottom.