### Bow Torque: How big an error?

 In the last post I provided the equations and Excel tools to calculate sight pin geometry.   With this capability it is now possible to compute the errors created from bow torque.  In this post, I will define torque as the rotation of the bow around the axis of the bow arm.   Two types of torque are possible.  Torque during release assuming the sight pin was on the target just before release, and bow torque during the sighting process.   The effect of bow torque on arrow placement can be significant.  Figure 1. shows the the sight angles experienced by an archer when viewed from the side.  A bow is aimed by aligning the eye with the peep sight, sight pin, and the target to achieve the desired arrow launch angle.  Proper aim requires that the plane of the nock to top and bottom of the bow be held vertical relative to the earth. Figure 1.  Side view of critical shot angles as detailed in a previous post.It is not easy to hold the bow perfectly vertical, and many archers find themselves torquing the bow left or right during the aiming process or during arrow release.  I will define bow torque as the angle of rotation around the axis of the shooting arm as shown in Figure 2. Figure 2.  Bow torque angle is the angle the bow is rotated along the shooting arm away from vertical (photo credit HuntingNet.com)Important in this discussion is the height of the arrow and sight pin above the axis of rotation as illustrated in Figure 3.  The further the arrow or sight pin is from the axis of rotation the greater they will move side to side and down with bow torque.  For a given torque angle, gamma, the arrow will move:horizontal arrow rest movement = arrow height {sin(gamma)}        (1)vertical arrow rest movement = arrow height {1-cos(gamma)}        (2)and for the sight,horizontal sight movement = sight height {sin(gamma)}          (3)vertical sight movement = sight height {1-cos(gamma)}          (4) Figure 3.  Schematic of angles and dimensions associated with bow torque.These movements will cause an error in the shot.  We will tackle the calculation for torque during the shot first since this is easier.   Imagine that you are shooting a perfectly tuned bow and that your aim is perfect.  However, during the shot you rotate your arm or wrist at the moment of release causing a torque on the bow.   This rotation will move the arrow rest right or left and down along the inner circle in Figure 3.  The amount of the movement is defined by equations 1 and 2.   The effect of this rotation on the shot vertical is computed by determining the pin position before torque for a given target distance, calculating the vertical movement (equation 2), subtracting the vertical movement from the pin position to obtain an effective pin height and shot angle, and computing the new trajectory of the arrow.  (The attached Excel sheet and previous post helps with these these calculations.)  This shot will always be a bit low, but not by as much as you might expect since the sine of a small angle is still very close to one.  (This is important!  Sine and cosine functions do not change by the same amount at all angles.)    The horizontal shot error is the horizontal movement of the arrow rest (equation 1) projected on the target.        horizontal target error = horizontal rest movement * (target distant/sight distance)   (5) Figures 4 and 5 show the calculated errors for shot torque as the blue lines.  I have attached an iPhone to my bow and used the level app to evaluate the range of expected torque angles.  It is easy to torque the bow one degree, it is very noticeable if you are torquing the bow five degrees so this is probably the maximum error.  I expect the bow torque for most archers to be in the zero to 3 degree range.   A two degree torque in the bow during launch will create less than a 1/4 inch downward error and a 3 inch error in the horizontal (you have got to love those trigonometric functions). Figure 4. Calculated errors associated with bow torque at different torque angles (angles listed above each point on the graph).  A perfect shot would hit the center at zero, zero.  The blue curve is the computed error for shot torque.  The red curve is for sighting torque.  Notice that the vertical axis is expanded relative to the horizontal (horizontal errors are bigger). Figure 5.  Same data as figure 4 with an expanded scale.The larger effect is bow torque during the sighting process.   Assume that you have a perfectly tuned bow, but the bow is torqued to the left during aiming.   The sight pins will move along the outer circle in Figure 3 positioning then down and left (equations 3 and 4).  Of course the archer doesn't realize that they are torquing the bow so they move the bow hand up and to the right to put the sight pin on the target.   A shot from a bow torqued left during sighting will fly high and to the right.   But things are a bit more complicated.  As the bow is torqued left the arrow rest is moved down and left, the entire bow is move up and right.  These two movements partially compensate each other. (Now is the time to get out your bow and practice aiming at the wall as you torque your wrist to understand the opposing effects.)  The upward and right movement wins because the sight is further from the axis of rotation than the arrow rest (objects move further on a bigger circle).   The effective arrow movements are:          Effective vertical movement = sight movement (eqn. 2) - rest movement (eqn. 4)           (6)         Effective horizontal movement = sight movement (eqn. 1)  - rest movement (eqn. 3)       (7) Once these movements have been calculated, the effect of this rotation on the shot vertical is computed by determining the pin position before torque for a given target distance, calculating the vertical movement (equation 6), subtracting the vertical movement from the pin position to obtain an effective pin height and shot angle, and computing the new trajectory of the arrow.  Again, the horizontal shot error is the horizontal movement of the arrow rest (equation 7) projected on the target.   These results are shown in Figures 4 and 5 as the red lines.   Notice that the error is always high and larger in magnitude than shot torque.  If you are not careful, it is easy to have a two degree torque in the bow during aiming.   This torque would produce a 1/4 inch error in the vertical, but a 5 inch error in the horizontal.    Bow torque produces significant horizontal errors!So what is the lesson from these calculations?   I have two very different sources of error when shooting under hunting conditions.  Bow torque during aiming can produce significant errors in the horizontal, and poor range estimation can produce equally large errors in the vertical.  Fortunately, these errors can be minimized by using a level mounted on the sight ring to minimize bow torque and a range finder to determine target distance.  Don't forget to only measure the horizontal range to the target when determining target distance.  The attached Excel file has a series of macros to help compute bow torque errors for your specific bow setup.  Clearly these calculations are over simplified because they assume that torque is not imparting a horizontal acceleration to the arrow, and the combined effect of bow shot torque and sight torque have not been considered.  The best strategy is to hold the grip with an open hand and sight with the bow as vertical as possible.
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Whitney King,
Aug 21, 2013, 10:28 AM
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