James Park
04-05-2003, 10:12 AM
I have often been asked how the bow tuning bit works:
In tuning either a recurve or a compound bow (fingers or release device), it is a matter of matching up the time it takes for the arrow to flex with the time it takes for the arrow to get from full draw position to the position where the nock leaves the bowstring.
Initially, the arrow flexes immediately following release. At the time the nock leaves the string we want the arrow to be straight, so we need the arrow to flex through 3/4 of a cycle of its flexing.
So: the first thing to calculate is how long it takes for the arrow to go from full draw to brace height. To do this we need the force-draw curve and the arrow's velocity on leaving the bow (which of course we know from the calculated velocity in Accurate Sights). With a small amount of calculus (two stepwise integrations) we can quite readily calculate the time the arrow is on the string. I have used a number of representative force-draw curves from which you can select the nearest for your bow - in fact the exact shape does not matter much in the calculations, so while you might be using the curve for my PSE to do the calculation for your Hoyt it will be still quite accurate enough.
Next: we need to know the resonant frequency of the arrow so that we can calculate the time it takes to flex through the 3/4 of a cycle. This I have measured for a range of arrows, and also calculated from first principles (using quite a bit of fancy engineering and some complex modelling). What we need are some rules of how the frequency changes as we change the arrow size, point weight, arrow length, etc. Hence, not so easy to do. To complicate it further, the frequency changes depending upon whether the arrow is in free flight on on the bow string, and it is different for recurves and compound while on the string. All this modelling is included in Accurate Sights.
We also need to know where the arrows nodes are, both while it is on the strong and also in free flight. In free flight they are easy to locate, while it is on the string it is a bit more difficult (especially for compound bows with release devices).
From that, we can calculate whether or not the arrow is straight at the moment it leaves the string, and if it is not whether it has flexed too quickly or to slowly.
After the arrow leaves the string the nodes shift and the resonant frequency changes. What we now need to do is to calculate where the fletches and nock are as they pass the launcher. This node and frequency shift is difficult to model (and even more difficult to show grapgically as in Accurate Sights).
To look for arrow clearance from the launcher or arrow rest, it is simply a matter of seeing whether any part of the arrow is sitting where they are as it goes past. This is of course quite important for the rear of the arrow.
If the arrow is not exactly straight as it leaves the string, I calculate the bow weight at which it should be straight, simply by redoing the calculation for how long it should take from full draw to brace height. It is, of course, necessary for you to input your bow weight for this to mean anything.
How accurate is all this?
For recurves - I think it should be quite good, as the modelling seems to me to be reasonably straightforward.
For compounds - it is a much more complex thing to model for a number of reasons. I have modelled it for a flat nock travel, and for many bows this is not the case. Hence the flex will not be exactly as in the program. However, for bows such as my PSE's the nock travel is in accord with how the arrow wishes to flex (which is good, and allows the arrow to behave a bit more closely to its free flight situation than for a flat nock travel bow). This means that the resonant frequency while the arrow is on the string may not be exactly in accord with my calculations, which could change the results (but only by a quite small amount). Also, for the compound with release device there will be some sideways flex as well, and I have not modelled it.
So: overall, I think the modelling should be reasonably representative of what happens, but you need to use it with care, remembering that we have a quite complex system and things could be a little different in reality.
In tuning either a recurve or a compound bow (fingers or release device), it is a matter of matching up the time it takes for the arrow to flex with the time it takes for the arrow to get from full draw position to the position where the nock leaves the bowstring.
Initially, the arrow flexes immediately following release. At the time the nock leaves the string we want the arrow to be straight, so we need the arrow to flex through 3/4 of a cycle of its flexing.
So: the first thing to calculate is how long it takes for the arrow to go from full draw to brace height. To do this we need the force-draw curve and the arrow's velocity on leaving the bow (which of course we know from the calculated velocity in Accurate Sights). With a small amount of calculus (two stepwise integrations) we can quite readily calculate the time the arrow is on the string. I have used a number of representative force-draw curves from which you can select the nearest for your bow - in fact the exact shape does not matter much in the calculations, so while you might be using the curve for my PSE to do the calculation for your Hoyt it will be still quite accurate enough.
Next: we need to know the resonant frequency of the arrow so that we can calculate the time it takes to flex through the 3/4 of a cycle. This I have measured for a range of arrows, and also calculated from first principles (using quite a bit of fancy engineering and some complex modelling). What we need are some rules of how the frequency changes as we change the arrow size, point weight, arrow length, etc. Hence, not so easy to do. To complicate it further, the frequency changes depending upon whether the arrow is in free flight on on the bow string, and it is different for recurves and compound while on the string. All this modelling is included in Accurate Sights.
We also need to know where the arrows nodes are, both while it is on the strong and also in free flight. In free flight they are easy to locate, while it is on the string it is a bit more difficult (especially for compound bows with release devices).
From that, we can calculate whether or not the arrow is straight at the moment it leaves the string, and if it is not whether it has flexed too quickly or to slowly.
After the arrow leaves the string the nodes shift and the resonant frequency changes. What we now need to do is to calculate where the fletches and nock are as they pass the launcher. This node and frequency shift is difficult to model (and even more difficult to show grapgically as in Accurate Sights).
To look for arrow clearance from the launcher or arrow rest, it is simply a matter of seeing whether any part of the arrow is sitting where they are as it goes past. This is of course quite important for the rear of the arrow.
If the arrow is not exactly straight as it leaves the string, I calculate the bow weight at which it should be straight, simply by redoing the calculation for how long it should take from full draw to brace height. It is, of course, necessary for you to input your bow weight for this to mean anything.
How accurate is all this?
For recurves - I think it should be quite good, as the modelling seems to me to be reasonably straightforward.
For compounds - it is a much more complex thing to model for a number of reasons. I have modelled it for a flat nock travel, and for many bows this is not the case. Hence the flex will not be exactly as in the program. However, for bows such as my PSE's the nock travel is in accord with how the arrow wishes to flex (which is good, and allows the arrow to behave a bit more closely to its free flight situation than for a flat nock travel bow). This means that the resonant frequency while the arrow is on the string may not be exactly in accord with my calculations, which could change the results (but only by a quite small amount). Also, for the compound with release device there will be some sideways flex as well, and I have not modelled it.
So: overall, I think the modelling should be reasonably representative of what happens, but you need to use it with care, remembering that we have a quite complex system and things could be a little different in reality.