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A Series of articles by Mike Warren (Designer of our successful Whitehart Bow and our new bow - Details to follow later in the year) looking at and challenging our understanding of bow design, efficiency and arrow mechanics. THE STRING-TENSION MODEL OR HOW A RECURVE BOW REALLY WORKS Earlier this year (2011) Perris Archery were good enough to send me some bow limbs to test on a piece of equipment I had built. The equipment is designed to check string-tension values in the drawn bow, from bracing height to full draw. Six bows were tested, a Hoyt, a Samick, a UUKHA, a White Hart, a Portland 2000 and one of my own limbs which is referred to as the ESP limb. The results showed conclusively that: • String tension was highest at bracing height and lowest at full draw. As the bow was drawn, string tension fell away rather than increased. Quite a surprise, since most archers would naturally assume the opposite. • Bracing-height string tension can be as much as twice the draw weight of the bow. A 38lb bow showed a maximum string tension value of 76.3lbs at bracing height. Other bows showed slightly more. This particular bow fell away to 45lb at full draw. • When the string-tension curve was plotted, (see the following diagram), it showed itself to be both a plot of reducing tension values and also an acceleration curve for the returning string. A relatively slow initial acceleration rate went up rapidly as the string approached bracing height and arrow release. This suggested that it is not so much the bow's draw weight that sends the arrow on its way, but the arrow's rate of acceleration from the loose in conjunction with the final maximum string tension at bracing height. They also gave a strong indication that: • Effective string length relative to actual string length can be a critical factor in bow cast. It would seem that the shorter it is (within limits) relative to actual string length, the faster the arrow leaves the string. This points to a possible direct relationship between relative string length and maximum string tension. It can be shown that in an over-braced bow, string tension drops and cast falls off. In the over braced bow, effective string length increases as the string is wound up. .
Copyright Mike Warren 2011 all rights reserved
ARROW, STRING and NOCK PERFORMANCE IN THE SHOT SEQUENCE High-speed video filming has made it possible to study the movement of the arrow from loose to the moment it leaves the string. It also reveals much about string movement during and after the arrows journey through the shot sequence and the part played by the arrow nock in influencing string movement. Of particular interest are the final few (6”-7”) inches of string return. This is the area of high acceleration on the String-Tension curve. Nock and string are well to the right of bow centre due to the arrow's oscillation as it passes the sight window. Its next oscillation (3rd in the shot sequence) carries it beyond and clear of the bow and nock and string make a diagonal journey across the mid-point at bracing height. Ideally the arrow comes off the string at this point while the arrow's diminishing pattern of oscillation continues down the line of aim. All observations and conclusions presented here are the result of close study of a number of Werner Beiter slow-motion videos. The diagrams accompanying this text, are an attempt to present the information visually. There would appear to be three critical nock and string positions in the shot sequence, two within the bow and one beyond after arrow release. Their journey to these points has been shown by straight lines rather than attempting to plot their actual path. DYNAMICS OF THE ARROW • At the loose, the string rolls off the tab to a position left of centre (right-handed archer) and the arrow lies at a small angular difference to the bow centre-line. Almost immediately, it takes the full impact of the draw weight delivered by the string and begins to buckle under the load. This buckling begins at a position just below the fletchings and moves down to the foot. Because the arrow lies at an angle to the centre line, the load-energy tries to turn the arrow clockwise and the foot of the arrow strikes the button. Werner Beiter in his observations of this phase of the arrow's travel, measured the deflection of the button at 2-3mm. • The arrow continues to bend and assumes the familiar curve as it passes the sight window. It has taken on energy from the loose and begins to dissipate that energy in rapid oscillations as it moves along the line of aim (diagram 1). Diagram 3 represents one full oscillation and reveals the axis of oscillation, about which the arrow is bending. In reality the arrow does not perfectly match this pattern because it is flexing along its length as it travels. We can call the pattern the arrow's ideal oscillation mode. It seems reasonable to assume that the more closely the arrow's movements match this ideal pattern in flight, the fewer will be the internal stresses in the body of the arrow. This points to the need for good arrow matching in conjunction with carefully tuned bracing height The axis passes through what are called the Nodes (points where the oscillation pattern crosses over from one side to the opposite side). These points cannot be accurately identified in the static arrow because they only arise within the arrows dynamic flight pattern of oscillations. • The most critical part of the shot sequence would seem to be within 6” or 7” of string return. Within this area (the high-acceleration phase in the STM) the nock and string move diagonally from the right, at position 2, passing through the mid-point at bracing height, where the arrow leaves the string. The arrow's actual departure point will depend upon high bracing-height string tension to pull the string firmly to the bow centre with minimal follow-through. Sloppy string tension will allow the arrow's departure point to vary one side or the other of bow centre. There will also be a lot of string movement in follow through. This strongly suggests that shot-accuracy is dependent on the arrow leaving the string at the bow mid-point in conjunction with high bracing-height string tension. At no time are the string and nock seen to be moving along the line of aim in a straight line.
Copyright Mike Warren 2011 all rights reserved
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