Post Shot Bow Rotation

How fast a bow rotates after the arrow has gone is a common discussion topic; surprising as it's completely irrelevant. The general view is that adding weight to the end of a long rod results in the bow rotating faster.

What actually happens is not obvious as both effects are possible depending on the bow configuration you start with and what change you make.

If for a given bow you increase the weight on the rod end then you increase the gravity torque on the bow - the "it rotates faster" argument. However adding weight to the rod end also increasing the bow moment of inertia which acts to reduce rotation rate - the "it rotates slower" argument. The overal rotation rate is complicated by a number of factors:

• The gravity torque on the bow changes as the bow rotates: maximum with the COG level with the grip and decreasing to zero as the COG swings vertically beneath the grip.
• The initial vertical position of the bow COG with respect to the grip (assumed pivot point) affects the gravity torque variation over time.
• Changing the end weight shifts the position of the bow COG which affects its rotaional characteristics

In an attempt to shed light on this issue a simple calculation is made of the time it takes for a bow to rotate from stationary with rod horizontal to the rod swinging down to the vertical with various end weights. A typical 25" riser with all up weight of 1200 grams is used.A weightless rod of length 70 centimetres is used. It's assumed that with the rod horizontal the COG is level with the pivot point. The time for the long rod to swing downwards from horizontal to vertical (i.e. through 90 degrees) is calculated.

As can be seen in this case adding weight to the rod end makes the bow rotate faster, in agreement with the general view. However the swing time difference between the 80gm and 270gm weight is only 16 hundreths of a second - not worth writing home about.

Incidentally increasing the gravity torque by increasing the length of the rod has the reverse effect i.e. it slows down the bow rotation rate (again by a trivial amount).If you push the bow centre of gravity forward with a longer extender or long rod, you can get the illusion that after the shot the bow drop away rotation speed is faster. This is because what archers look at is the movement of the end of the long rod. For a fixed riser rotation speed the longer the rod the faster the end of the rod moves - the speed is directly proportional to the distance the end of the rod is from the grip. So if you double the rod length, with the same riser rotation rate, the end of the rod moves twice as fast giving the illusion of a faster rotation rate.

Last Revision 16 March 2011