Feb. 22, 1913 
FOREST AND STREAM 
239 
Effect of Variable Point of Balance 
on the Flight of Arrows 
By E. J. RENDTORFF 
S OME time ago I received a letter from Dr. 
Hertig stating that the new arrows he had 
just purchased possessed a lack of unifor¬ 
mity in the position of their point of balance or. 
center of gravity. He wished to know whether a 
variation of one-half inch would produce an ap¬ 
preciable difference in their flight. My answer 
was that I did not know. As I have never seen 
the subject discussed, and admit my ignorance 
The physical principle involving the action 
of the center of gravity of an arrow can be 
stated as follows: The motion of the center 
of gravity of a system acted on by any force 
is the same as if all the mass were collected at 
the center of gravity and all the force (viz., 
that of the bow string) were applied at that 
point, parallel to its former direction. 
An arrow tliat rotates or turns in the plane 
first a drift, and second an angular displace¬ 
ment of the shaft from its actual direction of 
flight. The pressure of the wind on the shaft 
in front of the center of gravity turtis the arrow 
in one direction, while the pressure on the 
feathered end turns it in the opposite direc¬ 
tion, with the center of gravity as a fulcrum 
or axis of rotation. This is best illustrated by 
the use of a diagram. 
In Fig. I, G is the center of gravity of the 
arrow, A and L the force of the wind, while B 
and C represent the pressures produced by the 
forward motion of the arrow along its path EK. 
The forces L and B tend to shift the arrow to¬ 
ward the line of flight EK, while forces A and 
C tend to turn it at an angle. 
The tendency of a force to produce rota- 
concerning it, I wish some archer would shed 
a little light on the subject. 
Instead of writing to some of our archery 
authorities concerning the solution of this 
question, I believe it would be better to have the 
question discussed in our official organ, so that 
other archers wdll receive the benefit of their 
knowledge. The chief function of an archery 
department in such a magazine as Forest and 
Stream lies in the mutual help that archers 
receive in general discussions of mooted prob¬ 
lems. In order to set the ball rolling I shall 
attempt to give my views on the subject, in the 
hope that the true answer will be forthcoming. 
My candid opinion is that the position of 
the center of gravity, or point of balance, makes 
but little difference in the flight of an arrow, 
unless the variation is quite marked; but when 
an authority like Dr. Weston says that it makes 
as much difference as a uniformity of weight, 
it becomes apparent that a considerable di¬ 
versity of opinion exists. 
of its shaft, due to the action of a strong wind, 
or for any other cause, will rotate about its 
center of gravity as an axis. An unfeathered 
shaft having the center of gravity in the middle 
would rotate easily and have a very eccentric 
flight. A similar arrow with the center of 
gravity near the pile would fly somewhat truer, 
as the friction of the air along the nock end 
of the shaft would make the center of gravity 
precede and drag the arrow behind it. If (he 
center of gravity is near the nock end, the 
arrow would turn through 180 degrees and fly 
with the pile toward the rear. The main func¬ 
tion of the feathers is to keep the center of 
gravity of the arrows in front, with the nock 
in the rear. The guiding force is the friction 
of the air. The greater the distance between 
the feathers and the center of gravity of the 
arrows, the greater will be the guiding effect, 
so that on a quiet day, with little wind, this 
arrow would have the steadier flight. 
Wind has two general effects on the arrow: 
tion about a given axis depends upon the mag¬ 
nitude of the force and upon the perpendicular 
distance from the axis of rotation to the line of 
direction of the force. This distance is called 
the “lever arm,” and the turning tendency the 
“moment” of the force. Thus the tendency of 
the force B to produce a rotation about the 
center of gravity G is equal to the force B 
times the distance GH. 
Now the forces A and C produce a rota¬ 
tion to the right, while L and B cause a rota¬ 
tion to the left. The arrow will turn until there 
is an equilibrium of the moments of these four 
forces, or until 
axfg+cxig=bxgh+lxgj. 
If the center of gravity of another arrow 
lies nearer the pile, the moment of the force 
of the wind A increases, while that of L de¬ 
creases. As the feathers are relatively large in 
area this will produce a greater angular dis- 
{Contiuued on page 241.) 
