Feb. 22, 1913 
FOREST AND STREAM 
241 
EFFECT OF VARIABLE POINT OF BAL¬ 
ANCE ON THE FLIGHT OF ARROWS. 
Continued from page 239. 
placement of the arrow. However, the moment 
of the force B increases at the same time, so 
that the tendency to move the arrow back to 
the direction of its line of flight is also in¬ 
creased. Conversely, if the center of gravity 
of the arrow is nearer the nock the power of 
the feather to right the arrow is decreased, but 
the wind will not be able to turn the shaft 
through as great an angle as before. Things 
thus seem to balance, and neither position of 
the center of gravity seems to possess a dis¬ 
tinct advantage over the other. 
I see but one other case where a variable 
position of the center of gravity can produce 
—a matter which to my knowledge has never 
been considered. 
In connection with Fig. i there are two 
other things I wish to discuss. If the arrow has 
an angular position with regard to its line of 
flight, as illustrated in the digram, the area 
exposed to the friction of the air, in the for¬ 
ward direction, is greater than that offered 
when the shaft lies in its trajectory. This extra 
friction would retard the velocity of the arrow 
and cause it to undershoot. According to 
theory it would therefore be necessary to ele¬ 
vate the arrow when shooting with a strong 
wind. I would like to inquire from our archery 
friends whether they have ever noticed this 
effect. 
The second inquiry is relative to the drift 
their flight. As stated in the article, I did not 
pretend to understand the matter and wrote 
mainly for the purpose of starting a discussion 
on the subject, in the hope that the true answer 
would be forthcoming. 
One week after this article was written, I 
believed I had thought out the solution of the 
problem and the article on the “Toxopholist’s 
Paradox” was the result. In the last paragraph 
of that article is explained why our arrows 
should have a uniform position of their center 
of gravity. That is my final conclusion. 
The explanation may be correct; but if we 
are ever to progress intelligently and become 
proficient archers, these matters must be dis¬ 
cussed. We will all make mistakes in these dis¬ 
cussions, but what is the difference, if in the 
different results, and that is at the moment 
when the arrow first leaves the bow. The 
string, on release, has a tendency to move to¬ 
ward the central axis of the bow, D, Fig. 2. 
The center of gravity of the arrow tends 
to move straight ahead, on account of its 
inertia, but the nock of the arrow is con¬ 
strained in its motion by the string, so that 
there is a tendency to move the pile toward the 
left. This introduces the three forces A, B and 
C, illustrated in the diagram. 
Now, if the center of gravity of the arrow 
is moved toward the pile, the tendency of the 
shaft to get an angular displacement, on release, 
is diminished, due to the greater moment of the 
force at G, which holds the arrow in line, and 
also due to the consequently larger moment of 
the force at A, which would move the string to 
the left and thus diminish the lateral displace¬ 
ment; but the arrow would therefore bend more 
and receive an extra wobble during its flight. 
The pressure B against the bow would be 
increased and the wear on the shaft aug¬ 
mented. 
If the center of gravity is moved toward 
the nock, the arrow on release would receive a 
slightly greater angular displacement, but the 
wear on the shaft would be decreased. The 
arrow would bend and wobble less and there¬ 
fore have a truer flight. 
In brief, every advantage gained by having 
the center of gravity near the pile is neutral¬ 
ized by a corresponding disadvantage, and vice 
versa. It is a case of six of one and half-a- 
dozen of the other. In solving the problem 
one is between the devil and the deep sea. I 
believe a slight variation of the position of 
the center of gravity of an arrow makes no 
material difference, at any rate, less than does 
a lack of uniformity in the stiffness of the shafts 
of the arrow in the direction of the wind. I 
have frequently been surprised at the relatively 
small drift produced by a strong cross wind. 
A wind of forty miles per hour moves about 
150 feet, while an arrow travels 100 yards. The 
drift of the arrow would, of course, be much 
less, but it should certainly be more than one- 
fiftieth of that amount, or about three feet; and 
still I doubt whether I have ever made a larger 
allowance for a cross wind while shooting at 
100 yards. How is this explained? 
On examining Fig. i, it will be seen that 
the pressure of the air, produced by the forward 
motion of the arrow, is much less on the wind¬ 
ward than on the other side of the shaft. This 
will produce a shifting of the arrow into what 
we sometimes call, the “teeth of the wind”— 
i. e., in the direction opposite to the wind. It 
is the same effect as that which causes a base¬ 
ball to curve when one-half of it is smoother 
than the other, as is the case with the “spit ball.” 
AN EXPLANATION. 
This article on “The Effect of a Variable 
Point of Balance of Arrows” was written first 
and intended to precede the “Toxopholist’s 
Paradox.” Through a mistake the articles 
were published in the reverse order. The dia¬ 
gram intended for Fig. 2 in the Paradox article 
was also omitted, and another, having no con¬ 
nection with the subject, substituted in its place. 
Fig. 2 of the “Balance” article was the one 
intended to be used. 
When the “Balance” article was written 
the explanation of Butt, Walrand and Ford, per¬ 
taining to the reason why arrows are not de¬ 
flected to the left, was considered the correct 
one, and on this basis I could not understand 
why a slight variation of the center of gravity 
of arrows made a very material difference in 
long run we manage to> get a better understand¬ 
ing of the subject? 
Pittsburgh Archers Organize. 
Pittsburgh, Pa., Feb. 10 .— Editor Forest 
and Stream: At a dinner given by J. C. Patch, 
an organization of the various archery clubs 
around and about Pittsburgh was effected. 
The dinner, a nice little affair, was held at 
the Pittsburgh Athletic Association club house. 
Fifteen archers were present. The name of 
the merger is the Pittsburgh Archery Associ¬ 
ation. Mr. Patch was elected President, Dr. 
W. H. Plaines was chosen Secretary-Treasurer, 
and Dr. O. L. Hertig was selected as Vice- 
President, target bearer, range sweeper, and 
general filler in of miscellaneous duties. He 
accepted after much argument, with the proviso 
that some one else be allowed the privilege of 
cutting the grass during the shooting season. 
Mr. Patch, the new president, is a man well 
fitted for the position. In addition to being 
an archer of much enthusiasm and great 
promise, he is a man who can, and more, who 
will dig down in his jeans when the occasion 
demands. You don’t have to go after him with 
a lasso and a pair of dental forceps when a 
worthy cause needs help. 
The members of the new association are 
counting the days in anticipation of spring’s 
arrival, and let me whisper—Jimmie Duff needs 
to get busy making some extra tough targets. 
We have been very much interested in the 
able articles which Mr. Rendtorff has been con¬ 
tributing to the cause. I am not sure, how¬ 
ever, that we all agree with him. I can ap¬ 
preciate the sentiment that, with animated 
verbage, puts every phase of our beloved sport 
into song, into verse, and into prose even more 
