From: email@example.com (John Bercovitz)
Subject: Hatcher's Notebook - errata
Organization: Lawrence Berkeley Laboratory, California
Several people have asked for this so here it is.
This is an old post of mine on the subject followed by another
I think "Hatcher's Notebook" is the finest accessible technical book
available to the enthusiast. The grapevine has it that Stackpole is just
now printing more of them up. Gen. Hatcher had a tremendous amount of
practical experience with firearms. He was also quite good on theory due
to so much exposure to it (theory).
However, the book is not without typos and not without misapprehen-
sions on the part of Gen. Hatcher. Over the years I've annotated my copy
(3rd edition, 2nd Printing) to correct the problems. So that Innocents will
not be led astray, I'm writing the errata list below. Page numbers refer to
the edition I have. I do not represent this list of errata as complete.
In general: Hatcher uses "f.s." which means "foot-seconds" for velocity.
Clearly, velocity is measured in feet per second, but in that era, f.s. was
used to mean fps. Throughout the book, the figure given for the accel-
eration of gravity is 32.16 f/ss; the standard, at least these days, is
32.174 f/ss. Can't think of why it should have changed.
Pg 283, Chap XII, "The Theory of Recoil" section: "Principles of Physics
Involved in Recoil Calculation" formula SHOULD read:
w = Weight of the bullet in pounds = (wt. in grains)/7000
P 287, C XII, sec. "Third Element of Recoil", formula:
Thrust = Net Gas Pres. @ Exit x Area of Exit x Mass Rate of Discharge
This is all wrong: the units don't even cancel out. If it's a typo, I can't
reconstruct the original. There are many ways of expressing this formula
correctly; here's one:
Thrust = (Mass Rate of Discharge x delta V) + ( Gas Pres. @ Exit - Pres. of
Atmosphere) x (Area of Exit) where delta V is the velocity to which the
propellant gases have been accelerated. All variables except Pres. of
Atmosphere and Area of Exit vary with time so to use this formula to get
impulse you'd have to integrate it with respect to time; I really don't think
it's worth it. Use experimental means to determine this quantity.
PP 291 & 293, C XII, sec. "Recoil Before the Bullet Leaves the Gun"
...."Thus we COULD say the bullet produced 25%, and the muzzle blast 75%,
but if we did, we would be wrong"... Actually we would be RIGHT. Here,
JSH is confusing the equality of impulse with the equality of energy. He
erroneously expands on this thought further on P 293.
For a simple analogy, think of the following: A car's brakes decelerate
it from 60 mph to 30 mph, and then from 30 mph to 0 mph. How much
energy did the brakes remove? Three times as much from 60 to 30 as
from 30 to 0. How much momentum did they remove? Equal amounts both
P 556, C XXIII, "Exterior Ballistics", sec. "The Greenhill Formula"
"... 33 1/3 x .30 = 9.99 or in round numbers, 10 inches."
I don't think you'd really have to round off the answer to get 10.
Next paragraph: ...."the spin as given by the formula".........
The Greenhill formula gives twist, not spin. He gives the Greenhill
formula in words rather than in the usual form. If you work through all
the words, it comes out thusly:
T = (150/L)*(D^2)*[(sp.wt. of bullet/10.9)^0.5]*[(density of air/density of
medium)^0.5] where T is the twist in inches, L is the length of the
bullet, D is the diameter of the bullet, medium is what the bullet is
traveling through if not air (e.g. water).
Table on Page 558, C XXIII, "Exterior Ballistics", sec. "Retardation of the
Bullet by Air Resistance", last column heading should read: "Negative
Acceleration DIVIDED by Gravity"
P 566, C XXIII, "Exterior Ballistics", sec. "Construction of a Ballistic
Table" Should read: "Looking at Ingalls' tables, p. 590,..."
P 568, C XXIII, "Exterior Ballistics", sec. "Pressure in Pounds on the Nose
of the Projectile"
wrong: ..." the air resistance of p pounds on its nose will be pw/g."
right: ..." the air resistance of r pounds on its nose will be pg/w."
P 573, C XXIII, "Exterior Ballistics", sec. "Instructions for using the chart"
The first formula should read: i = (2/n)*[(4n-1)/7]^0.5
The second formula should read: n = 2*L^2
P 576, C XXIII, "Exterior Ballistics", sec. "Dimensional Analysis"
alpha beta gamma
The first formula should read: t = kL M g
alpha beta gamma
The second formula should read: T = L M (LT^-2)
P 576, C XXIII, "Exterior Ballistics", sec. "Application to Air Resistance"
alpha beta gamma
The 2nd formula should read: MLT^-2 = L (LT^-2) (ML^-3)
P 618, C XXIII, "Exterior Ballistics", sec. "Extension of Ingalls' Table I to
5000 Feet Velocity" Rumor has it, and my calculations confirm, that this
is a lousy extrapolation. Don't use it.
Considering the size of the book and the enormity of the task, I think
Hatcher's done an excellent job. Note that most of this book's faults must
be lain at the feet of the publisher/editor. Caution: Do check my work for
yourself; I'm not above the occasional transcription error either.
John Bercovitz (JHBercovitz@lbl.gov)
Here's some more:
Col. Ingalls tables were reprinted in Artillery Circular M, Revised
in 1917. The title page says INGALLS' BALLISTIC TABLES Computed by
Colonel James M. Ingalls, U.S. Army 1893, REVISED, UNDER THE DIRECTION
OF THE ORDNANCE BOARD, 1917 Washington, Government Printing Office
1918. At that time a number of errata were noted. Here are the errata
for Table I, which is also found in Hatcher's Notebook on pages 590-616.
I've used "D" to represent the capital Greek delta.
Value of U Column Correction
3,390 T(u)D For 0.008 read 0.009
3,350 S(u) For 794.1 read 694.1
3,350 I(u) For 0.03450 read 0.03509
3,010 I(u) For 0.04122 read 0.4142
2,870 I(u) For 0.04456 read 0.04459
1,118 T(u)D For 0.01 read 0.018
961 T(u)D For 0.01 read 0.019
540 I(u)D For 0.00878 read 0.00876
407 I(u)D For 0.20048 read 0.02048
367 I(u) For 5.68654 read 4.68654
323 T(u) For 50.749 read 50.747
189 T(u) For 97.689 read 97.685
--henry schaffer n c state univ