From: bercov@bevsun.bev.lbl.gov (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 from Henry. JHB ---------------------------------------------------------------------------- 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 times. 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) ---------------------------------------------------------------------------- #From Henry: 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

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