< Previous54T H E R I F L E M A N . September, 1918. sterling R,C. On -Vuguiit 30, on the club rifie range, the eight finalists in the Archer trophy shooting handicap had a close struggle to gain the handsome trophy, and also the four leading postions which en t i t l e d t h e s u c c e s s f u l f o u r t o u s e f u l p r i z e s . Tw o l a d i e s fi g u r e d in the final. Nurse Martin having to shoot off for fourth prize with Mr. H. I'reater, the latter prov ing successful. The Hon Secre t a r y o f t h e r i fl e c l u b s e c t i o n , Mr . A. Pegrum, and Mr . A. Palmer , a' well-known O . - i g e n h a m s p o r t s m a n , h a d t o shoot oft for the trophy, the latter proving victorious. Mr . \V. E. .-V rcher , the donor of the trophy, presented the prizes to the winners. Mr . J. Linwood, on behalf of the committee, proposed a vote o f t h a n k s t o t h e d o n o r o f t h e chief prize. RIFLEMEN'S SALES AND EXCHANGE. A d v e r t i s e m e n t s i n t h i s c o l u m n will he inserted at the rate of id. p e r w o r d p e r i n s e r t i o n f o r p r i v a t e A d v e r t i s e m e n t s a n d I d . p e r w o r d f o r T r a d e . A n n o u n c e m e n t s i f p r e paid. In consequence of the o r d e r r e c e n t l y i s s u e d u n d e r the Defence of the Realm R e g u l a t i o n s i t i s n e c e s s a r y f o r b o t h b u y e r a n d s e l l e r t o obtain a special permit to purchase and sell respec t i v e l y b e f o r e a n y . 2 2 o r . 3 0 3 r i fl e s c a n b e d i s p o s e d o f b y m e m b e r s o f R i fl e C l u b s . S u c h p e r m i t s m u s t b e o b t a i n e d f r o m t h e C o m p e t e n t M i l i t a r y A u t h o r i t y f o r t h e d i s t r i c t . W a r O f fi c e M i n i a t u r e a n d S h o r t L e e - E n fi e l d R i fl e s w a n t e d i n a n y c o n d i t i o n b y A . G . P a r k e r & C o . , L t d . , B i s l e y Wo r k s , W h i t t a l l S t r e e t , B i r mingham. For Sale.—.loi Martini Henry service rifles without bayonets, subject consent of authorities. Offers 4th (Volunteer) Battalion .A.P.W.O. Yorkshire Regiment, Drill Hall, North Street, Scar borough. CHALLENGES. Inserted free of charge. Post Matches wanted. Finch- ley Special Constabulary, 25 yards range, 8 to shoot, all to count; first team, average 96; second team, average 90.—E. G. WEST LONDON LEA( P o s i t i o n s o k t h e C l u b s i n t h e C.rosvenor Kensington Harrodian Borough of Wandsworth Wimbledon Park H a m m e r . s m i t h I r o n W o r k s . . . B Division Metropolitan Police L.G.O.C. .\ L.G.O.C. B Chiswick H a m m o n d , 2 3 , S q u i r e s L a n e , Church End, Finchley N.3. Royal Marine Barracks (Chat h a m ) R . C . w o u l d l i k e P o s t Matches, 25 yards, open or aperture sights and slings, 8 or 10 men a-side, counting out o p t i o n a l . — D r u m - M a j o r V. G . Bacon, R.M. Barracks, Chat ham. P o s t M a t c h e s w a n t e d , 1 0 t o shoot, 8 to count; aperture sights and slings ; to extend throughout week. Southgate R.C.—W. H. L a s t , 4 1 , Wa r w i c k R o a d , N e w Southgate, N.ii. W a n t e d P o s t M a t c h e s f o r both First and Second T eams (averages 96 and 93), 8 or 10 a-side (latter preferred), 7 or 8 to count. Open dates from end of .August. — Replies to A. E. Rasell, .Associated Equipment R.C., Blackhorse Lane, W al- thamstow, E.17. Post Matches wanted, 25 yards range, 10 to shoot (8 to count), open sights, no slings, on 50 y a r d s c e n t r e b u l l ; e x t e n d throughout week.—E. C. Stearn, 50, Belvoir Road, Cambridge. Endon R.C. would like to ar range Post Matches, 25 yards' range (outdoor), aperlure sights, 8 to shoot, 6 to count; average 9 2 . A l s o L a d i e s ' t e a m w i s h t o arrange Post Matches, 25 yards, 6 to shoot, 4 to count, aperture sights, single bull. Matches to extend throughout week.—J. T. Robinson, Florence T errace, Endon, Stoke-on-Trent. P o s t m a t c h e s w a n t e d , 8 t o shoot, 6 to count, aperture sights and slings, extend throughout week, 25 yards. Herrington R.C., Secretary, J. Y'ounger, 16, Garden Street, Newbottle, Co. Durham. M e t r o p o l i t a n E l e c t r i c R i fl e Club wish to arrange post matches on " Gauge Handicap " t e r m s ( s e e J u l y R i fl e m a n ) . Teams of 8 or 10, 6 or 8 to count. 25 yards. Handicapping scale, for 'team averages of 98, 97, 96, 95, etc., the corresponding gauge n u m b e r s w i l l b e — I , o , I , 2 , etc., respectively. Metropolitan gauge=: No. 3. H. J. Taylor, Metropolitan Electric Supply Co., Acton Lane, Willesden, N.W.io. W i m b l e d o n P a r k R i fl e C l u b would like to arrange post matches, 8 or 10 a side, all to count, 25 yards, aperture sights, S.M.R.C. match targets. A ver age of first team 97, second team 95. D. S. Oakey, 202, Revel- stoke Road, London, S.W.18. E O F R I F L E C L U B S . MMER SEIASON TO SEPTEMBER 8. s.\V .L. D.p. 75 1111 6 5I olO 752o lO 54() 1 0 5 320 6 73 40 6 5 2 3 o 4 3 I2 02 202o O 6 0 6 0o WA R B O O K S THE FOLLOWINC BOOKS ARE OBTAINABLE FROM THE S.M.R.C. AT THE PRICES QUOTED:- " Rifle Training for War." E. H. ROBINSON. " Musketry Instruction and Miniature Range Shooting." BY Q.M.S.-Instf. D. JAMES (School of Musketry, Hylhe). " Musketry Training for War.' Reprinted from the " Rifleman." " H o w t o S h o o t . " E. H. ROBINSON una S. CHANTLER. " H o w t o D r i l l . " BY E. H. ROBINSON. " Rifle and Carton." BY E. H. ROBINSON. Specially written in non technical language for those who desire to train tliemselves for war. Fully illustrated. 1/-, POSTAGE 2d. D e a l s t h o r o u g h l y w i t h Musketry Training in the Field. Invaluable to In s t r u c t o r s o f t h e N e w ' Army . Considerable Space devoted to the miniature weapon. 1/-, POSTAGE id. 2d. POSTAGE FKBH How to use a rifle. How to shoot straight Shoot i n g i n W a r . H i n t s o n marksmanship. 2d., POSTAGE Id. An elementary guide for the absolute beginner. 2d., POSTAGE Id. S o m e N o t e s 0 11 Ta r g e t aliooting witli the .22 calibre rifle, as a eport, and in preparation for w a r. W i t l i a c h a p t e r o n tlie formation and man agement of Miniature Rifle Cluhs. 1/-, POSTAGE 2d. " T h e M e c h a n i s m o f t h e E n fi e l d (1914) Rifle Visualised." 6d., POSTAGE Id. A few practical suggea- t i c n s i l l u s t r a t e d b y d i a grams. I/-, POSTAGE 2d. 6d., POSTAGE id. " The Rifleman's Dictionary and Riiief snd _ „ , „ R i f l e S h o o t i n g . P"""' 6d., POST AG. Id. BY E. H. ROBINSON, " Quick Training for War." BY L t . - G e a . S i r R . B A D E N - P O W E L L . " straight Tips for Subs." H i n t s O A C o m m i s s i o n s , A l l o w a n c e s , K i t s , Duties, Etc. Musketry (Skill-at-Arms) Hand- b o o k a n d B . S . A . M u s k e t r y S c o r e B o o k f o r G e n e r a l M u s k e t r y C o u r s e . The following are based on Official Manuals, and are wrillen by Officers of the Regular Army: " F i e l d E n t r e n c h m e n t s . " (Spade Work for Riflemen). " Musketry." I/-, POSTAGE id. ('303 and '22 Cartridie). Physical Training." J u n i o r a n d S e n i o r C o u r s e s , ' Machine-Gun Training." ('303 and '22 Cartridges,) 1 /3, POSTAGE 2d. I /3, POSTAGE 2d. 1/3, POSTAGE 2d. 1 /3, POSTAGE 2d. WWW.RIFLEMAN.ORG.UKOCTOBKU, 1918.T H E R I F L E M A N . 44 DOMINION" BRAND. T H E B E S T BRITISH AMMUNITION FOR BRITISH MARKSMEN. NOBEL'S EXPLOSIVES COMPANY, LTD., G L A S G O W & L O N D O N . P. C . B . WWW.RIFLEMAN.ORG.UK56T H E R I F L E M A N . OCTOBKU, iniS. RICKARBY'S RIFLE CRICKET TARGET SlaUonna' Hall). 25 Yds Supplied by the S.M.R.C, only. Price 16/= per 1,000. SPECIAL NOTICE. A f fi l i a t e d C l u b s c a n n o w b e s u p p l i e d with Britisb=made Ammunition, viz.:— ELEY'S '22 Long Rifle Smokeless Subject to Club Terms. P e r r . o o o . P e r C a s e l o . o o o . cl. £ s . _ c l . C a s e L o t s o f l o . o o o only, Cash with Order Strictly Xett.. £ s . c l . 17 0 8 10 0 7 17 0 Thefse pHcca are comlifioval on the iroodeii tonvx and fin cuscp in which ihc avimuvition is packed being returned to ihc S.M-H.O. [Carriage paid on Case Lois.) OrtfO S o c i e t y o f M i n i a t u r e R i fl e C l u b s ^ Arundel House, Arundel Street, London, W .C.2. wmcf fssrm 22 LONG RIFLE "LESMOK" GARTRIDQES were used successfully in the following Competitions at the S.IVI.R.C. Meeting, June, 1916. "DAIL Y EXPRESS." " D A I L Y T E L E G R A P H . " ^ ^ " D U K E O F W E S T M I N S T E R . " " S T E V E N S V A S E . " < & ■ " B E N H A M . " ^ ^ ^ In all kinds of shooting they continue to excel. No matter vshat the make of your favourite arm is, you can bring out its possibilities to the fullest degree by using " Winchester " make of cartridges. S o l e D i s t r i b u t o r s i n t h e U n i t e d K i n g d o m : LONDON ARMOUR Y COMP ANY L TD., 3 1 , B u r y S t r e e t , S t . J a m e s ' , L o n d o n , S . W. I . WWW.RIFLEMAN.ORG.UKThe Rifleman T H E O F F I C I A L O R G A N O F t h e S O C I E T Y O F M I N I A T U R E R I F L E C L U B S . Te l e g k a i ' h i c A u u k e s s : '■ R i f i c s l i o f , E s t r < i i t i l , L o n d o n . " Te l e p h o n e : G e r r a r d 2 9 5 2 — Vol. XV. No. 100 (New Series). LONDON, OCT OBER, 1918. Monthly , One Penny . B O M B - D R O P P I N G F R O M A I R C R A F T . (Continued.) B y " B a l i s t i c a . " Calculation of the Path of a Bomh Falling in .'\ir F R O M A T r a v e l l i n g A i r c r a f t . WE are now in a position to calculate the path described by the bomb falling in air. formula required are :— The C = /- w £1 = U = nkd" E + e 2 V c o s E c o s E ' (14) (13) 2 cos E' (tan E — tan c) I ( « ) = I ( U ) + ^ ( 1 6 ) cc = Ccos E' { S («) —S (U) } i j — X t a n . . . f = C { T ( « ) - T ( U ) } u cos E ^ V = • ■ . • c o s e U7) (18) (19) (20) The method of calculation here adopted is known as the " small arc " method, the path of the bomb being calculated piecemeal. In Figure III. the path described bv the falling bomb is represented in part by the curve A B C D. Whilst the bomb is describing the arc from A to B the vertical height (y) fallen is AE and the hori zontal range (x) is KB. In formula (14) to (20) the other svmbols are defined as follows :—E is the angle which the path of the bomb makes with the horizontal at._A and e is the angle which the path of the bomb makes w i t h t h e h o r i z o n t a l a t B . E ^ i s t h e m e a n o f t h e s e t w o angles. U is a fictitious or pseudo velocity, obtained from the initial velocity, V, of the bomb by (15). v is the velocity at B and u the corresponding pseudo velocity as defined in (20). t is the time of flight from A to B. I (U), I («)' S (U), S(m), T (U) and T (it) are Inclina tion, Space and Time functions determined from the laws governing the resistance of the air as defined by formula (10) in the manner shown later. Having determined the elements of the bomb's path w h i l s t t h e b o m b m o v e s o v e r t h e a r c f r o m A t o B , w e proceed in the same way to deal with'the next portion of the path from B to C, and calculate and y^. E now becomes the angle at B, c the angle at C, and E^ the mean of these two angles. The pseudo velocity U at B is obtained by replacing the of (15) by the v of the previous arc. :y 1 \ V \ c x — - y - > 1 y \ h\ Fi(!. III. Calculation ol the path of a falling tomb by " amall arcs." Calculatio.n of the Inclination, Space, and T ime Functions. The Inclination (I), Space (S), and Time (T) func tions for values of the pseudo velocities, U or u, can be determined from the following series of formulae :— Velocities between o f.s. and 790 f.s. I I ( w ) = [ 5 . 8 3 7 4 2 4 6 ] 0 . 4 1 9 5 9 1 . ( 2 1 I u- S (ii) = 158436.8— [4-6923243] log u . (22) I T ( 11 ) = [ 4 . 3 3 0 1 0 8 6 ] 1 5 - 4 5 9 5 • • ( 2 3 > 21 WWW.RIFLEMAN.ORG.UK58 Velocities between 790 i.s. and 970 f.s. I I («)= [8.5577817] 0.050275 . (24) S (m) = [7.2265570] 5571.36 . . (25) T (w) = [6.9255270] 1.8801 . . (26) ni2 Velocities between 970 j.s. and 1,230 f.s. I I (m) = [14.3075048] h 0.109117 . (27) S {u) = [12.7210075] — + 6034.48 . (28) T (u) = [12.5960688] — + 2.6089 • (29) N.B.—The figures within the square brackets [ ] in formuln; (-21) to (29) are logarithms. In the example of calculation of the bomb falling in air from a travelling aircraft which follows the U em ployed for the first arc is 142.2 f.s., and by formulae (21), (22) and (23) the corresponding values of I (U), S (U) and T (U) are determined in the following manner : Calculation of I (142.2). log constant = 5.8374246 2 log 142.2 = 4.3057992 log 34.0115 = 1.5316254 I (142.2) = 34.0115 — 0.4196 = 33.5919 Calculation of S (142.2). log 142.2 = 2.1528996 log (log 142.2) = 0.3330239 log constant = 4.6923243 log 106010.3 = 5.0253482 S (142.2) = 158436.8— 106010.3 = 52426.5 Calculation of T (142.2). log constant = 4.3301086 log 142.2 = 2.1528996 log 150.3861 = 2.1772090 T (142.2) = 150.3861 — 15.4595 = 134.9266 T h e s m a l l d i ff e r e n c e s t o b e o b s e r v e d b e t w e e n t h e values of I, S and T for 142.2 f.s. as calculated above, and those employed in the first column of the calculation set out below, are due to the fact that the latter are taken direct from the tables calculated by Colonel Ingalls. Example of Calculation. As an example we may take the case of a bomb of 81 inches in diameter weighing 6olb. let drop from an afrcraft travelling at a speed of 140 feet per second at a height of 6,000 feet. Our data are then;— V = 140 f.s. ; t c = 6 o l b . ; d = 8J inches. and, assuming that shiipe and steadiness of the bomb are the normal of the experiments on which the air resistance laws were determined, and that the air density at the ground is al.so normal, therefore n = I k = I IV and = 0.830. nkd^ To commence, we take convenient values of E and c. Assuming tjiat the arc AB in Figure III. represents the path of the falling bomb, whilst its inclination to the horizontal changes from 'e = o° to e = 20° and the arc EC whilst the inclination changes from E = 20° to 6 = 30°, the calculation of the x and y corresponding to the arcs and BC is as follows. We have to allow for the value of / in the formula by guessing a value of y ; should the value of y as calculated be very different to its as sumed value the calculation has to be repeated, using the y found by the first calculation. The y for the arc .'\B is .seen to be 40 feet, that is to say, the bomb falls to a height of 5,960 feet whilst the inclination is changing from E = o° to c = 20°; the / adopted is, therefore, for the mean height for the arc, that is for 5,980 feet. is the height to the lower limit of anv arc. U = tan E E t o e0° to 20° 20° to 30° E'10° 25° y= 40 feet 5(5 feet y Y — - = 5,980 feet 5.933 feet f r. 2 0 1.20 w = / = 0.996 0.996 nlul^ V = 140 f.s. 140.7 f.s. V COS E = 142.2 f.s. 145.9 f.s. c o s E ' tan e = 0.36400.5774 tan E = 0.0000 0.3640 i — tan e 0.36400.2134 2 c o s E ' = 1.9696 1.8126 2 c o s E ' = 1.976 1.821 2 cos E^ (tan E — tan c) c = 0.7194 0.3881 I(U) = 33.5927 31.8891 I(tt) =34.312132.2772 u = 140.7 f.s. 145.0 1 S{u) = 52653.4 52009.5 S(U) = 52426.6 51877.2 S (M) — S (U) 226.8 132.3 C COS E' = 0.9814 0.9032 X = 223 feet ir9 feet y — x tan E^ = 39 feet55 feet T(«) = 136.53 132.02 WWW.RIFLEMAN.ORG.UKT H E R I F L E M A N . 59 T(U) = 134.93 T (u) — T (U) = 1.60 C = 0 . 9 9 6 i = C(T(«) — T(U)} = 1.59 see. u = 140.7 f.s. u c o s E ' V = = 1 4 0 . 7 f . s . c o s £ • 0.91 0.996 0.91 sec. 145.0 f.s. 151.8 f.s. A glance at Figure III. will serve to show what has ■heen ascertained by the foregoing calculations. The first column informs us that the bomb in passing from .-\. to B has covered a range, x, of 223 feet and has fallen through a vertical height, y, of 39 feet; the time of Hight for the arc is 1.59 seconds and the velocity at B is 140.7 f.s. In the same way the other column of our calculation gives 29=119 f'Cet, l/' = 55 feet, the time of flight from B to C is 0.91 second, and the velocity at C is 151.8 f.s. T h e c a l c u l a t i o n h a s b e e n c o n t i n u e d t o c o v e r t h e c o m plete flight of the bomb to the ground, eight columns of calculation similar to the above being involved in all. 9Te collected results of the complete calculation of eight small arcs are given in the following table :— Wliilst inclination Horizontal Yei tical T ime V elocity o f l i o n i b ' s r a i i i i c l i e i y l i t o f a t e n d t r a j e c t o r y c h a n g e s c o v e r e d f a l l e n f a l l . o f f r o m : i s : i s : i s : a r c i s ; feet. feet. sees. f.s. 0° to 20" 20° to 30° 30^ 40' to 40° to 50° to 60° 60° to 70 70° to 80° 80® to 80.3° 223 11 9 142 188 274 474 1037 57 39 55 99 188 392 1017 3870 340 1-59 0.91 1.08 1-45 2-15 3-87 9.69 0-59 140.7 151.8 170.2 200.3 251-7 348-3 555-7 564.1 From the foregoing table another table may be con structed giving the range, height fallen, time taken to fall, and the velocity at the end of each arc:— Wlien Horizontal Ve r t i c a l Ti m e Ve l o c i t y Inclination of raiifje heightofat end trajccloiy i s : covered fallenfall.of arc i s :i s :i s :i s : degs. feet.feet. sees. f.s. 0 0 00.000 20 223391-59 140.7 30 342 94 2.50 151.8 40 484 193 3-58 170.2 50 672381 5-03200.3 60 946 773 7.18 .251-7 70 1420 1790 11 . 0 5 348-3 802457 5660 20.74555-7 80.3 2514 6000 21-33 564.1 To calculate the Quadrant Angle of Depression, a, to the point where the bomb strikes the ground, we have, by formula (3) and the appropriate figures from the table .above :— ]i 6,000 Tangent a = — = :— X 2 , 5 1 4 = 2.387 a =67.3 degrees. In still air and under normal conditions of atmospheric temperature and pressure an aviator, therefore, would release his bomb at a height of 6,000 feet to strike a t a r g e t 2 , 5 1 4 f e e t h o r i z o n t a l d i s t a n c e f r o m t h e p o i n t vertically beneath him when his line of sight was at a quadrant angle of depression of 67.3 degrees. The striking velocity of the bomb being 564.1 f.s., the striking energy, employing formula (9) and Table \T., is:— S.E. = Aw = 4943x60 = 2 9 6 5 8 0 f o o t - p o u n d s V = 1 3 2 4 f o o t - t o n s . A\'ith the assistance of the figures given in the last table the path of the falling bomb may be plotted on squared paper. This has been done in Figure I\". The firm curve, .4, is the curve of the bomb falling in air, the dotted curve, B, that of the bomb falling in vacuo plotted by using the figures given in Table II. I t i s t o b e n o t i c e d t h a t a i r r e s i s t a n c e h a s c a u s e d a loss in horizontal range of 189 feet, an increase in the time of flight of about 2 seconds, an increase in the quadrant angle of depression of i4 degrees, a diminution in striking velocity of 73 f.s., an increase in the angle of descent of 3 degrees and a loss in striking energy of 36^ foot-tons. These facts are obvious from the com parative table giving the elements of the trajectory of a bomb of 6olb. weight, 84 inches diameter, let fall from an aircraft travelling at 140 f.s. at a height of 6,000 feet, in air and in vacuo, which follows:— Bomb falling. Element. . ' , In air . 2,514 feet. 21.33 sees. In vacuo. 2,703 feet. 19.31 sees. Range ... Time of flight ... Quadrant angle of de pression ... ... 67.3 degs. 65.8 degs. S t r i k i n g v e l o c i t y . . . 5 6 4 f . s . 6 3 7 f . s . Angle of descent ... 80.3 degs. 77-3 degs. S t r i k i n g e n e r g y . . . 1 3 2 4 f o o t - t o n s 1 6 9 f o o t - t o n s . We remarked in the opening instalment of these articles (Riflem.vn, June issue) that when the bomb is a heavy one and of comparatively small diameter, that is to say, when the sectional density as measured bv the ballistic coefficient, C, is small, the effect of air resistance is minimised to a large extent. In the case with which we have been dealing the average value of the ballistic coefficient may be taken to be w c = r nlid- 30) where /' is the value of the altitude factor for two-thirds of the height from which the bomb is dropped. (In a parabolic trajectory, such as the curve B in Figure IV., the average height of the ordinates is exactly two-thirds o f th e m a x i mu m o rd i n a te ; th e tw o -th i rd s a s s u mp ti o n , in the case of trajectories in air, is frequently made in ballistic calculations.) The value of for a height equal to thirds of the complete fall, that is for 4,000 feet, is 1.12, so that bv (30) C = 1.12 X 0.830 = 0 . 9 3 0 or rather less than unity. Our calculation informs us that with an average value of C slightly under unity the loss in range when compared with the fall in vacuo is 189 feet, or about 7 per cent, of the range. For a value of C of 2 we might therefore expect the loss in range when compared with the fall in vacuo to be rather less than a hundred feet, or say 3 or 4 per cent, of the range. WWW.RIFLEMAN.ORG.UK60 T H E R I F L E M A N . OCTOBEE, 1918. C-4LCUL.\TI0N OF THE PATH OF A BOMB FALBIXG pERPEyDICULARLY IN AlE FROM A ST.4.TI0NARY AIRCRAFT. From the point of view of accurate bomb dropping- the dirigible balloon possesses certain advantages over the aeroplane. It is possible for the balloon to hover over a jwsition, to adjust its aim for level of keel, and to drop its bomb fierpendicularly on to the target. Pro vided there is no disturbance from below in the nature of anti-aircraft fire (which can, of course, be particularly effective in the region of the vertical), and that there is a still atmosphere, accuracy of aim should not present great difficulties. We will calculate the time of fall of the 6olb. bomb of inches diameter, falling perpendicularly from a height of 6,000 feet. Our data are, assuming, as before, normal conditions for the coefficients of shape and steadi ness of the bomb, and for the air density at ground le\-el:— V = o f.s. ; w = 6 0 l b . d = 8h inches ; n = i ; k = 1 : u- and = 0.830. nkd- The formulae to be used are:— (V + v) (V — v) V ^9 (i — P/C) \T — V 9{^-VlC) y and t = o r t = — . (31) • ( 3 2 ) (33) Of formulae (32) and (33), the latter is the easier to use, and it gives results agreeing with (32). T h e c a l c u l a t i o n i s p e r f o r m e d p i e c e m e a l i n t h i s manner. Convenient intervals of increment in velocity are chosen such as and v, the value of p (the resistance of the air in pounds to the standard projectile of one inch diameter) for the average of these velocities, v^, is taken, and y the height fallen, whilst the velocity is increasing from V to V is then determined. The time of fall, t, is given by dividing the y for the interval by the corre sponding 71', if we employ formula (33). The calculation is now set out at length for a couple of intervals corresponding to two successive increments of 100 f.s. in velocity of the falling bomb:— V t o u = o f . s . t o 1 0 0 f . s . 1 0 0 f . s . t o 2 0 0 f . s . C = / — 50 f.s. 150 f.s. p = 0.0036 lb. 0.0327 lb. y = 160 feet300 feet y Y = 5 , 9 2 0 f e e t 5,694 feet / = 1.20. 1.18 w f = 0 . 9 9 6 0.980 nkd^ V — = 0.00362 c V •— = 0.99638 c 29 = 64.38 V = 64.1 (V + v) (V — 7;) = 10,000 7/ = 156 feet Y — y = 5,844 feet y t = — = 3.12 sees. v'^ 0-0334 0.9666 64.38 62.2 30,000 482 feet 5,362 feet 3.21 sees. 6000 Direction of Ftipht- 5000 :j. 4000 .-s 3000 zooo 1000 J W.HlCKS. V v \\ \> \\ Vx \x \\ \\ \\ \ V \ x X \ \ [ \ \ \ \ \ \ ^ \ \ \ X \ \ \ \ \ \ \ \ \ \ ^ \ a\ \ B \ \ \ \ ^ \ ^ \ X 1000 ZOOO 3000 R R N G E ( N F E E T Fig- IV. Path of bomb falling from an aircraft travelling at a speed of 143 feet- per second (or 93 miles per hour) at a height of 6,(XX) feet. A. In air . B. In a vacuum It may be well to follow the steps of calculation employed above in detail. The initial velocity for the first column of the calculation is, of course, V = o f.s. An increment of loo f.s. is chosen so that u=ioo f.s. The mean velocity is 50 f.s. and the value of p for the mean velocity is calculated by formula (11). Formula (i r) gives R, the resistance in pounds for a bomb of any diameter d. WWW.RIFLEMAN.ORG.UKOctober, 1918. T H E R I F L E M A N . 61 For the .specific case of the unit projectile of i inch d i a m e t e r w e t a k e Av ' " - P = • • • ( 3 4 ) (I For the mean velocity of 50 f.s. we have 46762 X 2500 P = 10'' X 32.19 = 0.00362 lb. / is taken for the mean height where V is the height at the commencement of the interval and ij the distance fallen during the interval. .\ value for )/ has to be guessed and the calculation repeated if the guess is found to be a bad o n e . T h e r e m a i n d e r o f . t h e c a l c u l a t i o n w i l l b e u n d e r stood readily on inspection, as it follows the steps neces sary in using formulsE (31) and (33). The results of the complete calculation down to the ground are contained in the following table :— W h i l s t v e l o c i t y H e i g h t T i m e o f of bomb fallen fall i n c r c a . s e s f r o m : i s : i s : feet. sees, o f . s . t o t o o f . s . 1 5 6 3 . 1 2 100 f.s. to 200 f.s. 482 3.21 200 f.s. to 230 f.s. 378 1.68 250 f.s. to 300 f.s. 483 1.76 300 f.s. to 350 f.s. 604 1.86 350 f.s. to 400 f.s. 748 1.99 400 f.s. to 430 f.s. 934 2.20 430 f.s. to 300 f.s. 1 184 2.49 300 f.s. to 333 f.s. 1031 1.99 I he height fallen and the time of fall at each selected interval of velocity is useful to have tabulated, and is easily derived from the foregoing table, thus:— When velocitv Height Ti m e of falling bomb fallen taken to fall is : is : is: ' f.s.feet. sees. 000.00 100156 3.12 200 638 fi-33 230 10168.01 30014999-77 350 2103 11.63 400 2851 13.62 450 378515.82 300 496918-31 535 6000 20.30 Referring to Figure I\". we may note that whilst the bomb takes 21.33 seconds to tra\ erse the curve -A, it takes 20.30 seconds to fall vertically. The remaining velocity at the end of the curved path is 364 f.s. as compared with 333 f.s. at the end of the vertical path. One other interesting point as regards Figure IV. is to be noticed. The horizontal velocity of the parabolic curve, B, being constant, the aircraft (assuming its tra velling speed to be uniform and its direction horizontal) would have covered a distance (2,703 feet) equivalent to that traversed by the bomb, and would therefore be imme diately over the point of fall of the bomb at the moment it reached the ground. Travelling in air (curve A) the bomb would have covered only 2,314 feet, whereas the aircraft would have moved 2,703 feet, so that the aircraft would have passed the perpendicular at the point of fall by 189 feet before the bomb reached the ground. (To he continued.) B U R R O U G H E S & W AT T S C O M P E T I T I O N , 1 9 1 8 . Conditions : Teams of four from any Club in the United Kingdom affiliated to the S.M.R.C. deliberate at 25 yards, on two S.M.R.C. Match targets. 20 shots per man D R . W V F O R P R E L I M I N . A R Y R O U N D . Newcastle and DistrictW'aiisend and Ncptiine it Team l i i c c t r i c i . i g i i t i n g ( t o . . \ Te a m . H a r r o w v. N o r w i c h E l e c t r i c Tr a m w a y s . ( i a r s t o n . \ Te a m v . H a z e i i s . A Te a m . AA'itnoy i'iatoon Oxford Volunteers .A Team v. I.uton and Disirict .A Team. Metro. Eiorlric It 'I'eam v. Thatcham Special Police C Team. _ ("arlton and District v . Silloth It 'Peam. 7- S. 9- 11. 12. C Co. 2nd A'orks V.R. .A Team v. Cambridge Railways .A Team. Harrington .A Team v. Tondu and District. Ctloucestcr AA'agon Works C Team v. Grimsby Central .A Te a m . D u m f r i e t a n d M a x w e l l t o w n v . H a m m e r s m i t h I r o n W o r k s B Te a m . L l a n e l l y v. H e n d o n . Roulton and Paul .A Team v. Borough of Portsmouth. DRA W FOR FIRST ROUND. 1. 2. .t- 4- ,v 6. / 8. 9- Wallscnd and Neptune B Team v. Hendon or Llanelly. Harrow v. Boulton and Paul A Team or Borough of Ports mouth. Garston A Team v. Vickers (Cravford) .A Team. Luton and District .A Team v. Wokingham Platoon. M e t r o . E l e c t r i c B Te a m v . M a i d e n h e a d a n d D i s t r i c t . S i l l o t h B T e a m v . A r b r o a t h . C Co. 2nd A'orks V.R. .A Team v. Bolsover Colliery. Tondu and District v. Gloucester City B Team. Grimsby Central .A Team v. Crayford C Team. D u m f r i e s a n d M a x w e l l t o w n o r H a m m e r s m i t h I r o n W o r k s B Team v. Charing Cross Electric. 11 . 12. •3- 14- Lv 16. 17- 18. 19. H.'irtley Wintney v. AA'est Ham National Reserve B Team. W i m b l e d o n P a r k B T e a m v . W e s t H a m N a t i o n a l R e s e r v e A Te a m . F l a l i n g B Te a m v. T h e t f o r d A ' . T. C . Brighton Railway .Athletic .A Team v. Royal Aircnift Establish ment D T eam. C C o . 2 n d A ' o r k s V . R . B T e a m v . H e w o r t h B T e a m . Jedburgh v. Metro. Electric .A Team. Stourbridge v. .Addiscombe .A Team. Metro. Police K Division Limehouse v. Metro. (Birmingham) A T e a m . D u n s t o n E x c e l s i o r v. S t . F a i t h ' s , B r e n t f o r d . WWW.RIFLEMAN.ORG.UK62 T H E R I F L E M A N . October, 1918. 20. Padiham v. Brincliffe and Ecclesall C Team. 21. Roval .Aircraft Establishment B Team v. Hammer.smith Iron \ \ ' o r k s A Te a m . 22. Lee B Team v. Gloucester Wagon Works .A Team. 23. Holmes Chapel Detachment Cheshire V.R. B Team v. Cray- f o r d B Te a m . 24. Sterling A Team v. .Metro. Police S Division A Team. 25. .Metro. Police P Division v.AA'allsend and N'eptiine C Team. 26. Perth City^ and County v. Ferryhill N'.E.R. 2-. Orrell and District v . Leven and District. 2S. L. and S. AA. Railway v. Newcastle and District Electric Lighting Co. B Team. 2 9 . L . P. S . H e a d q u a r t e r s B Te a m v. C a s t l e f o r d A ' o l u n t e e r s B Te a m . 30. Pitsmoor A Team v. Fuilers Electrical AA'orks. 31. Garston B Team v. Luton and District C Team. 32. AA'althamstow Ensign .A Team v. Llandudno. 33. N.E.R.. York, B Team v. Ruston and Hornsby's Boiler AVorks B J ' e a m . 34. Old Grammarians (Brighton) v. No." 2 Platoon -A Co. ist AyB. Devon Regt. 35. Borough of AA'andsworth v. Portslade B Team. 36. .Mann Egerton v. I..G.O.C. B Team. 37. North Staffs Railway v. Vickers Crayford C Team. 38. Gloucester Civil Service v. N.E.R., York, .A Team. 39. Metro. Police S Division B Team v. Metropolitan (Birmingham) B T e a m . 40. Clitheroe National Reserve .A Team v. Luton and District B Te a m . 41. .Arcadia B Team v. Upper Tooting Church Institute. 42. Hazells B Team v. ,A Co. Hunts. Volunteers .V Team. 43. Sissons V. Metro. Electric C Team. 44. Railway Transport Depot R.E. D Team v. L.G.O.C. .A Team. 45. Silloth .A Team v. Faversham National Reserve. 46. G.E.R. .Alechanics' Institute A Team v. Southgate. 47. AAestwood AA'orks B Team v. L.G.O.C. C Team. 48. AA'estwood AA'orks -A "I'eam v. Thatcham Special Police A Team. 49. .Midland Railway, Kettering, B Team v. X Division Special Constabulary. 30. R..N. Barracks, Devonport, B Team v. Pitsmoor B Team. 51. Brighton Railway .Athletic B Team v. Devonport A Team. 32. .Associated Equipment Co. B 'Team v. Railway Transport Depot R.E. C Team. 3 3 . . A C o . i s t N o r t h a n t s A ' . R . v . . A t l a s B T e a m . , 3 4 . G r i m s b y C o r p o r a t i o n . A Te a m v. B r i n c l i ff e a n d E c c l e s a l l A Te a m . 33. .Appleton B Team v. Lancaster. 36. Chiswick V. A" Division Special Constabulary. 37. Blackfriars v. St. Botolph's, Bishopsgate. 3 8 . H o r s h a m A Te a m v. H a m a n d P e t e r s h a m B Te a m . 59. Bicester Town and District v. .Alitcham. 60. .Appleton A Team v. Cripplegate. 61. Kensington v. R.M., Chatham B 'Team. 62. Finchley Special Constabulary B Team v. AA'allsend tynd Neptune .A Team. 6 3 . S te r l i n g B Te am v. R enfield B Tea m. 64. AA'althamstow Ensign B Team v. R.N. Barracks. Devonport, .A T eam. 63. G.E.R., Liverpool Street, .A Team v. Horsham C Team. 66. .Appleton C Team v. Upper Mills .A Team. 67. 14th and i6th Platoons D Co. 2nd AMI. AA'est Riding Regt. v. .A Co. Morayshire A'.R. B Team. 68. Lyne v. Castleford A'olunteers .A Team. 6<). 3th I.iskeard Platoon B Co. 2nd Cornwall A'.R. v. Ham and P e t e r s h a m A T e a m . 70. Globe AA'orks v. J. S. AA'hite and Co., Cowes, C Team. 71. J..A.P. V. Devonport B Team. 72. Sperryn Athletic B Team v. Royal Marines, Chatham, .A Te a m . 7 3 . .Al id l a nd R ai l w a y, D erby, v. G ranvi lle Ca na di an s A Team . 74. Midland Railway, Nottingham, v. D Co. 4th V.B. Middlesex Regt. 73. Hendon and Crirklewood A Team v. Meigle and District A 'i'eam. 76. Liverpcxil B Team v. L.P..S. Headquarters .A 'Team. 77. Lee A 'Team v. AA'imbledon Park C 'Team. 78. A Co. ist .Morayshire A'.R. v. .A lAivision Special Constabularv A T e a m . 79. Clitheroe National Reserve B 'Team v. A Division Special C o n s t a b u l a r y B Te a m . 80. AA'hite and Poppe B Team v. Upper Mills B Team, 81. Finchley Special Constabulary C Team v. .Midland Railway, Kettering, A Team. 82. British Electric Transformer v. Gloucester AVagon AVorks B Te a m . S3. Finchley Special Constabulary .A leam v. J. S. AA bite and Co., Cowes, D Team. 84. Sperryn Athletic A Team v. Bishop Auckland. 83. Innerleithen and District v. .Alanchester City. 86. Royal Aircraft Establishment C Team v. Renfield C Team. 87. Hvde Park B Team v. A Co. Hunts. A olunteers B 'leam. 88. G.E.R. .Mechanics' Institute B Team v. A Co. i/ist Northern Counties Highland A'.R. B Team. 8g. Hartlepool v. Grimsbv Central B Team. 90. Harrods Territorial Association v. .Meigle and District B Team. 91. Railway Transport Depot R.E. B i earn v. Barnslcy and District. 92. Boulton and Paul, Ltd., B Team v. Portslade A Team. 93- West Ham Police v. Arcadia A Team. 94. Hanlev Y.M.C.A. v. Ealing A I'eam. 95- Gloucester City A 'I'eam v. Bethnai Green Tradesmen's. 96. 'Thatcham Special Police B Team v. Caxton B leam. 97. Hyde Park A Team v. Railway 'Transport Depot R.E A Team. 98. Garswood Hall Collieries v. Lee C Team. 99. G.E R., Liverpool Street, B Team v. Southampton Corporation Tr a m w a y s . 100. A Co. i/ist Northern Counties Highland ALR. A Team v. P i t s m o o r C T e a m . 101. Crayford A Team v. A Co. 17th County of London. 102. .Associated Equipment Co. A 'I'eam v. lyth and i8th Platoons E Co. 2nd A'.B. Yorks Regt. 1 0 3 . H o r s h a m B Te a m v. C a x t o n A Te a m . 104. A Co. 4th V.B. AA'elsh Regt. v. Reading A Team. 105. Frederick Steel and Co., Ltd., B 'I'eam v. Granville Canadian B T e a m . 106. Holmes Chapel Detachment Cheshire ALR. A Team v. Port land Sports Club. 107. Grimsby Corporation B Team v. Brincliffe and Ecclesall B Te a m . 108. Barrow v. Reading B Team. 109. Renfield A Team v. Heston A Team. n o . G u i l d f o r d a n d D i s t r i c t v. A C o . H u n t s Vo l u n t e e r s C Te a m . 111. Darlington Railway Athletic v. B Co. ist V.B. O.xford and B u c k s L . I . 112. E'rederick Steel and Co., Ltd,, .A Team v. Ruston and Hornsby's B o i l e r A A ' o r k s . A Te a m . 113. Holmes Chapel Detachment Cheshire V.R. C Team v. Hendon a n d C r i c k l e w o o d B T e a m . 114. Ellengowan v. Deal and District. 115. Cheani v. Cowes. 116. City of London National Reserve v. Liverpool A Team. 11 7 . R u s t o n A i r c r a f t v. i s t B a t t a l i o n C r o y d o n N a t i o n a l R e s e r v e . 11 8 . H a r r i n g t o n B Te a m v. H e w o r t h A Te a m . 119. Ucklield v. AA'imbledon Park A Team. 120. AA-'allasey v. Hampstead Special Constabulary. 121. Royal .Aircraft Establishment A Team v. 3rd Faversham Troop Boy Scouts. 122. 8th Platoon B Co. 2nd A.P.AALO. Yorks Regt. v. Herrington, 123. Monmouth and District v. Metro. Police N Division. 124. Prestwich and District v. Addiscombe B Team. 123. Cambridge Railways B Team v. Heston B Team. 126. J. S. AA'hite and Co., Cowes, A Team v. A^ickers Crayford B Te a m . 1 2 7 . A t l a s A Te a m v. N o . i P l a t o o n 2 n d A ' . B . A . P. A A L O . Yo r k s Regt. 128. AA'hite and Poppe .A Team v. J. S. AA'hite and Co., Cowes, B Te a m . N O T I C E T O C L U B S E C R E T A R I E S . The Society of Miniature Rifie Clubs has no local agents. All conimunications shojild be addressed direct to:—The Secretary, S.M.R.O., Arundel House, Arundel Street, London, W.C.2. WWW.RIFLEMAN.ORG.UKOcTOBElt, 1918. T H E R I F L E M A N . 63 REGISTER OF WINNERS. 1 l a T 1916 1916 1917 I917 1917 1917 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 1918 igiS 1918 1918 1918 1918 191S 1918 1918 1918 1918 Club. Leven and District Holmes Chapel Bombay Port Trust Leven and District Castleford Volunteers Kossie Rossie St. Faiths (Brentford) .'Vrmy Service Corps (M.T.t Kempton Park Sperryn Athletic Wa l l a s e y Manchester City 5th Essex Volunteer Regiment (Barking Coy.) 4th Suffolk Volunteer Regiment D Coy. (Brantham Platoon) L e w i s h a m N a t i o n a l R e s e r v e We s t L o n d o n L e a g u e Prestwich and District 3rd Glamorgan Volunteer Regi ment, D Coy. Holmes Chapel Associated Equipment Coy. Royal Air Force (Grain) Sissons Northants Volunteer Regiment, ist Batt., A Coy. Roj'al Naval Barracks, Devon- port King's School, Pontefract Royal Berkshire Volunteer Regi ment, ist Batt. 12th Platoon (Wokingham) Camberwell Special Constab- lary Lowestoft Railway Essex Cadet Regiment 4th Batt. (Hornchurch Coy.) D u m f r i e s a n d M a x w e l l t o w n A r m y O r d n a n c e C o y. N o . i Section, Aldershot County of London Volunteer Regiment, 13th Batt. D (Put ney) Coy. South Suburban Gas Coy. (Cray Wo r k s ) S t . G i l e s Ya r n e r s D C o y . 4 t h B a t t . ( D . C . O . ) Middlesex Volunteer Regiment M i d l a n d R a i l w a y ( H i g h g a t e Road) Grimsby Central H a m a n d P e t e r s h a m Uckfield Mobberly No.Bell Medal. Daily E.xfress Medal. 1920 J. G. Thomson J. G. Thomson 2423 Pte. W . Benson L/C. G. Davies 244a G. Baker R. Collyer 1920 ^ T. R i t c h i eT. R i t c h i e 1366 G. FellS. Stewart 1657W. M a r t i nJ. S. Smith ih57 J. McLaren W. M a r t i n 274 Mrs. J. W .H. S. Alford Croxford gSS 3000a W. J. Wright T. L e v i t t 495 G. H. Trapnell R. Billby 506 A. T . Mof fat 1918 4th East Yorks. Regt. (T.F.) 3214a 2747a 3445 2699 3227 2017 2423 3221 3230 2732 1949 2573 3874 2018a T912 2809 3122a 1051 3262a 3121a 2570 2010 2681a 3164 2972 365 3584 303a 3337a Lieut. F.W .O. L/Cpl. H. Bond Sergt. J. G. Tice Sergt. Willan A. E. Cooke A. T . Craston E. S. Chapman Pte. S. Dakin F. Newberry J. W. Fowler C. S. M. Miller C.P .O. Martin G. Reynolds L/Sergt. Denton Sergt. T. Knight Sergt. D, Macmillan W. Hope Pte. A. Brown L/Cpl. C. J. Stone W. C . S w e a t m a n J. Scott Sergt. P. G. Mitchell T. W . G i l l W. S o u t h o n Lt. Thos. Prince Pte. F. Murphy Pte. J.N.SIinger Wa t s o n Sergt. J. G. Tice Cpl. Crook F. H a r v e r s o n J. J. Stobo T. B . W a t s o n Pte. H. Bolshaw C. K. Edwards 2/Lt. Gammon Pte. Edgoly C.P.O. Madge F. J. Finn L/Sergt. Denton Sergt. T. Knight E. Garrod C.S.M. R. Holloman W. H o n e S.Q.M.S. McGraw L/Cpl. S. J. White W. T. G . Gillham C. McGregor Cpl. H. A. Peters H. O. Coverley E. Southon W. B. Sargeant Lt.V. H. Sugden Daily Telegraph Certihcaie. J. G. Thomson Pte. W . Simm R. Collyer T. R i t c h i e J. Hollings W. M a r t i n C. W atson W. G o o d m a n J. H. Cox G. H. Roscoe D a i l y H a i l Certificate. J. G. Thomson Pte. W . Benson F. J. Warder T. R i t c h i e S. Stewart D. Bruce J. B. McGibbon M". Goodman Pte. G. A. VYgar E. T oulouse E. P . Cottier W. B u c k l e Ladv's Medal. Sergt. J. W. Rungay | 2;Lt. Sproxton Sergt. J. G.Tice Sergt. Jones W. F . B u t l e r G. T . Oakes E. S. Chapman Sergt. S. Oakes G. A.Jones A. M. Newstead Pte. Y\'ingrove C.P.O. Jones H. Gledhill Pte. A. Leonard E. Garrod C.S.M. R. Holloman T. H. Boyd Pte. Buckingham L/Cpl. J. J. Hedges H. Gillham C. McGregor Pte. S. F . Sainsbury B. Hardy E. Southon Lt.Thos. Prince H. Fildes C. H.Edwards E. W . Palmer J. S. Oliver T. B . W a t s o n Pte.T. Hursfield T. K n o w l e s L. M. Pearce Cpl. Ashby C.P.O. May C. H. Sizer Pte. L. J. Griffith E. Garrod Pte. Clause T. H. Boyd Pte. H. Jackson Pte. E. Evans J. C. Harland C. McGregor Pte. W . H. Cocks A. E. Gray W. C o l l i n s Lt.Thos. Prince Cpl. H. H. Law M i s s G . Daplvii Mrs. M. Chilcott P O S T F R F F O r d e r s f o r " T h e R i fl e m a n " i n q u a n t i t i e s o f m o r e 1 i-w L-, than two dozen copies will be sent Post Free. WWW.RIFLEMAN.ORG.UKNext >