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RANGE TABLE FOR

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Originally appearing in Volume V03, Page 276 of the 1911 Encyclopedia Britannica.
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RANGE TABLE FOR 6-See also:

INCH See also:GUN. Projectile Palliser shot, Shrapnel See also:shell. See also:Weight, See also:loo lb. Muzzle velocity, 2154 f/s. Nature of mounting, See also:pedestal. Jump, nil. To strike 5' See also:elevation or Fuse 50 % of rounds alters an See also:object depression See also:scale for should fall in. Remain- to ft. Slope of impact. T. and P. See also:Time Penetra- point of See also:ing high De- Later- Eleva- Range. See also:middle of tion into Velocity. range See also:scent. ally or tion.

No. 54 See also:

Flight. Wrought must be Range. Verti- Marks I., Length. Breadth. Height. known to cally. II., or III. fjs. yds. in. yds. yds. yds. yds. yds. yds. secs. in. 2154 ,.

.. o•o0 0 0 0 .. .. .. 0•O0 13.6 2I22 1145 687 125 0.14 0 4 100 ; .. 0.4 o•16 13.4 2091 635 381 125 0.29 0 9 200 0.4 0'31 13.2 2061 408 245 125 0.43 0 13 300 1 .. 0.4 .. 0.47 13.0 2032 316 190 125 0.58 0 17 400 Iq .. 0.4 .. o•62 12.8 2003 260 156 125 0.72 0 21 500 If .. 0.5 0.2 0.78 12.6 1974 211 127 125 .0.87 0 26 600 2 .. 0.5 0'2 0.95 12.4 .1946 183 1I0 125 I.OI 0 30 700 21 .. 0.5 0.2 I•II 12.2 1909 163 98 125 1.16 0 34 800 2 .. 0.5 0.2 1.28 12.0 1883 143 85 125 1.31 0 39 900 3 .. o•6 0.3 - 1.44 II.8 1857 130 78 125 1.45 0 43 1000 311 .. o•6 0.3 1•6t II.6 1830 118 71 125 160 0 47 II00 3a o•6 0.3 I.78 II.4 1803 110 66 125 1.74 0 51 1200 4 o•6 0.3 I.95 I1.2 1776.

IOI 6, 125 I•$9 0 55 1300 4± .. 0.7 0.4 2.12 11.0 1749 93 56 125 2.03 0 59 1400 41 .. 0.7 04 2.30 to.8 1722 86 52 125 2.18 I 3 1500 5 .. 0.7 0.4 2.47 Io•6 1695 8o 48 125 2.32 I 7 1600 5Z 25 o•8 0.5 2.65 10.5 1669 71 43 125 2.47 1 II 1700 51 25 0.9 0.5 2.84 10.3 1642 67 40. too 2.61 I t6 i800 64 '25 1•0 0.5 3.03 10•I 1616 61 37 100 2.76 I 22 1900 62 25 1.1 o•6 3.23 9.9 1591 57 34 100 2.91 127 2000 7 25 I.2 0•6 3.41 9.7 The last See also:

column in the Range Table giving the inches of penetration into wrought See also:iron is calculated from the remaining velocity an empirical See also:formula, as explained in the See also:article See also:ARMOUR PLATES. _ High See also:Angle and Curved See also:Fire.-" High angle fire," as defined and See also:row officially, " is fire at elevations greater than 15°," and "curved (53) fire is fire from howitzers at all angles of elevation not exceeding 15°." In these cases the curvature of the trajectory becomes considerable, and the formulae employed in See also:direct fire must be modified; the method generally employed is due to See also:Colonel Siacci of the See also:Italian See also:artillery. Starting with the exact equations of See also:motion in a resisting See also:medium, also (56) dy_Cgsecitani. dq f (q sec i) ' (57) di _ Cg dq _q sec i . f (q sec i)' (58) d tan i C g sec i __ dq q •f(q sec i)' from which the values of t, x, y, i, and tan i are given by integration with respect to q, when sec i is given as a See also:function of q by means of (51). Now these integrations are quite intractable, even for a very See also:simple mathematical See also:assumption of the function f(v), say the quadratic or cubic See also:law, f(v) = v2/k or v'/k. But, as originally pointed out by See also:Euler, the difficulty can be turned if we See also:notice that in the See also:ordinary trajectory of practice the quantities i, See also:cos i, and sec i vary so slowly that they may be replaced by their mean values, n, cos n, and sec n, especially if the trajectory, when considerable, is divided up in the calculation into arcs of small curvature, the curvature of an arc being defined as the angle between the tangents or normals at the ends of the arc. Replacing then the angle i on the right-See also:hand See also:side of equations (54) -(56) by some mean value n, we introduce Siacci's pseudo-velocity u defined by (59) u = q sec n, so that u is a quasi-component parallel to the mean direction of the tangent, say the direction of the chord of the arc. by and eliminating r, (45) dx d2ydy ex_- dx dt dt2 _ dt dt2 - gdt' and this, in See also:conjunction with (46) tan i=dv_dy dx dt~dc' 2 .di dx d2y - dy d2x dx sec idt= (at d2i dt di2) (dt) 2 (47) reduces to (48) di tan i _- g dt = - v g COs . Or d dt - v cos i the See also:equation obtained, as in (18), by resolving normally in the trajectory, but di now denoting the increment of i in the increment of time dt.

Denoting dx/dt, the See also:

horizontal component of the velocity, by q, so that (49) v cos i=q, equation (43) becomes (5o) dq/dt= -r cos i, and therefore by;(48) (51) It is convenient to notation (See also:a2) (43) 2 _ - -r cos i = -rds' (44) d2 = - See also:sin i- = -rdsr dqdq dt_ry di=dt di-g' See also:express r as a function of v in the previous Cr=f(v), vf(v) di_ Cg ' an equation connecting q and i. Now, since v=q sec .t (54) dt _ sec i dq -Cf(q sec i)' and multiplying by dx/dt or q, (55) dx C q sec i dq f(q sec il' and multiplying by dy!dx or tan i, Integrating from any initial pseudo-velocity U, u du t=(. f f~u)f di -6=Crcosn fuf, tan 47—tan 6= Cgsecn du J u.f(u) But according to the See also:definition of the functions T, S, I and D of the ballistic table, employed for direct fire, with u written for v, Now calculate the pseudo-velocity ins from (81) uo=vi cos 4) sec n, and then, from the given values of 4 and 0, calculate ue'from either of the formulae of (72) or (73) :-- (82) I(ue) -I(u4) —tan ) —tang c( sec n °—6° D(ue)=D(us)— cos n. Then with the suffix notation to denote the beginning and end of the arc 4—6, (84) mte =C[T (u4)-T{ue)I, (85) 0+xe =C cos n [S(uo) —S(ue)], y _ DA (Y-Csecn I(u~)—S A now denoting any finite See also:tabular difference of the function between the initial and final (pseudo-) velocity. x=C cos n f f~u) y=C sin rt f f(u); and supposing inclination . to 0 radians the arc. (63) (6o) (61) (62) over (64) (83) (86) (65) fu ufn(t =J gp=T(U)—T(u), (66) J u du =S (U) —S (u), (u) (67) `g du J =I(U)—I(u)> uf(u) and therefore (68) t =C [T(U) —T(u)], (69) x=C cos n [S(U) —S(u)], (70) y=C sin n [S(U) —S(u)], (71) 47—0=C cos n [I(U) —I (u)], (72) tan 4—tan B=C sec n [I(U)—I (u)], while, expressed in degrees, (73) 0°—6°=C cos n [D(U)—D(u)]. The equations (66)—(71) are Siacci's, slightly modified by See also:General Mayevski; and now in the numerical applications to high angle fire we can still employ the ballistic table for direct fire. It will be noticed that n cannot be exactly the same mean angle in all these equations; but if n is the same in (69) and (70), (74) y/x = tan n, so that n is the inclination of the chord of the arc of the trajectory, as in Niven's method of calculating trajectories (Prot. R. S., 1877): but this method requires n to be known with accuracy, as i %, variation See also:inn causes more than 1 % variation in tan n. The difficulty is avoided by the use of Siacci's See also:altitude-function A or A(u), by which y/x can be calculated without introducing sin n or tan n, but in which n occurs only in the See also:form cos n or sec n, which varies very slowly for moderate values of n, so that n need not be calculated with any See also:great regard for accuracy, the See also:arithmetic mean 2(47+6) of y and 0 being near enough for n over any arc ¢—B of moderate extent. Now taking equation (72), and replacing tan 0, as a variable final tangent of an angle, by tan i or dy/dx, (75) tan 4—=C secn [I(U)—I(u)] and integrating with respect to x over the arc considered, (76) But (77) f o I (u)dx = fuI (u)dudu =C cos n f UI(u)udu 9f (u) =C cos n [A(U) —A(u)] in Siacci's notation; so that the altitude-function A must be calculated by summation from the finite difference AA, where (78)' AA=I(u) 9uAu P `I(u)AS, or else by an integration when it is legitimate to assume that f(v) =v'0/k in an See also:interval of velocity in which m may be supposed See also:constant. Dividing again by x, as given in (76), (79) tan 4— =Csecn[I(U)—S(U)—S((u))] from which y/x can be calculated, and thence Y.

In the application of Siacci's method to the calculation of a trajectory in high angle fire by successive arcs of small curvature, starting at the beginning of an arc at an angle ¢ with velocity v4), the curvature of the arc ¢—0 is first settled upon, and now (8o) n=1(0+6) is a See also:

good first approximation for n. N, M' Qz Ns Also the velocity tie at the end of the arc is given by (87) ve=u0 sec 0 cos n. Treating this final velocity vo and angle 0 as the initial velocity vo and angle 47 of the next arc, the calculation proceeds as before (fig. 2). In the See also:long range high angle fire the shot ascends to such a height that the correction for the tenuity of the See also:air becomes important, and the curvature 4—0 of an arc should be so chosen that ¢ye, the height ascended, should be limited to about moo ft., See also:equivalent to a fall of 1 inch in the See also:barometer or 3 % diminution in the tenuity See also:factor r. A convenient See also:rule has been given by See also:Captain See also:James M. Ingalls, U.S.A., for approximating to a high angle trajectory in a single arc, which assumes that the mean See also:density of the air may be taken as the density at two-thirds of the estimated height of the vertex; the rule is founded on the fact that in an unresisted parabolic trajectory the See also:average height of the shot is two-thirds the height of the vertex, as illustrated in a See also:jet of See also:water, or in a stream of bullets from a See also:Maxim gun. The longest recorded range is that given in 1888 by the 0.2-in. gun to a shot weighing 38o lb fired with velocity 2375 f/s at elevation 40°; the range was about 12 m., with a time for flight of about 64 sec., shown in fig. 2. A calculation of this trajectory is given by See also:Lieutenant A. H. Wolley-Dod, R.A., in the Proceedings R.A.

Institution, 1888, employing Siacci's method and about twenty arcs: and Captain Ingalls, by assuming a mean tenuity-factor r=o•68, corresponding to a height of about 2 m., on the estimate that the shot would reach a height of 3 m., was able to obtain a very accurate result, working in two arcs over the whole trajectory, up to the vertex and down again (Ingalls, Handbook of Ballistic Problems). Siacci's altitude-function is useful in direct fire, for giving, immediately the angle of elevation 4 required for a given range of R yds. or X ft., between limits V and v of the velocity, and also the angle of descent ,B. In direct fire the pseudo-velocities U and u, and the real velocities V and v, are undistinguishable, and sec n may be replaced by unity so that, putting y=o in (79), tan 4)=C [I (V)--AA. S]• Also (89) (90) tan /3=C [S—I(v) or, as (88) and (90) may be written for smal angles, (91) sin 24) 2C [I (V) —AA] AS' (92) sin 2/3=2C [oS — I (v)]' To simplify the See also:

work, so as to look out the value of sin 2¢ without the intermediate calculation of the remaining velocity v, a See also:double-entry table has been devised by Captain Braccialini Scipione x tan 4'—y=C sec n [xI (U)—f I(u)dx]. (88) tan 4—tan 13=C II(V) -L (v)] so that 7 (Problemi del Tiro, See also:Roma, 1883), and adapted to yd., ft., in. and lb See also:units by A. G. Hadcock, See also:late R.A., and published in the Proc. R.A. Institution, 1898, and in Gunnery Tables, 1898. In this table (93) sin 20=Ca, where a is a function tabulated for the two arguments, V the initial velocity, and R/C the reduced range in yards. The table is too long for insertion here. The results for and /3, as calculated for the range tables above, are also given there for comparison.

See also:

Drift.—An elongated shot fired from a rifled gun does not move in a See also:vertical See also:plane, but as if the mean plane of the trajectory was inclined to the true vertical at a small angle, 2° or 3°; so that the shot will See also:hit the See also:mark aimed at if the back sight is tilted to the vertical at this angle 5, called the permanent angle of deflection (see See also:SIGHTS). This effect is called drift and the See also:reason of it is not yet understood very clearly. It is evidently a gyroscopic effect, being reversed in direction by a See also:change from a right to a See also:left-handed twist of rifling, and being increased by an increase of rotation of the shot. The See also:axis of an elongated shot would move parallel to itself only if fired in a vacuum; but in air the couple due to a sidelong motion tends to See also:place the axis at right angles to the tangent of the trajectory, and acting on a rotating See also:body causes the axis to precess about the tangent. At the same time the frictional See also:drag damps the See also:nutation and causes the axis of the shot to follow the tangent of the trajectory very closely, the point of the shot being seen to be slightly above and to the right of the tangent, with a right-handed twist. The effect is as if there was a mean sidelong thrust w tan S on the shot from left to right in See also:order to deflect the plane of the trajectory at angle S to the vertical. But no formula has yet been invented, derived on theoretical principles from the See also:physical data, which will assign by calculation a definite magnitude to S. An effect similar to drift is observable at See also:tennis, See also:golf, See also:base-See also:ball and See also:cricket; but this effect is explainable by the inequality of pressure due to a vortex of air carried along by the rotatingball, and the deviation is in the opposite direction of the drift observed in artillery practice, so artillerists are still awaiting theory and See also:crucial experiment. After all care has been taken in laying and pointing, in accordance with the rules of theory and practice, See also:absolute certainty of hitting the same spot every time is unattainable, as causes of See also:error exist which cannot be eliminated, such as See also:variations in the air and in the muzzle-velocity, and also in the steadiness of the shot in flight. To obtain an estimate of the accuracy of a gun, as much actual practice as is available must be utilized for the calculation in accordance with the See also:laws of See also:probability of the 5o% zones shown in the range table (see PROBABILITY.) II. INTERIOR See also:BALLISTICS The investigation of the relations connecting the pressure, See also:volume and temperature of the See also:powder-See also:gas inside the See also:bore of the gun, of the work realized by the expansion of the powder, of the V See also:dynamics of the See also:movement of the shot up the bore, and of the stress set up in the material of the gun, constitutes the See also:branch of interior ballistics. A gun may be considered a simple thermo-dynamic See also:machine or See also:heat-See also:engine which does its work in a single stroke, and does not See also:act in a See also:series of periodic cycles as an ordinary See also:steam or gas-engine.

An See also:

indicator See also:diagram can be See also:drawn for a gun (fig. 3) as for a 21 20 .u..ESMMMEiiiiiiiiiie?CC ENNEEMiMEMMEM~iiiiiMEINIM.'.MO m~mmmussmommmmms sonommmmmmmsummummummammmm~ IMMMIRMEEMEEEMMMMMMEMMMOUNUMMMMMMENEEMENECdOMSM UMMEEPMEMEEMPEEEMESEMEMEMMMMMUENWIMMMMOREAMIll 11 ENNUMmIROMEMEMEMMMMMMMENSIMMMEMMMUMMMMIN11'aERAMMMIME 111:MMIEMEMEMMMEEEMMEEIMMIUMEMMEBIMOW. MM 'A MM nAMEMIEC..M1011 ". 11SIMMMMM11MM&EEMOREMISMEMIMIMEMM111M/MlMSZWEIMMMIMOEMM 1M MMMEMIMIMMIMMEMINEEMMMMISIM2WaTelOOMMIENNUME14:: 1ECISEMMMEEMMEMMUSMEMMMIOMMAMERMPEEMMMMEMMMMIMMSMINE 11!..!!^^!!!!!!!!!!!li7Ca!!!!!.!!!!!!!!.!!!!!!!!!! .! .!!!_!!!MMMIM1,~.~ /!!!!!!..!!!!!! ^!!!!!!!!!. ^•^!!! !.^!!lS-..a.S!!.!.!!l..S!!!!!See also:iM^!.!!!l.ar3 w6 •so 0.3 Rai/See also:lathe 20 lbs. 18 See also:French 8.N 25 20 „ See also:Amide See also:Lot 232 32 „ R.L.G2 23 EXE 42 Plugs O 346 8 7 8 9 10 tt 12 t9- —_i }--5 ~~---'~--16----1I 0 22 24 26 28 30 32 34 36 38 40 42 44 46 Travel in feet __ Pressure Curves, from Chronoscope experiments in 6 inch gun of :oo calibres, with various See also:Explosives. ' ;,n Observed Pressures.

End of Article: RANGE TABLE FOR

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