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AMCP 706-140 Trajectories, Differential Effects, And Data for Projectiles

Search inside document. The uandbooks are authoritative reference books of practical information and quanti- tative facts helpful in the design and development of Army materiel so that it will meet the tactical and the technical needs of the Armed Forces. It includes consideration of the various elements which, in considerable variation, may constitute the explosive train of an item, The main charge of an explosive item, such as projectile or warhead filler, is also covered, Data are given on the physical and explosive characteristics of typical explosives und references are cited in which additional data will be found.

Since these Siacci tables were arranged primarily fr se in cmpting aircraft firing tables, they were called Aircraft Tables; hwever, they can be sed fr ther prpses, as explained belw, in lie f ther frms. In these Aircraft Tables the argment is the cmpnent alng the line f departre f the velcity relative t the air, which is assmed mtinless. Althgh the Aircraft Tables are nt accrate in cmpting cmplete trajectries at high elevatins, they can be sed t btain trajectry data at sperelevatins belw 15" fr the derivatin and applicatin f the fllwing frmlas, see Reference These tables can als be sed fr the flat part f antiaircraft trajectries, where the sperelevatin is less than 15 fr the derivatin and applicatin cf the fllwing frmlas, see Reference The interval cf x shld be chsen small engh s that the integratins may be perfrmed accrately by Simpsn's rle: nt mre than feet.

The density fnctin H y has been tablated Reference 11 ; it gives the same vales. Simpsn's rle was sed, bt the trapezid rle gives fr the last vale.

Description:

The ther vales were cmpted by Eq. The vales f after the first were fnd in the Aircraft Table by inverse interplatin, sing the first tw terms d Taylr's series. Simpsn's rle gives fr the last vale, bt the trapezid rle was sed in rder t btain intennediate vales. The sqare f Cl. Cl, Simpsn's rle gives fr the last vale, bt the trapezid rle was sed s as t btain mre vales. Cmpted by Eq.


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Simpsn's rle gives ft fr the final vale. These tables are especially sefl fr aircraft fire fr ths derivatin and applicatin f the fllwing frmas, see References 34 and SO7 Eq.

AMCP 706-179 Explosive Trains Clean]

Reference 6 cntains a table f mdified Siacci fnctins based n the drag cefficient fr the mm High Explsive Antitank Shell T, which has rigid fins. These tables can be sed fr ther similar prjectiles, althgh they are nt sitable fr all tin-stabilized prjectiles. The fllwing fnctins and their derivatives are tablated as fnctins f Mach nmber M : Space Time Inclinatin 2.

The fllwing frmlas are applicable fr cmpting trajectry data at sperelevatins belw The angle f departre fr y 0 may be fnd by the frmla ap, r A M -A M. Mre detailed explanatins are given in References 21, 22, 23 and Effects n Range 1 Height f Target. Tw methds may be sed fr determining die effect f the height f the target with respect t the gn: ne by means f the trajectry chart, and anther by a crrectin t the angle f departre. The trajectry that passes thrgh the pint determined by the given hrizntal range and altitde can be fnd.


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  7. The ttal range f this trajectry is the range where it crsses the axis. The difference between the given range and the ttal range is die effect f the height f target Fr greater accracy, the exterir ballistic tables may be sed in lie f the charts. At shrt ranges, the effect may be cmpted mre accrately by sing the Siacci tables, as explained abve. The vacm frmla Eq.

    It shld be nted that the effect is small in the vicinity f the maximm range and, f crse, is negative at elevatins abve that crrespnding t the maximm rancp. Since the Exterir Ballistic Tables give the range as a fnctin f mzzle velcity fr cnstant vales f elevatin and ballistic cefficient, the effect f an increase in mzzle velcity may be fnd frm the differences.

    At shrt ranges, the eseect may be cmpted by sing the Siacci tables. In vacm, the range is prprtinal t the sqare c the velcity, as shwn in Eqatin 6; in air, this is a gd apprximatin if the ballistic cefficient is large. Since the Exterir Ballistic Tables give the range as a fnctin f ballistic cefficient fr cnstant vales f mzzle velcity and elevatin; the effect cf an increase in lg C may be fnd frm the differences. At shrt ranges, the effect may be cmpted by sing the Siacci tables. The vale f n may be btained frcm interir ballistic tables.

    Ballistic Trajectories - Differential Equations in Action

    It is apprximately 0. The retardatin de t air resistance is prprtinal t the air density and inversely prprtinal t the ballistic cefficient, as indicated m Eq. Therefre, t a first apprximatin, the effect n range f an increase in air density is eqal t the effect cf the same percentage decrease in C.

    An increase in the temperatre f the atmsphere affects the range in tw ways: it increases the density cf the air and the velcity cf snd. Fr a given pressre and hmidity, the density is prprtinal t the abslte tenperatre.

    How guns fire bullets

    The effectf density n range has been treated abve. Fr a given hmidity? Fr a given prjectile velcity, the Mach nmber is inversely prprtinal t the acstic velcity. A change in M prdces a change in the drag fnctin. A new trajectry cld be cmpted with, the varied fnctin; hwever, it is simpler t se an apprximate frmla dedced frcma semi-empirical frmla derived by Dr. A rear wind las three effects: it mves the crdinate system alng with h relative t the earth; it increases the angle f departre relative t die air; and h decreases die mzzle velcity relative t die air.

    The ttal effect n range may be expressed as fllws: A. Effects n Deflectin 1 Wind. A crsswind has tw efiects: it mves the crdinate system with it and it changes the directin f mtin relative t the air. After the yaw de t initial distrbances has damped ct, a spinning shell has a yaw f repse de t the crvatre cf fhe trajectry. This yaw is mainly t the right cf the trajectry if the shell has right-handed spin; t the left if it has left-handed spin. It-may be determined at shrt ranges by firing alternately frm barrels with right and left hand twists f rifling, r at lng ranges by crrecting the bserved deflectin fr the effects cf wind, cant cf trnnins, and rtatin cf earth.

    Dts dente time derivatives, and the initial cnditins are i. Ballistic Density, Temperatre, and Wind In treating the effects f variatins in the atmsphere, it has been assmed that the percentage variatins frm standard density and temperatre and the wind are cnstant all alng the trajectry.

    Actally, they vary with altitde, s that weighted mean vales mst be sed. The weighting factrs are determined by the prprtin cf the ttal effect that a variatin ccrring in each altitde zne wld have. Instead f cmpting a set f wenghhirrj factrs fr each trajectry, a few representative crves are sed. The sn f the prdcts cf the znal variatins by their weighting factrs is called the ballistic density, temperatre, r wind. The reslts are then treated as cnstants in cmpting the effects n range and deflectin. Internatinal Civil Aviatin Organizatin. Standard Atmsphere Tables and Data fr Altitdes t 65, feet.

    Am Handbk Flight Series, Characteristics. Drag Cefficient B,. Drag Cefficient Bj,. File N-I Drag Cefficient B 8.


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      External ballistics - Wikipedia

      Dcment These tables pertain t Prjectile Type 1. Table f G ri. Table f G,,. Bmb Ballistic Tables. Altitde is in meters in N-I; yards in N-I Charbnnier and Galy-Ache,. Nte sr la resistance de fair a mvement de prjectiles. Men de l'art, de la marine, Ballistic Tables, Art. Circlar t Rev.