Note on internal ballistics with composite charge

4 Pages·0.294 MB·English

by  Ray Asim.

A NOTE ON INTERNAL BALLISTICS WITH COMPOSITE CHARGE
Calcutta Technical School, C'alcutta
(Received 8 Jan. 65; revised 8 Sept. 65)
In the present note, it has been pointed out that under certain conditions the internal ballistics
of orthodox guns during the first stage of burning of a compf>siter hargc can be obtained n?it.h
the help of Hunt-Hinds tables.
Internal ballistics of orthodox guns using composite charges has been ciiscussed by
Kapurl, Aggarwa12. Venkatesan and Patni3, Kapur4 made an attempt to deduce the
internal ballistics in case of composite charges with help of Hunt-Hinds5 (1951) tables
by equivalent charge method, but as pointed out by him, there is error in the solution
because of inherent error in the estimation of the form-factor of the equivalent charge.
In another paper Kapur6 observed that if the composite charge consists of two compo-
nents both in the form of tube the solution for the first stage of burning can be obtained
by Hunt-Hinds tables. We shall, however, see in the present note that when the compo-
nents of the composite charge are of some specific sizes and shapes the internal ballistics
for the first stage of burning can be obtained with the help of Hunt-Hinds tables. In
passing we would like to mention that in the present discussion we have taken the ratios
of specific heats of gases produced by the components to be all equal, since in practice
4
this will be found to be almost true.
Fundamental equations
With the assumption about specific heats and with notations of Kapur4 the aquat,iolls
for the first stage of burning can be written as below : +
dv dv
v- -
W1 dx -dt = A p .
--WI
To calcnlate the ballistics for this stage of burning the above equations are to be integ-
rated with given initial conditions. The values of various variables at the end of this
1'
stage of burning will correspond to fi=O. In the next section we demonstrate
that under certain condition the solution of the above equations can be obtained with
help of Hul~t-Hindst ables,
43
4 5 Dm., SCI. J., 1'0t. IG, JASUARlY!W
~1frr.inr eszt Tt
From the c~i~un.tionins (2) we have
which ilitrqrutiori, silhjcet lo the collditiou tlial ,fi's are 1 to start ~vit~il,@ ve
011
. -
-DPIl (1 f = D, ( 1 -f )-- ............ -- -- -D(IGl - f n 1
Pn
P2
from ((7) 1~avr
SO TVI:
'
7
Z; - K'- 1 L.0 , I -- -srll (1 -1 t?lsiil
L'
or.- ~ i t h($1
z Ti" i;
-
. 4
;=
7
@I
RAY: A Note on Internal Ballistics with Composite Cha,rge
With (9) and noting that = 1, equation (1) can be written as
Xom we write
Therefore the above equation reduces to
With the above equation we take (4) a.nd first equat,ioifi (i = I) in (2) and (3) i.~.,
Thus to calculate the ballistics for the first stage of burning it is sufficient to integrate
(12), (13), (14) slid (4) with given initial conc'litions pro\-ideci (8) I~olds. The Hnnt-Hinds
tables give the solnlion of exactly tlicsc system of cc~n;tiiuns( I?), (13). (1s)il d (4). Norv
oqua,tion (8) svts 11p n~1etion.sb (?tn.rcn the size and shape of s~~ccensivoeo nlpoue~itsw d
t h e o f tlic first conlpo~~ent.T hus if the size and sl~apcU S t!lc comj,onents are col~ncc-
t ~ bdy this relation (S), the interid ballisties for the first stage of burning ca.11 he
obtained nitlh help of Hunt-Hinds tables. We note that if all the Bbs are zero, necessarily
(8) holds. Thus I<apor's6 observation that ballistics for the first stage of burnillg
arc obtainable by Hunt-Hinds tables, in case all the coml~onentsa re in the form of tubes,
is only a particular case of (P). The values of vazious ballistic wriables at the cud of the
first stage of bnr*nii,g mill correspond to ,fl 0.
=:
REFERENCES
1. KAPERJ, . N., Proc., Nat. Inst. Sci. India, 23A (1957), 16.
2. AQGARWAL6,. P., Ibid., 21A (1955), 321 & 342.
3. VENKATESANN,. S. & PATNIG, . S., Def. Sci. J., 3 (1953): 51.
4. k m r , J. PIT, Proc. h'at. Inst. Sci. India, 2,2A (1956), 63.
5. "Internal Ballist,ics." (H.M.S.O. 1951).
6. KAPUR3,. N., Def. Sci. J., 7 (1957), 26.