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MEMORANDUM REPORT

©.S^Ä^JÖJL i?®Wl©3l5i IFÄ®^®®^

RESEARCH & DEVELOPMENT DEPARTMENT

■■ ■ CONFIDENTIAL

7C>

55A/\ 44799 %

Mmi^ m*****m*

NOTICE: THIS DOCUMENT CONTAINS INFORMATION AFFECTING THE

NATIONAL DEFENSE OF THE UNITED STATES WITHIN THE MEANING

OF THE ESPIONAGE LAWS, TITLE 18, U.S.C., SECTIONS 793 and 794.

T'HE TRANSMISSION OR THE REVELATION OF ITS CONTENTS IN

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Uo S, MAVAJ.. POWIBR FACTOi;Y EESEAIiGH A1ID ISISIOPKSIT JSPiXBBSn

INDI.VN BEAD, KAE7USD

Il0o 10)»

15 Joly 1955

REVISION OF ADtlTITE VmSUXSS FOR TIG SIMPL3 CALCULATION OF

ThERMOCHEMIGAL PHOPSRTIES FOR USE IN BALLISTICS

B>

B. W. lev/Is S. OolclJi^n

This materiel contains inforration a:fecting tiia naclonal deffisc of the 'Onlted States wltiin the meaning of the Espionage laws Title 18, U. S, C, Section« 793 aai 79^, tae transmission or the revelation of which In en^ tnanner ;o an uniuthorlzed per- son is prohibited by la.

Reprodvction of the docuient In anj corm by other than naval activities is not authorized except by special approval of t.ae Secretary o^ the Karj. or the Chlff of Neva'. Operations, as appropriate.

55A A !47 99

coNFn i | MR 104

FCBBtfoaD

9

This räv.;.sion of thermochemical additive constants and

equations for calcnlating them was performed under Bureau of

Ordnance Task Assignment NPF-B2d-02"15-5^o It is port of a

program to kef'P methods of calculating thermochemical prop-

erties of propellants up to date. Values of constants are

published with the reservation that they nay be modified by

future vori£ aj.d new data in the literature. The data are as

of 1 April 1955.

Approved by:

Sol Skolnil; Director, J:esearch and

Development Department

Released by:

Georpo Eo ling captain, Utaavy Ccmmandiiig Officer

W, C. Ca^le Head, Chemical

Physics i'/ivision

mt li

ONF/I ■ i

GÜNTERS

e Heading

X Or" W OX '■! •»• ■> tm00»o990O9O3<»o-t u^O9««0«Oii0c>i><l«««e0003O

Data ,, ,,,,, »...•••••••..

K6TXS6C1 £l QUSlL . I OQ S »•«•»«••«a«>«f«««oo**«r'«-'»*tfa«*«'>oi'

Calculated Additive Constants for Selectsd Pro-

ppllant In,jre^ients ..........•.».•....•••.«••«*.

Use of Additive Constants ,. , <,., „,„

References u.r.

Calculation of the Additive Constants for Basic:

Lead Carbooate and Potassium Sulfats .........

Appendiz B

ConventionM Used at NPF fo? the Estimation of the

Composi'.ion of Total Volatiles in Conventional

Cue. Pro,)ellant8 Using EtLsr-Alcohol Solvent .,

MR 10*

Page nop

Al

v

1

2

9

9

12

14

21

TAB LBS

I. Theraociemical Data for Combustion Products

of P.-opellant In^re-.dlents ,......„ ,.

II» Thermochernical and Molecular Data for Selected

Propnllant Ingredients ...... ' o * i i>o*oe»oo

■ lii

COMFIDEi m^ ."A',,.; ME 104

III, Gram-Atomic Weights of Elemental Constituents

per Gram of Ingredient for Selected Pro-

pellimt Compounds o...,....».,..<...,,<,...»oooo

IV, Thermochemical Additive Constanta for Pro-

pellc.nt ingredients o.,<><>««e«(>«<a«<>«i>»o>,

V, Tlaermocheraical Data for Selected Substances ,.

10

18

cc m IT

cm^rni ä NB m

ABSTRACT

Tl-ie equal.ions for the calculation of the thermochemical

additive conslants of propellant ingredients, originally pre-

sented by Hirschfelder and Sheraan in 1942, are revised to

accommodate the later thermochemical data of combustion prod-

ucts and in^rrdients. The new constants,, which are for the

terms energy released (E), mean heat capacity (Cy)3 and

number of molfs of gas (n), were calculated and are tabulated

for a number of thj most used ingredients. Separate unique

consideration is given for potassium sull'ate and for basic

lead carbonat«;, resulting in larger differences in constants

than are obta ned for the generalized treatment of organic

ingredients.

r ^ ••r MR 104

HEVloION OF ADDITIVE CONST/JJTS FOR THE SIMPLh' CALCUIATION OF THERMOCHEKICAL PROPERTIES FOR USE IN BALLISTICS

In 19^2 Hirschfelder and Sherman^ pi'esented a

method for tii<j simplified calculation of thermochemical prop-

erties for propellants by means of additive constants. Since

then there ha^e been a number of changes in the values of the

thermochemical data used for these calculations. It is the

purpose of tlus report to tabulate the newer data, to revise

the equations for the additive constants on the basis of these

data, and to calculate new constants for some of the most used

ingredients. The revisions have been made following the pro-

cedures given by Hirschfeld«r and Sherman.^'

DATA

Experime ita] uttta were obtained from as many sources as

were availabl? to the autbors„ Reasonable estimates were

made when no iata coula be found« Changes from previous data

involved the energy of formation at 0° R of cexbon monoxidu

and carbon dioxide, the heat capacity of graphite and water(g)r

and correctioi of molar properties to conform with the latast

international atomic weight for carbon, ioC, 12o011o^^

Values for th3 heat capacities of hydrogen, nitrogen, carbon

dioxide,, and :arbon raonoxidt: had also changed slightly» Tae

CONFiCEWTIAL m 104

# data used for the calculation of the equations for the con-

stants are gi^en in Table !„ The thermocheniical and molecular

data for ingredients are given in Table II« The atomic com-

position data for ingredients are given in Table III.

REVISED EQUATIONS

The reviued equations for the calculation of the addi-

tive constant» Ej and Cy. are as follows:

Ei ■ FJH)i 38966^ 6252^- 520730; 67211^

Cy =• L809Cj ♦ 3.2641^ - äOöööj « 3 SSäNj

For Bj an alternative equation may be used

Ej * UC - 1330ISCj • 40019.^ * 520730: 6721)4;

The eq\iation .-'or n^ remains the samep i.e.,

£1» Cvi» an<i ni are tiie additive constants for energy re-

leased, mean heat capacity, and number of moles of gas for

ingredient I, respectively, C^, H^,, Oi, and K^ are the num-

ber of gram-a;oms of the elements per graa of ingredient i„

E(l)i is the negative of the energy of formation at 15° C

(288.16° K) o;' the ingredient in cal/gram i0e.p ^(15° C) M

where AE is tiie molar quantity and H is the molecular weight»

H. C. is the heat of combustion of the insrsdierit in calor'.es

per gram at 1,'»° C for liquid-vater product and constant vo'.-

urae„ These e-iuations are only changed in tue values of the

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numerical coefficients and have beea arrived at by adherence

to the method;; and procedures of Hirschfelder and Sherman» ^'

CALCVUTW) ADDITIVE CONSTANTS FOR SSLECKD PtOPELLAKT INGIEDIENTS

The additive constants Ei, Cy., and n^ have been calcu-

lated from tht; above equations fcr a number of the most common

propellant InfTedients and are given in Table 17, Numerous

changes in energy of formation of ingredient;a including the

nitrocellulost'S were noted. For the inorganic salts, basic

lead carbonat«: and potassium sulfate, the calculations had to

be made by considering the effects of these ingredients to be

unique. The calculations of the constants for these salts

are given in appendix A.

USE OF ADDITIVS CONSTANTS

The adiabatic flame temperature and impetu« of a propel-

lant are calculated by means of equations given by Hirschfelder

and ahenBan,'-' These equations are:

and

CONFIDENT,«AL

«

ISB MR 104

Table IV

TKERMOCHSMICAI ADDITIVS COESTAITS FOR nSPSLLOt DRSBEDISHTS

Comjound H Cvi H Butyl stearate -3726., .5675 .12919

Dibutyl phthalite -2693. .4336 .09700

Dioctyl phthalite -3101. .4796 .11010

Diphenylamine -300?. „3600 .10636

Ethyl alcohol -2772. ,6121 .10853 Ethyl centralise -2882. „4013 .10434

NitrocelluloseV lloOp^ N -30.4 .3528 ,0438? ii 1105C^ N 41 ..5 .3496 .04278 R 12.00^ N 113.2 .3464 .04169

12.20^ H 141.9 .3451 .04125

12o6Q^ N 199.1 „3426 .04038

12o8C^ B 228.2 ,3413 .03994

13o00^ N 256.6 .3401 .03951 13.15^ N 278,4 .3391 .03918

:i 13o25^ U 293,0 »3385 .03896 II 13*50$ H 329.1 .3369 .03342 u 14 a V ii 421.2 .3328 „03702

2-Nltrodipheny .anlne -1949. .3317 .08402 Nitro^lycerin 951.5 03388 .03082 Nitroguanidlne -5?o4 .3690 .04804

Petrolatum -4113„ .6123 ,14510 RDX 639 o0 ,3391 .0^052 Water{liq) -1552„2 .6403 .05551 Basic leaä c^u'bonate -199.7 ,0910 .0038? Potassium sulfi^te »1226.5 .2708 -,005?$/

^'le.'-'/Midiir T. virf;-I-MJ ■:;».. o'ib«; po&Mialteg« ffi.%«g«n njuo^anoJoee« nay ba OSVMEIUCNI by

-No"« (hwt hn nt.^m *m ist Sn^iuional Sc» Ajopendir A fait- dti'.vejsion,

aftfiw%^Wi: moEmm 10

A

I COWFID.ENTIÄL «'<*

vhere T0 is the adiabatic flane tenperature in "K, x^ Is the

veight fraction of the .ith ingredient; in the propellant, f is

the impetus in ft-lb/lb when R the gas constant is 2781.7 ft-

lb-gran/deg-lb-mole, and StiEi, StjCv , and SsiBi are the sums

of the product of the weight fraction and the additive constants

for all ingredients of the propellant. In connection with the

calculation of these ballistic properties it is necessary to

lenow the compoaltion of the propellant including that of the

volatiles. Usially the volatiles are determined as a total,

and one must estimate what they are composed of and in what

weight ratio, Knowledg*? of the type of powder and its manu-

facture may give one a basis for the estioiation. The con-

ventions used by the authors, based on experience with ether-

alcohol solveni>sxtruded propellants, are given in Appendix B.

L

COWFIDÖWilAL ..^ v^'fw* n #f

'" ■ ■ fei Iffl 10'+

REJÜSEKCES

0) Hlrsclifelder, J. O,» and Jack Sheroan» SiniplJ Calculation

of Thönaoc/iemical Properties for üse :.n Biilllstics, National

Defense Retsarch Cociriittee Report Ho. A-101 (OSRD 935) October

1942., COHPIDEITIAI

(2) tUrsc}afeld3rp J 0,, and Jack Shermaiu Simple Calculatlort

of TüörraocJieiricil Properties for Use in Ballistic?» Addenda to

National Defensa Research Coaraittee Report. A-101 (OSRD 1300)

March 19^3, COSPIDENTIAL

(3) HodgTMya, C, D., Editor., Eaodbook of Chemist.-y and Physics^

32nd Edition, Cleaical Rubber Publishing.Co«, Cleveland, Ohio,

1950.

(4) Jessup, Ralph S , and Edward J Proses. Heats of Conbus«-

tion and Format Ion of Calluloae and Nitrocallulos? (Cellulos;

Nitrate) J, Research Na:l. 3ur. Standards, 44, 387-93 (1950).

(5) Kelle.y, £„ K, Contributions tc the Tata on Theoretical

Metallurgy, X, h S, Bureau of Mines, Bulletin 47.}, 1949.

(6) Kelley, K„ K, Contributions to the Data on Theoretical

Metallurgy., 11, U, S Bureau of Mines, Bulletin 477,, 1950c

(?) Landolt-Bfimsteln, Kiysikalisch-Chemische Tabellen,

Jullua Springer, Bar/in. 1923»

(6) Lswi? Beriarl xvi Guenther Yon Elbe, Comb.is .ion, Plainea

and Explosions )f Oases, Academic Press, Inc., B. I., 1951»

% <#

1.2

%

'

I AL MR io4

(9) iu Do Lit ,le, Inc3 Report on Study of Pure Explosive

Compounds to the Office of Chief of Ordnance, Part IV, Contract

No. DA-19-020~OR]>4?, Hay 1, 1952. C0NFID3NTIAL

(10) Perry, J, H», Editor. Chemical Engineers' Handbook, 3rd

Edition, McGraw-Hill Book Co., H. T., 1950.

(11) Prosen, S, J,, and R, Gilmont. Heats of Combustion sind

Formation of DLethylphthalate, Dibutjlphthalate, Dinitrotoluene,

Diethyldiphenylurea and Nitroguanidlre, National Defense Re-

search Committee Report A-197, (OSRD-1590), July 19^. OOTPI-

DEKTIAL

(12) Rossini, F. Do, D. D. Wagraan, esii otherSp Selscted

Values of Chemical Thermodynamic Propertiss, National Bureau

of Standards Circular 500, February 1, 19.52o

(13) Rossini, F„ D», and others. Selected. Values of Chemical

Thermodynamic Properties, Series III,, National Bureau of

Standards.

(1^) Wa3hburE, Eu W,, Editoro International Critical Tables

of Numerical Tata, Physics, Chej.istry and Technology, McGrav-

Hill Book Co., H. I., 1926.

(15) Wichers, Edward» Report of the Committee on Atomic Weights

of the Americen Cheaical Society. J, Am,, Chem. SoCo, 76, 2033-

35 (195*).

4 *

^ili H. HE 104

APEEITDIX A

CALCUUTIOtf OF THE ADDITIVE CONSTANTS FOR BASIC IBAD CARBONATE AND POTASSIUM SULFATE

m Basic Lead Carbonate, 2PbC03''P"b(0H)2

Basic lead carbonate was considered to contribute to the

water-gas equilibrium and to contribute liquid netallic lead

in the form of fine droplets. Examination of the critical tem-

perature and pressure of lead indicated that the most probable

state under gai conditions was the liquid,. Thus the calcula-

tions of Ei and Cy. had to allow for the production and pres-

ence of lead,,

Calculation of E«;

E, - JX1) ♦ E(2) * m) E(4)

according to Hirschfelder and Sherman.'^' In this case the

presence of leid affects only the values of A(2) and E(4)„ E(l)

was estimated to be 55/'«5 cal/gram from the data for heat of

reaction giver in reference (14)„

E(2) is the energy envolved when the elements present are

cooled from 268<>l60 to 0° K. The contribution of the lead in

this compound to E(2) was estimated to be 5c^9 cal/gram0

E(4) is the energy necessary to heat the product gases

(and/or finely divided liquids and solids) from 0° to 2500eKc

The contribution of lead in this compound to E(4) was estimated

to be 6802 cal/gram and the contribution to E(2) - E(4) was

CONFIDE 'M 14

f^vK'-T-;' :r; T ■■Mi MR 104 '•£¥■"" |fi(# ::-

^S,,? cal/gram for the lead in this coapound. This figure »M

then added to the value of Si obtained for this compound on the

basis of the regular Ej equation.. Thus:

Es 'ElU 389e6Cf 6252U » 53073Os - 62 7 ■ - 199 7 cel/gnun

Calculation of Cy,:

The assumption vas made that the fine droplets of liquid

lead were In ti.ermal equilibrium with the gas and therefore a

term for lead iad to be added to the Cy. equation. Thus:

■ 09102 cal/degpMHgpatiio

Calculation of n«:

The fine <!roplets of lead were not considered to contri»

bute to the nunber of moles of gas per gram» Thus:

«4-V 1/2yi

■ 003867 rooSw/pranj

The data used ;.n the above calculations are Listed in the

various tables of this report»

Potassium Sulfate, KgSO.!;,

The constitats were previously estimated by Kirschfelder

and Shermajp ^ on the assumption that,, in guns, potassium Sul-

fate vaporizes as potassium colfate molecules. It was felt,

that this treatment was not a realistic one. when reducing gases

were present, A qualitative study was made of the products of

explosion of a powder containing %o potassium sulfate« Thl;>

m

t OlMl^iOHP^ i f741 MB tftit

powder vas fired in a calorimetric borabj and the gases were

found to contain a considerable quantity of hydrogen sulfide.

The residue left in the bomb was dissolved in water and tested

for the presence of sulfate ion. This test showed a negligible

amount of sulfate present. From this experiment it wa«? felt

that a more accurate estimate of the reaction of potassium

sulfate in a picpellant was:

The hydrogen vculd be furnished by the water-^as equilibrium,

which would ad.ust itself to the required condition» The cal-

culations were made on the basis of the above assumptions with

the aaditional products taken into coasiduratlon.

Calculation of Ei:

E(l), the negative of the energy of formation per gran0

tfas calculated in a straight-forward manner from the heat of

formation and vas found to be 1959»6 cal/greiru

F.(2), the energy to lower the teraperature of the elements

from ü88(>l60to 0° K, was calculated from the usual type equa-

tion,

fi^S) « 1630^ ♦ 129^ * 7130^

a 42 5 cal/^ram

E(3) is the energy of formation of the conrtnistion product3<

Equations for E(3) were obtained for the two eitreae cases;

(a) no carbon dioxide formed and (b) no water formed,. These

CC IDEi AL ~ "

MR 104

cases followed the method of Hirschfelder and Sherman^' but

included the EoSOh + ^Hg react ion«, This inclusion was made by

considering th* reaction to be:

CBOM < KjSO^ —* H20 ♦ U, > CO, < CO ♦ H^S ♦ KOil ♦ Nr

'Ilien the equations relating the number of moles of products to

ehe grajn-atoms of elements of the reactants vrere as follows:

nrrv - 4S - 1/2H ♦ 0 C > aH ^■^JJ a «CO - aCU 0 * 1/2H 4S an

■HO « 1/2H - SS UH

aI£OH

aH?S

!, 2\

K -2S

where the n's t>xe in moles per gram and the C, H, 0, H, K,

and S are in gi-am-atoms per gran of the elements in the povder,

Thus for the tvo cases:

{(l) win n ttf-Q ' 0

nu - C ♦ 1/I>H 0 4i>

»CO 'iC

«H?0^0 C.2S

(b) when »H O ' ^

a« ■ V2H • 2S "s

KOt - O - C 2S

OQQ • act * Q -> 95

«

CO? 17

m •

^Fll ■■ m 104

The other concentration expressions remained the same in both

cases,, The values for the separate cases vere each substi-

tuted into the S(3) expression;

B(3) " (nÖ)H 0 »{vmco * iti»)cQ « (nßjy s <> (nQ^Qy

where 8 is the energy of formation at 0° K of the various

produce conpounds as given in Table I and Table V, Thus two

expressions were obtained, E(3)a and E(3)b in terms of con-

stants and gram-atoirs per gram of elements«

Table V

THSRMOCHEMICAL DATA FOR SSLEGTEC SUBSTANCES

Substancö Cv? Cal/de^-raole AE, Kcal/mole Of :388,160 K 200Cp 3000° Kj Fonmtion 0° K 0o~2500PK

K(crys) 5,63?^ —. 0

s(rh) 4,480^/ «-^ 0 -«-

H2S(g) -— 14Ü23S// 4,123^ 21 „82^/

KOH — la.os/ 102O376S/ 49,440fi/

^ H*feT«nce (13)

^Refercacc 45)

^As«b.t«.T8 «tfimaac

C(4) Is the energy to heat all the products from 0° to

2500° K, E('+) equations were obtained for the two cases in a

manner quite similar to that for E(3) from the equation:

BU) ■ (n«)ij o ^^'H * ^^CO ^^CO * ^hl S '* ^"^KOH H> ^B«3^l>i

f -7: V ■■■» ■

18

0

•■ , . . te 104

-Aäere the a*s en the margjP to heat the respective products

from 0° to 2500° E. Thus B(4)a and ^(^)!? egressions were oto-

tainedo

Accordirig to Hirschfelder and Sherußii ':

E(3) « 0 77E(3)' v0 23E(3;fe

and E(.l) « 0 77EC4)a « 0 2aE(4)?

and thus

E(2)^ EC-S) -0 77CE{3>e B(4)*) < 0 2»,ECs:h E(4)-)

A. expression vre.s derived, from this for B(3) - S(^) in terms of

constants end the grExi-atoms per grain of elements« A similar

3(3) - S(4) exrreaaion was obtained for the CHOH system alonep

and this expression v/as auhtracted from that for the CHON plus

potassium sulfste to givr i express.ion for the potassium su3-

fate alone« Tins the expression:

(Etf) E(4)); - 77^<1>H 0 - ( Sj < .WKi)^ ZSKi^CO, '

waa obtained, where *-AEf0o^ AE2500ao0K

for the -vürioiiE products» Substituting the numerical values

^ave;

(EXS) < £(4)^ - 1293485,

" 690.6 cal/grim

combJmag- B(U «• E^ > Wb' E(4) gave;:

E, =- 122& 5 csl/graro

CC, ■ ■ AL «w»

Calculation of ^i'-

An expression for Gr* was obtained, from

c„ -W^B o • UC^n ♦ <BC.>CO. »WS^OO * CnCT)H s * (DCJK0H * (nCft)N 8 * * ■ ■

together with the saoe concentration axpressions and the two

extrene cases: (a) no carbon dioxide and (b) no water. Ex-

pressions were obtains! for Cya and Z-J3 for both the GHOMKS

and CHON systems and the difference was obtained. Both Cy8-

and CVD were given equal weight in ootaining the final ex-

pression, iod.,

\

The resultant equation was:

Calculation of nj;

On the basis of the reaction that was assumed between

potassium sulfate and bydrogen, it was seen ttiat the net ef-

fect was the consumption of 1 mole of gas rather than 1

furnishing of ,3as , Thus the value of nj hid to be negativ?,

and

n. * .5,

■ -.005738 mdsVffr«"

^O^FlPSMIIAi. zo

%

m

lA*. MR 104

APFEiroiX B

CONVENTIONS UJED AT NPF FOR TIE ESTIMATION OF THE COMPOSITION OF TOTAL 70LATILES IN CONVENTIONAL GUN PROPELLANTS

USING ETHER-ALCOHOL SOLVENT

Lgy Total Volatiles

When total volatiles are 0o7^ or less, the volatiles are

considered to be only water. This convention covers most

nltroguanidlne and most RDX powders that are solvent extrudedo

High Total Volatiles

When the propellant has a high total-volatile content,

the volatiles are. considered to consist of 00^ water, and the

remainder is considered to be ethyl alcohol This convention

covers single- and double-base solvent-exliruded powders»

*L 21

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