A Reliable Method for Predicting the Specific Impulse of Chemical Propellants

Frem, Dany

doi:10.5028/jatm.v10.945

Dany Frem

FREM Co. - Beirut - Lebanon

http://orcid.org/0000-0001-6647-2359

Correspondence author: Dany Frem | FREM Co. | Beirut - Lebanon | E-mail: frem.dany@gmail.com

Section Editor: Adam Cumming

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Figure 1
Structural formulas of different C-H-N-O, CNO and N_x (x = 6,8,10) monopropellants.

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Figure 2
Specific impulse values of twenty monopropellants calculated using and versus values computed using ISPBKW code.

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Figure 3
Structural formulas of C-N-O organic oxidizers used in composite propellants.

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Table 1
Comparison between the specific impulse values calculated using the ISPBKW code and Eq. 5 for different monopropellant compositions. Percentage deviations in parentheses.

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Table 2
Coefficients, standard errors, t-statistics, statistical significance (P-values), the lower and upper bounds of the 95% confidence intervals of Eq. 5 obtained by multiple regression analysis (R 2 adjusted = 0.945).

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Table 3
Comparison between the specific impulse values calculated using Eqs. 5 and 8 to ISPBKW code results for different monopropellant compositions. Percentage deviations in parentheses.

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Table 4
Atomic compositions and heat of formations of different ingredients used in triple-base and CMDB propellant compositions.

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Table 5
Comparison between the specific impulse values calculated using the ISPBKW code and Eq. 5 for single-base, double-base, triple-base and CMDB propellant compositions. Percentage deviations in parentheses.

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Table 6
Comparison between the specific impulse values calculated using the ISPBKW code and Eq. 5 for nitramine-based pseudo-propellant compositions. Percentage deviations in parentheses.

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Table 7
Comparison between the specific impulse values calculated using the ISPBKW code and Eq. 5 for ADN, AN, HNF, and organic oxidizer-based composite propellant compositions. Percentage deviations in parentheses.

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Table 8
Comparison between the specific impulse values calculated using the ISPBKW code and Eq. 5 for liquid monopropellant compositions. Percentage deviations in parentheses.

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Table 9
Comparison between the specific impulse values calculated using the ISPBKW code and Eq. 5 for liquid bipropellant compositions. Percentage deviations in parentheses.

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Table 10
Comparison between the specific impulse values calculated using the ISPBKW code and Eq. 5 for hybrid propellant compositions. Percentage deviations in parentheses.

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(2)

(3)

(4)

(5)

(6)

(7)

(8)

Compositions	∆Hº_f (kcal mol^–1)^a a Heat of formations (HOFs): (Dobratz and Crawford 1985) otherwise stated;	N_g	Q/ (kcal g^–1)	I_sp/(Ns g^–1)^c c Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008);	I_sp(Eq. 5)/(Ns g^–1)^d d To convert to the more conventional units of seconds, divide by 0.00981 Ng–1.
PETN	–128.7	0.0316	1.514	2.58	2.55 (–1.23%)
TNT	–16.0	0.0253	1.291	2.11	2.17 (2.62%)
HMX	17.93	0.0338	1.477	2.62	2.57 (–1.86%)
RDX	14.71	0.0338	1.482	2.62	2.57 (–1.81%)
Tetryl	4.67	0.0270	1.420	2.35	2.35 (0)
NM	–27.0	0.0369	1.364	2.46	2.54 (3.23%)
HNS	18.7	0.0233	1.367	2.19	2.19 (0%)
Comp-B	1.28	0.0308	1.410	2.42	2.43 (0.52%)
PBX-9404	0.08	0.0337	1.414	2.55	2.51 (–1.90%)
PBX-9011	–4.05	0.0333	1.358	2.43	2.44 (0.59%)
LX-14	1.5	0.0336	1.423	2.54	2.51 (–1.04%)
Pentolite (50/50)	–23.9	0.0285	1.402	2.37	2.37 (0)
HNAB	67.9	0.0243	1.445	2.32	2.30 (–0.92%)
NG	–88.6	0.0319	1.591	2.53	2.63 (3.67%)
NQ	–22.1	0.0385	0.898	2.11	2.11 (0)
Octol (75/25)	2.78	0.0317	1.431	2.50	2.47 (–0.95%)
TATB	–36.85	0.0291	1.075	2.01	2.03 (1.26%)
PA	–51.3	0.0251	1.283	2.18	2.15 (–1.47%)
Cyclotol (60/40)	1.15	0.0304	1.406	2.42	2.42 (0)
DEGDN	–99.4^b b (Meyer et al. 2007);	0.0332	1.392	2.42	2.47 (2.20%)
PBX-9007	7.13	0.0324	1.392	2.39	2.46 (2.83%)
PBX-9501	2.28	0.0336	1.442	2.56	2.53 (–1.29%)
DIPAM	–6.80	0.0253	1.298	2.16	2.17 (0.49%)
BTNEU	–76.91^b b (Meyer et al. 2007);	0.0311	1.467	2.52	2.49 (–0.89%)
BTTN	–97.04^b b (Meyer et al. 2007);	0.0322	1.509	2.59	2.56 (–1.18%)
FOX-7	–32.00^b b (Meyer et al. 2007);	0.0338	1.199	2.38	2.30 (–3.40%)
DDNP	46.39^b b (Meyer et al. 2007);	0.0238	1.391	2.27	2.23 (–1.93%)
DNDMOxm	–73.00^b b (Meyer et al. 2007);	0.0316	1.171	2.22	2.21 (–0.26%)
DNOC	–47.80^b b (Meyer et al. 2007);	0.0253	1.109	1.93	1.96 (1.34%)
DNPH	11.95^b b (Meyer et al. 2007);	0.0278	1.173	2.07	2.11 (1.87%)
DINA	–65.88^b b (Meyer et al. 2007);	0.0333	1.472	2.56	2.55 (–0.44%)
DIPEHN	–233.79^b b (Meyer et al. 2007);	0.0315	1.422	2.49	2.46 (–1.03%)
ETN	–114.76^b b (Meyer et al. 2007);	0.0325	1.365	2.34	2.43 (4.02%)
EDDN	–156.18^b b (Meyer et al. 2007);	0.0403	0.966	2.20	2.23 (1.49%)
EDNA	–24.81^b b (Meyer et al. 2007);	0.0367	1.303	2.46	2.48 (0.69%)
GUNI	–92.52^b b (Meyer et al. 2007);	0.0410	0.662	1.90	1.91 (0.31%)
FOX-12	–85.09^b b (Meyer et al. 2007);	0.0371	0.898	2.15	2.07 (–3.95%)

	Coefficients	Standard Error	t-Stat	P-value	Lower 95%	Upper 95%
Intercept	–4.459	0.437	–10.193	7.13 10^–12	–5.348	–3.570
*N_g*	121.81	8.62	14.135	8.51 10^–16	104.29	139.32
Q	4.697	0.193	24.328	4.36 10^–23	4.305	5.090

Compositions	∆Hº_f (kcal mol^–1)	N_g	Q/(kcal g^–1)	I_sp/(Ns g^–1)^j j Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008).	I_sp (Eq. 5) (Ns g^–1)	I_sp(Eq. 8) (Ns g^–1)
1a	9.88^a a (Meyer et al. 2007);	0.0245	1.368	2.22	2.22 (0)	2.21 (–0.55%)
1b	–161.53^a a (Meyer et al. 2007);	0.0310	1.609	2.48	2.62 (5.71%)	2.81(13.30%)
1c	–84.31^a a (Meyer et al. 2007);	0.0426	0.947	2.16	2.27 (5.13%)	2.49 (15.22%)
1d	144.5^b b (Dobratz and Crawford 1985);	0.0238	1.692	2.65	2.53 (–4.63%)	2.65 (0)
1e	207.53^c c (Christe et al. 2015);	0.0300	1.978	2.90	2.91 (0.48%)	2.77 (–4.49%)
1f	161.02^c c (Christe et al. 2015);	0.0288	1.936	2.95	2.85 (–3.24%)	2.68 (–9.11%)
1g	106.74^d d (Fischer et al. 2012);	0.0381	1.432	2.65	2.63 (–0.70%)	2.79 (5.27%)
1h	36.33^e e (Göbel et al. 2010);	0.0372	1.344	2.61	2.53 (–3.36%)	2.59 (–0.75%)
1i	73.76^e e (Göbel et al. 2010);	0.0324	1.681	2.65	2.72 (2.52%)	2.58 (–2.63%)
1j	52.27^e e (Göbel et al. 2010);	0.0366	1.597	2.73	2.74 (0.30%)	2.63 (–3.51%)
1k	32.67^e e (Göbel et al. 2010);	0.0368	1.085	2.27	2.26 (–0.29%)	2.26 (–0.43%)
1l	61.28^e e (Göbel et al. 2010);	0.0378	1.171	2.37	2.38 (0.48%)	2.18 (–7.81%)
1m	112.69^e e (Göbel et al. 2010);	0.0394	1.286	2.49	2.53 (1.34%)	2.02 (–18.93%)
1n	56.96^f f (Klapötke et al. 2015);	0.0347	1.198	2.30	2.32 (1.20%)	2.38 (3.67%)
1o	67.38^f f (Klapötke et al. 2015);	0.0381	1.391	2.54	2.59 (1.97%)	2.43 (–4.28%)
1p	58.66^g g (Ghule et al. 2011);	0.0282	1.860	2.72	2.78 (2.24%)	2.56 (–5.78%)
1q	43.90^h h (Rahm et al. 2014);	0.0278	1.915	2.74	2.81 (2.64%)	2.47 (–9.78%)
1r	345.6ⁱ i (Lempert et al. 2009);	0.0357	4.114	4.22	4.38 (3.87%)	2.56 (–39.28%)
1s	406.7ⁱ i (Lempert et al. 2009);	0.0357	3.631	4.11	4.12 (0.11%)	2.61 (–36.53%)
1t	473.4ⁱ i (Lempert et al. 2009);	0.0357	3.381	4.04	3.97 (–1.73%)	2.80 (-30.62%)
RMSD (Ns g^–1)^* * RMSD = Root-Mean-Square Deviation.					0.08	0.602

^a
(Meyer et al. 2007Meyer R, Köhler J, Homburg A (2007) Explosives. 6th ed. Weinheim: Wiley-VCH.);
^b
(Dobratz and Crawford 1985Dobratz BM, Crawford PC (1985) LLNL Explosives Handbook: properties of chemical explosives and explosives simulants. (UCRL-52997-CHG-2) Lawrence Livermore National Laboratory Report.);
^c
(Christe et al. 2015Christe KO, Dixon DA, Vasiliu M, Wagner RI, Haiges R, Boatz JA, Ammon HL (2015) Are DTTO and iso-DTTO worthwhile targets for synthesis? Propellants, Explosives, Pyrotechnics 40(4):463-468. doi: 10.1002/prep.201400259
https://doi.org/10.1002/prep.201400259... );
^d
(Fischer et al. 2012Fischer N, Fischer D, Klapötke TM, Piercey DG, Stierstorfer J (2012) Pushing the limits of energetic materials - the synthesis and characterization of dihydroxylammonium 5,5'-bistetrazole-1,1'-diolate. J Mater Chem 22(38):20418-20422. doi: 10.1039/C2JM33646D
https://doi.org/10.1039/C2JM33646D... );
^e
(Göbel et al. 2010Göbel M, Karaghiosoff K, Klapötke TM, Piercey DG, Stierstorfer J (2010) Nitrotetrazolate-2N-oxides and the strategy of N-Oxide introduction. J Am Chem Soc 132(48):17216-17226. doi: 10.1021/ja106892a
https://doi.org/10.1021/ja106892a... );
^f
(Klapötke et al. 2015Klapötke TM, Kurz MQ, Schmid PC, Stierstorfer J (2015) Energetic improvements by N-oxidation: insensitive amino-hydroximoyl-tetrazole-2N-oxides. J Energ Mater 33(3):191-201. doi: 10.1080/07370652.2014.963743
https://doi.org/10.1080/07370652.2014.96... );
^g
(Ghule et al. 2011Ghule VD, Sarangapani R, Jadhav PM, Tewari SP (2011) Theoretical studies on polynitrobicyclo [1.1.1]pentanes in search of novel high energy density materials. Chem Pap 65(3):380-388. doi: 10.2478/s11696-011-0002-9
https://doi.org/10.2478/s11696-011-0002-... );
^h
(Rahm et al. 2014Rahm M, Bélanger-Chabot G, Haiges R, Christe KO (2014) Nitryl cyanide, NCNO2. Angew Chem Int Ed 53(27):6893-6897. doi: 10.1002/anie.201404209
https://doi.org/10.1002/anie.201404209... );
ⁱ
(Lempert et al. 2009Lempert DB, Nechiporenko GN, Soglasnova SI (2009) Energetic potential of compositions based on high-enthalpy polynitrogen compounds. Combust Explos Shock Waves 45(2):160-168. doi: 10.1007/s10573-009-0021-9
https://doi.org/10.1007/s10573-009-0021-... );
^j
Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008Mader CL (2008) Numerical modeling of explosives and propellants. 3rd ed. Boca Raton: CRC Press. doi: 10.1201/9781420052398
https://doi.org/10.1201/9781420052398... ).
^*
RMSD = Root-Mean-Square Deviation.

Compositions	Atomic compositions	∆H º_f (kcal mol^–1)
NG	C₃H₅N₃O₉	–88.6^a a (Dobratz and Crawford 1985);
NC (12% N)	C₆H_7.74N_2.26O_9.52	–173.7^a a (Dobratz and Crawford 1985);
NC (13.35% N)	C₆H_7.29N_2.71O_10.41	–163.0^a a (Dobratz and Crawford 1985);
NQ	CH₄N₄O₂	–22.1^a a (Dobratz and Crawford 1985);
RDX	C₃H₆N₆O₆	+14.71^a a (Dobratz and Crawford 1985);
BDNPA-F (50/50 BDNPA/BDNPF)	C_2.347H_4.068N_1.254O_3.134	–46.39^a a (Dobratz and Crawford 1985);
DEP	C₁₂H₁₄O₄	–179.99^b b (NIST 2017);
2-NDPA	C₁₂H₁₀N₂O₂	18.40^b b (NIST 2017);
AP	NH₄ClO₄	–70.58^a a (Dobratz and Crawford 1985);
ADN	H₄N₄O₄	–35.99^c c (Gadiot et al. 1993);
HNF	CH₅N₅O₆	–17.21^c c (Gadiot et al. 1993);
TAGAZ	C₄H₈N₂₂	257.0^d d (Sivabalan et al. 2004);
Carbamite	C₁₇H₂₀N₂O	–105.06^e e (Meyer et al. 2007).
DNC 90/7/3 NC(12% N)/NG/Carbamite	C_2.329H_3.017N_0.886O_3.535	–62.27
CL 78/20/2 NG/DEP/2-NDPA	C_2.22H_3.07N_1.05O_3.47	–46.48

Single-base propellants	∆H º_f (kcal mol^–1)^a a Chemical compositions and heat of formations (HOFs): (Baer and Bryson 1961) otherwise stated; Other chemical compositions:	N_g	Q/ (kcal g^–1)	I_sp/ (Ns g^–1)^f f Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008).	I_sp(Eq. 5) (Ns g^–1)
M1	–53.80	0.0291	1.213	2.12	2.19 (3.07%)
M1A1	–57.40	0.0292	1.179	2.07	2.15 (3.80%)
M6	–53.80	0.0292	1.228	2.16	2.21 (2.00%)
M10	–59.30	0.0298	1.256	2.27	2.25 (–1.02%)
M12	–56.80	0.0296	1.245	2.23	2.23 (0)
M14	–54.10	0.0292	1.242	2.20	2.22 (1.06%)
IMR	–56.80	0.0296	1.247	2.24	2.24 (0)
Double-base propellants	∆H º_f (kcal mol^–1)^a a Chemical compositions and heat of formations (HOFs): (Baer and Bryson 1961) otherwise stated; Other chemical compositions:	*N_g*	Q/ (kcal g^–1)	I_sp/ (Ns g^–1)^f f Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008).	I_sp(Eq. 5) (Ns g^–1)
M2	–55.90	0.0304	1.319	2.37	2.33 (–1.75%)
M5	–56.80	0.0303	1.304	2.35	2.31 (–1.55%)
M7	–48.30	0.0302	1.387	2.45	2.39 (–2.27%)
M8	–47.50	0.0305	1.410	2.48	2.42 (–2.17%)
M9	–47.70	0.0305	1.422	2.50	2.44 (–2.47%)
M18	–55.70	0.0295	1.232	2.17	2.22 (2.11%)
M26	–50.40	0.0300	1.307	2.31	2.31 (0)
T25	–52.10	0.0299	1.295	2.30	2.29 (–0.47%)
Triple-base propellants	∆H º_f (kcal mol^–1)^a a Chemical compositions and heat of formations (HOFs): (Baer and Bryson 1961) otherwise stated; Other chemical compositions:	*N_g*	Q/ (kcal g^–1)	I_sp/ (Ns g^–1)^f f Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008).	I_sp(Eq. 5) (Ns g^–1)
M15	–30.20	0.0346	1.094	2.19	2.21 (0.97%)
M17	–31.90	0.0349	1.137	2.30	2.26 (–1.65%)
T34	–33.10	0.0347	1.088	2.20	2.21 (0.50%)
28/22.5/1.5/48 NC (12% N)/NG/Carbamite/Picrite^b b (Sanghavi et al. 2003);	–37.56	0.0343	1.131	2.28	2.24 (–1.63%)
28/22.5/1.5/48 NC (13.35% N)/NG/Carbamite/Picrite^b b (Sanghavi et al. 2003);	–35.20	0.0343	1.157	2.32	2.27 (–2.09%)
20.8/20.6/3.6/55 NC (13.35% N)/NG/Carbamite/Picrite^b b (Sanghavi et al. 2003);	–32.00	0.0347	1.107	2.25	2.23 (–0.81%)
28/22.5/1.5/38/10 NC (12% N)/NG/Carbamite/Picrite/RDX^c c (Sanghavi et al. 2006);	–34.77	0.0339	1.189	2.33	2.29 (–1.77%)
28/22.5/1.5/33/15 NC (12% N)/NG/Carbamite/Picrite/RDX^c c (Sanghavi et al. 2006);	–33.38	0.0336	1.219	2.36	2.32 (–1.75%)
28/22.5/1.5/28/20 NC (12% N)/NG/Carbamite/Picrite/RDX^c c (Sanghavi et al. 2006);	–31.98	0.0334	1.248	2.38	2.34 (–1.86%)
CMDB propellants	∆H º_f (kcal mol^–1)^a a Chemical compositions and heat of formations (HOFs): (Baer and Bryson 1961) otherwise stated; Other chemical compositions:	*N_g*	Q/ (kcal g^–1)	I_sp/ (Ns g^–1)^f f Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008).	I_sp(Eq. 5) (Ns g^–1)
29.5/32/8/1/29.5 DNC/NG/DEP/2-NDPA/AP^d d (Gore et al. 2002);	–54.96	0.0329	1.251	2.42	2.33 (–3.95%)
29.5/32/2/1/29.5/6 DNC/NG/DEP/2-NDPA/AP/BDNPA-F^d d (Gore et al. 2002);	–52.88	0.0334	1.302	2.49	2.39 (–4.01%)
29.5/32/8/1/29.5 DNC/NG/DEP/2-NDPA/RDX^d d (Gore et al. 2002);	–35.30	0.0311	1.339	2.38	2.37 (–0.50%)
29.5/32/2/1/29.5/6 DNC/NG/DEP/2-NDPA/RDX/BDNPA-F^d d (Gore et al. 2002);	–33.23	0.0316	1.390	2.47	2.43 (–1.58%)
29.5/32/8/1/29.5 DNC/NG/DEP/2-NDPA/ADN	–45.82	0.0331	1.314	2.45	2.40 (–2.10%)
29.5/32/8/1/29.5 DNC/NG/DEP/2-NDPA/HNF	–40.03	0.0320	1.372	2.47	2.43 (–1.65%)
30/40/30 DNC/CL/TAGAZ^e e (Sivabalan et al. 2004);	–16.68	0.0334	1.177	2.18	2.27 (3.96%)

Pseudo-propellant compositions	∆H º_f (kcal mol^–1)^a a Heat of formation (HOF) and chemical composition of GAP and BAMO: (Gadiot et al. 1993); (HOF) of BTTN and CL-20: (NIST 2017) and (Meyer et al. 2007), respectively;	N_g	Q/(kcal g^–1)	I_sp/(Ns g^–1)^b b Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008).	I_sp(Eq. 5) (Ns g^–1)
80/20 RDX/GAP	10.96	0.0336	1.392	2.46	2.48 (1.03%)
71/9/20 RDX/GAP/BTTN	–0.96	0.0334	1.445	2.55	2.53 (–0.87%)
70/30 HMX/GAP	12.73	0.0335	1.342	2.35	2.43 (3.61%)
80/20 RDX/BAMO	17.26	0.0335	1.408	2.49	2.50 (0.16%)
70/30 HMX/BAMO	22.17	0.0334	1.367	2.41	2.46 (1.91%)
70/30 CL-20/GAP	23.89	0.0314	1.416	2.44	2.45 (0.48%)
80/20 CL-20/BAMO	29.56	0.0312	1.488	2.58	2.51 (–2.47%)

ADN-based compositions	∆H º_f (kcal mol^–1)	N_g	Q/(kcal g^–1)	I_sp/ (Ns g^–1)^f f Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008). Heat of formation (HOF) values: AN (Dobratz and Crawford 1985); AB, PMVT and PVMDO (Manelis and Lempert 2009); TMETN (NIST 2017); HTPB (HOF) and atomic composition (Maggi and De Luca 2011); 3u and 3v (Shastin and Lempert 2014).	I_sp(Eq. 5) (Ns g^–1)
80/20 ADN/GAP^a a (Wingborg et al. 2010);	–17.55	0.0388	1.326	2.60	2.55 (–1.99%)
75/25 ADN/GAP^a a (Wingborg et al. 2010);	–14.69	0.0384	1.307	2.57	2.52 (–1.89%)
70/30 ADN/GAP^a a (Wingborg et al. 2010);	–11.82	0.0381	1.289	2.53	2.50 (–1.29%)
65/35 ADN/GAP^a a (Wingborg et al. 2010);	–8.96	0.0377	1.270	2.48	2.47 (–0.37%)
60/40 ADN/GAP^a a (Wingborg et al. 2010);	–6.09	0.0373	1.252	2.42	2.44 (0.77%)
50/50 ADN/GAP^a a (Wingborg et al. 2010);	–0.36	0.0366	1.215	2.29	2.39 (4.21%)
74/26 ADN/AB^b b (Manelis and Lempert 2009);	–26.17	0.0384	1.397	2.47	2.60 (5.53%)
85/15 ADN/PMVT^b b (Manelis and Lempert 2009);	–20.16	0.0390	1.279	2.57	2.51 (–2.36%)
80/20 ADN/PVMDO^b b (Manelis and Lempert 2009);	–23.21	0.0391	1.367	2.62	2.59 (–0.97%)
AN-based compositions	∆H º_f (kcal mol^–1)	*N_g*	Q/(kcal g^–1)	I_sp/ (Ns g^–1)^f f Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008). Heat of formation (HOF) values: AN (Dobratz and Crawford 1985); AB, PMVT and PVMDO (Manelis and Lempert 2009); TMETN (NIST 2017); HTPB (HOF) and atomic composition (Maggi and De Luca 2011); 3u and 3v (Shastin and Lempert 2014).	I_sp(Eq. 5) (Ns g^–1)
75/25 AN/AB^b b (Manelis and Lempert 2009);	–86.28	0.0410	1.054	2.29	2.34 (2.44%)
75/25 AN/PMVT^b b (Manelis and Lempert 2009);	–88.16	0.0420	0.889	2.24	2.20 (–2.10%)
85/15 AN/PVMDO^b b (Manelis and Lempert 2009);	–92.66	0.0423	0.986	2.34	2.31 (–1.47%)
60/20/20 AN/GAP/TMETN^c c (Oyumi et al. 1996);	–112.41	0.0393	0.614	1.85	1.79 (–3.27%)
70/15/15 AN/GAP/TMETN^c c (Oyumi et al. 1996);	–111.56	0.0404	0.696	2.01	1.93 (–4.16%)
60/15/15/10 AN/GAP/TMETN/NC(12%N)^c c (Oyumi et al. 1996);	–107.24	0.0390	0.721	1.99	1.92 (–3.70%)
40/15/15/30 AN/GAP/TMETN/NC(12%N)^c c (Oyumi et al. 1996);	–98.61	0.0362	0.772	1.94	1.89 (–2.43%)
40/15/15/30 AN/GAP/TMETN/HMX^c c (Oyumi et al. 1996);	–77.04	0.0374	0.856	2.08	2.03 (–2.46%)
HNF-based compositions	∆H º_f (kcal mol^–1)	*N_g*	Q/(kcal g^–1)	I_sp/ (Ns g^–1)^f f Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008). Heat of formation (HOF) values: AN (Dobratz and Crawford 1985); AB, PMVT and PVMDO (Manelis and Lempert 2009); TMETN (NIST 2017); HTPB (HOF) and atomic composition (Maggi and De Luca 2011); 3u and 3v (Shastin and Lempert 2014).	I_sp(Eq. 5) (Ns g^–1)
80/20 HNF/GAP^d d (Gadiot et al. 1993);	–1.86	0.0361	1.481	2.66	2.63 (–1.40%)
80/20 HNF/PGN^d d (Gadiot et al. 1993);	–18.95	0.0358	1.522	2.65	2.66 (0.22%)
80/20 HNF/PLN^d d (Gadiot et al. 1993);	–19.55	0.0372	1.539	2.70	2.70 (0)
80/20 HNF/BAMO^d d (Gadiot et al. 1993);	4.44	0.0360	1.498	2.68	2.64 (–1.63%)
80/20 HNF/HTPB	–10.29	0.0351	1.383	2.40	2.51 (4.57%)
Organic oxidizer-based compositions	∆H º_f (kcal mol^–1)	*N_g*	Q/(kcal g^–1)	I_sp/ (Ns g^–1)^f f Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008). Heat of formation (HOF) values: AN (Dobratz and Crawford 1985); AB, PMVT and PVMDO (Manelis and Lempert 2009); TMETN (NIST 2017); HTPB (HOF) and atomic composition (Maggi and De Luca 2011); 3u and 3v (Shastin and Lempert 2014).	I_sp(Eq. 5) (Ns g^–1)
85/15 1f/AB^e e (Shastin and Lempert 2014);	85.02	0.0295	1.853	2.88	2.80 (–2.69%)
85/15 3u/AB^e e (Shastin and Lempert 2014);	60.58	0.0295	1.609	2.72	2.59 (–4.78%)
85/15 3v/AB^e e (Shastin and Lempert 2014);	76.92	0.0295	1.772	2.83	2.73 (–3.37%)
85/15 1e/AB	85.49	0.0304	1.889	2.86	2.85 (–0.49%)

Chemical compositions:
^a
(Wingborg et al. 2010Wingborg N, Andreasson S, de Flon J, Johnsson M, Liljedahl M, Oscarsson C, Pettersson Å, Wanhatalo M (2010) Development of ADN-based minimum smoke propellants. Presented at: 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit; Nashville, USA. doi: 10.2514/6.2010-6586
https://doi.org/10.2514/6.2010-6586... );
^b
(Manelis and Lempert 2009Manelis GB, Lempert DB (2009) Ammonium nitrate as an oxidizer in solid composite propellants. Progress in Propulsion Physics 1:81-96. doi: 10.1051/eucass/200901081
https://doi.org/10.1051/eucass/200901081... );
^c
(Oyumi et al. 1996Oyumi Y, Kimura E, Hayakawa S, Nakashita G, Kato K (1996) Insensitive munitions (IM) and combustion characteristics of GAP/AN composite propellants. Propellants, Explosives, Pyrotechnics 21(5):271-275. doi: 10.1002/prep.19960210511
https://doi.org/10.1002/prep.19960210511... );
^d
(Gadiot et al. 1993Gadiot GMHJL, Mul JM, Meulenbrugge JJ, Korting PAOG, Schnorkh AJ, Schöyer HFR (1993) New solid propellants based on energetic binders and HNF. Acta Astronautica 29(10-11):771-779 doi: 10.1016/0094-5765(93)90158-S
https://doi.org/10.1016/0094-5765(93)901... );
^e
(Shastin and Lempert 2014Shastin AV, Lempert DB (2014) Energy potential of some triazine derivatives. Russian Journal of Physical Chemistry B 8(5):716-719. doi: 10.1134/s1990793114050212
https://doi.org/10.1134/s199079311405021... );
^f
Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008Mader CL (2008) Numerical modeling of explosives and propellants. 3rd ed. Boca Raton: CRC Press. doi: 10.1201/9781420052398
https://doi.org/10.1201/9781420052398... ). Heat of formation (HOF) values: AN (Dobratz and Crawford 1985Dobratz BM, Crawford PC (1985) LLNL Explosives Handbook: properties of chemical explosives and explosives simulants. (UCRL-52997-CHG-2) Lawrence Livermore National Laboratory Report.); AB, PMVT and PVMDO (Manelis and Lempert 2009Manelis GB, Lempert DB (2009) Ammonium nitrate as an oxidizer in solid composite propellants. Progress in Propulsion Physics 1:81-96. doi: 10.1051/eucass/200901081
https://doi.org/10.1051/eucass/200901081... ); TMETN (NIST 2017NIST (2017) Standard Reference Data Base Number 69; [accessed 2017 April 21]. http://webbook.nist.gov/chemistry
http://webbook.nist.gov/chemistry... ); HTPB (HOF) and atomic composition (Maggi and De Luca 2011Maggi F, De Luca LT (2011) Assessment of rocket exhaust pollution through thermochemistry. Presented at: 4th European Conference for Aerospace Sciences (EUCASS); Saint Petersburg, Russia.); 3u and 3v (Shastin and Lempert 2014Shastin AV, Lempert DB (2014) Energy potential of some triazine derivatives. Russian Journal of Physical Chemistry B 8(5):716-719. doi: 10.1134/s1990793114050212
https://doi.org/10.1134/s199079311405021... ).

Liquid monopropellant compositions	∆H º_f (kcal mol^–1)	N_g	Q/(kcal g^–1)	I_sp/ (Ns g^–1)^e e Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008).Heat of formation (HOF) values: HAN (Meng et al. 2009); MeOH, H2O, EtOH, 1-PrOH, Glycine and Urea (NIST 2017); H2O2 (70%) (Constantine and Cain 1967).	I_sp(Eq. 5) (Ns g^–1)
69.7/0.6/14.79/14.91 HAN/AN/MeOH/H₂O^a a (Chang et al. 2002);	–141.34	0.0445	0.915	2.27	2.29 (1.14%)
77.25/0.67/17.19/4.89 HAN/AN/MeOH/H₂O^a a (Chang et al. 2002);	–113.94	0.0433	1.085	2.43	2.43 (0%)
72.3/0.62/11.62/15.47 HAN/AN/EtOH/H₂O^b b (Wucherer et al. 2000);	–135.98	0.0440	0.927	2.31	2.29 (–0.50%)
73.41/0.63/10.26/15.70 HAN/AN/1-PrOH/H₂O^b b (Wucherer et al. 2000);	–133.49	0.0439	0.938	2.31	2.30 (–0.58%)
63.63/0.54/22.22/13.61 HAN/AN/Glycine/H₂O^b b (Wucherer et al. 2000);	–142.33	0.0425	0.771	2.15	2.08 (–3.08%)
60/30/10 ADN/MAN/Urea^c c (Ide et al. 2015);	–57.54	0.0411	1.105	2.45	2.40 (–2.17%)
40/40/20 ADN/MAN/Urea^c c (Ide et al. 2015);	–73.95	0.0415	0.902	2.20	2.20 (0)
30/40/30 ADN/MAN/Urea^c c (Ide et al. 2015);	–84.31	0.0416	0.744	1.97	2.03 (2.68%)
59.86/25/15.14 H₂O₂(70%)/AN/EtOH^d d (Martin et al. 2006);	–172.85	0.0460	0.908	2.27	2.33 (2.56%)
80/8/12 H₂O₂(70%)/H₂O/EtOH^d d (Martin et al. 2006);	–213.13	0.0477	0.828	2.19	2.29 (4.51%)
36.67/51.20/12.13 H₂O₂(70%)/ADN/EtOH^d d (Martin et al. 2006);	–108.13	0.0434	1.137	2.47	2.48 (0.45%)

Liquid bipropellant compositions	∆H º_f (kcal mol^–1)	N_g	Q/(kcal g^–1)	I_sp/(Ns g^–1)^e e Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008). Heat of formation (HOF) values: N2O4, Toluene, Methylcyclohexane, n-heptane, Ethylene oxide, Nitroethane, N2H4, DETA, MA and TNM (NIST 2017); HEH and UDMH (Keshavarz et al. 2011); RFNA (Wright 1977); O2, NO, RP-1, NH3 (U.S. Army Material Command 1969).	I_sp(Eq. 5) (Ns g^–1)
N₂O₄/HEH (O/F = 1.94)^a a (Keshavarz et al. 2011);	–24.10	0.0372	1.511	2.68	2.68 (0)
N₂O₄-UDMH/HEH (80/20) (O/F = 2.45)^a a (Keshavarz et al. 2011);	–2.58	0.0374	1.660	2.79	2.81 (0.92%)
N₂O₄-UDMH/HEH (90/10) (O/F = 2.55)^a a (Keshavarz et al. 2011);	–0.42	0.0374	1.679	2.80	2.83 (1.06%)
N₂O₄/UDMH (O/F = 2.60)^a a (Keshavarz et al. 2011);	2.05	0.0374	1.696	2.81	2.84 (1.17%)
N₂O₄-UDMH/HEH (60/40) (O/F= 2.32)^a a (Keshavarz et al. 2011);	–5.94	0.0374	1.641	2.77	2.79 (0.87%)
RFNA/UDMH (O/F = 2.92)^a a (Keshavarz et al. 2011);	–43.83	0.0393	1.460	2.68	2.68 (0)
RFNA-UDMH/HEH (90/10) (O/F = 2.85)^a a (Keshavarz et al. 2011);	–45.77	0.0393	1.444	2.67	2.67 (0)
RFNA/HEH (O/F = 2.14)^a a (Keshavarz et al. 2011);	–64.32	0.0390	1.304	2.57	2.53 (–1.43%)
O₂/RP-1 (O/F = 2.60)^b b (U.S. Army Material Command 1969);	–18.41	0.0323	2.146	2.94	3.09 (5.27%)
O₂/N₂H₄ (O/F = 0.91)^b b (U.S. Army Material Command 1969);	15.16	0.0476	1.905	3.07	3.21(4.62%)
O₂/Toluene (O/F = 1.87)^c c (Greenfield 1960);	–5.19	0.0279	2.026	2.84	2.91 (2.58%)
O₂/Methylcyclohexane (O/F= 2.04)^c c (Greenfield 1960);	–21.69	0.0327	2.007	2.87	2.99 (4.29%)
O₂/n-heptane (O/F = 2.05)^c c (Greenfield 1960);	–24.03	0.0341	2.017	2.88	3.03 (5.09%)
O₂/Ethylene oxide (O/F = 1.10)^d d (U.S. Army Ordnance Corps 1960);	–29.72	0.0326	1.985	2.87	2.97 (3.72%)
O₂/Nitroethane (O/ F= 0.65)^d d (U.S. Army Ordnance Corps 1960);	–31.58	0.0345	1.818	2.81	2.88 (2.61%)
O₂/EtOH-75% (O/F = 1.30)^d d (U.S. Army Ordnance Corps 1960);	–93.22	0.0379	1.640	2.71	2.80 (3.29%)
TNM/N₂H₄ (O/F = 1.40)^d d (U.S. Army Ordnance Corps 1960);	18.38	0.0438	1.586	2.85	2.89 (1.27%)
H₂O₂ (90%)/N₂H₄ (O/F = 1.50)^d d (U.S. Army Ordnance Corps 1960);	–79.15	0.0522	1.335	2.70	2.86 (5.90%)
RFNA-DETA/MA (80/20) (O/F = 3.00)^d d (U.S. Army Ordnance Corps 1960);	–54.24	0.0388	1.364	2.61	2.58 (–0.94%)
RFNA/Hydine (O/F = 3.17)^b b (U.S. Army Material Command 1969);	–48.55	0.0387	1.433	2.65	2.64 (–0.36%)
N₂O₄/N₂H₄ (O/F = 1.30)^b b (U.S. Army Material Command 1969);	13.52	0.0456	1.584	2.87	2.92 (1.70%)
N₂O₄/Aerozine-50 (O/F = 2.00)^b b (U.S. Army Material Command 1969);	6.32	0.0405	1.658	2.83	2.87 (1.41%)
N₂O₄/NO (70/30)-MeOH (O/F = 2.10)^d d (U.S. Army Ordnance Corps 1960);	–45.03	0.0373	1.528	2.67	2.70 (0.90%)
N₂O₄/NO (70/30)-NH₃ (O/F = 2.10)^d d (U.S. Army Ordnance Corps 1960);	–20.17	0.0459	1.393	2.73	2.77 (1.38%)

Chemical compositions:
^a
(Keshavarz et al. 2011Keshavarz MH, Ramadan A, Mousaviazar A, Zali A, Shokrollahi A (2011) Reducing dangerous effects of unsymmetrical dimethyl hydrazine as a liquid propellant by addition of hydroxyethylhydrazine, Part II, Performance with several oxidizers. J Energ Mater 29(3):228-240. doi: 10.1080/07370652.2010.514320
https://doi.org/10.1080/07370652.2010.51... );
^b
(U.S. Army Material Command 1969U.S. Army Material Command (1969) Engineering design handbook elements of aircraft and missile propulsion. (AMCP 706-285) Washington: US Army Materiel Command.);
^c
(Greenfield 1960Greenfield S (1960) An experimental evaluation of rocket propellant data. In: Penner SS, Ducarme J, editors. The Chemistry of Propellants. Paris: Pergamon. p. 169-227 doi: 10.1016/B978-1-4831-9626-8.50011-8
https://doi.org/10.1016/B978-1-4831-9626... );
^d
(U.S. Army Ordnance Corps 1960U.S. Army Ordnance Corps (1960) Ordnance engineering design handbook, ballistic missile series: propulsion and propellants. (AMCP 706-282) Washington: US Army Materiel Command.);
^e
Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008Mader CL (2008) Numerical modeling of explosives and propellants. 3rd ed. Boca Raton: CRC Press. doi: 10.1201/9781420052398
https://doi.org/10.1201/9781420052398... ). Heat of formation (HOF) values: N2O4, Toluene, Methylcyclohexane, n-heptane, Ethylene oxide, Nitroethane, N2H4, DETA, MA and TNM (NIST 2017Dobratz BM, Crawford PC (1985) LLNL Explosives Handbook: properties of chemical explosives and explosives simulants. (UCRL-52997-CHG-2) Lawrence Livermore National Laboratory Report.); HEH and UDMH (Keshavarz et al. 2011Keshavarz MH, Ramadan A, Mousaviazar A, Zali A, Shokrollahi A (2011) Reducing dangerous effects of unsymmetrical dimethyl hydrazine as a liquid propellant by addition of hydroxyethylhydrazine, Part II, Performance with several oxidizers. J Energ Mater 29(3):228-240. doi: 10.1080/07370652.2010.514320
https://doi.org/10.1080/07370652.2010.51... ); RFNA (Wright 1977Wright AC (1977) USAF propellant handbooks. Nitric acid/nitrogen tetroxide oxidizers. Volume II. (AFRPL-TR-76-76) AFRPL Technical Report.); O2, NO, RP-1, NH3 (U.S. Army Material Command 1969U.S. Army Material Command (1969) Engineering design handbook elements of aircraft and missile propulsion. (AMCP 706-285) Washington: US Army Materiel Command.).

Hybrid propellant compositions	∆H º_f (kcal mol^–1)	N_g	Q/(kcal g^–1)	I_sp/(Ns g^–1)^e e Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008). Heat of formation (HOF) values: DCPD (Shark et al. 2013); H2O2 (92%) and H2O2 (86%) (Rajesh et al. 2003); H2O2 (90%) and H2O2 (98%) (Constantine and Cain 1967); N2O (Heister and Wernimont 2007); Paraffin wax (Bernard et al. 2011); PE (Risha et al. 2007).	I_sp(Eq. 5) (Ns g^–1)
O₂/HTPB (O/F = 2.30)^a a (Heister and Wernimont 2007);	–10.91	0.0303	2.144	2.91	3.05 (4.82%)
H₂O₂ (90%)/PE (O/F = 7.80)^a a (Heister and Wernimont 2007);	–144.43	0.0442	1.385	2.63	2.73 (3.78%)
H₂O₂ (98%)/PE (O/F = 7.00)^a a (Heister and Wernimont 2007);	–125.53	0.0433	1.540	2.71	2.84 (4.56%)
H₂O₂ (98%)/DCPD (O/F = 6.20)^a a (Heister and Wernimont 2007);	–112.37	0.0413	1.600	2.70	2.84 (5.33%)
H₂O₂ (86%)/HTPB (O/F = 7.50)^b b (Rajesh et al. 2003);	–117.89	0.0436	1.633	2.76	2.92 (5.60%)
H₂O₂ (92%)/HTPB (O/F = 6.50)^b b (Rajesh et al. 2003);	–116.24	0.0428	1.609	2.75	2.88 (4.89%)
RFNA/HTPB (O/F = 4.90)^c c (Venugopal et al. 2011);	–57.08	0.0344	1.457	2.54	2.56 (0.87%)
RFNA-HTPB/AP (90/10) (O/F = 3.80)^c c (Venugopal et al. 2011);	–56.01	0.0343	1.427	2.56	2.54 (–1.09%)
N₂O/Paraffin wax (O/F = 7.00)^d d (Bernard et al. 2011);	32.64	0.0344	1.359	2.60	2.47 (–4.77%)
N₂O/HTPB (O/F = 7.40)^a a (Heister and Wernimont 2007);	37.38	0.0334	1.396	2.61	2.48 (–4.84%)
HAN(95%)/HTPB (O/F = 9.60)^a a (Heister and Wernimont 2007);	–89.89	0.0410	1.189	2.49	2.47 (–0.55%)

Chemical compositions:
^a
(Heister and Wernimont 2007Heister S, Wernimont E (2007) Hydrogen peroxide, hydroxyl ammonium nitrate, and other storable oxidizers. In: Chiaverini MJ, Kuo KK, editors. Fundamentals of Hybrid Rocket Combustion and Propulsion. Virginia: AIAA. p. 457-488. doi: 10.2514/5.9781600866876.0457.0488
https://doi.org/10.2514/5.9781600866876.... );
^b
(Rajesh et al. 2003Rajesh K, Kuznetsov KA, Natan B (2003) Design of a lab-scale HP/HTPB hybrid rocket motor. Presented at: 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit; Huntsville, USA. doi: 10.2514/6.2003-4744
https://doi.org/10.2514/6.2003-4744... );
^c
(Venugopal et al. 2011Venugopal S, Ramanujachari V, Rajesh KK (2011) Combustion experiments of HTPB/RFNA mixed hybrid propellants. Indian Journal of Science and Technology 4(10):1267-1272. doi: 10.17485/ijst/2011/v4i10/30170
https://doi.org/10.17485/ijst/2011/v4i10... );
^d
(Bernard et al. 2011Bernard G, Brooks MJ, Beaujardiere JP, Roberts LW (2011) Performance modeling of a paraffin wax / nitrous oxide hybrid rocket motor. Presented at: 49th AIAA Aerospace Sciences Meeting; Orlando, USA. doi: 10.2514/6.2011-420
https://doi.org/10.2514/6.2011-420... );
^e
Equilibrium specific impulses were calculated using the ISPBKW thermochemical code (Mader 2008Mader CL (2008) Numerical modeling of explosives and propellants. 3rd ed. Boca Raton: CRC Press. doi: 10.1201/9781420052398
https://doi.org/10.1201/9781420052398... ). Heat of formation (HOF) values: DCPD (Shark et al. 2013Shark SC, Pourpoint TL, Son SF, Heister SD (2013) Performance of dicyclopentadiene/H2O2-based hybrid rocket motors with metal hydride additives. J Propul Power 29(5):1122-1129 doi: 10.2514/1.B34867
https://doi.org/10.2514/1.B34867... ); H2O2 (92%) and H2O2 (86%) (Rajesh et al. 2003Rajesh K, Kuznetsov KA, Natan B (2003) Design of a lab-scale HP/HTPB hybrid rocket motor. Presented at: 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit; Huntsville, USA. doi: 10.2514/6.2003-4744
https://doi.org/10.2514/6.2003-4744... ); H2O2 (90%) and H2O2 (98%) (Constantine and Cain 1967Constantine MT, Cain EFC (1967) Hydrogen Peroxide Handbook. (AFRPL-TR-67-144) ARFPL Technical Report.); N2O (Heister and Wernimont 2007Heister S, Wernimont E (2007) Hydrogen peroxide, hydroxyl ammonium nitrate, and other storable oxidizers. In: Chiaverini MJ, Kuo KK, editors. Fundamentals of Hybrid Rocket Combustion and Propulsion. Virginia: AIAA. p. 457-488. doi: 10.2514/5.9781600866876.0457.0488
https://doi.org/10.2514/5.9781600866876.... ); Paraffin wax (Bernard et al. 2011Bernard G, Brooks MJ, Beaujardiere JP, Roberts LW (2011) Performance modeling of a paraffin wax / nitrous oxide hybrid rocket motor. Presented at: 49th AIAA Aerospace Sciences Meeting; Orlando, USA. doi: 10.2514/6.2011-420
https://doi.org/10.2514/6.2011-420... ); PE (Risha et al. 2007Risha GA, Evans BJ, Boyer E, Kuo KK (2007) Metals, energetic additives, and special binders used in solid fuels for hybrid rockets. In: Chiaverini MJ, Kuo KK, editors. Fundamentals of Hybrid Rocket Combustion and Propulsion. Virginia: AIAA. p. 413-456. doi: 10.2514/5.9781600866876.0413.0456
https://doi.org/10.2514/5.9781600866876.... ).

[1] Correspondence author: Dany Frem | FREM Co. | Beirut - Lebanon | E-mail: frem.dany@gmail.com

Brasil

Brasil

A Reliable Method for Predicting the Specific Impulse of Chemical Propellants

ABSTRACT