APPENDIX B
MISSION OPTIMIZATION PROGRAM - OPT-4; MDRE COMPONENTS

FREE-SPACE V MISSION PERFORMANCE

Step	Instructions	Input data/units	Keys
1	load sides 1 and 2
2	store constraints into secondary registers
	store:	1.656X10-10	STO 0
	store one set of the following constraints: MDRE/MDLL
	0.122 / 0.142		STO 1
	7.194X10-4 / 7.973X10-4		STO 2
	0.005 / 0.014		STO 3
3	rotate storage		P S
4	set format SCI 3
5	store values and mission parameters
	all units MKS
	propellant acceleration a, m/sec2	a	STO A
	propellant launch rate ,Hz		STO B
	exhaust velocity ve, m/sec	ve	STO C
	propellant lump (payload) mass, kg	m1	STO D
	missionv, m/sec	v	STO E
	mission thrust time, tB, sec	tB	STO I
6	start program. Output data printed as follows:		[A]
	caliber D, m
	SCR mass, kg
	winding mass, kg
	feeder=capacitor mass, kg
	MDRE total mass, kg
	total power, W
	efficiency, fraction
	total radiator mass, kg
	overall MD specific powerplant mass, kg/w
	powerplant, total mass, kg
	MDRE mass/overall initial mass, fraction
	payload mass.overall initial mass, fraction
	initial mass Mo, kg
	payload mass delivered at destination, Mpay, kg
	propellant mass used,Mpro, kg
	note: last five items apply only to MDRE calculations
7	for length, m		[B]
8	for thrust, N		[C]

OPT-4 PROGRAM DESCRIPTION (EQUATIONS, VARIABLES)

MDRE constants are used and identified by by ( )

• caliber (mean diameter of drive coils) =0.197m, m₁ = payload (pellet) mass
• SCR mass = 1.65X10^-10 v_e³ a m
• winding mass = (0.122)v_e
• feeder = capacitor mass + (7.196X10^-4v_e [a]m₁
• kinetic power = 1/2m₁v_e² = P_kin
• kinetic power mass = (0.005)* kinetic power = M_kinetic
• waste power = [M_wind + M_feed]/[(0.005) + 0.02] = P_waste
• total MDRE mass = 1.5* [M_scr +2M_wind + 3M_feed + M _kin] = M_tot
  which is also = 1.5*[M_scr +M_wind + M_feed + M _cap + M_rad + M_pow]
• P_tot = P_kin + P_waste
• power plant mass = (0.005)* P_tot
• radiator mass = M_rad = 0.02* P_waste
• efficiency = 1-P_waste/P_tot
• overall MD specific power plant mass = M_tot/P_tot
• characteristic velocity v_c = ,v_e* = v_e/v_c
• M_pay/M_o = e ^-v/v_e-v_e*²(1 - e ^-v/v_e)
• initial acceleration = a_o = [v_e/t_B] [1 - e ^-v/v_e]
• initial mass = M_o = m₁ c/a_o
• mission payload mass M_pay = M_o *M_pay /M_o
• propellant mass M_prop = M_o [1 - e ^-v/v_e]
• m_bucket/m₁ = 2.263
• overall MDRE length S_tot =1.694v_e² /2a
• thrust = m₁ v_e

001	*LBLA	056	x	111	x	166	CHS
002	.	057	3	112	STO5	167	RCL5
003	1	058	1/X	113	PRTX	168	+
004	9	059	yx	114	1	169	STO6
005	7	060	x	115	RCL9	170	PRTX
006	RCLD	061	RCLD	116	RCL8	171	1
007	3	062	5	117	PRTX	172	RCL5
008	1/X	063	ENT	118		173
009	yx	064	9	119		174	RCLC
010	x	065		120	STO	175	x
011	PRTX	066	yx	121	PRTX	176	RCLI
012	PS	067	x	122	RCL9	177
013	RCL	068	STO3	123	5	178	STO8
014	PS	069	PRTX	124		179	1/X
015	RCLC	070	RCLB	125		180	RCLD
016	3	071	RCLD	126	STO4	181	x
017	yx	072	x	127	PRTX	182	RCLB
018	x	073	RCLC	128	RCL5	183	x
019	RCLA	074	x2	129	RCL8	184	RCLC
020	x	075	x	130		185	x
021	RCLD	076	2	131	STO6	186	STO9
022	3	077		132	PRTX	187	PRTX
023	1/x	078	STO8	133	RCL8	188	RCL6
024	yx	079	P S	134	P S	189	x
025	x	080	RCL3	135	RCL3	190	PRTX
026	STO1	081	P S	136	P S	191	1
027	PRTX	082	x	137	x	192	RCL5
028	P S	083	STO6	138	PRTX	193
029	RCL1	084	RCL2	139	SPC	194	RCL9
030	P S	085	RCL3	140	RCL	195	x
031	RCLC	086	+	141	2	196	PRTX
032	1	087	.	142	x	197	P S
033	.	088		143	RCL1	198	RTN
034	5	089	2	144	x	199	*LBLA
035	yx	090	P S	145	RCL6	200	RCLC
036	x	091	RCL3	146		201	X2
037	RCLD	092	PS	147		202	RCLA
038	RCLB	093	+	148	STO7	203
039	x	094		149	RCLC	204	.
040		095	STO9	150	Y	205	8
041	x	096	ST+8	151		206	4
042	STO2	097	RCL6	152	x2	207	7
043	PRTX	098	RCL2	153	RCLE	208	x
044	P S	099	2	154	RCLC	209	PRTX
045	RCL2	100	x	155		210	RTN
046	P S	101	+	156	CHS	211	*LBLC
047	RCLC	102	RCL3	157	ex	212	RCLB
048	5	103	3	158	P S	213	RCLD
049	ENT	104	x	159	STO5	214	x
050	3	105	+	160	CHS	215	RCLC
051		106	RCL1	161	1	216	x
052	yx	107	+	162	+	217	PRTX
053	x	108	1	163	x	218	RTN
054	RCLA	109	.	164	STO4	219	R/S
055	RCLB	110	5	165	PRTX	End of Program

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