Project Longshot to Alpha Centauri - part 7

Phew, lots of formulae today and even more tomorrow. Only nine pages left though and then it'll be time to upload the whole thing to scribd.com. This is Project Longshot, a proposed mission to Alpha Centauri, the closest star system to our own.




4.0 SPACECRAFT DESIGN

The general structure of the probe consists of five main components. The probe head, fuel tanks, central truss, fission power reactor and fusion drive system.

The actual probe will house all of the necessary instruments and data processing equipment. There will also be a particle shield in front to protect the spacecraft during the interstellar flight phase. The particles may not be all that large, but the spacecraft will be traveling and velocities near 5 percent of the speed of light; therefore, they will have a tremendous amount of energy.

The fuel tanks were designed to be cylinders. This shape was picked for its ease in construction. The calculations on the sizing of the fuel tanks are in the appendix. The tanks are connected to a central framework using explosive bolts which will permit their jetisioning when empty. A detailed structural analysis on the sizing of the tanks may be found in the Appendix.

The central truss will be a collapsable space frame and fulfill several functions. Its primary role is to connect the probe head with its power source while providing adequate separation for thermal and radiation protection. Additionally, it will house the attitude determination and control systems and support the fuel tanks during the interstellar transit phase of the mission.

The fission power reactor will be attached to the aft end of the main truss behind a thermal reflector. This shield will protect the cryogenic fuel from the heat generated by the drive as well as the reactor. The rear end of the reactor will incorporate a flange for mounting the fusion drive. This connector will contain pyrotechnic elements to separate the drive system once the spacecraft reaches Alpha Centauri.

The fusion drive system was described in the Propulsion section. It will serve the additional function of providing attach points for the after particle shield and the chemical upper stages. The rear shield is needed during the decceleration phase of the flight when the spacecraft is flying backwards.

A weight table is included in the appendix as well as a diagram of the structure.




APPENDIX

Delva-V Calculations

Assumptions:

space station orbit altitude = 300 km
space station orbit inclination = 28.5 deg
obliquity = 23.5 deg
1 AU = 149.6x10^6 km
Earth radius = 6378 km
f earth = GMe = 398,601.2 km^2/sec^3
f sun = 1.3271544x10^11 km^2/sec^3
f Jupiter = 1.268x10^8 km^2/sec^3

(1) Velocity of probe about the earth:
Vp = (GMe/Rcircular).5 = (398,601.2/6678).5 = 7.7258 km/sec

(2) Amount of plane change:
i* = 61x - (28.5x + 23.5x) = 9x

(3) Delta-V for 9x plane change:
Delta-Vpc = 2 x Vp x sin(i/2) = 1.2123 km/sec

(4) Earth escape velocity:
Ve-escape = (2GMe/R).5 = 10.9260 km/sec

(5) Delta-V to escape earth:
Delta-Ve-esc = Ve-esc - Vp = 3.2002 km/sec

(6) Velocity of probe around sun:
Vp-sun = (f sun/1 AU).5 = 29.7849 km/sec

(7) Solar system escape velocity:
Vsun-escape = (2 f sun/1 AU).5 = 42.1221 km/sec

(8) Delta-V to escape the solar system:
Delta-Vsun-esc = Vsun-esc - Vp-sun = 12.4273 km/sec

(9) Total Delta-V required to escape solar system:
Delta-Vtotal = 16.8398 km/sec


Rough calculations for Delta-V's for orbit changes to take the probe out to Jupiter (to take on fuel) are made using Hohmann transfer equations as an approximation (actual orbits would be patched-conics). The first six calculations are the same for this analysis:

(1) Energy of Hohmann transfer orbit:
Et * - f sun/6.2 AU = -143.0894 km^2 / sec^2

(2) Perigee velocity of transfer orbit:
V1 = [2(f sun/1 AU + Et)].5 = 38.6171 km/sec

(3) Delta-V to enter transfer orbit:
Delta-V1 = V1 - Vp-sun = 8.8223 km/sec

(4) Apogee velocity of transfer orbit:
V2 = [2(f sun/5.2 AU + Et)] = 7.4157 km/sec

(5) Velocity required to orbit Jupiter at an altitude of 500,000 km:

V3 = (f Jupiter/571370).5 = 14.8971 km/sec

(6) Delta-V to inject into orbit about Jupiter:
V3 - V2 = 7.4814 km/sec

(7) Jupiter escape velocity:
V3-escape = (2 f Jupiter / 571370).5 = 21.0676 km/sec

(8) Delta-V to escape Jupiter:
Delta-V3-esc = V J-esc - V J = 6.1705 km/sec

(9) Velocity of probe about sun at Jupiter distance:
Vp-sun-3 = (f sun/5.2 AU).5 = 13.0601 km/sec

(10) Velocity to escape sun at Jupiter distance:
V sun-esc-J = (2 f sun/5.2 AU).5 = 18.4697 km/sec

(11) Delta-V to escape sun at Jupiter distance:
V sun-esc-J - Vp-sun-J = 5.4087 km/sec

(12) Total Delta-V for Jupiter analysis Delta-V
Vtotal = 32.2954 km/sec

This is nearly twice the Delta-V required for the first case. This fact, along with the difficulties involved in mining the atmosphere of Jupiter, getting the fuel to a million kilometr orbit around the planet, etc., has made it obvious that obtaining fuel from Jupiter is not feasible.



Acceleration and Velocity Profiles

1. Accelerations. The accelerations for the mission were found using the equation F=ma. Since it is a constant thrust, the acceleration will increase at a constant rate. The acceleration was found by dividing the thrust by the mass left at the time. This gives the acceleration chart on page.

2. Velocity. Since the acceleration changed at such a small rate, it was assumed that an average value for the acceleration could be used for computing the velocity. The acceleration at the beginning of a phase and at the end of a phase were averaged. This acceleration was then multiplied by the time interval for which it pertained. This delta V was then added to the previous velocity. The turning point for the mission was found with the computer program on the next page. Different turnig points were tried until one was found that gave a final velocity of about 32.935 km/s.


DESII 07 Apr 88 17:23

100 REM *** THIS PROGRAM ASSUMES THAT THE ACCELERATIONS***
110 REM *** CAN BE AVERAGED SINCE THEIR VALUE IS SMALL***
120 REM ** AND THEY DO NOT CHANGE MUCH.***
130 REM
140 PRINT "ENTER THE TURNING POINT."
150 INPUT TP
160 LET A1A=(.00464+.00577)/2
170 LET V/A1A*33.35*3147E7
180 REM
190 REM *** VELOCITY AT RELEASE OF TANKS 1 AND 2 ****
200 REM
210 LET A2A=(.00619+.0084)/2
220 LET V=V+A2A*33.35*3.147E7
230 REM
240 REM **** VELOCITY AT RELEASE OF TANKS 3 AND 4 ****
250 REM
260 LET A3A=(.00931+ATP)/2
270 LET V=V+A3A*(TP-66.7)*3.147E7
280 REM
290 REM ****VELOCITY AT TURNING POINT ****
300 REM
310 LET A4A=(.021+ATP)/2
320 LET V=V-A4A*(100.05-TP)*3.147E7
330 REM
340 REM **** FINAL VELOCITY ****
350 REM
360 PRINT V/1000, ATP
370 PRINT "GO AGAIN?"
380 INPUT ZZ$
390 IF ZZ$="Y" THEN 150
400 END

Ready