ROCKET PHYSICS

Some factors to take in consideration when designing a space vehicle.

With increased specific impulse-ISP- propellant mass is reduced.  On the low end, small increases in ISP allow massive reductions in propellant, so boosting a solid or hybrid rocket's performance from 250 seconds to 285 seconds makes a big difference.  ISP*0.0098=exhaust velocity in kilometers per second. The lines in the graph above are for delta Vs of 2.4, 4.8 and 7.2 kps.  As the delta V increases, higher ISPs and/or larger propellant masses are required given the same mass of the rocket and payload.  For this rocket to travel at 4.8 kps it will need 1050 tons of propellant with an ISP of 200 seconds but only 400 tons of propellant with an ISP of 300 seconds.

Curiously enough, the least amount of energy is needed for an exhaust velocity about  2/3 that of the delta velocity.  This is found simply by taking 1/2 the propellant mass from graph one in kilograms and multiplying times the exhaust velocity in meters/second squared to get the kinetic energy of the exhaust in joules and plotting the graph.  At exhaust velocities below the minimum energy point, the energy required slopes upwards steeply.  Above that, energy requirments increase with increases in ISP in a linear relation.  Even so, we must consider the cost of producing and transporting the increased propellant masses of a lower ISP versus the higher energy demands of a higher ISP.  This is very important when designing nuclear electric or solar electric propelled vehicles.

As we can see,  beyond the minimum energy point, the energy that must be imparted to the reaction mass climbs directly with increases in ISP.  If we want to minimize propellant masses launched up from Earth or the Moon to save costs, a higher ISP makes sense.  If we seek higher and higher ISPs from NEP or SEP, we must have larger and larger powerplants or take longer and longer to energize the propellants (reaction mass) and achieve the desired delta V with a given powerplant.  Larger powerpants=less payload, more uranium or more solar panel area. A compromise must be found for reaction mass cost, flight time, energy cost and powerplant mass/payload mass ratio.  More information, see: NEOFUEL

To put it all another way, when lifting off from Earth or another planet you want to maximize payload mass and reduce propellant fraction by using the highest exhaust velocity possible (highest specific impulse) and have enough thrust to overcome gravity.  The best propellants in use are LH2 and LOX although there are more powerful fuels like LH2&LFl, beryllium or lithium with hydrogen and liquid fluorine, but these have drawbacks.  A nuclear thermal rocket with LH2 would yeild about twice as much exhaust velocity as LH2/LOX but nuclear accidents are feared.  Higher thrust also means faster acceleration and less gravity loss of theoretical velocity as determined by  V=c logeMR  MR= Mo/Mbo  Mo=mass initial  Mbo=mass at burn out Once you are in space you don't need to overcome gravity and you don't need  as much thrust so a smaller rocket motor works well for long slow accelerations.  The ship can have a higher propellant fraction and higher mass ratio if the problem of obtaining propellant (reaction mass) is solved by tapping resources from the Moon or asteroids. With an exhaust velocity of about 0.6 the delta V you get the most energy efficiency.  This doesn't matter much for chemical fuels but it does matter for nuclear thermal and nuclear electric propulsion if you want to make the most efficient use of uranium, use the smallest lightest powerplant (reactor) and deliver the energy to the reaction mass in the shortest possible time; this last point being of great significance with electric drives that a long time to accelerate. Some will say that electric drives accelerate slowly because of their low thrust, but thrust levels are dependent on energy supply and electric drive thrust levels can be increased by clustering numerous units. See: Electric Drives With plenty of reaction mass available by mining the Moon and launching it into space inexpensively with mass drivers a higher mass ratio, higher propellant fraction and exhaust velocity only 0.6 the delta V make sense.  Exhaust velocities lower than 0.6 dV are even less efficient than higher ones as you can see from the graphs above.  With higher exhaust velocities you go faster by a factor of about 1.6 for efficiency.  With a fusion drive and 20,000 kps exhaust V the most efficient dV is 33,333 kps.  If c=0.6(dV) then dV=(0.6dV)logeMR or e^(dV/0.6dV)=MR  MR=5.29 The most energy efficient MR for a NTR or NEP system is about 5.3  Dense reaction mass substances for NTR like H2O, CH4, NH3 yield lower exhaust velocities than LH2 but perfectly fine, yeild higher mass ratios because they are dense and can be stored in smaller tanks, don't have to be kept as cold as LH2 and are space storable for long periods of time.  Plenty of H2O, CH4 and NH3 could be mined on Mars and launched with mass drivers  to rockets orbiting Mars, or could be mined on the ice moons of Jupiter or Saturn and launched up to orbiting rockets for travel between the moons of these planets. Dense reaction mass substances for NEP like sodium, lithium, mercury or magnesium will yeild good NEP performance, are storable indefinitely without and boil off, and are very compact yeilding high mass ratios.  Lithium and mercury are rare. The Moon has a little sodium but plenty of magnesium.  The use of magnesium for NEP must be explored.  An NEP system with only 3000 seconds ISP would have an exhaust velocity of 29.4 kps and be most efficient for a delta V of 49 kps.  VASIMR is interesting because it can vary its specific impulse and exhaust velocity to get the most energy efficient exhaust velocity for various delta Vs.  Since VASIMR heats reaction mass to hundreds of thousands of degrees and magnesium boils at only 1120 C. it is probable that vaporized magnesium could be used in VASIMR, although hydrogen has been used in VASIMR experiments.  Solid blocks of magnesium could be slowed vaporized by electrical heating to provide vapors to VASIMR that are then heated until they ionize and heated further electrically and ejected from a magnetic nozzle.  See: Spaceships