How efficient is Orion?

The question comes up. Also on the web. And blogs.

The are four types of efficiency to consider.

1- Most simply; payload fraction, the part of the launched mission that is useful.

    a) Orion - 40+% is common for easy missions.
      i)  880 Ton test vehicle 34%: 300 tons to 300 mi orbit
      ii) 4000 Ton Interplanetary
          one)   40% 1600 tons to orbit
          two)   30% 1200 tons to Lunar landing
          three) 20% 800 tons to lunar surface and back
          four)  20% 800 tons to mars orbit and back
          five)   5% 200 tons to Venus orbit then Mars orbit then Earth orbit.

      iii) Advanced Interplanetary 10,000 tons
          one)   61% 6100 tons to orbit
          two)   57% 5700 tons to Lunar landing
          three) 53% 5300 tons to lunar surface and back
          four)  53% 5300 tons to mars orbit and back
          five)  45% 4500 tons to Venus orbit then Mars orbit then Earth orbit.
          six)   13% 1300 tons to Enceladus and back

     iv) 10m 1963 Orion Design from Ga-5009
        300 day Mars mission from earth orbit and back 103,300 ft/sec
        6.4%: 1145 mt gross 72.8 mt payload

      v) 10m 1963 Orion Design from Ga-5009
         450 day Mars mission  97,355 ft/sec
         8.3%: 73 mt payload 880 mt gross

     vi) 20m 1963 Orion Design from Ga-5009
         450 day Mars mission  72,850 ft/sec
         26%: 300 mt payload 1141 gross


    b) Shuttle - Cargo 1.6% (LEO) to 0.8% (ISS) , non cargo missions do a  
      little better.

    c) Apollo can be broken down into fundamental tasks, that contribute to the
       total payload. Oversimplifed the payload fraction is 25/3000 = .83 %, this
       combination is invalid, but the breakdown
       will be useful when looking at energy.

         i) Place the 15 metric ton Lunar Module on Luna
         2) Move the 5 metric ton Ascent Stage to Lunar orbit.
         3) Return the 5 metric ton Command Module to earth.

    d) Viking -  632,970 Gross mass
         i) 2328 kg Orbiter in LMO  : 0.36 %
        ii) 572 kg Lander on Mars      : 0.09 %

    e) Voyager 1 -  0.114 % 721.9 kg /  632,970 Gross mass

2- ISP - A measure of efficiency developed early in rocket research.

Project Orion - Compared to other high performance options .

3- Energy efficiency - Especially apealing to children of the seventies.

    a) Project Orion - A detailed analysis of the 880 ton Orbital Orion Test Vehicle. 
       450 KT  yields 4.87 kt. of orbital energy. 1.66 KT of cargo energy. 
       Efficiency is therefore .37% percent.

    b) Shuttle - The external tank starts with 1.2 Kt of , the SRB's with 3 for  
       a total of 4.2 Kt. The ISS cargo energy is .11 Kt, for an efficiency of 2.5%.

    c) Viking - The 572 kg Lander on Mars has .007 Kt more potential energy than
       before launch. The 2 metric ton orbiter has 0.03 Kiltons of extra energy.
       Launch fuel:  530 Tons mixed, energy to be calculated.

    d) Voyager 1 - Solar Altitude 14,919,000,000 km, v 17,147 m / sec
       mass 721.9 kg, total potential and kinetic energy added by mission: .19 KT
       Launch fuel:  530 Tons mixed, energy to be calculated.

4- Cost efficiency - Most complicated, but most important.
Dyson 8 million ton Super Orion was as efficient as 5 cents per pound.

Relationships and examples to be calculated...

----------------
Constants

From:               To:                [m/s]             MegaJoules/KG

Earth surface       Low Earth Orbit     9300             43
Low Earth Orbit     GTO                 2500
GTO                 GEO                 1500
GTO                 Earth escape         700
Earth escape        Low Lunar Orbit      700
Earth escape        Mars Transfer Orbit  600
LEO                 Mars surface        4800
LEO                 Solar escape        8700
Lunar Lunar         Lunar surface       1600
Mars surface        Low Mars Orbit      4100
Mars capture orbit  Mars low-energy      900
Low Mars Orbit      Phobos Transfer      900