Abstract:
A system, apparatus and method for mitigating the shock front of a rocket or aerospace plane flying at hypersonic speeds while simultaneously distilling liquid chemical elements regeneratively from the ambient air by means of vortex inversion splines. The splines may additionally be tuned by geometry to function as both centripetal and/or isentropic thrust augmentation attribute and/or double-decker Joule-Thomson refrigeration means. Because of the stochastic stagnation flux that reaches into the absolute zero zone by means of precooling, a splined stochastically switched hypersonic nosecone may be constructively tuned into a complex Carnot refrigeration engine commanding both personal and enterprise liquid Helium distilling means with orders of magnitude efficacy gains over existing methods.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application is Continuation in part of U.S. patent application Ser. No. 15/083,128 filed on Mar. 28, 2016, entitled as “Apparatus and Methods for a Hypersonic Stochastic Switch” and claims the benefit of U.S. Utility patent application Ser. No. 14/564,024, filed on Aug. 12, 2014 and entitled “Apparatus and Methods for Hypersonic Nosecone”, U.S. Utility patent application Ser. No. 14/313,976, filed on Jun. 24, 2014 and entitled “Thermally Conductive Hypersonic Nosecones” and U.S. Provisional Patent Application No. 61/838,454, filed on Jun. 24, 2013 and entitled “Hypersonic Vortex Tube”, which is herein incorporated by reference in its entirety. 
     
    
     BACKGROUND 
       [0002]    This inventive subject matter relates to the systems, apparatus, and methods for the reduction of drag in a spacecraft or missiles. The reduction of drag in spacecraft and missiles is of particular concern as atmospheric friction can cause the nosecone to increase beyond the failure point. Clearly ways to reduce would benefit missiles, allowing them to travel at higher speeds, and spacecraft, allowing them to reenter the atmosphere without the fear of destruction. 
         [0003]    Also described are the details and means to transform an isentropically expanded hypersonic stochastic vortex flux (Z-plane singularity) back into isentropic (Y-plane) mode by means of (micro/planetary) splines that reset the hypersonic stochastic vortex flux back into a supersonic isentropic front by means of contra rotating micro or planetary splines. 
       SUMMARY 
       [0004]    The inventive subject matter is about a thermally reactive nosecone mounted on a projectile for achieving hypersonic transport comprising: an incipient shockwave, the incipient shockwave being transformed into an isentropic flux via a stochastic switch. A core component of the thermally reactive nosecone is a stochastic switch (a singularity), which is the consequence of isothermal compression and/or hypersonic liquefaction and/or regenerative cooling and/or Joule-Thomson throttling and complex cryogenic Carnot refrigeration (triggered via sudden expansion and/or a porous plug integrated into the discharge end of the thermally reactive nosecone) whereby a linear continuum of the incipient shockwave is transformed into a gyrating perfectly random stochastic vortex/stagnation flux. In order to transform the stochastic vortex flux (back) into isentropic streamlines grooved isentropic splines (in the inside the discharge nozzle and/or peripheral of the nosecone of the nozzle of the thermally reactive nosecone) has been proposed in lieu of the porous plug triggering Joule-Thomson throttling and complex Carnot refrigeration simultaneously. In addition to Joule-Thomson throttling and complex Carnot refrigeration an extrinsic cryogenic resource may be applied to pre/sub cool the thermally reactive nosecone to supercharge the refrigeration power of the shockwave piercing stochastic switch. Liquid nitrogen and/or a liquid cryogenic propellant may be applied as the extrinsic cryogenic resource to supercharge the switching power of the shockwave thermally reactive shockwave piercing nosecone mounted on a projectile for achieving hypersonic transport. The thermally reactive nosecone may additionally be optimized for throttling and triggering complex Carnot refrigeration liquefaction of atmospheric oxygen to drive a rocket propulsion engine of a hypersonic transport. 
         [0005]    In another embodiment of the invention the thermally reactive nosecone may be configured with an independent/freestanding isentropic hypersonic expansion nozzle to drive the thermally reactive nosecone as a cryogenic refrigeration apparatus wherein the isentropic hypersonic expansion nozzle of the thermally reactive nosecone is optimized to distill liquid helium. Liquid helium hydrogen in the range of 1-5% of helium may additionally be introduced into the isentropic expansion nozzle to boost the liquefaction capacity of liquid helium. The thermally reactive nosecone may be additionally configured as a (micro) personal and/or enterprise (scaled) freestanding thermally reactive nosecone to distill liquid helium directly distilled out of compressed helium by means of the addition of isentropic splines within an (hypersonic) expansion nozzle in addition to (tanked) liquid nitrogen to (1) precool and (2) refrigerate the expanded helium proximal to the saturation curve of helium at absolute zero. 
         [0006]    In another embodiment the thermally reactive nosecone is coupled within the confinements of rocket missile and/or aerospace plane with a centripetal thrust augmentation nozzle whereby (1) the centripetal thrust augmentation nozzle is equipped with grooved (isentropic) splines that transform/switch the stochastic vortex flux (back) into isentropic streamlines and (2) whereby the grooved (isentropic) splines centripetal thrust augmentation nozzle is equipped with (enumerated) supersonic ram detonation (SURD) propulsive means in addition to grooved (isentropic) splines in isolation. 
         [0007]    The inventive subject matter also comprises a system, apparatus and methods for a reduction of drag in a missile using a vortex tube as well as augmenting the thrust of a centripetal nozzle system with (micro) planetary splines. 
         [0008]    In an embodiment is illustrated a method for reducing drag at hypersonic speed that includes the steps of mounting a liquefaction nosecone on the forward portion of a projectile; where the projectile is either a missile or spacecraft. 
         [0009]    In another embodiment is described a method for reducing drag at hypersonic speed also having the steps of drawing an atmosphere external to the liquefaction nose cone an intake aperture or a discharge shaft. 
         [0010]    In yet another embodiment is presented the details of a supersonic isentropic splines switching the stochastic hypersonic flux from the Z-plane back into the Y-plane to (1) maximize regenerative cooling of the shockwave piercing nosecone and (2) maximizing propulsive thrust augmentation of the stochastic or inversed centripetal supersonic ram detonation nozzle system. 
         [0011]    This specification is not limited to a single embodiment, rather the methods and systems presented should be construed broadly and further incorporate the material presented in the drawings. 
     
    
     
       DESCRIPTION OF THE DRAWINGS 
         [0012]      FIGS. 1A and 1B  illustrates a stochastic regenerative hypersonic shockwave piercing nose cone. 
           [0013]      FIGS. 2A and 2B  illustrates a stochastic regenerative hypersonic nose cone with annular splines in conjunction with the annular exit. 
           [0014]      FIGS. 3A and 3B  illustrates a stochastic regenerative hypersonic nose cone with both annular and peripheral splines in conjunction with the annular exit. 
           [0015]      FIGS. 4A and 4B  illustrates a stochastic regenerative hypersonic nose cone driven by a high pressure supersonic/isentropic expansion nozzle. 
           [0016]      FIGS. 5A and 5B  illustrates a hybrid aerospace plane with stochastic regenerative hypersonic nosecone in conjunction with an elemental splined centripetal thrust augmentation nozzle. 
           [0017]      FIGS. 6A and 6B  illustrates a hybrid aerospace plane with stochastic regenerative hypersonic nosecone in combination with an array of centripetal supersonic-detonation hypersonic Constellation propellant injectors in conjunction with splined annular exit. 
           [0018]      FIGS. 7A and 7B  illustrates a stochastic regenerative hypersonic nose cone with both annular and peripheral spline cavities in conjunction with splined annular exit. 
           [0019]      FIGS. 8A and 8B  illustrates an elemental centripetal splined thrust augmentation nozzle in conjunction with splined annular exit. 
           [0020]      FIGS. 9A and 9B  illustrates a centripetal splined supersonic-detonation thrust augmented nozzle driven by an array of hypersonic Constellation micro propellant injectors in conjunction with splined annular exit. 
           [0021]      FIG. 10  illustrates the micro splines in a Z/Y-plane gear transformation. 
       
    
    
     DETAILED DESCRIPTION 
       [0022]    Persons skilled in the art will recognize that many modifications and variations are possible in the details, materials, and arrangements of the parts and actions which have been described and illustrated in order to explain the nature of this inventive concept and that such modifications and variations do not depart from the spirit and scope of the teachings and claims contained therein. 
         [0023]    In an embodiment,  FIG. 1A  denotes a typical hypersonic system  100 , wherein streamline  101  entering the funneled supersonic nosecone intake  102  is transformed into a hypersonic stochastic vortex flux  107  at contact  103  with the regenerative chilled slanted surface  105  in the cryogenic zone regenerative chilled via Joule-Thomson throttling/refrigeration  104  and hence exiting via nozzle aperture  106 . Referring to  FIG. 1B , which illustrates a cross-sectional view  150 , depicting an outer nozzle, inner nozzle and shaft structure represented by  108 / 109  and shaft  110  respectively. 
         [0024]    In an embodiment,  FIG. 2A  denotes a system  200 , wherein hypersonic streamline  201  entering the funneled supersonic nosecone intake  202  whereupon being transformed into a hypersonic stochastic vortex flux  207  at contact  203  with the regenerative chilled slanted surface  205  in the cryogenic zone regenerative chilled via Joule-Thomson throttling/refrigeration  204  and hence exiting via the splined nozzle aperture  206  whereby the primary vortex  207  is being transformed into a numerocity of contrarotating micro spline vortices  213  that generates an isentropical transformed propulsive supersonic front  212  in accordance with the 2 nd  law of thermodynamics (preservation of internal energy) whereby dU=δQ+δW=δQ [with an isothermal (regenerative) cryogenic shockwave piercing nozzle system with δW=0] and dU=δQ+δW=δW [with an adiabatic/ceramic lined (centripetal) thrust augmentation propulsive nozzle system with δQ=0]. Referring to  FIG. 2B , which illustrates a cross-sectional view  250 , depicting an outer nozzle, inner nozzle and shaft structure represented by  208 / 209  and shaft  210  respectively. 
         [0025]    In an embodiment,  FIG. 3  illustrates a system  300 , wherein a hypersonic streamline  301  entering the funneled supersonic nosecone intake  302  whereupon being transformed into a hypersonic stochastic vortex flux  307  at contact  303  with the regenerative chilled slanted surface  305  in the cryogenic zone which is regeneratively chilled via Joule-Thomson throttling/refrigeration as a consequence of (1) sudden expansion of the core shaft  304  and (2) the (splined) nozzle apertures  306  whereby the primary vortex  307  is transformed into a numerocity of contrarotating (micro) SPLINE vortices  313  that generates the (ISENTROPICAL) transformed (propulsive) supersonic front  312  in accordance with the 2 nd  law of thermodynamics (preservation of internal energy) whereby dU=δQ+δW=δW given δQ=0. Likewise, the peripheral splines  314  transforms the peripheral vortex  315  into a numerocity of (micro) SPLINE vortices  317  in according to the 2 nd  law of thermodynamics (preservation of energy) dU=δQ+δW=δQ given δW=0 vis-a-vis. Referring to  FIG. 3B , which illustrates a cross-sectional view  350 , depicting an outer nozzle, inner nozzle and shaft structure represented by  308 / 309  and shaft  310  respectively. 
         [0026]    In an embodiment,  FIG. 4  illustrates a system  400 , wherein a hypersonic streamline  401  driven by high pressure hypersonic-isentropic expansion nozzle system  420 / 425  entering the funneled supersonic nosecone intake  402  whereupon being transformed into a hypersonic stochastic vortex flux  407  at contact  403  with the regenerative chilled slanted surface  405  in the cryogenic zone regenerative chilled via Joule-Thomson throttling/refrigeration within the sudden expansion  404  hence exiting via the internally splined nozzle aperture  406  whereby the primary vortex  407  is being transformed into a numerocity of contrarotating micro spline vortices  413  that generates the isentropical transformed supersonic front  412  according to the 2 nd  law of thermodynamics (preservation of energy) whereby dU=δQ+δW=δW given δQ=0. Referring to  FIG. 4B , which illustrates a cross-sectional view  450 , depicting an outer nozzle, inner nozzle and shaft structure represented by  408 / 409  and shaft  410  respectively. 
         [0027]    In an embodiment,  FIG. 5  illustrates a system  500 , wherein a hybrid aerospace plane with stochastic regenerative hypersonic nosecone (stochastic switch) in conjunction with an elemental splined centripetal thrust augmentation nozzle (isentropic switch) whereby a hypersonic streamline  501  enters the funneled (supersonic) nosecone intake  502  whereupon being transformed into a stochastic vortex flux  507  at contact  503  with the regenerative chilled slanted surface  505  in the cryogenic zone via Joule-Thomson throttling/refrigeration in accordance with the 2 nd  law of thermodynamics (preservation of energy) whereby dU=δQ+δW=δW given δQ=0 Likewise, the (funneled) vortex flux  507  is transformed into a numerocity of contrarotating (micro) SPLINE vortices  513  that generates the (isentropical) transformed (propulsive) supersonic front  512  in accordance with the 2 nd  law of thermodynamics (preservation of internal energy) whereby dU=δQ+δW=δW given δQ=0. Likewise, the peripheral splines  514  transforms the peripheral vortex  515  into a numerocity of micro spline vortices  517  in according to the 2 nd  law of thermodynamics (preservation of energy) dU=δQ+δW=δQ given δW=0 vis-a-vis. Referring to  FIG. 5B , which illustrates a cross-sectional view  550 , depicting an outer nozzle, inner nozzle and shaft structure represented by  508 / 509  and shaft  510  respectively. 
         [0028]    In an embodiment,  FIG. 6  illustrates a system  600 , wherein a hybrid aerospace plane with stochastic regenerative hypersonic nosecone (stochastic switch) in combination with an array of centripetal (supersonic-detonation) hypersonic (Constellation) propellant injectors in conjunction with splined annular exit (isentropic switch) whereby a hypersonic streamline  601  enters the funneled supersonic nosecone intake  602  whereupon being transformed into a stochastic vortex flux  607  at contact  603  with the regenerative chilled slanted surface  605  in the cryogenic zone via Joule-Thomson throttling/refrigeration in accordance with the 2 nd  law of thermodynamics (preservation of energy) whereby dU=δQ+δW=δW given δQ=0. Likewise, the funneled vortex flux  607  is transformed into a numerocity of contrarotating (micro) SPLINE vortices  613  driven by an array of hypersonic Constellation (micro) propellant injectors  617  that generates the (isentropical) transformed (propulsive) supersonic front  612  in accordance with the 2 nd  law of thermodynamics (preservation of internal energy) whereby dU=δQ+δW=δW given δQ=0. Likewise, the peripheral splines  614  transforms the peripheral vortex  615  into a numerocity of (micro) SPLINE vortices  617  in according to the 2 nd  law of thermodynamics (preservation of energy) dU=δQ+δW=δQ given δW=0 vis-a-vis. Referring to  FIG. 6B , which illustrates a cross-sectional view  650 , depicting an outer nozzle, inner nozzle and shaft structure represented by  608 / 609  and shaft  610  respectively. 
         [0029]    In an embodiment,  FIG. 7  illustrates a system  700 , which depicts a stochastic regenerative hypersonic nose cone whereby the hypersonic streamline  701  is transformed into a stochastic vortex flux at contact  703  with the regenerative chilled slanted surface  705  in the cryogenic zone which is (regeneratively) chilled via Joule-Thomson throttling/refrigeration. The peripheral splines  714  transforms the peripheral vortex  715  into a numerocity of (micro) spline vortices  715  in according to the 2 nd  law of thermodynamics (preservation of energy) dU=δQ+δW=δQ given δW=0 vis-a-vis. Referring to  FIG. 7B , which illustrates a cross-sectional view  750 , depicting an outer nozzle, inner nozzle and shaft structure represented by  708 / 709  and shaft  710  respectively. 
         [0030]    In an embodiment,  FIG. 8  illustrates a system  800 , which depicts an elemental splined centripetal thrust augmentation nozzle (isentropic switch) whereby the funneled vortex flux  807  is transformed into a numerocity of contrarotating (micro) spline vortices  813  that generates the (isentropical) transformed (propulsive) supersonic front  812  in accordance with the 2 nd  law of thermodynamics (preservation of internal energy) whereby dU=δQ+δW=δW given δQ=0. Referring to  FIG. 8B , which illustrates a cross-sectional view  850 , depicting an outer nozzle, inner nozzle and shaft structure represented by  808 / 809  and shaft  810  respectively. 
         [0031]    In an embodiment,  FIG. 9  illustrates a system  900 , which depicts an enumerated splined centripetal thrust augmentation nozzle isentropic switch whereby the funneled vortex flux  907  is transformed into a numerocity of contrarotating micro spline vortices  913  driven by an array of hypersonic Constellation (micro) propellant injectors  917  that generates the (isentropical) transformed (propulsive) supersonic front  912  in accordance with the 2 nd  law of thermodynamics (preservation of internal energy) whereby dU=δQ+δW=δW given δQ=0. Referring to  FIG. 9B , which illustrates a cross-sectional view  950 , depicting an outer nozzle, inner nozzle and shaft structure represented by  908 / 909  and shaft  910  respectively. 
         [0032]    In an embodiment,  FIG. 10  depicts a planetary splines gear transmission analogy  1000 , wherein  1008 / 1009 / 1010  represent the outer/inner shell and the central shaft respectively and  1015  representing the contrarotating spline vortex flux. According to design rules (1) dU=δQ+δW=δQ [dU=δQ with δW=0 and dU=δW with δQ=0. Isentropic switch in accordance with the 2 nd  Law of Thermodynamics (preservation of energy) and (2) the sum of the splines induced (micro/inversed) vortices YY=power of the incipient/shafted vortex. 
         [0033]    In accordance with the First Law of Thermodynamics, conservation of energy, whereby energy can be neither created nor destroyed (1) generally and/or (2) specifically in a sudden expansion in a duct or nozzle system whereby dU=δQ+δW=δQ. Here the splinesconstitute a sudden/grooved expansion in a supersonic expansion nozzle whereby (1) micro (contra rotating) vortex streams are spawned (via sudden expansion) which mirrors the master/mother vortexflux succinctly (2) the sum total of the (micro/spline) vortices equals the incipient master/mother vortex flux (3) the micro/spline flux negates (wipes out) the incipient master/mother vortex and (4) because the operation of the 1 st  Law of Thermodynamics, the (incipient) master/mother vortex flux is spatially transformed/reincarnated into (supersonic) isentropic streamlines whereby dU=δQ+δW=δQ. In event of a (regenerative) cryogenic shockwave piercing nozzle system  dU=δQ+δW=δQ  [with δW=0] and in event of an adiabatic/ceramic lined (centripetal) thrust augmentation propulsive nozzle system  dU=δQ+δW=δW  [with δQ=0]. 
         [0034]    However because the equation of state dU=δQ+δW=δQ must be satisfied in accordance with the First Law of Thermodynamics, the supersonic splines isentropic switch functions as (1) (supercharged) Joule-Thomson refrigeration engine in the cryogenic zone and (2) supercharged (thrust augmentation) expansion nozzle whereby dU=δQ (δW=0) with a (splined) crusonix shockwave piercing nozzle and dU=δW (δQ=0) with a centripetal SURD (supersonic ram detonation) thrust augmentation propulsive nozzle. 
         [0035]    In order to model the dynamics of the splines hypersonic/stochastic and supersonic/isentropic transformation computationally vector matrix power factor analogy in conformance with electrical power transmission (perfect alignment of the voltage and current vectors so as to max energy/work transmission) is being applied whereby in a purist isentropic potential field the stagnation and velocity vectors are in perfectly alignment/symmetry (to max work performed) in compliance with the 1st Law of Thermodynamics (dU=δQ+δW=δW (δQ=0). Given that in a perfect electrical/fluidic (potential) field the current/voltage and stagnation pressure/velocity are in perfect alignment the power factor [COS(Ø)] must be UNITY (i.e. cos(Ø)=1.0) both ways. However, in event of current/voltage lead/lag and velocity/stagnation pressure divergence the power factor will be smaller than unity (i.e. cos(Ø)&lt;1). In order to enumerate actual (real time) splines power factor divergence actual. (cryogenic) regression [−180 C/−170 C/−150 C/−140 C/−120 C/ 23 C] (M5 stagnation pressure) data sets has been employed that rendered cos( 527  )=0.41/0.35/ 0.32/0.31/0.30/0.27 [66/70/71/72/73/74deg] as to purist (isentropic) and cos(Ø)′=0.36/0.33/0.30/0.30/0.29/0.26 [69/71/72/73/73/75deg] as to purist stochastic/random transformation respectively. 
         [0036]    With the power factor postulation in place backed up with and actual measured (M5) hypersonic/cryogenic stagnation transformation “regression” data, the splines isentropic transformation may be modeled by an isentropical expansion as follows: 
         [0000]    M=((Pr)̂0.286−1)×5)̂0.5 generally and Me=((Prixcos(Ø)′)̂0.286−1)×5)̂0.5 specifically and (2) T2=T1×(1+0.2Mê2)̂−1 consequently. 
         [0037]    Applying the data cos(Ø)′=cos(Ø)×0.887, Me=[((150×0.41×0.887) ̂0.286−1)×5]̂0.5=[(3.14−1)×5]̂0.5=[10.7]̂0.5 =3.3 Conversely given Me=3.3, T2=93×(1+0.2×3.3̂−1=93×(2.18)̂−1=93/2.18=42.7K=−230.5C. Noteworthy is that although the exit Mach number Me=3.3 is 30% lower than the incipient (isentropic) front @M5, the Mach number impairment is minimal taking in account that (1) (regenerative/isothermal compression shockwave piercing utility and (2) turning the splines into a powerful refrigeration engine. See tabulation as to the VT3 data spread −180/−170/−150/−140−120/23C in totality. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 1. dU = δQ + δW = δQ [with δW = 0][ISOTHERMAL] 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Me/C. 
                 −180 
                 −170 
                 −150 
                 −140 
                 −120 
                 23 
               
               
                 Me/K 
                 93 
                 103 
                 123 
                 133 
                 153 
                 296 
               
               
                 cosØ 
                 0.41 
                 0.35 
                 0.32 
                 0.31 
                 0.30 
                 0.27 
               
               
                 Ø 
                 66 
                 70 
                 71 
                 72 
                 72.5 
                 74 
               
               
                 R ′   
                 8.87 
                 9.53 
                 9.54 
                 9.57 
                 9.59 
                 9.66 
               
               
                 Pr 
                 150 
                 127 
                 117 
                 113 
                 110 
                 100 
               
               
                 Me 
                 3.3 
                 3.1 
                 3.0 
                 2.9 
                 2.9 
                 2.8 
               
               
                 Te/K 
                 29.7 
                 35.4 
                 44.3 
                 48.7 
                 57.0 
                 116.1 
               
               
                 Te/C. 
                 −243.3 
                 −237.6 
                 −228.7 
                 −224.3 
                 −216.0 
                 −156.9 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 2. dU = δQ + δW = δW [with δQ = 0] [ADIABATIC] 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Ti/C. 
                 −180 
                 −170 
                 −150 
                 −140 
                 −120 
                 23 
               
               
                 Ti/F. 
                 −292 
                 −274 
                 −238 
                 −220 
                 −184 
                 73 
               
               
                 Ti/R 
                 168 
                 186 
                 222 
                 240 
                 276 
                 533 
               
               
                 Qpr 
                 20000 
                 20000 
                 20000 
                 20000 
                 20000 
                 20000 
               
               
                 Apr 
                 12 
                 12 
                 12 
                 12 
                 12 
                 12 
               
               
                 Qpr ′   
                 1667 
                 1667 
                 1667 
                 1667 
                 1667 
                 1667 
               
               
                 ΔTpr ′   
                 6667 
                 6667 
                 6667 
                 6667 
                 6667 
                 6667 
               
               
                 Tmax/F. 
                 5000 
                 5000 
                 5000 
                 5000 
                 5000 
                 5000 
               
               
                 Qstoich 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
               
               
                 Rstoich 
                 30 
                 27 
                 23 
                 21 
                 18 
                 9 
               
               
                 Me 
                 12.0 
                 11.4 
                 10.4 
                 10.0 
                 9.3 
                 6.5 
               
               
                 Isec 
                 3,769 
                 3,581 
                 3,195 
                 3,031 
                 2,742 
                 1,593 
               
               
                   
                 12.0 
                 11.4 
                 10.4 
                 10.0 
                 9.3 
                 6.5 
               
               
                   
                 29.7 
                 35.4 
                 44.3 
                 48.7 
                 57.0 
                 116.1 
               
               
                   
               
             
          
         
       
     
         [0038]    As for work performed the nominal splines isentropically expanded Mach number Me=3.3/3.1/3.0/2.9/2.9/2.8 respectively. However, in event of SURD (supersonic ram combustion) the exit Mach number is boosted in conformance with 1 st  law of Thermodynamics to Me′=12/11.4/10.4/10/9.3/6.5 respectively in accordance with the enumerated spreadsheet. 
         [0039]    In a preferred embodiment, a thermally reactive nosecone mounted on a projectile for achieving hypersonic transport is described. Wherein an incipient shockwave is transformed into an isentropic flux via a stochastic switch. The stochastic switch is a singularity switch whereby a linear continuum is transformed into a gyrating stagnation flux and the singularity is a consequence of isothermal compression and hypersonic liquefaction of the incipient shockwave onto the thermally reactive nosecone. The isothermal compression and hypersonic liquefaction is achieved via regenerative cooling of the thermally reactive nosecone. 
         [0040]    In a preferred embodiment, the singularity/isothermal compression transforms the insipient hypersonic streamlines into a harmonic stochastic vortex flux. wherein isothermal compression of the thermally reactive nosecone is achieved via regenerative cooling of the thermally reactive nosecone via Joule-Thomson throttling and complex cryogenic Carnot refrigeration. Wherein Joule-Thomson throttling and complex Carnot refrigeration is triggered via sudden expansion and/or a porous plug integrated into the discharge end of the thermally reactive nosecone. Wherein Joule-Thomson throttling and complex Carnot refrigeration is triggered via grooved isentropic splines (in lieu of the porous plug) inside the nozzle of the thermally reactive nosecone. with grooved isentropic splines that transform the vortex flux into isentropic streamlines. 
         [0041]    In a preferred embodiment, the isentropic switch is integrated onto a discharge and/or peripheral of the thermally reactive nosecone is described. wherein an extrinsic cryogenic resource is applied to precool the thermally reactive nosecone in addition to the stochastic switched hypersonic stagnation front to supercharge the switching power of the shockwave piercing stochastic switch. Wherein the extrinsic cryogenic resource to supercharge the switching power of the shockwave piercing stochastic switch is liquid nitrogen and/or a liquid cryogenic propellant. The thermally reactive nosecone is optimized for throttling and triggering complex Carnot refrigeration liquefaction of atmospheric oxygen to drive a rocket propulsion engine of a hypersonic transport. wherein an isentropic hypersonic expansion nozzle is applied to drive the thermally reactive nosecone as a cryogenic refrigeration apparatus. wherein the isentropic hypersonic expansion nozzle of the thermally reactive nosecone is optimized to distill liquid helium. wherein hydrogen in the range of 1-5% of helium is introduced into the isentropic expansion nozzle to boost the liquefaction capacity of liquid helium. wherein liquid helium is directly distilled out of compressed helium. A freestanding thermally reactive nosecone comprising of isentropic hypersonic expansion nozzle wherein liquid helium is directly distilled out of compressed helium. 
         [0042]    In a preferred embodiment, a freestanding thermally reactive nosecone comprising of isentropic hypersonic expansion nozzle with isentropic splines is described. Wherein liquid helium is directly distilled out of compressed helium. which is scaled as a personal helium distillation plant driven by tanked and compressed Helium and Liquid Nitrogen. which is scaled as an enterprise Liquid Helium production facility with Liquid Nitrogen and with the addition of Hydrogen. Which is scaled as an enterprise Liquid Helium production facility without Liquid Nitrogen and without the addition of Hydrogen. which is scaled as an enterprise Liquid Helium production facility with Liquid Nitrogen and with the addition of Hydrogen. which is scaled as an enterprise Liquid Helium production facility without Liquid Nitrogen without the addition of Hydrogen. Wherein the thermally reactive nosecone is coupled within the confinements of rocket missile and/or aerospace plane with a centripetal thrust augmentation nozzle. the centripetal thrust augmentation nozzle is equipped with grooved isentropic splines that transform the vortex flux into isentropic streamlines. the grooved isentropic splines centripetal thrust augmentation nozzle is equipped with enumerated supersonic ram detonation (SURD) propulsive means in addition to grooved isentropic splines in isolation. 
         [0043]    In a preferred embodiment, a double/isentropic switch adaptation of the stochastic switch comprising of a supersonic isentropic splines switch, a planetary splines switches, an incipient stochastic vortex, a contrarotating splines vortices, a transformed/switched isentropic jet is described.