The experimental discovery of the super-deep penetration of microparti
cles into strong materials by hypervelocity impact documented the real
ity of earlier predictions of fracture mechanics concerning the anomal
ously low drag of a body moving like a wedge in a brittle medium. In t
he present paper, some wedge-embedded penetration regimen models, taki
ng into account arbitrary friction and plastic deformations near conta
ct areas, shaving effects, and a complex or even fractal geometry of a
cracking front, are advanced. The equation for drag is derived using
the author's invariant GAMMA-integral equivalent to the energy conserv
ation law. The thrust of a motor necessary to propel a projectile or v
ehicle in hard rock is evaluated. It is shown that the thrust of the N
ASA space shuttle's rocket booster suffices to provide the penetration
of a small projectile or vehicle in strong granite for the distance o
f a mile during a short span of time. Super-deep penetration of microp
articles is examined using results from fracture quantum mechanics. Th
e hypothesis is advanced that the super-deep penetration of microparti
cles represents the self-propagation of a specific internal solitary w
ave forming a cavity with a projectile moving inside the cavity withou
t drag. This solitary wave is named the rayleighon, because it propaga
tes with the Rayleigh speed. It is suggested that this paper would pro
vide a possible stimulus for conversion of some Department of Defense
rocket motor industries towards civil exploration of the Earth, which
is studied much less than the cosmos.