  We present a 3D dynamical model of the orbital induced curvature of the
wind-wind collision region in binary star systems. Momentum balance equations
are used to determine the position and shape of the contact discontinuity
between the stars, while further downstream the gas is assumed to behave
ballistically. An archimedean spiral structure is formed by the motion of the
stars, with clear resemblance to high resolution images of the so-called
``pinwheel nebulae''. A key advantage of this approach over grid or smoothed
particle hydrodynamic models is its significantly reduced computational cost,
while it also allows the study of the structure obtained in an eccentric orbit.
The model is relevant to symbiotic systems and Gamma-ray binaries, as well as
systems with O-type and Wolf-Rayet stars.
  As an example application, we simulate the X-ray emission from hypothetical
O+O and WR+O star binaries, and describe a method of ray tracing through the 3D
spiral structure to account for absorption by the circumstellar material in the
system. Such calculations may be easily adapted to study observations at
wavelengths ranging from the radio to Gamma-ray.
