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Re: MS info and some formulas

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  • captcurt2000
    Thanks Barry This is great info. I have seen it before but every time I look at it, I pick up more. Curt
    Message 1 of 2 , Nov 12, 2009
      Thanks Barry

      This is great info. I have seen it before but every time I look at it, I pick up more.

      Curt

      --- In wsjtgroup@yahoogroups.com, "Barry Garratt" <bgarratt@...> wrote:
      >
      >
      > There is a lot of material available if one wishes to really understand
      > meteor scatter, or, as it is more commonly known, as forward scatter.
      >
      > If you understand the geometry of forward scatter you'll realize that the
      > expression "one way rocks" doesn't really compute.
      >
      > In order to cause a forward scatter reflection, the meteor trail must lie
      > within a plane (called the tangent plane) which is tangent to an ellipsoid
      > having the transmitter and receiver as its foci. The entire reflection path
      > will also lie within a plane (called the plane of propagation), which
      > contains the transmitter, reflection point, and receiver.
      > The plane of propagation will be normal to (at right angles to) the meteor
      > tangent plane.
      >
      > The meteor itself can be at any orientation within the tangent plane - it
      > need not be normal itself to the propagation path.
      > There is, however, greater signal loss when the meteor trail is
      > perpendicular to the propagation plane than when it is parallel to the
      > propagation plane.
      >
      > A third constraint is that most meteor reflections will occur within the
      > narrow altitude band of about 85 to 105 km altitude. Thus, the sphere formed
      > by the 95 km altitude band, the meteor tangent plane, and the ellipsoid
      > having the transmitter and receiver as foci must all meet (or be tangential)
      > at the reflection point.
      >
      > The "classical" equations for forward-scatter from a meteor trail, which
      > have been derived from theory and validated empirically during the heyday of
      > radiometeor astronomy (1945-
      > 1970) , are as follows:
      >
      > Underdense trails (electron line density, Q < 1E14 electrons / meter):
      >
      > Underdense Echo Power
      >
      > The echo power received at the receiving station in a forward scatter
      > underdense echo is given as the product of two fractions:
      >
      > P_r = ((P_t * g_t * g_r * lambda^3 * sigma_e) / (64pi^3)) * ((Q^2 *
      > sin^2(gamma)) / ((r1 * r2) * (r1 + r2) * (1 - sin^2(phi) * cos^2(beta)))),
      >
      > where:
      > P_r = power seen by receiver (Watts),
      > P_t = power produced by transmitter (Watts),
      > g_t = gain of transmitting antenna (dB),
      > g_r = gain of receiving antenna (dB),
      > lambda = RF wavelength (m),
      > sigma_e = scattering cross section of the free electron (m^2),
      > Q = electrons per meter of path,
      > r1 = distance between meteor trail and transmitter (m),
      > r2 = distance between meteor trail and receiver (m),
      > phi = angle between r1 line and normal to meteor path tangent plane, or
      > phi = 1/2 angle between the r1 and r2 lines,
      > beta = angle between meteor trail and the intersection line of the tangent
      > plane and plane of propagation,
      > gamma = angle between the electric vector of the incident wave and the line
      > of sight to the receiver (polarization coupling factor).
      >
      > A useful substitute for sigma_e is:
      >
      > sigma_e = 1.0E-28 * sin^2(gamma) m^2,
      >
      > which reduces in the back-scattter case to simply:
      >
      > sigma_e = 1.0E-28 m^2.
      >
      > Underdense Echo power decay
      >
      > A second useful expression for the exponential decay over time of the
      > underdense echo power is given as an exponential (e^x) raised to a
      > fraction):
      >
      > P_r(t)/P_r(0) = exp(- (((32pi^2 * D * t) + (8pi^2 * r0^2)) / (lambda^2 *
      > sec^2(phi)))),
      >
      > where:
      >
      > P_r(t)/P_r(0) = normalized echo power as a function of time (t),
      > t = time in seconds (sec),
      > D = electron diffusion coefficient (m^2/sec),
      > r0 = initial meteor trail radius (m).
      >
      > The diffusion coefficient, D, will increase roughly exponentially with
      > height in the meteor region. An empirical derivation from Greenhow &
      > Nuefeld (1955) is given for meteor altitudes of h = 80 km to h = 100 km:
      >
      > log10(D) = (0.067 * h) - 5.6,
      >
      > for D in m^2/sec.
      >
      > The initial meteor trail radius is another empirically derived value, given
      > in two studies as:
      >
      > log10(r0) = (0.075 * h) - 7.2,
      >
      > h = meteor altitude (75-120 km)
      > r0 = trail radius (m)
      >
      > and
      >
      > log10(r0) = (0.075 * h) - 7.9.
      >
      > Underdense echo duration
      >
      > An approximate expression for the duration of an underdense trail is given
      > by:
      >
      > t_uv = (lambda^2 * sec^2(phi)) / (16pi^2 * D)
      >
      > Overdense trails (electron line density, Q > 1E14 electrons / meter):
      >
      > The classical expressions for the overdense trails contain many more
      > assumptions and estimations than for the underdense trails. Their full
      > theory is still under development today. However, the classical equations
      > can still be used to glean some of the basic characteristics of these
      > events. I am showing these here in their final form, skipping some
      > intermediate steps and approximations.
      >
      > Overdense echo power
      >
      > P_r = 3.2E-11 * ((P_t * g_t * g_r * lambda^3 * Q^(1/2) * sin^2(gamma)) /
      > ((r1*r2) * (r1+r2) * (1 -sin^2(phi) * cos^2(beta)))).
      >
      > Overdense Echo Duration
      >
      > An approximate expression for overdense echo duration is given by:
      >
      > t_ov = 7E-17 * ((Q * lambda^2 * sec^2(phi)) / D).
      >
      > If you wish to delve more into forward scatter then a good book to read is
      > "Meteor Science and Engineering," D.W.R. McKinley, (McGraw-Hill, 1961)
      >
      > As I mentioned at the beginning there is a lot more to forward scatter than
      > just pointing in the general direction of the meteors and hoping for the
      > best. I'm not suggesting that you sit and do the calculations all the time
      > but they do explain a lot of the varibles in play when you are running with
      > someone.
      >
      > Bottom line have fun and don't get discouraged if you don't always get the
      > result you expected.
      >
      > 73,
      >
      > Barry KS7DX
      >
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