Re: MS info and some formulas
- Thanks Barry
This is great info. I have seen it before but every time I look at it, I pick up more.
--- In email@example.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)))),
> 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
> P_r(t)/P_r(0) = exp(- (((32pi^2 * D * t) + (8pi^2 * r0^2)) / (lambda^2 *
> 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)
> log10(r0) = (0.075 * h) - 7.9.
> Underdense echo duration
> An approximate expression for the duration of an underdense trail is given
> 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
> Bottom line have fun and don't get discouraged if you don't always get the
> result you expected.
> Barry KS7DX