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

>