![[geometric view]](common.gif)
The basic geometry of NDT is straightforward when it occurs by forward scatter. Assume that we have a transmitter at one point on the earth's surface, whose signals are being received by a receiver at another point which is beyond line of sight from the transmitter. The following diagram shows the situation, and illustrates the common volume in which scattering is assumed to take place. Note that the earth's curvature is (as always) greatly exaggerated.
Illustration of Terms and Geometry
The common or scattering volume is determined by the geometric circumstances, the beam widths of both transmitter and receiver, their takeoffs, and the height of the tropopause. If one of the stations has a poor takeoff, then the lower edge of its beam will be higher, and will reduce the common volume. Although high gain antennas are beneficial in other ways, they will have narrower beam widths, and thus result in a smaller common volume (and remember that this diagram should have a third dimension). The height of the tropopause is another major determinant for longer DX. In the worst case, in winter low pressure systems, it may be as low as 8 km, which will eliminate any common volume for longer DX.
The effect of the height of the tropopause on common volume, and thus the effectiveness of NDT propagation, can be illustrated by some recent data from 4 m contests. On 27 September 1998, I could barely hear Stewart GM4AFF, just being able to decipher his callsign at the top of the QSB (slow fading), although occasional meteor scatter 'pings' to S9+ confirmed that he was transmitting. From my QTH, he is about 700 km distant, with the midpoint of the path quite close to the MST radar site, about 350 km north of here. Using a 4/3 earth model for the signal path up into the upper troposphere, and assuming a 'normal' rate of change of radio refractive index, the lowest point of the common volume should have been at a height of around 8.6 km above the earth's surface; a simple earth model predicts that same point at about 11 km altitude. At that time, the MST radar was indicating that the tropopause was at an altitude of about 11.2 km, providing insufficient common volume for a QSO without running higher effective radiated power (for instance).
In contrast, Steve G0AEV, with a path midpoint at about 300 km north of his QTH, should have had a common volume extending upwards of 6.5 km (4/3 earth) to 8.3 km (simple earth) altitude, giving a significantly greater common volume for scattering. He was therefore able to hear GM4AFF more easily. Indeed, earlier on in the day, when the MST radar suggested a slightly higher tropopause, at 11.4 km altitude, G0AEV completed with GM4AFF.
During a previous 4 m contest on 9 August 1998, I worked GM4DHF/P over a similar length path to that between G0AEV and GM4AFF. At that time, the tropopause height indicated by MST radar was about 11.9 km above the ground, and the QSO quite easy to complete.
There are inevitable simplifications in this model. Of course, the common volume does not have sharply bounded edges. Some scatter may still take place above the tropopause, or the tropopause may even reflect or refract radio waves to help such transmission. On the lower VHF bands, in particular, NDT propagation may occur by refractive modes rather than forward scatter: see my more speculative pages (accessed from the Inner Sanctum) for more on this.
Last updated 27 Dec 1998
Howard Oakley
Mail howard@quercus.demon.co.uk