ngles (i.e., nearer the vertical) only partial or no refraction occurs. This is illustrated in Figure 8.8. Similarly, for a given angle of incidence, refraction decreases with an increase in fre- quency, SO at a critical frequency the wavefront will pass through the layer. As the wavefront passes through an ionized layer, it imparts energy to the electrons, and a small amount of this energy is lost as heat. In the D layer, this transfer of energy is sufficient to completely High-Frequency Sky Wave Propagation lonosphere Critical Angle Skip Zone Fig. 8.8 Critical angle of Earth ionospheric refraction. Take-Off Angle (degrees) Great Circle Distance Fig. 8.9 Take-off angle for single-hop sky wave paths. absorb medium frequencies during daylight, but at higher frequencies it causes some attenu- ation in the refraction process. Refracted waves also undergo a change of polarization that is due to the complex movement of the free electrons; this phenomenon is called Faraday rotation. In planning an HF sky wave link, it is necessary to know the distance between the transmitter and receiver, or the area to be covered, and this can be calculated by equations 8.10 and 8.11. It is desirable to minimize the number of "hops" (i.e., refractions from the ionosphere and reflections from the Earth's surface) to minimize path attenuation and the inherent variability associated with ionospheric refraction. Maximum radiation from the antenna should therefore be at an angle (the take-off angle) that results in refraction from the ionosphere onto the target area. Figure 8.9 is a diagrammatical representation of the surface of the Earth from which the optimum take-off angle of radiation from the antenna can be derived if the distance and refracting layer height are known. A lower take-off angle is required for longer distances, and for distances of greater than 2000 km two or more hops are normally required. In practice, a number of different propagation modes can be established on multihop links, which makes field strength predictions 