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r <br />li <br />y > ’ ic* • <br />Fig 3 —Distance plottea against wave angle (one-hop <br />trans.nission) for the nominal range of virtual heights <br />for the E and F2 layers, and for the F1 layer. <br />The second important point to be recognized in <br />mult'hop propagation is that the tngcnometry of the first <br />hop generally establishes the tfgonometrv for all <br />succeeding hops. Ano't is the raoiation angle at the <br />transmitter which sets up the trigonometry for the first <br />hop. Solving a propagation triangle is simplified with the <br />aid of the graph in Fig 3 ’ In this graph the radiation angle <br />in degrees is given on the left, and the smqie-hop <br />distance for the effective layer height along the bottom. <br />Table 1 shows the optimum propagation distance for <br />various radiat'on angles. The data for this taoie was read <br />from the graph of Fig 3, based on an assumed F-layer <br />height of I3i miles <br />From Table 1, if the radiation angle from a given <br />transmitting antenna is concentrated at 30®. the first and <br />succeeding heps m radio propagation will span about <br />650 miles each With a usaoie mdAimurr, limit of f ve hops <br />under the best of conditions, one can pr-jiect ina« <br />the greatest distance for ootimum communications for <br />a 30® wave angle is five times 650 miles, or 3250 miles. <br />For effective communications ove' greater distances, it <br />wduld be necessary to lower the radiation angle at the <br />transmirer antenna site As will be oiscussec shoniy, this <br />can be done only py increasing the height of the hori­ <br />zontal transmitting antenna. <br />Although the discussion m the preceding para ­ <br />graphs has been m terms of a transmitting antenna, the <br />same principles apply when the antenna is used for <br />reception A high antenna will receive low-angle signals <br />more effectively than will a low antenna The point of <br />these several paragraphs may be summarized briefly; <br />The vertical angle of radiation is the key factor in <br />d®termining effective communications distances <br />beyond line of sight. <br />Table 1—Propagation Distance versus <br />Radiation Angle <br />(Data extracted from Fig 3) <br />RaAation Ootimum <br />Ang‘6.f'ooagaior <br />Degrees Distance, \t-ies <br />2 2250 <br />i 2100 <br />3 1650 <br />10 1500 <br />15 1200 <br />20 1000 <br />30 650 <br />40 450 <br />Scientists and engineers recognize that modes <br />other than signal hoppmg account for the prcpagafior <br />of radio waves over fhousanas of miles However <br />studies of actual radio propagation m which the write' <br />has participated have displayed signals with as many as <br />5 hops, so the hopping mode is one distinct possibility * <br />Whatever the propagation mode, there is unanimous <br />agreement that the most effective communications at HF <br />most often accompany the lowest radiation angle. <br />Horizontal Antennas <br />A simple antenna that is commonly used for HF <br />communications is the horizontal half-wave dipole. The <br />dipole IS a straight length of wire (or tubing) into which <br />radio-frequency energy is fed at the center Because of <br />Its simplicity, the dipole may be easily subjected to <br />theoretical performance analyses Furtherjhe results <br />of prooer analyses are borne out in practice. For these <br />reasons, the half-wave dipole becomes a convenient <br />performance standard against which other antenna <br />systems can be compared. The dipole antenna, when <br />viewed from one end. radiates an equal amount of power <br />in all directions. <br />Because the earth acts as a reflector for HF radio <br />waves, the directive properties of any antenna are <br />modified considerably by the ea.ih underneath it If a <br />dipole antenna is placed horizontally above the earth, <br />most of the energy rad ateo downward from the dipole <br />IS reflected upward The reflected waves combine with <br />the di.'ect waves (those raaiated at angles above the <br />horizomari m various ways, depending on the height of <br />the antenna, tne frequency, and the electrical character­ <br />istics of the ground under and around the antenna <br />At some vertical angles above the horizon, the direct <br />and reflected waves may be exactly in phase —that is. <br />the maximum signal or field strengths of both waves are <br />reached at the same instant at some distant point. In this <br />'From The ARRL Antenna Boox. 1-itned tion. Cnaoter 1. Fig 12. <br />-HF backscaner studies by Rayineon (Company under contract <br />with Rome Air Development Center. Gritfiss AFB. NY. A part <br />of this study was done at Raylheon s South Dartmouth, <br />Mass, field site. Jan-Jun, i960.