AP 3302 Pt. 3 Section 1 CHAPTER 1 PULSEMODULATED RADAR dimensional picture. Such radars are in fact often called 3D radars. It is not usual however to show all the factors on a single c.r.t. display. Normally two c.r.t.s are used, one to show range and bearing (e.g. a p.p.i.) and the other to show range and height. To find the height of a target we use an aerial array which can swing the radiated beam up and down. Fig 21 shows two aircraft which are both at a ground range of 20 miles but are flying at different heights. Two important facts can be obtained from the diagram: a. The actual distance between the radar and aircraft B is much greater than that between the radar and aircraft A. The distance to the target in each case is called the slant range. b. With the radar beam directed at aircraft A the angle between the beam and the horizon (the angle of elevation) is 200. For aircraft B it is 400. Thus the greater the height of an aircraft, at a given ground range, the greater is the angle of elevation. We shall now see how these facts are used to find the height of an aircraft and its true ground range. The known factors are slant range r and angle of elevation 0 of the aerial. From Fig 22: Sin q = Height/r therefore Height = r sin q Cos q = Ground range /r therefor Ground range = r cos q Example. If the slant range of an aircraft is measured as 30 miles and the angle of elevation as 5^{o} Height = 30 sin 5^{o} = 30 x 0.0872 = 2.6 miles or 13,720 feet. Ground range = 30 cos 5^{o} = 30 x 0.9962 = 29.89 miles.
How Height is Indicated In practice it is not necessary to calculate the height and ground range of each target because modern radar equipment includes a suitably designed indicator which shows these factors directly. The aerial used for heightfinding radiates a beam which is narrow in the vertical direction but which spreads horizontally (Fig 23a). It is first turned towards the azimuth bearing of the target (obtained from the p.p.i.) and then it nods up and down between the limits to be scanned. The indicator used with this aerial has a form of brightup (intensitymodulated) display. The trace is formed in much the same way as for a p.p.i., the trace moving in synchronism with the aerial; but since the aerial swings in a vertical arc the illuminated part of the c.r.t. is a sector in elevation (Fig 23c). Ground range and height are precalculated and are marked on a scale placed over the face of the c.r.t. 

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