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Other losses can only be estimated from statistical data, and some of these are dependent on weather conditions, especially on rainfall. The first step in the calculations is to determine the losses for clearweather or clear-sky conditions. These calculations take into account the losses, including those calculated on a statistical basis, which do not vary significantly with time. Losses which are weather-related, and other losses which fluctuate with time, are then allowed for by introducing appropriate fade margins into the transmission equation.

B = rChargeLevel()

As a first step in the loss calculations, the power loss resulting from the spreading of the signal in space must be determined. This calculation is similar for the uplink and the downlink of a satellite circuit. Using Eqs. (12.1) and (12.2) gives the power-flux density at the receiving antenna as

27.10 (a) n (for all integers n); (b) 2 n (for all integers n); (c) + 2 n (for all integers n); (d) k (for all odd integers k); 2 3 3 (e) + 2 n (for all integers n); ( f ) + 2 n (for all integers n); (g) + 2 n and + 2 n (for all integers n); 2 3 4 4 (h) + 2 n (for all integers n). 6 27.11 (a) 12 sin2 x cos x; (b) cos x 2 sin x; (c) x cos x + sin x; (d) 2x(cos 2x x sin 2x); (e) (f) x cos x sin x ; x2

(12.6)

If the battery is 70 percent depleted, B will have the value 30, indicating that there is 30 percent capacity remaining. Run the program in Fig. 13.1 and leave it running for a while. The program makes the robot move back and forth on the screen and reports its battery charge level. Once

The power delivered to a matched receiver is this power-flux density multiplied by the effective aperture of the receiving antenna, given by Eq. (6.15). The received power is therefore PR

MainProgram: rLocate 50,200,90 rIgnoreCharge false while true XYString 3,3,"Charge=",rChargeLevel(),"% rForward 700 rTurn 180 wend End

Recall that r is the distance, or range, between the transmit and receive antennas and GR is the isotropic power gain of the receiving antenna. The subscript R is used to identify the receiving antenna. The right-hand side of Eq. (12.7) is separated into three terms associated with the transmitter, receiver, and free space, respectively. In decibel notation, the equation becomes [PR] [EIRP] [GR] 10 loga 4 r b l

x sin x + 2 cos x 2 ; (g) 5(3 cos x cos 3x sin 3x sin x); (h) 4 cos 2x sin 2x = 2 sin 4x; (i) 4x sin (2x 2 3); x3 sin 2x ( j) 15 sin2 (5x + 4) cos (5x + 4); (k) ; (l) 6(sin2 (sin2 x))(cos (sin2 x)) sin x cos x. cos 2x 27.12 (a) 1 2 4 1 ; (b) 0; (c) ; (d) 1; (e) ; ( f ) ; (g) 0; (h) 3; (i) 3; ( j) 0; (k) 1; (l) 0. 3 3 5 4

(12.8)

the battery is depleted the next statement that tries to make the robot move will cause an error as shown in Fig. 13.2. Real robots will have to connect themselves (or be connected) to a terminal to recharge the battery, and the process may take hours. It serves no purpose for a simulator to simulate hours of recharging. Our robot can be recharged with the command:

The received power in dBW is therefore given as the sum of the transmitted EIRP in dBW plus the receiver antenna gain in dB minus a third term, which represents the free-space loss in decibels. The free-space loss component in decibels is given by [FSL] 10 loga 4 r b l

27.13 Figure A-19 shows the graphs for one period of each function, except in the case of the aperiodic function ( f ). 27.14 (a) max = 2 (at 2 ), min = 0 (at 0); (b) max = 3 , min = 1(at 0); 2 at 4 5 5 3 3 5 (c) max = at and , min = 1 at 0, and ; (d) max = , min = ; 3 at 3 at 4 6 6 2 2 3 2 3 1 5 ; (e) max = (at ), min = 0 at the two roots of cos x = 4 4

ExprN is an expression that results in a value between 1 and 100. If you pass a value outside these limits RobotBASIC will assume the closer limit. This command instantaneously recharges the battery to the level you specify. Simulating time delays or having to be at a particular place and orientation can be done programmatically. The following sections will explore methods to accomplish this.

(12.9)