Add detail of radar equation for marine a scope

CLAUDE.md

@@ -65,6 +65,8 @@ is compiled, which in this case would be the build subdirectory of the project
 directory, you would type ./radar_simulator, or use a full path name
 of {PROJECT_DIR}/build/radar_simulator.
 
+In the CMakeLists.txt, plese use the name radar_simulator for the add_executable call.
+
 There will be three main areas of the screen. On the right hand side will be the radar
 scope.
 
@@ -259,6 +261,7 @@ Individual scope informations
    2-1 Chain Home A Scope
 
    ==========================================================
+
    Downward PIP and mixing calibration pips with target pips and noise grass
 
    Very important. The Chain Home A Scope is upside down. That is, the baseline
@@ -390,7 +393,8 @@ Individual scope informations
    creates a curved waveform; not just a line.
 
    A photograph for this display show no graticule at all. Only range pips formed by an oscillator.
-   Those oscillator pips are fixed. Range settings do not affect them.
+   Those oscillator pips are fixed. Range settings do not affect them. There is a baseline at the
+   bottom, etched in glass, that is side illuminated by incandescent lamps.
 
    Like Chain Home, the Marine A-scope sums noise, calibration pips, and target echoes into a
    single signal before the deflection plates — this is a hardware reality of any CRT A-scope.
@@ -411,6 +415,45 @@ Individual scope informations
    3. 6.0 miles; marker pips every 1.0 miles
    4. 12.0 miles; marker pips every 2.0 miles
 
+   RADAR EQUATION FOR MARINE A SCOPE
+
+   Here are the fixed values (those values that can be declared as 
+   uniforms) for the marine a scope radar. I suggest these for the uniform names
+
+   peak_power = 500 KW
+   wavelength = 10 centimeters
+   antenna_gain = 30 db
+   pulse_rep_frequency = 500 hz
+   horizontal_beamwidth = 2.5 degrees
+
+   Now we have some stuff for the settings file:
+
+   SYSTEM_TEMPERATURE ($T_s$): Usually 290K; used to calculate the noise floor
+   NOISE_FIGURE ($F$): A value in dB that determines how much "grass" your 
+     specific receiver adds to the signal.
+   BOLTZMANN_CONSTANT ($k$): $1.38 \times 10^{-23}$, essential for the thermal 
+     noise part of your simulation.
+
+   Now, here is a snippet of pseudo code:
+
+   /* Uniform Variables provided by CPU */
+   uniform float u_AntennaBearing; // Current rotation of knob/motor
+   uniform float horizontal_beamwidth;      // Fixed for the scope (e.g., 2.5 degrees)
+
+   /* Logic for each Target (calculated on CPU or in Geometry Shader) */
+   float angle_diff = abs(target.bearing - u_AntennaBearing);
+
+   // Handle the 359 to 0 degree wrap-around
+   if (angle_diff > 180.0) angle_diff = 360.0 - angle_diff;
+
+   // BeamFactor: 1.0 at center, drops to 0.5 at horizontal_beamwidth/2
+   // This creates the "fade in / fade out" effect as you turn the knob
+   float beam_factor = exp(-2.77 * pow(angle_diff / horizontal_beamwidth, 2.0));
+
+   // Final received power Pr
+   float Pr = (peak_power * pow(antenna_gain, 2) * pow(wavelength, 2) * target.rcs * beam_factor) / 
+           (pow(4.0 * PI, 3.0) * pow(target.range, 4.0));
+
 2. PPI Scope
 
    PPI stands for Plan Position Indicator