# ITU Certified Graphs All figures below are regenerated from the canonical `botb_itu_analysis.py` library with values byte-for-byte matching the ITU Calculator spreadsheet (see [[ITU_Calculator_Reference]]). The `ITU_Calc_` prefix flags them as part of the synced set. **Physics:** 31.5 MHz vertical polarisation, 3 kW TX into 26 dBi broadside array, equisignal 5° squint loss (CROSSOVER_dB = −19.87), noise floor ≈ 0.08 μV at the 50 Ω receiver input. **Two-line comparison throughout:** - **Sommerfeld-Norton FE** (green): flat-Earth solution with surface reflectivity. Direct ray plus ground-reflected plus surface-wave term (ITU Handbook on Ground Wave Propagation 2014 §3.2.1). - **ITU-R P.526-16 Fock** (magenta): globe creeping-wave diffraction past the radio horizon. This is the International Telecommunication Union's own standard for smooth-Earth obstruction loss. --- ## 1. Beam Maps ### 1.1 Telefunken July 1939 over-sea test cycle (animated) A 1-second-per-frame loop through the five nominal Telefunken test ranges (400 / 500 / 700 / 800 / 1000 km). Kleve's beam stays fixed while a cyan halo marks the target under test. Green and pink wedges along each equisignal show SN-flat vs Fock-globe reach: the solid pink segment marks the region where the globe prediction still clears the noise floor, and the hatched pink "UNUSABLE" segment marks the shadow zone. ![[ITU_Calc_knickebein_beam_map_telefunken_cycle_1s_mega 1.gif]] ### 1.2 Operational raid geometry: Kleve and Stollberg beams crossing over Derby The Large Knickebein setup for a Midlands raid. Kleve (111 m, overland) fires the director beam through Spalding. Stollberg (72 m, sea path) fires the cross beam through Beeston. Both yellow equisignals are scaled to a common 1000 km reference so reach is visually directly comparable. Kleve's Fock wedge holds solid out to roughly 600 km; Stollberg's collapses inside 560 km because of the shorter TX and the sea path's lower β clamp (ITU-R P.526 Eq. 16). ![[ITU_Calc_knickebein_beam_map 1.png]] ### 1.3 Telefunken snapshot: 400 km target Closest test range. SN predicts 1024 μV equisignal; Fock predicts 20.6 μV. Both well above the 0.08 μV noise floor, so the globe prediction and the flat-Earth prediction agree on USABLE. ![[ITU_Calc_knickebein_beam_map_telefunken_400km 1.png]] ### 1.4 Telefunken snapshot: 500 km target SN still at 827 μV, Fock down to 3.95 μV. Last range at which the globe model predicts a usable equisignal. ![[ITU_Calc_knickebein_beam_map_telefunken_500km 1.png]] ### 1.5 Telefunken snapshot: 700 km target Fock crosses the noise floor: 0.047 μV, a factor of 1.7 below usable. SN still predicts 507 μV. The hatched pink band visualises exactly this gap. ![[ITU_Calc_knickebein_beam_map_telefunken_700km 1.png]] ### 1.6 Telefunken snapshot: 800 km target Fock drops to 0.0039 μV, roughly 26 dB into the shadow. SN still predicts 401 μV. If the 1939 report logs a signal at this range, the globe model cannot account for it. ![[ITU_Calc_knickebein_beam_map_telefunken_800km 1.png]] ### 1.7 Telefunken snapshot: 1000 km target Fock bottoms out at 2.7 × 10⁻⁵ μV, about 69 dB below noise. SN holds at 269 μV. The 1939 test log reports successful reception at this range (BArch RL 19-6/40 ref. 230Q8 App. 2), so the globe prediction misses the observation by more than 60 dB. ![[ITU_Calc_knickebein_beam_map_telefunken_1000km 1.png]] --- ## 2. Master Bar Charts: Signal Strength per Target Each bar pair shows the SN flat-Earth prediction (green) and the P.526 Fock globe prediction (magenta) for equisignal voltage at the aircraft receiver input. The white noise-floor line at ≈ 0.08 μV is the USABLE / UNUSABLE threshold. Diagonal-hatched pink marks the gap between a UNUSABLE Fock prediction and the corresponding SN bar. ### 2.1 Kleve → operational UK targets Kleve at 111 m firing overland into Spalding (440 km), Retford (512 km), Derby (530 km) and Birmingham (550 km). Both models clear the noise floor at every target. Fock stays within one order of magnitude of SN at these ranges because the paths are still inside the usable globe-diffraction regime. ![[ITU_Calc_master_bargraph_kleve_operational 1.png]] ### 2.2 Kleve → Telefunken 1939 over-sea test ranges Same TX (111 m) but over sea, aimed at the TF test targets. The Haversine distances Kleve → target (shown in parentheses) are shorter than the Stollberg-labelled nominals because Kleve sits southwest of Stollberg. Fock crosses the noise floor between the 500 km test (3.95 μV) and the 700 km test (0.047 μV). ![[ITU_Calc_master_bargraph_kleve_telefunken 1.png]] ### 2.3 Stollberg → operational UK targets Stollberg 72 m over sea into Beeston (694 km), Derby (711 km), Birmingham (754 km) and Liverpool (791 km). Every Fock prediction sits below the noise floor: Beeston 0.019 μV, Liverpool 0.0013 μV. SN meanwhile predicts 326 to 402 μV across the same paths. This is the zero-crossing the null hypothesis is testing against historical raid logs. ![[ITU_Calc_master_bargraph_stollberg_operational 1.png]] ### 2.4 Stollberg → Telefunken 1939 over-sea test ranges The historical test geometry: Stollberg-to-target ranges 400 / 500 / 700 / 800 / 1000 km. Flat-Earth stays usable across the entire set. Fock is already below noise by the 500 km test and roughly 10⁷ times too weak by 1000 km. ![[ITU_Calc_master_bargraph_stollberg_telefunken 1.png]] --- ## 3. Distance Sweeps: SN vs Fock over continuous range Continuous curves from 50 km out to the beam end, showing where each model's equisignal crosses the noise floor. Blue dotted verticals mark the operational or test targets. The dashed grey line is the 4/3-Earth radio horizon computed from both TX and RX heights. ### 3.1 Kleve → Midlands sweep TX 111 m, RX 6000 m, overland. SN stays near 1 kμV across the whole 900 km sweep. Fock tracks close to SN until the 354 km radio horizon, then falls off a cliff and crosses the noise floor near 600 km. Retford (512), Derby (530) and Birmingham (550) labels are staggered across rows because they sit within 40 km of each other. ![[ITU_Calc_sweep_kleve_operational 1.png]] ### 3.2 Stollberg → Midlands sweep TX 72 m, RX 6000 m, sea. Same cliff-edge pattern as Kleve but the Fock crossover happens earlier, near 560 km, because of the lower TX height and the sea path's β clamp at 31.5 MHz (below the 300 MHz cutoff for vertical polarisation over seawater). By the time the beam reaches Beeston (694 km), Fock predicts 0.02 μV while flat-Earth predicts 402 μV. ![[ITU_Calc_sweep_stollberg_operational 1.png]] ### 3.3 Telefunken July 1939 over-sea test sweep Same Stollberg 72 m TX but with the aircraft at 4000 m (the 1939 test altitude per BArch RL 19-6/40 ref. 230Q8 App. 2). Horizon drops to 296 km. Fock crosses the noise floor just past 500 km; SN stays usable to 1200 km and beyond. This is the calibration case for the null hypothesis: if the 1939 report logs a signal at 700, 800 or 1000 km, the globe model cannot reproduce it and the flat-Earth model can. ![[ITU_Calc_sweep_telefunken 1.png]]