Why the Antenna Table and the Wavelength Table Agree

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Why the Antenna Table and the Wavelength Table Agree

The chapter gives two separate ways to size a remote antenna: a wavelength formula, wavelength equals wave speed over frequency, and a half-wave dipole formula, length approximately 143 divided by frequency in megahertz, giving 28.6 m at 5 MHz, 16.5 cm at 868 MHz, and 6.0 cm at 2.4 GHz. Lower frequencies help propagation, but the chapter warns they make installation harder because the antenna becomes a physical structure. This audit asks the question those two tables invite: are the wavelength table and the dipole-length table secretly describing the same physics, and why don’t their numbers match exactly?

Companion to the chapter Infrastructure-Denied IoT Connectivity — every number here comes from that chapter.

Ada: The chapter gives two separate tables – wavelength lambda = c / f and half-wave dipole length L = 143 / f_MHz – and they are secretly the same physics. Let me tie them together with the chapter’s own values, c = 3 x 10^8 m/s.

• Wavelength at 5 MHz: 3e8 / 5e6 = 60 m; at 2.4 GHz: 3e8 / 2.4e9 = 0.125 m = 12.5 cm. Both match the table.
• A free-space half wavelength at 5 MHz is 60 / 2 = 30 m. But the dipole table says 143 / 5 = 28.6 m.

Those differ on purpose. The dipole constant 143 is not arbitrary: a free-space half wavelength uses 150 / f_MHz metres (since lambda / 2 = (300 / f_MHz) / 2), and 143 / 150 = 0.953. That ~0.95 is the standard velocity/end-effect shortening of a real dipole – so 28.6 m is just 30 m trimmed by about 5%. The same factor holds at 2.4 GHz: 143 / 2400 = 5.96 cm versus a 6.25 cm half wavelength, again 0.953.

The design meaning is the scale, not the trim. That 28.6 m HF dipole is about 28.6 / 0.0596 = 480x longer than the ~6 cm 2.4 GHz dipole. This is precisely why the chapter says lower frequencies “make installation harder because the antenna becomes a physical structure” – the math turns a favourable propagation choice into a literal 29-metre construction problem the field team must raise, tension, and weatherproof.

Every number above is taken from the chapter’s own material and re-derived step by step.