Avionics

d \approx 1.23\sqrt{h}

Maximum line-of-sight range to the radio horizon for a VHF antenna, driven by antenna height and the curvature of the Earth.

Radio Wavelength

\lambda = \dfrac{c}{f}

Wavelength of a radio signal is the speed of light divided by its frequency; it sets antenna length and dish sizing.

DME Slant Range Correction

d = \sqrt{D_s^2 - h^2}

DME measures the direct (slant) distance to the beacon; the true ground distance is found by removing the height component.

ILS Glideslope Height

h = D\tan\theta

Height an aircraft should be above the runway threshold when established on the ILS glideslope at a given distance.

One-in-Sixty Rule

\theta = \dfrac{60 \times d_{off}}{d_{flown}}

Rule-of-thumb linking a lateral track error to an angular deviation: 1 nm off after 60 nm is about 1° of error.

Mode C Altitude Reporting

FL = \dfrac{PA}{100}

A Mode C/S transponder reports pressure altitude referenced to 1013.25 hPa; dividing by 100 gives the flight level, independent of the local altimeter setting.

Free-Space Path Loss

FSPL_{dB} = 20\log_{10}d + 20\log_{10}f + 32.44

Signal power lost simply by spreading through free space, growing with both distance and frequency.

Effective Isotropic Radiated Power

EIRP_{dBW} = P_t + G_t - L_c

Apparent power a transmitter would need if it radiated equally in all directions; combines transmit power, antenna gain and cable loss.

Radar Maximum Unambiguous Range

R_{max} = \dfrac{c}{2\,PRF}

Farthest range at which a pulse echo returns before the next pulse is sent; beyond it, targets appear at false (aliased) ranges.

Radar Range Resolution

\Delta R = \dfrac{c\tau}{2}

Smallest separation at which two targets appear as distinct echoes, set by the transmitted pulse width.

Radar Doppler Shift

f_d = \dfrac{2v_r}{\lambda}

Frequency shift of an echo from a moving target; the factor of two accounts for the round trip to the target and back.

Nyquist Sampling Rate

f_s \geq 2 f_{max}

To digitise an analogue avionics signal without aliasing, the sampling rate must be at least twice the highest frequency present.

Parabolic Antenna Gain

G = \eta\left(\dfrac{\pi D}{\lambda}\right)^2

Gain of a dish antenna rises with aperture area and falls with wavelength, scaled by aperture efficiency.

Radar Range Equation

P_r = \dfrac{P_t G^2 \lambda^2 \sigma}{(4\pi)^3 R^4}

Received echo power for a monostatic radar, combining transmit power, antenna gain, target size and range.

GPS Pseudorange

\rho = c\,(t_r - t_t) + c\,\delta t

Measured distance to a GPS satellite from signal travel time, biased by the receiver clock error — hence “pseudo” range.

GPS Position Error (DOP)

\sigma_{pos} = GDOP \times \sigma_{UERE}

Overall positioning error is the geometry factor (dilution of precision) multiplied by the per-satellite ranging error.