Avionics

Radio navigation, radar, communications, antennas, GPS and signal-processing formulae behind aircraft electronic systems

Avionics brings together the key formulae behind aircraft navigation, radar, communications, antennas, GPS, and signal processing, from radio horizon and wavelength to DME, ILS, and radar performance calculations. It’s useful for students, exam candidates, and engineers in real-world aviation work, where these equations help interpret signals, estimate ranges and altitudes, and keep airborne systems accurate, reliable, and safe.

Radio Horizon (line of sight)

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

NEWIntermediate

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

NEWIntermediate

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

NEWIntermediate

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

NEWIntermediate

\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

NEWIntermediate

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

NEWIntermediate

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.