# Head-up display > [[PORTAL_Aviation|Aviation]] · [[PORTAL_Avionics|Avionics]] spine. <!-- MICROSIMGEN:BEGIN v1.7 — hand-placed to match siblings; regenerate with g08_place_microsims.py (§15) --> ## Microsims — three.js ### Head-up display (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Head-up_display.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Head-up display — three.js microsim"></iframe> </div> **Open it full-screen:** [Head-up_display.html](https://wikitube-3d-microsims.netlify.app/Head-up_display.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles: - [[Fly-by-wire]] - [[Autopilot]] - [[Glass_cockpit]] - [[Terrain_awareness_warning_system]] - [[Aircraft_flight_dynamics]] - [[Avionics]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4).* <!-- MICROSIMGEN:END --> ## Overview A **head-up display** is a transparent display that presents flight information in the pilot's forward field of view. The description is accurate and almost entirely misses the point. What separates a HUD from a bright screen bolted to the windscreen is one optical property: the image is **collimated**, focused at optical infinity, so that each symbol is a *direction* rather than a *place*. The consequence is **conformality**. If the symbology lives at infinity and is drawn with the same perspective mapping the eye uses, a symbol can be placed so that it lies exactly over the piece of the real world it refers to. A horizon line can sit on the horizon. A pitch ladder rung labelled 10 can lie along the locus of directions ten degrees above the horizontal. A runway outline computed from a navigation database can be drawn over the runway itself, even when the runway is invisible in fog. And the **flight path vector** — a small winged circle marking the direction the aircraft is actually travelling — can sit on the patch of ground the aeroplane is going to arrive at. That last symbol is the reason the microsim above puts the aircraft in a crosswind. On approach with a crosswind from the right, the aeroplane must point into the wind to hold the extended centreline. The nose is aimed several degrees off the runway. The boresight symbol, which is fixed to the airframe, is aimed several degrees off the runway with it. Everything the pilot's body feels is normal — wings level, ball centred, no sideslip whatever — and the nose is nevertheless lying. Only the flight path vector tells the truth, because it is drawn from the velocity vector and knows nothing about which way the fuselage happens to be facing. Slide the head sideways with collimation switched on and the flight path vector stays welded to the touchdown point. Switch collimation off, so the same symbology is painted on a panel-mounted display 0.65 m away, and eight centimetres of head movement swings it nearly seven degrees off the world. That difference is the whole argument for a HUD's optical system. The second thing a HUD buys is a **scan**. Information that would otherwise sit on the instrument panel, requiring a head-down glance of a second or two at the worst possible moment, is available without looking away from the window. This is why HUDs migrated from combat aircraft into airline cockpits: they are worth most in the approach and landing phase, in poor visibility, where the outside cues are marginal and the cost of a downward glance is highest. The lineage is a gunsight. The **reflector sight**, patented by Sir Howard Grubb in 1900 and fielded widely in the Second World War, projected an illuminated reticle off a partially reflecting glass so that the aiming mark appeared at infinity and did not shift when the gunner's head moved — exactly the parallax argument above, arrived at half a century early and for exactly the same reason. **Gyro gunsights** of the 1940s added a computed lead angle to the reticle. Extending a computing gunsight to present attitude, speed and flight path is a short conceptual step, and it was taken in the late 1950s and 1960s: the Blackburn Buccaneer is generally credited as the first production aircraft whose head-up "strike sight" served as a primary flight reference, and the LTV A-7 Corsair II of the late 1960s is usually described as the first aircraft whose HUD carried the full set of information needed to fly it. Around the same time the French engineer Gilbert Klopfstein developed the conformal approach symbology — flight path vector, flight path angle reference, conformal runway — from which most later HUD formats descend. The civil line began in earnest in the 1980s with the Flight Dynamics Head-up Guidance System, adopted by Alaska Airlines and used to fly low-visibility approaches into airports where a conventional autoland installation was impractical. Regulators subsequently allowed HUD-based credit in low-visibility operations, and HUDs are now offered on most transport aircraft. The current frontier is the **Enhanced Flight Vision System**, in which an infrared or millimetre-wave sensor image is drawn on the same combiner, conformal with the world, allowing an approach to continue below the ordinary decision altitude on the strength of a sensor image of the runway environment; in the United States this is governed by 14 CFR 91.176. The successor line is **head-worn**: helmet-mounted displays in combat aircraft, where the symbology follows the pilot's line of sight instead of the airframe's, and wearable head-up displays now certified on some civil aircraft. The advantage is a display that is no longer limited to the small window a fixed combiner provides; the costs are head-tracking accuracy, weight on the neck, and a much harder alignment problem. ## The physics ### Collimation and the parallax argument Take a symbol drawn on a surface at range *L* from the eye, in a direction that is correct when the eye sits at the design eye position. Move the eye by a distance *d* perpendicular to that line of sight. The direction in which the eye now sees the symbol changes by eps = arctan(d / L) ~= d / L (small angles) and that angular change is the **registration error**: the amount by which the symbol has slipped off the world feature it was drawn over. Nothing about the symbol has moved. The eye has. The two cases in the microsim differ only in *L*: | Case | *L* | *d* = 8 cm | error | |---|---|---|---| | Panel display at the combiner plane | 0.65 m | 0.080 m | 123 mrad = 7.05° | | Collimated combiner (modelled) | 4 km | 0.080 m | 0.020 mrad = 0.0011° | | Collimated combiner (real) | infinite | 0.080 m | 0 | A real collimator achieves this by placing the image source at the focal plane of a relay lens assembly. Light from a single point on the source leaves the optics as a **parallel bundle**, and a parallel bundle is, by definition, an image at infinity: every eye position that intercepts the bundle sees the point in the same direction. The combiner then folds that bundle into the pilot's eye without changing its direction, using a partially reflecting plate — modern combiners are usually holographic or dichroic, reflecting the narrow spectral band of the display source while transmitting roughly 80 % of everything else. That transmittance is why the world is slightly dimmer inside the HUD's window than outside it, an effect the microsim reproduces. The optics view (view 3) draws the bundle explicitly: diverging from the image source, parallel after the collimating optics, and still parallel arriving at the eye box. At the reader's own desk the same experiment is available without an aeroplane: hold a finger up in front of a distant building and move your head. The finger moves against the building; the building does not move against the horizon. A HUD is engineered so that its symbology behaves like the horizon rather than like the finger. ### The conformal mapping A HUD computes symbol positions as directions in aircraft body axes, then projects them onto its raster with a gnomonic (tangent-plane) mapping about the boresight. If **d** = (*d*<sub>x</sub>, *d*<sub>y</sub>, *d*<sub>z</sub>) is a unit vector in body axes with *x* to the right, *y* up and the nose along −*z*, the raster coordinates are u = u0 + f * (dx / -dz), v = v0 - f * (dy / -dz), f = (W/2) / tan(FOV_H / 2) which is the same projection a pinhole camera — or an eye — performs. Because the projections match, a symbol drawn at the projection of a world direction lands on top of the world feature in that direction. That single identity is conformality, and everything else follows from it. Attitude enters through the body-to-world rotation: the microsim composes it as an aviation 3-2-1 sequence (yaw, then pitch, then roll) and transforms every conformal element — horizon, pitch ladder, heading scale, runway outline, flight path vector — through the same quaternion, so that all of them stay registered under any attitude rather than being separately fudged. Note that this is a *directional* mapping. It is exact for features at infinity (the horizon, the pitch ladder) and approximate for features at finite range (the runway outline), where the true direction depends slightly on where the eye is. At the ranges involved the difference is negligible: 15 cm of head movement against a runway threshold 1.6 km away is 94 microradians. ### The flight path vector, angle of attack and drift The flight path vector is drawn in the direction of the aircraft's velocity. Decompose the offset between the boresight and the FPV: - **Vertically**, the gap is the **angle of attack**. Pitch attitude θ, flight path angle γ and angle of attack α satisfy θ = γ + α in symmetric flight, so the vertical separation between the waterline symbol and the FPV is α directly. A HUD therefore gives an angle-of-attack readout for free, drawn to scale, without an AoA gauge. - **Laterally**, the gap is the **drift angle** — the angle between where the nose points (heading) and where the aircraft goes (track). In a crosswind the drift angle comes from the wind triangle. With true airspeed *V*, a pure crosswind component *V*<sub>xw</sub> and the ground track held on the runway centreline at a commanded ground-referenced flight path angle γ, the air-relative velocity is (*V*<sub>xw</sub>, *w*, −*V*<sub>gh</sub>) and its magnitude must be *V*. Eliminating the vertical component gives a closed-form solution with no iteration: V^2 = Vgh^2 * sec^2(gamma) + Vxw^2 => Vgh = cos(gamma) * sqrt(V^2 - Vxw^2) w = sin(gamma) * sqrt(V^2 - Vxw^2) Vg = sqrt(V^2 - Vxw^2) drift = atan2(Vxw, Vgh) Groundspeed is the Pythagorean difference of airspeed and crosswind; the crab angle is asin(*V*<sub>xw</sub>/*V*) to within the cosine of the path angle. At the sim's defaults — 140 kt true, 15 kt crosswind, γ = −3° — this gives a drift angle of 6.16°, a groundspeed of 139 kt and a descent rate of −740 ft/min, all of which the readout displays live. The crucial point for the lesson is that a **coordinated crab has no aerodynamic sideslip**. The aeroplane is flying straight through the air mass; the air mass is moving sideways. The slip-skid ball is centred, the wings are level, nothing feels wrong, and the nose is still pointing six degrees away from the runway. There is no bodily cue for drift. This is precisely the sort of thing that instruments exist to supply, and precisely the sort of thing a conformal display supplies best, because it does not report drift as a number to be interpreted — it draws the answer on the runway. Angle of attack in the model is inverted from a simple lift relation, CL = 2*mg*/(ρ*V*²*S*) and α = (CL − CL<sub>0</sub>)/CL<sub>α</sub>, using the published wing geometry of a narrow-body twin (*S* = 124.6 m², *b* = 34.32 m) at a 60 t landing mass with representative flaps-30 coefficients. The coefficients are chosen so that the model reproduces a checkable number: the stall speed it implies is 57.3 m/s, so *V*<sub>ref</sub> = 1.23 *V*<sub>s</sub> = 137 kt, within a couple of knots of the real reference speed for that aeroplane at that mass. At 140 kt the model returns α = 5.4°, and hence a body attitude of about +2.4° on a three-degree path — again the right answer for the real aircraft. ### Field of view, and why it is small A HUD's **total field of view** is the angular size of the combiner aperture as seen from the design eye position: FOV_H = 2 * arctan( a / (2 L_c) ) For an aperture *a* = 35 cm at *L*<sub>c</sub> = 0.65 m this is 30°; the sim uses 30° × 24°, representative of a modern transport HUD. Combat HUDs are similar or smaller — the F-16's is commonly quoted at about 25° total. Against a windscreen that spans most of a hemisphere, this is a small window, and it is a *hard* limit: making it larger means a bigger combiner, a bigger collimator, and a larger, heavier projection unit in a glareshield that has no room. Worse, the **instantaneous field of view** — what a particular eye position can see through that aperture — is smaller still and shrinks asymmetrically as the head moves: FOV_H(dx) = arctan( (a/2 - dx) / L_c ) + arctan( (a/2 + dx) / L_c ) Move the head 8 cm to the right and the left edge of the symbology disappears behind the combiner frame. The microsim models this exactly, by clipping the symbology against four planes through the *actual* eye and the four edges of the aperture, so that with collimation on and the head displaced you see the correct behaviour: the symbology does not move, but part of it is no longer visible. This is why HUD installations specify an **eye motion box**, a volume of a few centimetres in each direction within which the full field of view is guaranteed, and why HUD-equipped aircraft take seat positioning seriously. Symbology that would fall outside the field is **caged** to the edge and drawn differently, rather than silently vanishing — the microsim does this for the flight path vector when a large crosswind or a steep flight path pushes it past the aperture. A display that quietly loses a symbol is worse than one that admits it has. ### Accommodation The third benefit is the one that is easiest to state and hardest to photograph. An image at optical infinity shares its focus with the distant scene, so the eye does not have to re-accommodate between symbology and world. A display at finite range *L* forces a dioptric error of *D* = 1/*L* on whichever of the two the eye is not focused on; a defocused point images as a blur circle whose angular diameter is simply the pupil diameter times the dioptric error: theta_blur = p * D For a panel display at 0.65 m, *D* = 1.54 dioptres, and with a 5 mm pupil the blur circle is 7.7 mrad, about 0.44°. That is a modest blur — which is why head-down displays work at all — and the microsim draws exactly that number rather than an exaggerated one, applying it to the symbology when the eye is focused outside and to the world when the eye is focused on the display. The real cost is not the blur but the **time**: accommodation takes on the order of a few hundred milliseconds in each direction, it degrades with age as presbyopia sets in, and it must happen at exactly the moment when the aircraft is closest to the ground. Honesty requires a caveat here, because the literature contains a genuine and long-running dispute. Stanley Roscoe and colleagues argued from the 1980s that pilots do not in fact accommodate to optical infinity when viewing a collimated display in a visually impoverished field, but instead relax toward their **dark focus** — an intermediate resting point typically around 1 dioptre — which would mean that HUD symbology is not seen as sharply, and distant objects not sized as accurately, as the optical design implies. Others have found the effect small in operational conditions. The prudent statement is that collimation removes the *optical* requirement to re-accommodate but does not by itself guarantee that the eye behaves as the optics intend. There is a second and better-attested human-factors cost: **attentional capture**, or cognitive tunnelling. Because HUD symbology and the world occupy the same visual direction and the same focal distance, attention devoted to the symbology can suppress detection of unexpected events in the scene behind it. The classic demonstration is Fischer, Haines and Price's NASA study of 1980, in which pilots flying HUD approaches in a simulator were slower to notice — and in some cases failed entirely to notice — an aircraft blocking the runway. This is not an argument against HUDs, which have a strong operational safety record; it is an argument that superimposing two information sources is not free, and that HUD symbology sets should be as sparse as they can be. Hence the declutter control. ## Controls -> what each maps to | Control | Symbol | Range | Units | What it does | |---|---|---|---|---| | Airspeed | *V* | 115 – 200 | kt (true) | Sets true airspeed. Drives the lift coefficient CL = 2*mg*/(ρ*V*²*S*), hence the angle of attack, hence the gap between the boresight and the flight path vector. Also sets groundspeed through the wind triangle. | | Flight path angle | γ | −8 – +4 | deg | The **ground-referenced** flight path angle, which is what the flight path vector displays and what the pilot flies. −3.0° is the standard ILS glidepath; at that setting the PAPI beside the runway shows two white and two red, as its ICAO setting angles (2.500, 2.833, 3.167, 3.500°) are designed to. | | Crosswind | *V*<sub>xw</sub> | −30 – +30 | kt | Pure crosswind component, positive from the right. Drives the crab: drift = atan2(*V*<sub>xw</sub>, *V*<sub>gh</sub>). The aircraft always tracks the centreline, so the entire effect appears as a heading offset — the lateral gap between the boresight and the FPV. | | Head lateral | *d*<sub>x</sub> | −15 – +15 | cm | Moves the eye sideways from the design eye position. With collimation on, nothing registers differently; with it off, the symbology swings by *d*<sub>x</sub>/0.65 radians. Also shrinks the instantaneous field of view on one side. | | Head vertical | *d*<sub>y</sub> | −12 – +12 | cm | The same experiment in the other axis. | | Declutter level | — | 0 – 2 | level | 0 full (conformal runway outline, full tapes, 5° heading ticks, pitch ladder to ±30°); 1 approach (outline and minor ticks removed, ladder to ±10°); 2 minimum (flight path vector, horizon, boresight and digital speed and altitude only). | | Collimation | *L*<sub>img</sub> | on / off | — | On: the image is at infinity (modelled at 4 km, residual parallax 25 µrad). Off: the identical raster is painted on a panel-mounted surface 0.65 m from the design eye. Nothing else changes. | | Flight path vector | — | on / off | — | Removes the velocity-vector symbol, leaving only airframe-referenced information — that is, leaving only symbols that cannot tell you where you are going. | | Eye focused on the display | *D* | on / off | dioptres | Accommodation. With collimation off, choosing the display defocuses the world by 1.54 D and choosing the world defocuses the symbology by the same. With collimation on neither is defocused, which is the point. | | View | — | pilot / outside / optics | — | Pilot eye; an external view showing the airframe crabbed against its own velocity vector; and a scale diagram of the optical path from image source through collimator and combiner to the eye box. | | Fly / Pause · Centre head · Reset | — | — | — | Freeze the approach, return the eye to the design position, or restore all defaults. | Every control is also reachable from the keyboard: arrow keys move the head, **C** toggles collimation, **F** the flight path vector, **D** declutter, **E** eye focus, **[** **]** airspeed, **−** **=** flight path angle, **,** **.** crosswind, **1**/**2**/**3** the views, space to fly or pause, **R** to reset. ## Learning objective After using the sim a reader should be able to: 1. **State what conformality is and demonstrate it.** The flight path vector lies over the point on the ground the aircraft will reach, and the sim marks that point independently with a cyan ring computed from the velocity vector and the terrain, so the claim is falsifiable on screen rather than merely asserted. 2. **Separate heading from track.** In a crab the nose and the velocity vector differ by the drift angle, there is no aerodynamic sideslip and therefore no bodily cue, and only a velocity-referenced symbol resolves the ambiguity. 3. **Explain why collimation is not decoration.** Registration error is *d*/*L*. Making *L* infinite is the only way to make the error zero for all eye positions, and the sim's readout quantifies the alternative: 8 cm of head movement on a 0.65 m display is 123 mrad, which at 1.6 km is 190 m of touchdown-point error. 4. **Describe the field-of-view constraint honestly.** A HUD sees 25–30° of a windscreen that spans far more, the instantaneous field shrinks as the head leaves the eye box, and symbology at the edges is genuinely lost. 5. **Give the accommodation argument and its caveats** — the optical benefit is real and quantifiable, the human response to it is contested, and attentional capture is a measured cost that motivates declutter. ## Limits and connections The flight model is **kinematic, not dynamic**. Nothing is integrated from forces: the sliders set true airspeed, ground flight path angle and crosswind, and the wind triangle is solved exactly. There is no autopilot, no turbulence, no wind shear, no flare, no gear or flap change, and the aircraft tracks the centreline perfectly, which is a considerable compliment to the pilot. Real crosswind approaches include a decrab or sideslip in the last few seconds before touchdown, which the model does not attempt. The optics are modelled at the level of **ray directions**, which is the level at which conformality and parallax live and no deeper. There is no tracing through real glass, no aberration, no distortion mapping, no chromatic error, no binocular disparity budget, no display latency and no boresight misalignment — and misalignment in particular is a genuine engineering problem, since a conformal display is only as conformal as the installation's alignment and the inertial reference's attitude accuracy allow. The combiner aperture is treated as a rectangle normal to the line of sight; real combiners are tilted plates, and the sim draws one, but their field of view is quoted as the aperture seen from the design eye, which is what is modelled. Several deliberate legibility compromises are flagged in the code. Symbol strokes and characters are drawn several times larger than a real HUD's roughly 1 mrad strokes and 6 mrad characters, so that a screenshot survives. Approach and runway lights are drawn with an angular size they do not have, because a real lamp is visible from kilometres away by *intensity*, which a non-HDR renderer cannot reproduce. The cyan impact ring's **position** is the true computed impact point, but its **size** is held at a constant angular diameter so it does not shrink to a few pixels at range. The conformal runway outline is generated from exact truth rather than from a navigation database, so it does not show the database and position errors that limit a real HUD-guided landing system. The connections run in several directions. The symbology's inputs — attitude, inertial velocity, air data — are the same signals that feed the [[Autopilot]] and the [[Fly-by-wire]] control laws, and a HUD is often the display through which a flight-director or autoland mode is monitored rather than flown. The information it presents is a re-projection of the same data that fills a [[Glass_cockpit]]; the difference is entirely one of where the data is put and in what frame. The pitch, angle-of-attack and flight-path relationships it draws are the kinematics developed in [[Aircraft_flight_dynamics]]. A conformal display is also the natural place to put a terrain warning, and a [[Terrain_awareness_warning_system]] alert drawn on a HUD can indicate *where* the terrain is rather than merely that it exists. Everything here sits inside the broader system described in [[Avionics]]. Two extensions are worth naming. **Enhanced and synthetic vision** put a sensor or database-generated image of the outside world on the same combiner, conformal with the real one; the standards for those systems are the natural next reading. And **head-worn displays** — helmet-mounted in combat aircraft, wearable in some civil installations — remove the fixed aperture entirely, at the price of needing to know where the head is pointing to a fraction of a degree, continuously, in a vibrating cockpit. That is a harder problem than collimation, and it is the reason the fixed combiner has survived for sixty years. ## References - Newman, R. L. *Head-Up Displays: Designing the Way Ahead.* Avebury Aviation / Ashgate, Aldershot, 1995. (The standard monograph on HUD design, symbology and certification.) - Weintraub, D. J.; Ensing, M. *Human Factors Issues in Head-Up Display Design: The Book of HUD.* CSERIAC State of the Art Report 92-2, Crew System Ergonomics Information Analysis Center, Wright-Patterson AFB, Ohio, 1992. - Fischer, E.; Haines, R. F.; Price, T. A. *Cognitive Issues in Head-Up Displays.* NASA Technical Paper 1711, NASA Ames Research Center, Moffett Field, California, 1980. (The original attentional-capture study; the unnoticed runway incursion.) - Prinzel, L. J. III; Risser, M. *Head-Up Displays and Attention Capture.* NASA/TM-2004-213000, NASA Langley Research Center, Hampton, Virginia, 2004. (A review of the intervening two decades of evidence.) - Wickens, C. D.; Long, J. "Object versus space-based models of visual attention: implications for the design of head-up displays." *Journal of Experimental Psychology: Applied*, vol. 1, no. 3, pp. 179–193, 1995. - Iavecchia, J. H.; Iavecchia, H. P.; Roscoe, S. N. "Eye accommodation to head-up virtual images." *Human Factors*, vol. 30, no. 6, pp. 689–702, 1988. - Roscoe, S. N. "The trouble with HUDs and HMDs." *Human Factors Society Bulletin*, vol. 30, no. 7, pp. 1–3, 1987. (States the dark-focus objection; see Newman for the counter-argument.) - SAE International. *Transport Category Airplane Head Up Display (HUD) Systems.* Aerospace Recommended Practice ARP5288. - SAE International. *Minimum Performance Standard for Airborne Head Up Display (HUD).* Aerospace Standard AS8055. - RTCA, Inc. *Minimum Aviation System Performance Standards (MASPS) for Enhanced Vision Systems, Synthetic Vision Systems, Combined Vision Systems and Enhanced Flight Vision Systems.* DO-315 series, Washington, D.C. - Federal Aviation Administration. *Criteria for Approval of Category I and Category II Weather Minima for Approach.* Advisory Circular 120-29A, 2002. - Federal Aviation Administration. *Straight-in landing operations below DA/DH or MDA using an enhanced flight vision system (EFVS).* Title 14 Code of Federal Regulations § 91.176. - Federal Aviation Administration. *Instrument Flying Handbook.* FAA-H-8083-15B, 2012. (Chapter on flight instruments and display systems.) - Federal Aviation Administration. *Pilot's Handbook of Aeronautical Knowledge.* FAA-H-8083-25C, 2023. - International Civil Aviation Organization. *Annex 14 to the Convention on International Civil Aviation, Volume I: Aerodrome Design and Operations.* (Precision approach path indicator setting angles and approach lighting geometry.) - International Civil Aviation Organization. *Manual of All-Weather Operations.* Doc 9365. - Hecht, E. *Optics*, 5th ed. Pearson, Boston, 2017. ISBN 978-0-13-397722-6. (Collimation, afocal systems, image formation at infinity.) - Smith, W. J. *Modern Optical Engineering: The Design of Optical Systems*, 4th ed. McGraw-Hill, New York, 2008. ISBN 978-0-07-147687-4. - Melzer, J. E.; Moffitt, K. (eds.) *Head-Mounted Displays: Designing for the User.* McGraw-Hill, New York, 1997. (The head-worn successor line, including the eye-box and exit-pupil arguments that carry over from HUDs.) - Rash, C. E.; Russo, M. B.; Letowski, T. R.; Schmeisser, E. T. (eds.) *Helmet-Mounted Displays: Sensation, Perception and Cognition Issues.* U.S. Army Aeromedical Research Laboratory, Fort Rucker, Alabama, 2009. - Etkin, B.; Reid, L. D. *Dynamics of Flight: Stability and Control*, 3rd ed. Wiley, New York, 1996. ISBN 0-471-03418-5. (Body axes, Euler-angle conventions and the theta = gamma + alpha relationship used throughout.) - Anderson, J. D., Jr. *Introduction to Flight*, 8th ed. McGraw-Hill Education, New York, 2016. (Lift coefficient, reference speeds and the approach condition.) **On the spine:** [[Avionics]] · [[Fly-by-wire]] · [[Autopilot]] · [[Head-up_display]] · [[Traffic_alert_and_collision_avoidance_system]] · [[Terrain_awareness_warning_system]] · [[Radio_navigation]] · [[Radiation_hardening]] · [[Radar]] · [[Air_traffic_control]] · [[Aviation]]. <!-- FLIGHTLINK:BEGIN g23 — generated from _registry/plans/AVIATION_AVIONICS_SECTIONS.md; do not hand-edit inside --> **Part of the [[Avionics]] hub** — main article for section X13, *Head-up display*. Related sections: Flight instruments · Instrument landing system. <!-- FLIGHTLINK:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Head-up_display) : [Wikitube](https://en.wikitube.io/wiki/Head-up_display) --- *PORTAL_Avionics three.js batch · 2026-08-05 · sim staged in `_3d_deploy_stage/`.*