Engine-Out Glide Range Calculator: Wind and Turns

The model uses a shallow, steady, engine-off glide and a parabolic drag polar. Callender (2025), attached pages 7–10, provides the aerodynamic basis. We calibrate it with the supplied best-glide ratio $G$ and speed rather than inventing aircraft drag coefficients.

Weight correction is $V_{E0}=V_{E,ref}\sqrt{m/m_{ref}}$ (Callender, bank-angle paper, attached p. 8). With density ratio $\sigma$, $V_0=V_{E0}/\sqrt{\sigma}$. True airspeed is treated as horizontal air-relative speed in this shallow-glide approximation.

For $x=V/V_0$, wings-level sink is $s(V)=V_0(x^3+x^{-1})/(2G)$. For a requested true bearing, resolve the wind into tailwind $w_\parallel$ and crosswind $w_\perp$. The ideal straight-track ground speed is $u=\sqrt{V^2-w_\perp^2}+w_\parallel$. A 32-iteration bounded derivative search maximizes $u/s(V)$ between the entered EAS limits after conversion to TAS. In axial winds this reproduces Callender's published headwind and tailwind examples. Equation 20 in that paper prints a second term without the required groundspeed factor; this implementation follows the dimensionally consistent derivative of its drag polar and Equation 19.

The turn model is derived here using FAA PHAK coordinated-turn kinematics (attached pp. 33–35 and 38–40): $n\approx\sec\beta$, $V_t=V_0\sqrt n$, $s_t=V_t n/G$, $\omega=g\tan\beta/V_t$, and $r=V_t/\omega$. Integrating the air-relative circular arc and adding wind times elapsed time gives the turn displacement. This preserves the best-glide lift coefficient; it is not a reproduction of the different fixed-speed turn examples in the Callender bank-angle paper.

After the response delay, a bearing solver searches left and right arcs up to 360° in 10° brackets and bisects crossings 25 times. It retains the longer positive endpoint on the requested ray. Straight-leg speed is the ideal no-turn wind solution for that ray, held fixed during the turn-endpoint search. Thus the result is a feasible route-family estimate, not a globally optimized trajectory. The footprint samples rays every 5°; its area is the sum of triangles between successive radial endpoints. Every route ends at the selected approach-height reserve.

• The entered glide ratio and reference speed describe the same clean configuration and engine/propeller state. Defaults are generic study values, not a particular aircraft.
• Convert published IAS to CAS with the aircraft's POH/AFM airspeed-calibration data before using CAS as an EAS approximation at low Mach. Uncorrected IAS carries additional instrument and position errors (FAA Instrument Flying Handbook 15B, printed p. 5-9; attached excerpt p. 1).
• Constant mass, density and uniform horizontal wind; no vertical air motion.
• Coordinated shallow glide with $L\cos\beta\approx W$; no sideslip or gust loads.
• During the delay, speed is already at weight-corrected best glide along the starting heading.
• Turn and straight-leg speed changes, roll-in/roll-out and kinetic-energy changes are instantaneous and are omitted from the height budget. The turn-speed increase preserves lift coefficient; the model does not predict stall speed or establish operating margins.
• The user supplies a valid current-mass EAS floor, cap, bank and approach reserve. The minimum-speed bound is not a stall model.
• Map coordinates are local east/north distances over one flat landing elevation. The filled contour interpolates a sampled set of modeled routes; it contains no terrain or landing-site information.

AVIATION — TRAINING ONLY. Not for operational flight planning, navigation, emergency decisions or runway-turnback guidance.

Use the aircraft POH/AFM, actual operating limitations and qualified instruction. No safe arrival, landing or return altitude is established.

This version requires a speed interval containing still-air best glide, wind below 95% of the minimum modeled TAS, and enough usable height for a full modeled turn so every ray can be solved. The preferred turn descent ratio is $n/G\le0.25$. Accuracy deteriorates for steep descents, very low density, extreme speeds, changing winds and configuration changes.

The numerical outline is a route-family estimate, not the full reachable set. Speed is wind-adjusted for the requested bearing before solving turn geometry. Additional optimization, multiple turns, approach alignment, flare, runway dimensions, obstacles, terrain, icing, propeller changes, pilot transients and vertical wind are not represented. Its interpolation and area do not certify that every enclosed point is a usable landing site.