Breguet Aircraft Cruise Range and Parabolic Polar (L/D)_max Formula

Link wing aspect ratio, Oswald span efficiency, and fuel mass fraction via Breguet’s equation

For a parabolic aircraft drag polar C_D = C_D0 + C_L^2 / (PI() * AR * e_osw), parasite drag equals induced drag at peak aerodynamic efficiency (L / D)_max = 0.5 * SQRT((PI() * AR * e_osw) / C_D0). Integrating fuel burn over steady cruise yields the jet Breguet Range Equation: R_km = (V_kmh / c_hr) * (L / D) * LN(W_init / W_final), where V_kmh is true airspeed (km/h) and c_hr is weight-specific fuel consumption (1/hr, i.e., kg fuel per kg thrust per hour).

Audit a twin-aisle transport with parasite drag C_D0 = 0.0200 (B2), wing aspect ratio AR = 10.0 (B3), Oswald efficiency e_osw = 0.80 (B4), cruise speed V_kmh = 850 km/h (B5), specific fuel consumption c_hr = 0.50 hr^-1 (B6), start-of-cruise mass W_init = 75,000 kg (B7), and end-of-cruise mass W_final = 50,000 kg (B8): (L/D)_max = 0.5 * SQRT(400 * PI()) = 10 * SQRT(PI()) = 17.7245, and Breguet range reaches 1,700 * 10 * SQRT(PI()) * LN(1.5) = 12,217.3593 km!

Parabolic Drag Polar Maximum Lift-to-Drag Ratio (L/D)_max Formula

Validate C_D0 > 0, aspect ratio AR > 0, and Oswald span efficiency 0 < e_osw <= 1.

=LET(cd_0, B2, ar_w, B3, e_os, B4, IF(OR(cd_0 <= 0, ar_w <= 0, e_os <= 0, e_os > 1), "Invalid Polar Input", ROUND(0.5 * SQRT((PI() * ar_w * e_os) / cd_0), 4)))

Jet Breguet Cruise Range R_km Formula

Enforce W_init >= W_final > 0 so fuel burned W_init - W_final is never negative (when W_init = W_final, LN(1) = 0 returns 0 km).

=LET(cd_0, B2, ar_w, B3, e_os, B4, v_kmh, B5, c_sfc, B6, w_in, B7, w_fn, B8, IF(OR(cd_0 <= 0, ar_w <= 0, e_os <= 0, e_os > 1, v_kmh <= 0, c_sfc <= 0, w_fn <= 0, w_in < w_fn), "Invalid Breguet Input", LET(ld_mx, 0.5 * SQRT((PI() * ar_w * e_os) / cd_0), ROUND((v_kmh / c_sfc) * ld_mx * LN(w_in / w_fn), 4))))

Further reading

• Arte Sheets Lesson — Rayleigh Flow Diabatic Compressible Thermal Choking Formula
• Microsoft Support — LN function