Breguet Aircraft Range Equation & Lift-to-Drag (L/D) Glide Distance formulas

Keep the cruise model and glide assumptions separate

Breguet range here assumes constant speed, lift-to-drag ratio and weight-specific fuel consumption over an idealized cruise segment. The initial and final masses bracket that segment; they are not automatically takeoff and landing masses. The ratio can use consistent mass or weight units.

B3 must be fuel weight flow divided by thrust, in inverse hours. Mass-based TSFC in kg/(N·h) requires multiplication by gravitational acceleration to obtain this convention; do not enter that mass-based value unchanged. With speed in km/h the result is kilometers.

This is not a dispatch range: climb, descent, reserves, wind, changing performance and operational constraints are not modeled. Zero mass consumed gives zero range in this fueled-cruise equation.

The separate glide uses height lost above the target elevation and its own glide L/D in B8. Constant steady glide in still air gives horizontal distance = height lost × L/D. Cruise L/D need not be the best-glide value. The result does not determine emergency reachability, speed, terrain clearance or landing suitability.

Breguet Jet Cruise Range in kilometers (or nautical miles)

Use positive cruise speed, fuel-consumption parameter, L/D and masses; final mass cannot exceed initial mass. The logarithmic ratio is dimensionless.

=IF(COUNT(B2:B6)<>5,"Invalid inputs",IF(OR(B2<=0,B3<=0,B4<=0,B5<=0,B6<=0,B6>B5),"Invalid inputs",ROUND((B2 / B3) * B4 * LN(B5 / B6), 1)))

Ideal steady still-air glide distance

B7 is nonnegative height lost in kilometers relative to the target elevation. B8 is the positive glide L/D for the assumed condition, independent of cruise L/D in B4.

=IF(COUNT(B7:B8)<>2,"Invalid inputs",IF(OR(B7<0,B8<=0),"Invalid inputs",ROUND(B7*B8,1)))

Further reading

• Microsoft Support — LN function
• MIT Unified Engineering — Breguet range equation
• NASA Glenn — Glide angle and height lost