SYST 660 NAME: ____________________________
1
Payload-Range Diagrams
1) Brueget’s Range Equation.
a. Derive Brueget’s Range Equation
b. Include units and show how units yield Range (nm)
c. List the assumptions for Brueget’s range Equation
a) R = (a/c) M (L/D) ln (Winitail / Wfinal)
b) (ft/sec) / (lbs fuel/sec/lbs thrust) = ft (convert to nm – 1ft = 0.00016457nm)
c) zero wind conditions, standard cruise speed, standard day conditions
(e.g., standard atmosphere) and standard domestic fuel reserves
2) Calculate the Range for the following aircraft.
Maximum Zero Fuel Weight = 600,000 lb aircraft
W fuel = 180,000 lbs
W final = 600,000 – 180, 000 lbs
Constant speed V = 642.9 ft/sec
Constant altitude = 30,000 ft
L/D = 18.712
c = 0.0002361 lbs fuel/sec/lbs thrust
R = (a/c) M (L/D) ln (Winitail / Wfinal) = (V/c) (L/D) ln (Winitail / Wfinal)
V = Ma
(642.9 ft/sec/0.0002361 lbs fuel/sec/lbs thrust) (18.712) (ln (600,000/(600,000 –
180,000))= 18173570 ft = 3442 nm
