Maximum Endurance (jet)
Longest time aloft for a jet, maximized at maximum L/D.
Formula
Variables
Example
A jet stays airborne longest when flown at its maximum lift-to-drag ratio.
How it works
This equation gives the maximum possible time a jet can remain airborne on a fixed fuel load, assuming it is flown at the speed and altitude that maximize the lift-to-drag ratio. It works because fuel flow is proportional to thrust required, and in steady cruise a jet needs thrust roughly equal to drag, so a lower drag for the same lift means less fuel burned per unit time. The logarithm appears because the aircraft gets lighter as fuel is burned, so the endurance depends on the ratio of initial to final weight rather than just the amount of fuel.
When to use it
Use this for planning or analyzing maximum endurance missions for jets, such as loiter, patrol, or holding patterns. It is appropriate when the goal is time aloft rather than range, and the aircraft is assumed to cruise steadily at the condition that maximizes lift-to-drag.
Worked example, step by step
Given: c = 0.60 hr^-1, L/D = 18, Wi = 60,000 kg, Wf = 48,000 kg Step 1: Compute the weight ratio: Wi/Wf = 60,000/48,000 = 1.25 Step 2: Take the natural log: ln(1.25) = 0.2231 Step 3: Multiply L/D by the log term: 18 × 0.2231 = 4.0158 Step 4: Divide by c: E = 4.0158 / 0.60 = 6.693 hr Final answer: Maximum endurance ≈ 6.7 hours
Common mistakes to avoid
- Using log base 10 instead of the natural logarithm ln
- Putting weight in the wrong order, which can give a negative endurance
- Applying the formula with a thrust-specific fuel consumption value in the wrong units
Did You Know?
To stay airborne longest, a jet flies for minimum drag, not maximum speed.
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