Two curves rule the cruise.
The power an aeroplane needs is two terms fighting: parasite drag grows with the cube of speed, induced drag — the cost of making lift — falls off as 1/v. Their sum is the power-required curve, a lopsided bathtub with a bottom. Above it sits the power your engine can deliver; the gap between the curves is yours to spend on climb, on speed, or — by throttling back — on fuel not burned.
Every cruise decision is a point on this curve. The interesting ones have names, and each name answers a different question: how long can I stay up, how far can I get, and how fast can I go without the fuel bill becoming silly.
Endurance is a minimum, range is a tangent.
Best endurance lives at the bottom of the curve — minimum power, minimum litres per hour, maximum hours aloft. It is uncomfortably slow, wallowing on the back side of the curve, and useful mainly for holding and for arguments. Best range is faster: it minimises litres per kilometre, not per hour, and geometrically it is the tangent from the origin to the fuel-flow curve — the same construction glider pilots met on the polar in the MacCready article, wearing an engine.
The two speeds are mathematically locked together: best endurance is best range divided by the fourth root of three, about 76% of it. The ratios survive any aircraft — only the absolute numbers belong to the type.
The power curve, priced in litres.
Slide a 20 km/h headwind in and watch the blue circle — best range over the ground — walk to the right: wind moves the tangent's origin, so a headwind demands faster flight, a tailwind rewards patience. Then park the red dot on CARSON and read the price of hurry: about 32% more speed than best range for 16% more fuel per kilometre.
Carson's speed: the least wasteful hurry.
Best range is efficient and slow; full throttle is fast and gluttonous. In 1980 B. H. Carson asked where the compromise stops being graceful and found a fixed point: at 1.316× the best-range speed, total drag has risen only by a factor of 2/√3 ≈ 1.155. You buy 32% more speed for 16% worse kilometres-per-litre — the best speed-per-fuel bargain the physics offers. Faster than Carson, the cube law starts charging properly.
For our schematic single that is 190 km/h against 144 for best range: an hour and forty minutes saved on a 1000-kilometre day, for about 13% of the tank's reach. Carson called it the least wasteful way of wasting; most real-world cruise settings land, knowingly or not, within a few knots of it.
In your cockpit.
This whole chart collapses to two live numbers on the panel: true airspeed and fuel flow. Divide them — the instrument does — and you have specific range, your position on the curve, updated every second and honest about wind, altitude and the state of your engine. Set the cruise by that number and the argument between the accountant and the schedule is settled with data.
What those litres per hour become at the other end of the tank — reserves included — is the fuel planning article.