Navigation & Flight

The crossing

U.C.F. hulls do not coast. A crossing is flown under power the entire way: thrust to the midpoint, flip end over end, and decelerate the rest of the distance so the ship arrives at rest alongside the berth rather than through it. Navigators call it the brachistochrone profile. Loaders call it the reason nothing in the hold is allowed to be round.

Because the drive never rests, distance and time are related by a single law. Half the crossing is spent accelerating, so d = a(t/2)², and flight time is therefore t = 2√(d/a). Time goes as the square root of distance, which is the one mercy in the whole arrangement: a run four times as far takes only twice as long.

The company's standard acceleration is fixed by its oldest published number. Earth orbit to Luna is quoted at eight hours, and 384,399 km in eight hours under this profile requires 1.8538 m/s². Every other figure in the timetable descends from that one promise.

What the drive costs

Speed is not the expensive part. Velocity is. A continuous-thrust crossing must buy its speed on the way out and then buy the same speed again to shed it on the way in, so the total velocity budget is Δv = 2√(dA). The figures are large, and they are meant to be.

Distances above are quoted at mean separation. A ship routed Earth orbit to Titania by way of Titan spends 8,147 km/s across the two legs, which is the largest single commitment on the published network.

Propellant is charged by the arithmetic that has governed every rocket ever built. To change velocity by a given amount, a ship throws away a fraction of its own mass, and that fraction climbs faster than the velocity does. At the company's 3,000 km/s exhaust velocity, Luna costs a hull under two percent of itself, Mars at mean separation costs about thirty eight percent, and Titan to Triton costs a freight train fifty four percent. The same Triton run on a torchship costs ninety two percent, which is a number the yards will quote a price for and then decline to build.

The three hulls

Pushing harder shortens the crossing but raises the velocity bill, because time falls as one over the square root of acceleration while delta-v rises as its square root. A hull cannot be fast and cheap. It can be fast, or it can carry things.

On the Earth to Mars run a freight train burns seventeen percent of itself as propellant and a torchship forty five. Out at Titan to Triton the same comparison is brutal: fifty four percent against ninety two. The freight train is not a lesser ship. It is the only class for which the outer runs close at all, and everything beyond Saturn moves because a freight train was willing to take four times as long about it.

The exception is cargo that spoils. Salmon mousse loses roughly a seventh of itself on a freight train to Titania and about a twentieth on a torchship, and on a full presentation-tin manifest that difference is worth several times the fuel. Perishables fly fast. Grain, ore, cometary ice, tinplate and bonded clay do not care how long they are in the dark, and they are loaded accordingly.

Amazonian Prime Freight operates three torchships and names them after delivery windows. We operate six freight trains and name them after naps. Both fleets arrive. Only one of them arrives with the whole manifest. Fleet Operations bulletin, Cannery Row

Seasons

The planets do not hold station for the convenience of the timetable. A lane is not the same lane twice, and the separation a navigator is quoted this morning is a fact about this morning.

Earth and Mars sit anywhere from 78 to 378 million kilometres apart depending on where each happens to be, and since flight time follows the square root of distance, the same run can take half as long in a good season as in a bad one for very nearly the same fuel. Luna is exempt. Luna comes with us.

The outer pairs are worth stating plainly. Titania and Triton are on a cycle no employee of this company has seen turn over, and the schedule between them is best described as permanent. That run belongs to the freight trains and always will.

Gravity assists

A close pass by a massive body rotates a ship's velocity vector, and in the Sun's frame that rotation is free speed. The gain is bounded by the body's mass and by how close a pilot dares fly, which is why Jupiter is worth a detour and Luna is not.

Company minimums place periapsis no nearer than three body radii. Closer than that is not a pass, it is a landing, and the paperwork differs considerably. In practice assists matter most on the short Jovian transfers, where a swing past Jupiter can buy back several hours on a twelve hour hop. On the long outer crossings the ship is simply moving too quickly for any planet to bend its course enough to matter, and the flight plan will say so.

A note on quoted distances

Published lane figures are quoted at root mean square separation, which is the honest long-run average of a pair over a full season rather than a convenient midpoint. For two roughly circular orbits this works out to the square root of the sum of the squares of the two orbital radii. It is the number a lane costs on average across every season it will ever have, which makes it the right basis for a rate card and the wrong basis for a departure.

Navigators file against the sky in front of them. Accounting files against the average. Both are correct and the difference is called a launch window.

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