The vehicle

A vehicle in Vivapse is a stack of stages with a payload on top. You choose very little about each stage directly: which engines, how many, how much propellant, how wide, what it is made of, and which recovery hardware it carries. Everything else — its dry mass, its length, its velocity budget, its thrust-to-weight on the pad and on the way down — is derived from those choices by the designer, and the physics flies what the designer derived.

That is the point of the arrangement. A rocket's numbers are not independent, and a designer that let you type in a dry mass would let you build a vehicle that cannot exist.

What a stage is made of

The Vehicle panel builds up to three stages. For each one you set:

• Engines: one or more engine groups, each a catalogue engine or a customised one, and a count.
• Propellant mass: how much the tanks hold. The propellant type follows from the engines, and every engine on a stage must burn the same one.
• Diameter, from 0.6 to 12 m.
• Material: aluminium-lithium, stainless steel, or carbon-fibre composite.
• Recovery hardware: landing legs, grid fins, a heat shield.
• RCS gas for the attitude thrusters, and for a stage with legs, the landing reserve its legs are built for.

The payload's mass is set once, for the whole vehicle.

Dry mass is computed

The dry mass of a stage is the sum of its parts, each sized by a rule in the structural model:

• Tanks from their surface area, which follows from the propellant's volume and the diameter, times the material's areal density. The walls get heavier per square metre as the diameter grows, as hoop stress says they should.
• Engines at their catalogue mass, and a thrust structure weighing 0.35 % of their vacuum thrust expressed as weight.
• Pressurisation at 0.4 % of the propellant, 0.6 % for hydrogen.
• Avionics, RCS hardware, and the interstage below the stage above.
• Legs at 6 % of the rest plus a term that grows with diameter, scaled up for a larger landing reserve; grid fins; a heat shield over the base and the side.

Here is where Aster's 8.45 t upper stage goes:

A quarter of it — the fins, the heat shield and the legs, 2.2 t — exists only to bring the stage home. That is the price of recovery, and it is paid in payload at the full rate, because on the top stage a kilogram of structure and a kilogram of payload are the same kilogram to the rocket equation. On the booster the exchange is far kinder: flown back to back with and without its recovery hardware, a kilogram of Aster's booster costs roughly a tenth of a kilogram of payload. This is why reusable boosters came first.

Materials

The wall figures are at the 3.66 m reference diameter. Steel is nearly twice as heavy as aluminium-lithium and survives more than twice the temperature, which is the whole argument for a steel upper stage that re-enters. On real launch sites steel methalox stages also carry hot-gas attitude thrusters, three times the thrust of cold nitrogen at an Isp of 250 s instead of 70.

Propellant

A propellant is a fuel, an oxidiser and the ratio between them, and what the designer needs from it is the density of the mix, because volume becomes tank and tank becomes mass.

Hydrogen's specific impulse is the best in the catalogue and its tanks are the worst: the same mass of hydrolox needs 2.9 times the volume of kerolox. Aster's booster holds 400 t of kerolox in 387 m³, which is 38.7 m of its 43.5 m.

On real launch sites, 1 % of each stage's propellant can never be burned. It sits in lines, sumps and tank bottoms, stays aboard as mass, and the engines flame out when the rest is gone. fc.propellant, fc.deltaV and fc.burnTime count only the usable part. On Aster's booster the residuals are 4 t; on its upper stage 1 t, worth roughly 300 m/s at the end of the stage's life.

Engines

The figures are approximate public ones. Each engine's thrust falls with the pressure of the air around its nozzle,

where $F_{\text{vac}}$ is its vacuum thrust, $p$ the ambient pressure and $A_e$ the area of its nozzle exit. The mass flow is set by the throttle alone, so as the air thins the same flow buys more thrust: a Merlin 1D's 845 kN at sea level becomes 932 kN in vacuum. A vacuum engine's wide nozzle makes that loss enormous in thick air, and worse: in air above its separation pressure the flow tears away from the nozzle wall and destroys it. That is 25 kPa for the Merlin Vacuum and 30 kPa for the Raptor Vacuum at full throttle — roughly 10 km up — and less at lower throttle: a Merlin Vacuum at 40 % is destroyed above 10 kPa. That is why the two vacuum engines have no sea-level figures. They are for stages that light above the air.

Two numbers in the table matter more on the way down than on the way up. The throttle floor decides whether a stage can hover, and the number of starts decides how many burns a flight gets: a boostback, an entry burn and a landing burn are three relights of a booster engine, and the RS-25 and RD-180 have one start in total.

On real launch sites an engine also gives no thrust at all for a moment after fc.ignite(): 0.3 s for the Merlins and the RD-180, 0.4 s for the Raptors and the BE-4, 0.5 s for the RS-25, 0.2 s for the Rutherford. Then it spools up. At 250 m/s, 0.3 s of nothing is 75 m.

Engine groups

A stage can carry up to four engine types and forty engines in all. Colossus II's ship is the example: three sea-level Raptors inside and three vacuum Raptors on an outer ring. Each group keeps its own thrust, specific impulse, throttle range, spool-up, ignitions and gimbal, and one fc.throttle() drives them all, each within its own range. A program chooses which groups burn with fc.setEngines(), which takes a number of engines, a count per group, or 'sea-level', 'vacuum' or 'all'; fc.engineGroups reports each group's state and whether it can fire at the current pressure. A vacuum Raptor cannot gimbal at all, so on that ship the sea-level engines do all the steering.

Engines sit on rings in the base of the stage, and they light in a balanced order: the centre first, then opposite pairs. An engine lost in flight moves the thrust line off the axis, and the autopilot has to trim the torque with the others.

Thrust-to-weight

Each stage card shows the stage's thrust-to-weight at ignition, with everything above it attached, at sea level and in vacuum, against its weight in standard gravity, $g_0=9.80665$ m/s². The designer judges the first stage on the sea-level figure and the others on the vacuum one. In flight, fc.twr is the thrust available now against the weight felt now, which on real launch sites is fc.effectiveGravity: gravity less the relief that horizontal speed gives.

On the pad the number has one job. Below 1 the engines cannot lift the vehicle, between 1 and about 1.15 they lift it so slowly that gravity takes most of what they produce, and above about 2.2 the vehicle reaches the thick air too fast and too hard. Those are the designer's thresholds, and it warns outside them. For an upper stage it warns below 0.45.

Gravity takes $g$ from the vehicle's speed for every second it spends climbing vertically, whatever its thrust. A rocket that lifts off at 1.45 spends 69 % of its thrust at release holding itself up. Every second of that is velocity it will never keep, which is why the pitch-over starts as soon as it is safe, and why the ascent's gravity losses on the overview's budget are the largest single loss.

More engines do not make that free. Each extra Merlin on Aster's booster adds 470 kg of engine and 333 kg of thrust structure before it lifts anything, and a higher thrust-to-weight means a harder pass through maximum dynamic pressure and a harder ride at the end of the burn, when the tanks are nearly empty: Aster's booster, at full throttle in vacuum with its tanks dry, would push 6.3 g.

The velocity budget

Each stage's velocity budget follows from the rocket equation, with everything above it counted as dead mass:

where $I_{\text{sp}}$ is the engines' specific impulse, $m_0$ the mass when the stage ignites and $m_f$ the mass when its propellant is gone. The designer reports each stage in vacuum and at sea level, and totals the vehicle with the first stage taken halfway between the two — a rough allowance for a stage that starts at sea level and finishes above the air.

Aster's booster is worth 4.19 km/s in vacuum and its upper stage 7.12 km/s, for a designer total of 11.11 km/s. Low Earth orbit costs about 9.3 to 9.6 km/s once gravity and drag have taken their share, and the designer warns below 9.3. The difference, about 1.7 km/s, is Aster's entire budget for coming home: the booster's return and the upper stage's de-orbit and landing. It is not large.

Landing thrust-to-weight

The last number on a stage card is the one that decides how the stage lands: one engine at its minimum throttle, at sea level, against the empty stage's weight. Above 1, the stage cannot hover. It must arrive at zero speed exactly as it arrives at zero height, which is the hoverslam.

The number is worse than the throttle floor suggests. Throttling down lowers the chamber pressure, and with it the vacuum thrust, but not the air's pressure on the nozzle exit. A Merlin 1D at its 40 % floor at sea level gives 0.4 × 932 kN − 87 kN = 286 kN: a third of its sea-level maximum, not 40 %.

On real launch sites the empty stage is not empty. Aster's booster carries its 4 t of residuals to the ground, and in the reference flight it touched down at 28.7 t with about 400 kg of usable propellant left; one Merlin at minimum then gives 1.04 times its weight. It cannot hover, but only just. Its upper stage, landing at 14.4 t on the same engine, cannot hover by a factor of two.

The presets

The Vehicle panel starts from one of seven presets. The first five are the classic range's vehicles; Aster 5 and Colossus II are real vehicles at real scale.

Dry masses exclude RCS gas. Δv is the designer's total, with the first stage halfway between sea level and vacuum.

• Aster is the default: a Falcon-class two-stager whose booster flies to the drone ship and whose upper stage comes home from orbit to Landing Zone 1. Its landing thrust-to-weight is 1.18 on the booster and 3.33 on the upper stage.
• Aster Expendable takes the legs and fins off the booster. The booster is 2.5 t lighter, and the payload doubles to 3 t; the total Δv falls because the payload is heavier, not because the vehicle is worse.
• Colossus is a 9 m stainless-steel methalox vehicle with a 33-engine booster that lands on legs. Its landing thrust-to-weight is 0.29 on the booster and 0.75 on the upper stage: both can hover on one Raptor. The Full mission example is tuned for boosters of up to nine engines and expends this one on purpose.
• Sparrow is a small carbon-fibre launcher with an expendable booster and 30 kg of payload. At 9.61 km/s it has almost nothing to spare, and with the reference program its upper stage does not survive re-entry.
• Hopper is a single-engine test vehicle for suborbital hops, with legs built to land with half its propellant still aboard. It lifts off at 2.87 and lands at 5.09: no hover is possible, ever.
• Aster 5 is a Falcon 9 Block 5 at real scale: a 411 t booster, a Merlin Vacuum upper stage with no legs, a 5.2 m fairing and 13 t of payload. The upper stage is expended, as the real one is.
• Colossus II is Super Heavy and Starship V2 at real scale. Its booster has grid fins but no legs — the real one is caught by its tower — so the reference program expends it. The ship carries a heat shield, legs, and grid fins in place of the real one's flaps.

Two more vehicles, Odyssey and Odyssey Mars, are built for the Moon and Mars; the Mission panel offers them for those destinations. Missions and destinations covers them.

What each number does to the flight

• Propellant buys velocity logarithmically and costs thrust-to-weight linearly. Doubling a stage's load does not double its Δv, and it makes the stage heavier on the pad, longer, and slower to accelerate.
• Engine count buys thrust-to-weight and costs dry mass: 803 kg of engine and thrust structure per Merlin on Aster. It shortens the time spent fighting gravity and hardens max-Q and burnout.
• Specific impulse is velocity directly. A vacuum nozzle's 37 extra seconds on the Merlin are worth about 12 % more Δv from the same tanks.
• Dry mass on the top stage is payload lost kilogram for kilogram, so every piece of recovery hardware there is paid for at full price.
• Diameter shortens the tanks for the same volume and widens the vehicle against the air; it also makes the walls heavier per square metre and spreads the legs.
• Landing reserve decides the landing mass the legs are built for. On the classic range that is the empty stage plus the reserve — 10 % of the propellant unless you say otherwise. On real sites the legs are built for the empty stage plus 2 %, or the reserve you set explicitly. The Hopper sets 50 %. Land heavier than the legs were built for and their crush cores give sooner.
• Minimum throttle and starts decide the way down. Landing thrust-to-weight above 1 means a hoverslam; too few starts means a burn you cannot have.

The quickest way to see all of it is to change one number on Aster and read the stage card before and after. The designer recomputes everything as you type.