First-order parametric dry-mass model for a rocket stage's pressure vessels and load-bearing structure. Walls are sized per axial station from the governing driver — internal pressure, station-dependent compression buckling, or max-Q bending — with honest structure factors, cryogenic material modifiers, differential-pressure common bulkheads, a pressurant-system module, and an uncertainty band. Engines and turbopumps are excluded; thrust structure is optional.
Tank sizing. Volume V = m/ρ × (1 + ullage&residual). Each tank is a cylindrical barrel capped by two domes of shape factor k (dome height = R/k). Barrel length solves so total volume fits; below a threshold the tank reverts toward a near-spherical shape (zero barrel).
Station-based loads. The stage is divided into segments from forward skirt down to aft skirt. Each wall carries axial compression N = g·gmax·(mass forward of it)/(2πR) — exact, so the upper tank does not carry the lower tank's propellant. Bending is an envelope max-Q approximation, not a true moment diagram: the side aero load q·C·D is treated as a running load and the moment at each station is the integral of the side load above it (½·w·x²) plus a forward tip term scaled by the bending-lever input. The axial bending stress ±M/(πR²) is added to the station's compression. Real moment distributions also depend on inertial relief, thrust line, and payload — not modeled here.
Wall thickness per station = max of: hoop (pressure) t = pR·SF/(σ·η); compression buckling t = √(N·SF·R/(γ·E)) with imperfection knockdown γ (0.20–0.40, user-selectable); combined axial+bending membrane t = (N+M/(πR²))·SF/(σ·η) — then clamped to min gauge. The buckling and bending checks are taken as separate candidates and the max selected; a true shell-stability interaction check is not performed.
Localized tank hardware. Smooth shell+dome+bulkhead area is the idealized minimum. Real tanks add heavy local structure the shell math misses: ports, penetrations, manholes, sensor bosses, dome-to-barrel joints, attach rings (local fittings), thicker weld seams and flanges (weld lands), and anti-slosh baffles / propellant management devices. These are applied as percentages of bare tank shell+dome mass and are the main reason ideal tank calculators read light.
Honest structure factors. The internal-structure efficiency (isogrid, stringer, balloon) reduces only the buckling-driven excess over the pressure-required thickness: t_eff = t_press + f·(t_buckle − t_press). Pure membrane (pressure) mass is never discounted. Domes get little or no rib benefit.
Pressure stabilization. Balloon tanks require a minimum operating pressure to avoid collapse; internal pressure adds stabilizing tension that offsets compression (N_eff = N − p·πR²/(2πR)). The tool reports the minimum pressure and warns if tank pressure is below it.
Common bulkhead replaces two adjacent domes with one shared bulkhead sized from the selected differential-pressure case (nominal ΔP, one-side-vented, or proof), not the larger absolute pressure. A cryo-pair insulation penalty (areal mass) is added explicitly.
Simplified cryogenic strength trend factors. Yield/ultimate get a temperature multiplier based on the colder propellant in contact (most alloys strengthen at cryo; CFRP is de-rated). These are trend factors for early sizing, not certified material allowables — welds, fracture toughness, ductility, fatigue, and processing all matter and are not captured. CFRP cryotanks also add a liner areal mass for the permeation barrier.
Pressurant module (pressure-fed): helium gas mass from ideal gas at tank pressure × blowdown factor, plus a COPV bottle mass from an empirical kg per stored litre, plus a regulator/valve allowance.
Uncertainty band. Conceptual mass-estimating relationships are good to roughly ±20–30%. The band shows 0.8× / 1.0× / 1.3× the nominal. Excluded: engines, turbopumps (thrust structure optional), TPS, fairing, payload, and unusable propellant beyond the residual allowance.