Free-piston displacer gas spring: double-acting Ø18 cylinder, gland and piston in a 2 in tri-clamp spool — dimension sheet
Source: Xem Studio, https://xemstudio.com/objects/fpse-displacer-gas-spring/  (CC BY 4.0)
Basis: Gas-spring stiffness k = γ p (A²/V₁ + (A − a)²/V₂) (two closed columns either side of the piston); tuned with the Redlich & Berchowitz linear dynamics of the generator
Catalog version: 2026-10-20

Sizes: see table below
- The displacer must resonate a little below the running frequency so that it leads the piston; with 365 g moving that takes about 28 kN/m at 10 bar helium. A flexure that stiff would be overstressed at the displacer's stroke, so the spring is gas: two 30 mm columns of the working charge either side of a Ø18 piston on the end of the stinger (7.63 + 7.42 cm³).
- It scales with the charge, as the engine's other gas forces do, so the displacer stays in tune from 1 to 10 bar. Its compression ratio is mild: ±15 % of the column at the design stroke.
- Tuning: the column height sets the frequency of the displacer and so its phase lead; my analysis puts 30 mm at about 70° lead. Shorter columns make it stiffer (less lead), longer columns softer. The analysis on the performance page shows the effect of ±10 % displacer mass.
- The cylinder is pressed into the top spool with its vent flats letting the bounce gas past to the port cap; the gland closes its bottom with a spigot and three M3 × 16; the stinger runs in the gland's Ø3 bore. Both clearances (piston and stinger) leak only between gas springs at the same mean pressure.

part  size
cylinder  Ø47.5 × 93.0, bore Ø18
piston  Ø18 × 25
gland  Ø47.5 × 10 + Ø18 × 3 spigot
columns  2 × 30 mm
stiffness at 10 bar He  27.9 kN/m

Files elsewhere (not hosted by Xem Studio; license as stated by the publisher):
- Proc. IMechE Part A: Redlich & Berchowitz (1985), Linear dynamics of free-piston Stirling engines — PDF — journal; method cited [verify license at link] — https://journals.sagepub.com/doi/pdf/10.1243/PIME_PROC_1985_199_025_02
- Wikipedia: Hagen–Poiseuille flow between parallel plates (clearance-seal leakage Q = π D δ³ Δp / 12 μ L) — web — CC BY-SA 4.0 (text) — https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation
- Long Earth Society: Engine builds — web, video — LES site — https://longearthsociety.com/engineering/

Free files (CC BY 4.0, Xem Studio; STEP + STL, 3 parts): https://xemstudio.com/files/hardware/fpse-displacer-gas-spring/index.json
API: https://xemstudio.com/api/geometry?object=fpse-displacer-gas-spring