← Catalogue · #024 V3 draft / A

Owl Mountains rack railway

Where does wheel adhesion alone end and the work of the rack begin? The weight stays vertical; the angle of the track is exaggerated here.

55 ‰gradient in the model · train 60 t (assumption)

Force diagram on an inclined track (wide frame) An original illustrative diagram, not a map and not a line profile. The diagonal is the track; beneath it is a schematic cross-section of the viaduct, above it a small train. Q is the weight of the whole train, vertically downward. N_drv is the load of the driving wheels (driving mass 28 t) on the rail, perpendicular to the track; it is not the load of the whole train. T is the component of the weight of the whole train down the track. Above the track are two bands: T, and adhesion with the red rack part; the dashed part marks the missing force. Force diagram on an inclined track (phone frame) The same original illustrative diagram in a tighter frame that fits all the arrows and labels: the train on the exaggerated, inclined track, the weight of the whole train Q vertically, the load of the driving wheels N_drv perpendicular to the track, the component T down the track, and the adhesion band with the red rack part.

Illustrative diagram, not a drawing of the structure or a line profile. Q and N_drv are drawn out of scale (broken arrows); the angle of the track is exaggerated.

1 · Climb
2 · Rack
3 · Limit

Adhesion provides 27.4 of the 32.3 kN. The missing 4.9 kN is taken over by the rack (6% of the 80 kN limit).Result of a static model with the assumptions below — not a safety assessment or a timetable.

What the rack changes

  1. Weight is vertical.Q = m·g acts downward regardless of the inclination of the track. The track does not rotate gravity; it only sets the directions into which we resolve it.
  2. The weight of the whole train splits into two components.Along the track: T = Q·sin α. At 55 ‰ (α ≈ 3.15°) that is only approx. 5.5% of the weight — which for the 60 t train in the model still comes to approx. 32 kN. Perpendicular to the track acts Q·cos α ≈ 588 kN for the whole train; the diagram does not draw this value.
  3. The driving wheels can grip only as much as friction allows.Only the load of the driving wheels counts: N_drv = m_drv·g·cos α, in the model a driving mass of 28 t, i.e. approx. 274 kN (this is not the load of the whole train). Hence F_adh = µ·N_drv at µ = 0.10: approx. 27.4 kN.
  4. The difference is the missing part of the force.F_rack = max(0, T − F_adh), but no more than the assumed limit. The rack does not change T; it adds a second path for transmitting force to the track. When the limit is too small, a dashed segment remains on the diagram and the model does not count the climb as achieved.
  • Q weight of the whole train — solid arrowhead, always vertical
  • N_drv load of the driving wheels (28 t) on the rail — dashed, perpendicular to the track; the rail's reaction acts in the opposite direction and is not drawn
  • T component of the weight of the whole train down the track — open arrowhead
  • F_adh adhesion — diamond
  • F_rack rack — red used only for it

The same train, two assumptions

A fixed comparison for 55 ‰ and 60 t. The same figures appear in the diagram after selecting “55 ‰” and switching the rack.

Without rack

−4.9 kN

T = 32.3 kN, F_adh = 27.4 kN. 4.9 kN is missing: in the model, adhesion is exceeded.

With rack, 80 kN limit

4.9 kN

The rack takes over the missing part, i.e. approx. 6% of the limit. This is only a force balance in the model.

The viaduct: no photograph for now

No document in the draftV2 pointed to a photograph of the viaduct (Wikimedia Commons, Tomasz Leśniowski, CC BY-SA 4.0). It is not embedded in this prototype: it works offline, and the file and licence have not been checked here. The cross-section in the diagram is a schematic — the number of spans and the proportions do not come from sources.

According to PTTK (data taken over from V1/V2, to be verified), the Srebrna Góra viaduct is 28 m high and was built in 1901.

PTTK warns against walking onto the viaduct because it has no railings. This is information from a source that still needs checking; the draft is not field guidance.

The line in four dates

  • 1900Dzierżoniów–Srebrna Góra via Pieszyce and Bielawa Zachodnia.
  • 1902Extension to Ścinawka Średnia; on the Srebrna Góra–Wolibórz section, part of the track had a rack.
  • 1903The railway reaches Radków.
  • 1931Closure of the Srebrna Góra–Wolibórz section; the track was dismantled in 1934.

Dates from the V1/V2 materials; they were not verified in this run.

Sources for further verification

Links carried over from V2; they were not opened in this run.

Limits: the model does not determine historical speeds, the load capacity of the rack bar or operating safety. Gradient, adhesion, masses and the rack limit require separate supporting evidence.