Water-Powered Forge

2D twin of the 3D forge: head tank, water wheel, cam shaft and helve hammer, using the same equations as the 3D page.

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Water, wheel and hammer

The wheel converts a share eta of the water power rho g Q H into shaft power; the shaft torque is P / omega, and four cams per turn lift the hammer by h so each blow carries m g h.

Model checks

The science

What is modelled

Water from a head tank turns a vertical wheel; the wheel shaft carries four cams that lift the tail of a pivoted hammer (a helve). The hammer is released and falls freely on the anvil. All the energy of the blows must come from the wheel shaft.

Equations

  • Water power P = rho g Q H; shaft power P eta; torque T = P_shaft / omega.
  • Energy per blow m g h, impact speed sqrt(2 g h), blows per minute = 4 x rpm.
  • Hammer work rate = energy per blow x blows per second, which can never exceed the shaft power.

Checks run in the page

  • Power chain from flow and head to shaft.
  • Torque from power and speed.
  • Numerical free fall against sqrt(2 g h).
  • The energy ceiling, including an infeasible case.

Honest simplifications

A single lumped efficiency, no hammer lever ratio, rebound or anvil losses, no wheel dynamics or friction, and a hammer drawn as a pivoted rod. An illustrative heritage-machine model, not a design tool.

What to try
  • Press Heavy hammer, fast wheel: the work rate passes the shaft power and the page flags it as infeasible.
  • Press Low river and watch the available power fall.
  • Raise the lift: energy per blow grows linearly with h while the blows per minute stay fixed.
Water, shaft and hammer power against flow
Shaft torque against wheel speed
Energy per blow against hammer lift
Hammer work against shaft power (energy ceiling)
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