A breast-shot water wheel receives water near axle height beside a curved breast. Explore the circular layout and calculate circumference, paddle spacing and an arc length measured at the wheel radius. These geometric results do not predict hydraulic or shaft performance.
Breast-Shot Layout Calculator
Enter wheel diameter, paddle count and breast-arc angle to calculate the circular layout. The wheel-width field does not enter these side-view calculations or change the drawing.
Equation Used
- The wheel is a perfect circle.
- N identical paddles are equally spaced and rotate rigidly.
- The declared breast is a concentric circular arc.
- Flow, head, immersion, clearances, forces, efficiency, speed, torque, power and safety are excluded.
Diameter, paddle count and breast-arc angle set the displayed layout and numerical results. The water markers and playback rate are illustrative; wheel width is not used by these calculations.
Water enters near mid-height beside a curved breast
National Park Service sources distinguish the breast wheel by water entering about halfway up its circumference, unlike bottom-fed undershot and top-fed overshot wheels. The curved breast is shown as a declared concentric arc, not as a hydraulic clearance.
The wheel, spokes and paddles rotate rigidly while qualitative water markers enter near axle height and follow part of the breast arc.
Historical mill topology
NPS historical material documents breast wheels as one of the vertical water-wheel forms used at mills. The Smithsonian preserves a teaching model comparing breast, undershot and overshot arrangements.
This page does not evaluate a site, restore a wheel or design hydropower equipment.
Declared circular and breast-arc geometry
gamma is in radians for arc length. These identities do not represent water capture or performance.
Declared layout example
For D=5.0 m, N=24 and gamma=100 degrees, circumference is 15.708 m, spacing is 15.00 degrees, rim pitch is 0.654 m and breast arc length is 4.363 m.
What this geometry omits
Real behavior depends on headrace, inlet, breast and paddle geometry, clearances, tailwater, load and losses. None is solved here.
The arc result uses the wheel radius D/2. It does not include a running gap or the thickness of a physical breast, and cannot specify the dimensions or output of a working installation.
Breast-wheel questions
Is breast arc a running-clearance specification?
No.
Does paddle spacing predict efficiency?
No.
Does phase represent RPM?
No.
Is the water path a flow simulation?
No.
Can this calculator size a generator?
No.
Breast-wheel references
- National Park Service, Saugus Iron Works history: breast-wheel water entry midway on the circumference.
- National Park Service, Hopewell Furnace Water Wheel: breast wheel receives water halfway up, between undershot and overshot arrangements.
- Smithsonian National Museum of American History, Water Wheel: documented comparative model.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
