Undershot Wheel

Part of Hydro Generator

The simplest water wheel type — paddles dipping into a flowing stream, driven by water current — requiring no dam or head, but with low efficiency.

Why This Matters

The undershot wheel requires almost nothing to deploy: no dam, no millpond, no elevated launder, no head. You build a wheel with paddles on the rim, set it in a stream with the paddles dipping into the current, and it turns. This simplicity made the undershot wheel the first type used in recorded history — Roman mills on the Tiber, medieval mills on slow European rivers — and it remains the easiest hydro device to improvise in an emergency.

The trade-off is efficiency. An undershot wheel converts only 25-35% of the water’s kinetic energy into mechanical work. The water pushes the paddles and then slides away, carrying much of its momentum downstream. Compare this to 65-85% for an overshot wheel. But in the right situation — a large river with strong current and little elevation change — an undershot wheel might be your only viable option, and 30% of something is infinitely better than 100% of nothing.

Understanding undershot wheel design also provides the foundation for the more efficient Poncelet wheel (a refined undershot design with curved buckets) and the underlying fluid mechanics that explain why gravity-type wheels outperform them.

When to Use an Undershot Wheel

Use it when:

• A river or fast-running stream has strong current but minimal elevation change
• You need power quickly and lack the time or materials to build a dam or diversion
• The stream floods regularly (an undershot wheel can be designed to ride out floods)
• The site has water rights issues that prevent building a dam

Consider other options when:

• There’s even a few feet of available head — a breastshot or overshot wheel extracts far more power
• The stream is slow and shallow — insufficient current velocity means little power from undershot
• You need maximum power from limited flow — undershot wastes most of the energy

Minimum useful current speed: about 0.5-0.75 meters per second. Below this, the wheel barely turns. Above 2 m/s (swift river current), an undershot wheel starts to become practical for meaningful power.

Basic Design

Paddles (float boards): Flat boards projecting radially from the wheel rim, dipping into the stream. Simple, easy to make, easily replaced when worn or damaged. Typical dimensions: 2-3 feet wide (face), 12-18 inches deep radially.

Wheel diameter: Larger diameter = slower rotation = more torque, but also requires a deeper stream. The paddles should penetrate about 1/3 of their depth into the water (with the wheel axle well above the water surface). For a stream that is 2 feet deep at the mill location, a 10-12 foot diameter wheel with 18-inch paddles is appropriate.

Paddle spacing: 6-12 paddles evenly spaced for small wheels. More paddles produce smoother power (always some paddles in the water) but each paddle is narrower and weaker. 8 paddles is a common compromise.

Axle height: The wheel axle must clear the highest flood level. Build on elevated abutments on each bank with the wheel hanging between them. For seasonal flood rivers, the wheel should be able to be raised out of the water or removed before flooding.

The Poncelet Wheel: Improved Undershot

Jean-Victor Poncelet (1788-1867) analyzed the losses in traditional undershot wheels and designed an improved version that achieves 55-65% efficiency — far better than flat paddles.

Key innovation: Curved, concave buckets instead of flat paddles. The buckets receive the jet of water without impact loss (the bucket velocity at entry should equal the water velocity, so the water “slides in” smoothly). The water decelerates smoothly in the bucket, transferring its momentum, then falls out with nearly zero residual velocity.

Bucket shape: A circular arc curve facing backward relative to wheel rotation, with entry angle about 20-30° from horizontal. Water enters tangentially, rises slightly in the bucket, decelerates, and exits near zero velocity. This is the same principle as the overshot wheel buckets but applied to kinetic energy rather than gravity.

Supplementary sill: A raised sill on the stream bottom below the wheel concentrates the stream flow into a jet directed at the wheel buckets. This sill (a simple masonry or plank dam) is much smaller than a full mill dam but significantly increases the velocity of water reaching the wheel. The Poncelet wheel is really a low-head reaction wheel that combines the best features of undershot and breastshot designs.

Construction: Same as flat-paddle undershot, but buckets require more careful shaping. A wooden template for the bucket curve ensures consistency across all 16-24 buckets.

Installation and Channel Design

Stream channeling: For any undershot wheel, narrowing the stream channel under the wheel increases current velocity. Build masonry or timber wing walls tapering the stream from its full width to slightly narrower than the wheel face. A narrowing to 80% of the natural channel width increases velocity by 25% (continuity equation: same flow through smaller area = faster flow).

Flashboards: Removable planks in the tailrace that raise the downstream water level slightly, increasing the effective head difference across the wheel. Adding even 6 inches of effective head to an undershot wheel can increase power by 30-50%. Many historical undershot mills used flashboards to fine-tune performance.

Flood management: The wheel must survive floods. Options:

• Raise the entire wheel clear of floodwaters before they arrive (requires a mechanism to lift or disassemble the wheel)
• Design the wheel to withstand being submerged (sturdier construction, no damage from debris passing through)
• Site the mill away from the flood zone with water delivered by a channel

Seasonal variation: River current varies with season. Design for minimum useful current; excess current in wet season simply drives the wheel faster (with more power). If current becomes dangerously high (flood), reduce the number of paddles in the water by raising the wheel or closing a diversion gate.

Maintenance

Paddle replacement: The most common maintenance. Paddles erode and break from impact with debris. Design paddles as bolted-on replaceable units, not integral to the wheel frame. Keep spare paddle boards cut and shaped, ready to swap in.

Axle and bearings: Undershot wheel axles run in bearings above the water. Protect from splash by a simple housing. Grease frequently (weekly for working mills) since the bearing environment is damp.

Debris management: The biggest operational problem. Logs, branches, and other floating debris can break paddles, jam the wheel, and in floods, carry enough force to demolish the entire mill structure. A trash rack (vertical bars) upstream of the wheel catches debris; someone must clear it regularly. During active flood, close gates and let flood pass without the wheel turning.