SLHS: Undershot Waterwheels

Is An Undershot Watermill Not Efficient ?

In this design, its name suggest, the headwater from the leet passes under the wheel (see the idealised diagram right).

Say the waterwheel is 4m in diameter and we’ll be generous in assuming that each paddle is perfectly sealed (which it definitely isn’t) and falls though a height of 1m. Then one would surely expect it to develop roughly 1/4 of the power of it’s overshot brother above ?

We can see what might be considered the paucity of the design if we look at where the headwater comes in. The top of the water level is at axel height. That is half the height of the wheel so 1m of available water height isn’t even used. One might assume therefore that 50% of the available energy is surely being wasted ?

In the big scheme of things one might think if there’s loads of water in winter who cares ? However outside of that time water isn’t so plentiful so why does this design work so well ?

Getting Mill Design Right

If any old carpenter bunged a wheel in the water it would certainly turn but constructing the whole building, the mill equipment and infrastructure to keep the grain flowing was an expensive business. Generally it took a wealthy family to set up a proper mill up and they would be looking for good profits on their outlay so it would be vitally necessary to bring a Mill Designer with excellent expertise and experience.

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Ideal Undershot Waterwheel ©Charlecote Mill

Efficient Undershot Watermills Are More Like A Turbine

Our assumption that the water at the bottom of the Control Gate just dribbles into the buckets, like an overshot wheel but underneath, is missing an important consideration. The higher the backed up water above the Control Gate the more the water squirts out the bottom of it at speed. This “Kinetic Energy’ pushes the waterwheel round more like a Pelton Turbine.

The equation for Kinetic Energy is:   E = 1/2 mv2          where  m = mass of the water   v = velocity of that water

This means that if the water speed, v, doubles one gets four times the energy !

This rule of thumb was the secret that the expereinced Mill Designers knew over those without the understanding including the mill owners themselves. This was their ‘black art’. Thus if the Control Gate is only lifted a little one doesn’t get much mass passing through but it’s moving fairly quickly. If one lifts it a little more then much more mass passes through and the water is ‘squirted’ though as quickly as it can. Lift it more and, whilst more mass passes though, the average water speed hardly increases so only a little more energy is available. Thus there is an optimum amount that the Control Gate should be lifted to get the most efficient extraction of power. Even modern turbine designers know this.

Thus if one wants to get more power then the gate shouldn’t be lifted higher but the gate and the waterwheel should be made wider ! Thus the Mill Designer has to ascertain how much water is available at this stretch of river and calculate the width of the water wheel accordingly- another one of his dainty arts !

If You Want More Power Should A Bigger Wheel Be Used ?

We are all aware of the variability of the river flow. Yet the Mill Designer needs his client’s mill design to be a one-size-fits-all flows ! Given the premise above he’d have to be a clever mill designer to make a wheel with variable width paddles and Control Gates and have them reliable for decades come. So what’s the answer ?

Well the answer quite simply is: To have two wheels. Albeit more expensive this has a large number of benefits:

A prime example of this is Charlecote Watermill..

Theory Behind Undershot Mills

Overshot Mills

Overshot Waterwheel

Pitchback Waterwheel

In layman’s terms let’s look at watermill designs. For completeness we will briefly look at overshot designs eventhough none exist in South Warwickshire.

Overshot Watermills Are Very Efficient

Water in an overshot mill (see near right) is fed at the top of the wheel and uses the weight of the water falling to turn the wheel due to gravity. Generally the water exits in the reverse direction that it came in. A second design turns the wheel in the reverse direction so that the water exits in the forward direction -usually continuing its course downhill.

Both get to be at least 90% efficient but require a large head height in the first place and that is rarely practical except in hilly places or where a considerably long leet exists.

For maximum efficiency the wheel needs to be as large as possible to use all the available height. This often means that the wheel will dip into the flow of the exit water. Thus that pool at the bottom must be made as shallow as possible otherwise the water flow will be slow and the wheel will drag in it reducing efficiency.

1. ADVANTAGES OF USING TWO WATER WHEELS
   

2. •greater efficiency than the one size fits all
   

3. •good use of low water availability in summer
   

4. •if something breaks there’s a whole spare system available
   

5. •enhancements, or routine replacement parts esp grindstones, can can be done while the other half operates (and your customers don’t get upset !)