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The strange world of Falkirk Wheel Statistics

Where the comparison of the Falkirk Wheel to Buses, Elephants and Kettles, came from I don't know, but it certainly has stuck, being repeated in numerous places. It doesn't help that not all the statistics agree, so here are my version of the statistics.

8 buses high

A good analogy, in its heyday Alexander's of Falkirk produced world class buses and coaches. A double decker bus is just over 4 metres high, the Falkirk wheel is 35 metres high, or across. However the difference in water level between the canals is only 24 to 25 metres. If you also consider that when rotating the lower part of the wheel sinks into a dry well in the lower basin, then the visible height of the structure is about 30 metres. Believe me, you have to see it, sitting in its natural amphitheatre the structure is truly impressive whatever size it actually is.

Can carry 100 African elephants

Where did that come from, left field? There is no connection between elephants and the Wheel. I donít thing so anyway. African elephants are bigger than Asian (or Indian) ones, adults are between 4 and 7 tonnes, so were talking 600 tonnes here, very heavy. Thatís 50 elephants going up as 50 come down, what a thought! Various figures are quoted for weight, 1800 tonnes for the total rotating mass, 80 tonnes for dry caissons or gondolas, and 300 tonnes for each caisson. A figure of 250000 litres of water per gondola is also mentioned. This all suggests to me that the gondolas are 50 - 80 tonnes dry and 300 tonnes wet or laden.

Uses the power of 2 kettles to rotate

This is the one that blows me away, even as an engineer I find this difficult to believe. There must be some huge Victorian style engine-room beneath the 21st century styling, making this thing work, mustn't there? In the UK kettles come in two types, normal 2Kwatt, and fast boil 3Kwatt, so we are looking for less than 6Kwatt (or 6, 1 bar electric fires). Lets look at this in a bit more detail, there are two things you need to overcome to make the wheel rotate, lets look at them one at a time:

Lifting Water

Now the wheel is in "perfect balance", so simplistically there is no work done in rotating the wheel, as one gondola rises the other falls. This is even so when there are boats in the caissons since they will displace their own weight in water, and balance will be maintained. But in the real world there will always be imbalance.
 

The intention is to keep the water levels in the caissons within 37.5mm, the operating difference. The plaque shown left, attached to the caisson itself indicates the maximum difference. There is a pumping mechanism to achieve this, although it it unclear whether this is in the caisson, the basin and aqueduct, or both. Anyway the worst case is that you need to lift 37.5mm of water 24 metres from the basin to the aqueduct in approximately 7 minutes. Spread over the surface area of the caisson this "extra" adds about 6000 litres or 6 tonnes to the caission.

The force (Newtons) required to lift 6000Kg is m x g 6000 x 9.81 = 58860 Newtons
The work done (joules) is force x distance 58860 x 24 metres = 1.41 Mjoules
Power (watts) is work done / time 1412640 / (7x60) = 3360 watts (3.4 Kwatts)

This is the average power for the lift, but the power will vary as the weight swings out in a semi circle. The maximum power is proportional to the speed of vertical lifting, i.e. pi/2. The peak lifting power is therefore 5.28Kwatts.

There is one factor I have not considered above, that is that you can only use the above water level rule for empty caissons. Boats in the caissons may displace their own weight in water but the water level will no longer be proportional to the difference in weight.

If your thinking of making one of these, remember to include a breaking device for when the water imbalance goes back down!

Friction

Friction is everywhere, tell that to the perpetual motion machine designer. It makes everything that moves slow down and everything that is stationary difficult to move. The force needed to overcome this friction and to overcome the weight imbalance in the water (covered in the last paragraph), is called torque. You have to expend energy to overcome the torque. This energy is lost in heating up the world. Eureka Findlay say that the torque required is very low, 2972KNm, because of the advanced bearing technology used on the wheels main axle. It is not clear whether this figure is for the bearings alone, or whether it takes account of the water lifting. However the torque created by lifting the water is:

6000Kg being lifted via a radial arm of 15 metres 6000 x 15 = 90 KNm

This is so low compared with the 2972KNm from the bearings as to be negligible in our consideration.

So the power required to overcome a torque of 2972KNm is:

Power (watts) is Torque/time (7 minutes) 2972000/(7x60) = 7076 watts (7Kwatts)

Because it is not clear whether the torque figure is to overcome friction alone, or friction plus the weight of water, then our answer varies from 5 to 12 Kwatt, 2 to 4 kettles. In any event the power requirement is surprisingly small, for two main reasons, the wheel is perfectly balanced, and the rotational speed is comparatively slow.

You can see more details on the hydraulic motors used to achieve this in the Drive Chamber.

QED.