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Engines in Comparison In order to be able to categorize the Transverpello properly, it is best to compare its power output with that of other water-powered prime movers. Let us first check whether it is superior enough to the best known water-powered prime mover involving no damming, the stream wheel, to be worthwhile. In order to have the same energy preconditions, we will consider a working width of 10 metres with a depth of 3 m. Assuming a gradient of 0.25 per mille, in accordance with the intended use in flat country, then according to the Manning equation, there will be a speed of flow of 2 m/s. Let this be increased to 2.5 m/s in this case, by an increase in surface roughness factor, we don´t want the stream wheel to come out too badly in the comparison. The equation for the
power output of the stream wheel is:
Let the wheel width b be 10 m,
and the depth of immersion hs be a favourable
0.45 m;
then for a mechanical efficiency h of 0.8, we obtain an output of: Official government bodies in the U.S.A. test the barrage-free use of water power and its marketability now and after further development, using free flow turbines. Due to the analogy to
wind power and the form and space requirement of flow flumes, no more
than two rotors, each with a diameter of approx. two metres, could be
accommodated in the example. If we take the density of water as being
850 times that of air, the following equation results according to Betz: Physically, this would be four times as much as with the stream wheel. And now for the Transverpello: Let its hydrofoil be 17 m long, and have a height of 2.8 m For
a designed cambered section,
we derive an average coefficient of lift ca of
0.9 from the profile characteristic.
If the resultant path is 9 m, the time 13 s, and the efficiency is 0,7, than according to the Kutta – Joukowski aquation, the output is: This more than is ten times the output of the stream wheel, with no more time or effort being required for its construction. Although one should keep in mind that there can be no question of competing with prevailing turbine technology where the topography is favourable to them, or a dam serves other purposes besides generating electricity, let us compare on the purely physical level with it, too. The
rule-of-thumb formula for output is generally: The
rate of flow Q is calculated from the continuity equation as 60
m³/s; let the head be 2 m
for a Kaplan turbine here. Then So a Transverpello facility which produces the same performance as the turbine installation would have to consist of 16 modules of the size in our example. If one takes into account the fact that the Transverpello does without the entire barrage, with all its extensive construction and many accompanying elements, such as regulation of the groundwater, embankments to protect other people's property, design and maintenance of the slopes, fish ladders, fine screens, locks, consideration of the bed load, and various others, these sixteen might not be more expensive. After taking into account all the losses within the system itself - and for the turbine after converting the flow-rate into a theoretical head - the approximate hydroelectrical performance ratio between the stream wheel, the free-flow turbine, the Transverpello and the turbine is 1:4:10:30; adjusted according to cost, the respective benefit sinks to 1:3:8:5 and transposed into the lower MW range, the turbine's leading margin reduces to 1:3:8:8. The physical performance ratio can be altered to the benefit of the stream wheel by reducing the depth of the water while retaining a constant cross-sectional area, but after cost adjustments, this increase in the benefit is very small. In addition to its use in flatlands the Transverpello could also be an attractive alternative to the turbine in locations where a dam is undesirable due to ecological reasons. Lutz Kroeber 2007 Transverpello |