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Tidal Power Density Assumptions

NOTE:

TIDAL FLOW IN BAY OF FUNDY = up to 3.28 m/s

The strongest flow in the Bay of Fundy region occurs through the Minas Passage, the relatively deep, thin channel that connects the Minas Basin to the Bay of Fundy.

The volumetric flowrate through the passage reaches roughly 106 cubic m/s and sustains time-averaged, depth-averaged tidal currents of up to 3.28 m/s.

http://www.math.mun.ca/~rhaynes/karsten_etal.pdf

Another approach for determining Peak Power Tidal Density has been made using Cumberland Sound GA data as shown below where the average annual Tidal Power Density was found to be 2,913 W / sq. m.

A common measure of the intensity of the hydrokinetic resource is kinetic power density (W/m2) which is given by:

K = .5 (p*F^3)

where, in this case, p is the density of seawater (nominally 1024 kg/m3) and F is the time-varying tidal flow speed (m/s).

The Northwest National Marine Renewable Energy Center at the University of Washington reports:

"In oceanographic terms, currents of 1 m/s are exceptionally strong, but currents at the most promising hydrokinetic sites may regularly exceed 4 m/s."

"For the purposes of feasibility assessment, kinetic power density is often reported as an annual average. The minimum economic threshold for site development is around 1 kW/m2 and for outstanding sites the kinetic power density may exceed 5 kW/m2."

http://depts.washington.edu/nnmrec/overview.html

The Tidal Power Density used in this calculator example is

3,000 W / sq. m

Tidal Turbine Efficiency Assumptions

The US office of energy efficiency and renewable energy in a paper available at:

http://www1.eere.energy.gov/water/pdfs/1023527.pdf

Reports on Tidal Device Efficiency:

Given that the Betz Law says that no more than 59% of the energy can be extracted by a turbine.

Then the overall efficiency has to be less that this,

and it is estimated that 45% overal energy efficiency (conversion of the total energy density) which is 76% of the 59% (Betz Law) turbine limit is reasonable for tidal stream turbines.

However if the much more experienced wind industry is actually achieving 26% efficiency then is is also reasonable that the new tidal industry is operating at a simialr efficiency.

Therefore for the purposes of the calculator example a 26% Tidal System Efficiency is being used.

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Extreme Tidal Location Example

(Bay Of Fundy = 3.28m/s at Minas Passage)

In this extreme tidal current location the flow estimated to be for 6,000 hrs per year (at avg. speed of 3.28 m /sec)

then: P = (.5*(1024* (3.28*3.28*3.28)) = 18,000 W / sq. m = 18 kW / sq. m / hr

times 6,000 hours per year = 108,000 kWh / year / sq. m

times .30 (for 30% Turbine Efficiency) = 32,400 kWh / year / sq. m

and at $.15 / kWh the income would be $4,860 per year / sq. m

if the cost of the tidal turbine system were $5,000 / sq. m

then this would be a very good & economical way to produce electricity.

TIDAL FLOW IN BAY OF FUNDY = up to 3.28 m/s

The strongest flow in the Bay of Fundy region occurs through the Minas Passage, the relatively deep, thin channel that connects the Minas Basin to the Bay of Fundy.

The volumetric flowrate through the passage reaches roughly 106 cubic m/s and sustains time-averaged, depth-averaged tidal currents

of up to 3.28 m/s

Recent surveys of potential tidal power sites have estimated the theoretical mean power of a flow through a channel, using a formula based on the kinetic energy flux in the undisturbed state

PKE = E (1/2 PU^3) (1)

where p is the density of water, E the cross-

sectional area of the channel and u the depth-

averaged, upstream current speed.

The term in brackets in equation (1) is the mean power density and is calculated by averaging u across the channel and over a tidal cycle.

In reference (3), a mean power density of 6.04 kW/m2 and a passage cross-sectional area of 2.74 x 106 m2 were used to give a power estimate of 1.9 GW for the Minas Passage, significantly less than the 10 GW estimate based on the mean potential energy.

From: http://www.math.mun.ca/~rhaynes/karsten_etal.pdf

Assessment of Tidal Current Energy in the Minas Passage, Bay of Fundy, R. Karsten, R.Haynes et al, Mathematics and Statistics, Acadia University, Nova Scotia, 2008