RESOURCE AVAILABLE
Information used for the purpose of this study is obtained from the Sarawak tidal stream tables; Sarawak hourly high and low tides tables, nautical charts, and onsite measurement.
THE SARAWAK TIDAL STREAM TABLES 2006
The Sarawak Tidal Stream Tables (known as stream tables in this report) was published by the Director of Marine, Sarawak, Malaysia back in year 2006. The tidal stream tables record the tidal stream flow rates for seven stations off the coast of Sarawak. These stations are known as Off Tanjung Po, Off Kuala Paloh, Off Kuala Rajang, Off Tanjung Sirik, Off Kuala Igan, Bintulu Port and Off Kuala Miri. Observations on these stations were carried out for a period of 14 days to 36 days. Their geographical locations are tabulated in Table 3.9.1.
STATIONS 
LATITUDE 
LONGITUDE 
OBSERVATION PERIOD 
Off Tanjung Po 
01° 48’ 00” N 
110° 33’ 00” E 
36 days 
Off Kuala Paloh 
02° 30’ 34” N 
113° 57’ 54” E 
36 days 
Off Kuala Rajang 
02° 07’ 32” N 
113° 00’ 04” E 
31 days 
Off Tanjung Sirik 
02° 55’ 00” N 
111° 45’ 00” E 
31 days 
Off Kuala Igan 
03° 37’ 00” N 
111° 30’ 00” E 
35 days 
Bintulu Port 
03° 15’ 46” N 
111° 01’ 37” E 
14 days 
Off Kuala Miri 
04° 23’ 52” N 
111° 08’ 41” E 
20 days 
Table 3.9.1: Geographical locations of the seven examined stations.
The analysis and prediction tasks for the tables are carried out by the Sarawak Marine Department (SMD). The tables illustrate the hourly tidal stream flows at the maximum rates (measured in knots), the flows direction (measured in degree) and the moon age (depicted by symbols). Figure 3.9.1 shows a tidal stream table for station Off Tanjung Po in February. As observed in Figure 3.9.1, the maximum speed of the tidal stream was recorded as 0.4 knots at hour 1100, 2nd February 2006, with a 13 degree in directions. The moon age consists of four stages, namely the new moon, the first quarter moon, the full moon and the last quarter moon. For instance, the first quarter moon happened on the 5th day of the month.
Figure 3.9.1: A screenshot of tidal stream tables published by the Director of Marine Sarawak.
SARAWAK HOURLY AND LOW TIDES TABLES 2008
The high and low tides tables (known as tide tables in this report) are compiled and published in a yearly basis by the Director of Marine Sarawak. The predictions had taken into account only the average seasonal variations which are largely meteorological.
Observations were performed mainly by the marine department but not all. A few other institutions were also involved in the observations work including Sarawak Land and Survey Department and the Directorate of National Mapping. Period of observation varies from 2 months the shortest to the longest 2 years.
Tides in Sarawak are mostly semidiurnal which means there will be two high and two low waters every day. Tides on the Atlantic coast of the United States are of the semidiurnal type. A diurnal tide on the other hand has only a single high and single low water occur each day. Tides in Kuala Baram, Kuala Niah, Kuala Similajau, Pelabuhan Bintulu, and Tanjung Kidurong are usually diurnal.
NAUTICAL CHARTS
Information about the speed of tidal stream is not accessible from available nautical charts. However, the charts give a quick appreciation of the physical characteristics of the sites.
READINGS OBTAINED FROM DIRECT MEASUREMENT
A current meter is deployed 5 meter below the water surface and is scheduled to log a reading of the speed of the stream every 5 minutes at the river mouth of Batang Lupar. The first reading is taken in the afternoon of 13May2010 and the meter logs for 50 hours nonstop.
FUNDAMENTAL TO TIDAL STREAM ENERGY EXTRACTION
The kinetic energy flux in a water channel is proportional to the cube of the speed of the water passing through the channel. The energy flux can be expressed as follows:
In the above equation, ρ is the density of sea water in kg/m3; U is the speed of tidal stream in m/s; A is the crosssectional area of the channel in m2.
Equation 1 can be simplified to express the kinetic energy flux without taking into consideration the crosssectional area. An energy flux without considering the crosssectional area is termed ‘density’. Finding a ‘density’, instead of a ‘flux’ for each of the site is the objective of this report. At times, the phrase “power density” is used instead of “flux density” and they can both be expressed as follows:
Equation 2 can be represented as in the following figure.
Figure 32: Presentation of kinetic energy flux density against the speed of tidal stream.
TERMINOLOGIES
The relationship between speed and energy is the fundamental idea behind this report.
The speed of the tidal stream reveals the available physical energy a site has. The phrase ‘kinetic energy flux’ will be used throughout this report to indicate power. The term ‘speed’ is used instead of ‘velocity’ to avoid confusion arises from the direction of tidal stream though many times a negative velocity denotes ebb and a positive velocity denotes flood.
Reports that were prepared by various parties were examined and found to have been using different terminologies for speed or perhaps even different types of speed. Examples of them are “average peak”, “mean spring peak”, and ‘peak’. Care has to be taken when choosing the type of speed to use for calculation because energy is related to the cube of the speed, as being expressed in Equation 1. Therefore, a small difference in the magnitude of speed will pose a significant difference in the calculated energy.
Some of the reports had not defined the kind of speed used but it is believed that ‘peak’ speed refers to absolute maximum speed (i.e., the highest speed that occurs for a few minutes or hours per year). For the purpose of this report, ‘speed’ indicates “average flood or ebb peak” as in accordance to the EPRI report.
On top of that, the terms ‘stream’ and ‘current’ though are interchangeable but for the consistency of this report and the ease of reading, only one single term is used throughout this report. The term ‘stream’ is chosen arbitrarily.
Site Screening and the Acquiring of Information
SITE SCREENING AND THE ACQUIRING OF INFORMATION
It has been stated earlier that the physical appearance of a site can be made a parameter for assessing tidal energy, as according to DTI and Robert Gordon University. It has also been proven by a few other reliable reports, including EC96, ETSU93, the Black and Veatch, the EUSUSTEL, the MERG, and the EPRI that the speed of the tidal stream can be used as a criterion to decide if a site has a potential for economic energy extraction.
The Director of Marine Sarawak or Jabatan Laut Sarawak (thereafter JLS) had published a set of tidal stream tables for seven sites in Sarawak in year 2006. The tables show the hourly speed of tidal stream at seven different sites throughout the year. The peak speed at each site is investigated to see if any one of them meets the 1.5m/s desired speed.
EXTRAPOLATION OF THE SPEED OF THE TIDAL STREAM
The speed increases when a stream enters a narrow channel from a wide channel. In the event that the measured speed of the stream is taken at the wider channel but the channel which is narrower seems to have a faster stream, it is possible to get the speed of the stream at the narrow channel without taking measurement at the site. Such approach to obtain the speed of the stream at different places is termed ‘extrapolation’. In this report physical channels are not assumed.
ACCOUNTING FOR DEPTH VARIATIONS IN SPEED
For a site to be considered suitable for turbine deployment, the site must be able to have a minimum of 15m depth left for the turbine. Added to the clearance needed for vessels and at the bottom, it is obvious that the site must be deep enough before it can be considered suitable. The following table summarizes all.
The speed of tidal stream varies from the surface of the sea to the bottom of the sea. A 1.5m/s speed on the surface does not necessarily imply a 1.5m/s speed at 20m below the surface. The speeds acquired from the tables published by JLS are examples of “surface speed”.
The variation of speed as according to the depth may be complex but has become common to be represented as follows:
Where:
U x is the horizontal component of the speed for tidal stream at x
ξ is the vertical distance above the seabed,
h is the depth of the water, and
w is the coefficient of power law
(Bryden et al, 2007)
There are a number of laws that illustrate the variation of speed as according to the depth. The Two commonly used power laws are the 1/7th and the 1/10th power laws. EPRI [7] chose to use the 1/10th law while Bryden et al (2007) [6] in his attempt to show the drawback of using surface speed to calculate extractable energy chose to use the 1/7th law. The coefficients used for both laws are shown in Table 3.14.
SOURCE 
POWER LAW 
COEFFICIENT OF POWER LAW, w IN EQUATION 3 
EPRI [7] 
1/10th 
10 
Bryden and Couch (2007) [6] 
1/7th 
7 
Table 3.12 (a): The power laws and the relevant coefficients. There is no such thing as which of the power law prevails. The use of power laws brings the overestimation of extractable energy to a lesser extent.
If the speed of the tidal stream is known to be 3 m/s at a depth 5m below the surface in a place where the depth of the sea is 25m, the constant, Const in the above equation can be easily obtained.
U x = 3m/s
ξ= 25m – 5m = 20m (remember this is the elevation from the bed of the sea)
h = 25m
w = 7, if the 1/7th power law is used.
Equation 3 becomes:
And therefore,
Const = 3.10
By substituting the constant value of 3.10 into Equation 3, the equation transforms to
By using this constant value of 3.10, the speeds of the tidal stream at various depths pertaining to that particular column of water are obtainable. The speed at 10m below the surface is therefore:
Both the EPRI [7] and Bryden et al (2007) [6] were in no way suggesting which law is the better. In fact, it is conceivable to use just a single power law throughout the tidal cycle because different power law sets in at the different stages of the tidal cycle. However, as a first approximation, a single power law might suffice (Bryden et al, 2007 [6]).
Instead of using the surface speed for the calculation of energy, which was proven to result in a substantial over estimate of the energy, the use of a “depthaveraged speed” result in a relatively ‘satisfactory’ deviation. The 1/10th law is chosen for use in this report. The “depthaveraged speed” can be derived as follows:
Let the horizontal speed of the tidal stream at some depth z be expressed as:
Where,
U0 is the reference speed at z
z is vertical distance above seabed, and
z0 is the reference depth
In the case above a 10th power law is used. For any reference velocity and depth, the depthaveraged speed is given by:
Let U0 be the surface speed and therefore the reference depth, z0 is equal to the depth of the sea (or channel). In such a case, h2 – h1 is also equal to z0 where h1 is zero. This gives:
The depthaveraged speed is therefore 90.9% of the surface speed. The depthaveraged speed if the 1/7th power law is used can also be derived in the same manner. A summary of the depthaveraged speed is given in the following table.
SOURCE 
POWER LAW 
COEFFICIENT OF POWER LAW, w IN EQUATION 3 
DEPTHAVERAGED SPEED, u 
E 
1/10th 
10 
90.9% of “surface speed”. 
Bryden and Couch (2007) [6] 
1/7th 
7 
87.5% of “surface speed”. 
Table 3.12 (b): The depthaveraged speeds for the power laws.
POWER LAW 
SURFACE SPEED, m/s 
DEPTHAVERAGED SPEED, ū > m/s 
KINETIC ENERGY FLUX DENSITY, Wm2 (EQUATION 1)

1/10th 
0.51 
=0.51*0.909 
=0.5*1024*0.46^3 
1/7th 
0.51 
=0.51*0.875 
=0.5*1024*0.45^3 
Table 3.12 (c): It is summarized in this table the use of “depthaveraged speed” in the calculation of kinetic energy flux density. The surface speed used is the actual peak speed found at Off Kuala Igan.
CROSSSECTIONAL AREA
Crosssectional area is one part of Equation 1. Integrating the area of a particular channel tells the total kinetic energy flux that particular channel has. As no crosssectional area is assumed in this report, a ‘density’ will be calculated instead. A numerical representation of density is expressed by Equation 2.
An assumption made throughout the EPRI report is that the speed of the tidal stream remains constant across the width of the channel. This assumption will overestimate the available energy because the speed is always lower at areas close to shore, as compared to at the middle of the channel. The EPRI report claimed that the assumption was necessary in the absence of other data and shall have no impact towards the relative resource ‘ranking’ of the sites investigated.
The word ‘ranking’ indicates the order in which the sites are arranged based on the total amount of energy the sites have. As all sites feel the same degree of overestimation, the order in which the sites are arranged will be the same as in the case where no assumption of constant speed is made. However, it has to be careful when making claim of the amount of tidal energy a site has as the amount claimed will always be larger than the actual value.
The assumption made by the EPRI report is equally applicable to the report presented here such that the available and the extractable tidal energy that the amount of energy obtained at the end of this report will be larger than the actual value.
CALCULATING AVAILABLE RESOURCE
The available resource of each site is the sum of instantaneous flux density throughout the year. Again, a ‘density’ is calculated instead of ‘flux’ because no physical channels are assumed in this report and thus the ‘areas’ which will be needed for the calculation of ‘flux’.
An example of how the density is calculated can be explained as follows:
Figure 3.16: A screenshot of the tidal stream tables published by JLS in year 2006. Off Kuala Rajang is one of the seven sites having published tidal stream data.
The speeds shown in the table are in knots and a conversion of unit from knots to m/s will therefore be needed. Also shown in the table are the coordinates of the site as well as the month of which the data is relevant to, and in this case, the month of July. The left most column shows the date and day whereas the top row represents hours. Numbers in italic are directions in degree and symbols right beside the day denote the age of the month.
At 0100 hr of July 11, 2006, the speed indicated is 0.6 knots or equivalent to 0.3m/s. The speed indicated is “surface speed’ and needs to be averaged. The depthaveraged speed based on the 1/10th law is:
The instantaneous kinetic energy flux density, as according to Equation 2 is:
Where 1024 is the density of sea water in kgm3.
The density of kinetic energy flux is calculated for all available speed and the sum contributes to the annual density. Only 15% of the available resource is allowed to be extracted so as not to pose any harm to the surrounding environment.
PRESENTATION AND INTERPRETATION OF RESULTS
PEAK SPEEDS AT SITES
None of the site has met the 1.5m/s requirement except for Pulau Triso at Batang Lupar. The highest speed recorded is 2.06m/s on 15May2010 at 08:52:29. About 28% of the readings logged throughout the 50 hours period exceeds the 1.5m/s threshold. On the 14th alone, about 27.7% of the readings recorded exceeds the 1.5m/s requirement. The longer the tidal stream stays at its peak speed, the more the energy can be extracted. The following table summarizes the peak speeds observed for all eight sites.
SITES 
COORDINATES 
PEAK SPEED, m/s 


Lat 
Long 
Throughout year 2006 (Except for Pulau Triso) 
Off Kuala Igan 
03° 37’ 00” N 
111° 45’ 00” E 
0.51 
Off Kuala Rajang 
02° 07’ 32” N 
1 11° 01’ 37” E 
0.36 
Off Tanjung Po 
01° 48’ 00” N 
110° 33’ 00” E 
0.36 
Off Kuala Paloh 
02° 30’ 34” N 
111° 08’ 41” E 
0.41 
Off Tanjung Sirik 
02° 55’ 00” N 
111° 30’ 00” E 
0.36 
Off Kuala Miri 
04° 23’ 52” N 
113° 57’ 54” E 
0.21 
Bintulu Port 
03° 15’ 46” N 
113° 00’ 04” E 
0.15 
Pulau Triso (Batang Lupar) 
01° 30’ 45” N 
110° 57’ 55” E 
2.06 
Table 3.17: The peak speeds at sites. The peak speed is the highest speed of tidal streams at sites as according to the predictions made in the tidal stream tables published by the Director of Marine and the direct measurement conducted at Batang Lupar.
CLEARANCES AT SITES
A site has to be deep enough for a turbine to be safely deployed. The water space left for turbine shall ideally be equal or larger than the minimum rotor diameter of 15m. The site Off Kuala Igan is the only site meeting the depth requirement. Table 3.18 (a) summarizes all.
Table 3.18 (a): Clearances required for vessels and for the deployment of turbines. The MLLWs were obtained from the tide tables published by the Director of Marine. The top clearance is 15m for oceangoing vessels. The bottom clearance is 1/10 of MLLW. The depths of the sites were obtained from the nautical charts published also by the Director of Marine. The reference numbers of the charts are indicated in column ‘Chart#’. The column “Space left for turbine” indicates the available space for turbines to be deployed safely.
None of the site has met the depth requirement except Off Kuala Igan. Though the MLLW of the site Off Kuala Igan was unavailable, but as the “bottom side requirement” contributes little to the total clearance, the site is considered to have met the depth requirement.
The MLLWs were extracted from the tide tables, not the stream tables. The predictions found in the tide tables and also the stream tables refer to different sites or ‘ports’. Although the name of the sites may not be the same in both tables but because some of the sites are in vicinity to each other, it is deemed appropriate to associate the data from the tide tables to the sites listed in the stream tables.
The MLLWs used in Table 3.18 (a) for the seven sites investigated by this report were extracted from the tide tables by using those sites that are located close enough to the seven sites. The only site that turned out to have no close match to the sites listed in the tide tables was “Off Kuala Igan”. A close match of the sites can be found in the following table.
Table 3.18 (b): Comparison of sites published by Stream Tables and Tide Tables. Though both the tide tables and stream tables share different sites for prediction but many of them are in vicinity to each other.
The water depth as well as the MLLW for Pulau Triso is based on the observation made by JLS during when the measurement activities were carried out.
EXTRACTABLE ENERGY AT SITES
The energy calculated in this report is in term of ‘density’. A ‘density’ does not carry the meaning of total annual kinetic energy flux. A total annual kinetic energy flux is a product of ‘density’ and the ‘crosssectional’ area of the channel (if there’s any).
It has been mentioned earlier in this report that “The speed of the tidal stream reveals the available physical energy a site has”. If Pulau Triso (Batang Lupar) has the strongest stream of all, it is reasonable to believe that the physical energy possessed by the site shall be the largest.
The “extractable” flux density is calculated based on “depthaveraged speed”. The mean monthly density is obtained by averaging monthly density, excluding the odd maximum and minimum. The amount of flux density possessed by the month of February is always the least. The shorter days Februaries have shall explain. The flux density for Pulau Triso is not calculated. The duration of the readings does not extend to one entire month.
Table 3.19: The total available as well as the extractable energy each site possessed.
Figure 3.19 (a): Peak speeds at sites (illustrated).