Calculations

    By using data from the National Data Buoy Center, I was able to find the actual power contained in the waves at four sites around Hawaii (the only four in this general area sites that are monitored by NBDC equipment).  Using historical data graphs, I calculated the average yearly wave heights and average yearly wave periods for all four sites (a map of these sites can be found below).  With these values, I was able to calculate the actual power per unit width contained in the waves around Hawaii.

T = wave period    L = wavelength    H = waveheight  n = group velocity parameter   g = gravity  ? = density of water
 
 

*I used the deep water wave assumptions of:         L = 1.56*T^2    &    n = 0.5

 

			Year Average (Jan-Dec)
Location of buoy	Station ID	n	T (sec)	L (m)	H (m)	Power (watts)	Power (MW)	Efficiency
185 miles SE of Hilo, HI	51004	0.5	6.48	65.50502	2.47	37813.12196	0.037813122	29%
215 miles SSW of Hilo, HI	51002	0.5	6.34	62.70514	2.43	35807.6177	0.035807618	31%
205 miles SW of Honolulu, HI	51003	0.5	6.66	69.19474	2.29	33405.56465	0.033405565	33%
170 miles W of Kauai Island	51001	0.5	6.79	71.9224	2.46	39301.90591	0.039301906	28%

    Multiplying the power per unit width by the diameter of each PowerBuoy (4.5 m) and by the number of buoys in the system (20), I was able to find the actual power contained in the ocean along the projected width of the system.  Dividing 1 megawatt by this number gave me the efficiency for each location.  The average of was 30%.

    Upon finding this efficiency, I set out to find out where the PowerBuoy system's power generating abilities would be maximized.  Out of regional curiosity, I decided to first check some locations in the Great Lakes.  I chose one NDBC location in Lake Superior and one in Lake Michigan.  My results were just as I had expected:  if the same system with a 30% efficiency was installed at either one of these locations, it would require many more than 20 buoys at both spots to generate the target power output of 1 megawatt.  My results are shown below.

 

			Year Average (Jan-Dec)					efficiency = 30%
Location of buoy	Station ID	n	T (sec)	L (m)	H (m)	Power (watts)	Power (MW)	PowerBuoys needed for 1MW system
Lake Michigan- 43 miles SE of Milwaukee, WI	45007	0.5	3.3	16.9884	0.765	1847.18517	0.001847185	401
Lake Superior- 200 ENE of Hancock, MI	45004	0.5	3.7	21.3564	0.92	2995.373628	0.002995374	247

    I then calculated, using the same method as above, the number of PowerBuoys needed to generate 1 megawatt in two more locations around North America; off the East coast (54 miles southeast off Nantucket) and West coast (310 north off Adak, Alaska).  The locations and my results are shown below.
 

    These results show that Nantucket (and most likely a large portion of the eastern seaboard) is not a very economically viable location to install the PowerBuoy system.  Off the coast of Alaska (and perhaps other far northwestern offshore locations) is an even more economically viable  location for the system to be installed, requiring less than 20 PowerBuoys to generate the target 1 megawatt of power.

    Since the above calculations were all done using average yearly wave heights and wave periods, the results would vary during the summer months and winter months.  Winter months usually yield more intense wind patterns, thus raising the average height and period.  Summer months usually are more calm, having the opposite effect.  Below are my calculations for the same locations using the number of buoys previously calculated for each respective site.

   
 

			Summer Average (Jun-Aug)
	Station ID	n	T (sec)	L (m)	H (m)	Power (watts)	Power (MW)	PowerBuoys	Power generated by system in summer (MW)
185 miles SE of Hilo, HI	51004	0.5	5.9	54.3036	2.17	26573.27625	0.026573276	20	0.7174785
215 miles SSW of Hilo, HI	51002	0.5	5.9	54.3036	2.2	27313.1001	0.0273131	20	0.7374537
205 miles SW of Honolulu, HI	51003	0.5	6.1	58.0476	1.9	21062.53598	0.021062536	20	0.5686885
170 miles W of Kauai Island	51001	0.5	5.83	53.022684	1.93	20770.97083	0.020770971	20	0.5608162
Lake Michigan- 43 miles SE of Milwaukee, WI	45007	0.5	2.75	11.7975	0.43	493.1534885	0.000493153	401	0.2669686
Lake Superior- 200 ENE of Hancock, MI	45004	0.5	2.65	10.9551	0.35	310.4956969	0.000310496	247	0.1035348
54 miles SE of Nantucket, MA	44008	0.5	5.93	54.857244	1.13	7242.44496	0.007242445	46	0.4497558
310 miles N of Adak, Alaska	46035	0.5	5.77	51.936924	1.57	13603.43986	0.01360344	17	0.3121989

 
 

			Winter Average (Nov-Feb)
	Station ID	n	T (sec)	L (m)	H (m)	Power (watts)	Power (MW)	PowerBuoys	Power generated by system in winter (MW)
185 miles SE of Hilo, HI	51004	0.5	7	76.44	2.8	52491.348	0.052491348	20	1.4172664
215 miles SSW of Hilo, HI	51002	0.5	6.88	73.841664	2.79	51223.64369	0.051223644	20	1.3830384
205 miles SW of Honolulu, HI	51003	0.5	7.5	87.75	2.69	51908.61561	0.051908616	20	1.4015326
170 miles W of Kauai Island	51001	0.5	7.75	93.6975	3.11	71696.19432	0.071696194	20	1.9357972
Lake Michigan- 43 miles SE of Milwaukee, WI	45007	0.5	4	24.96	1.25	5977.96875	0.005977969	401	3.2361734
Lake Superior- 200 ENE of Hancock, MI	45004	0.5	4.6	33.0096	1.5	9899.51625	0.009899516	247	3.3009937
54 miles SE of Nantucket, MA	44008	0.5	6.3	61.9164	2.17	28374.8543	0.028374854	46	1.7620785
310 miles N of Adak, Alaska	46035	0.5	7.325	83.702775	3.65	93339.82472	0.093339825	17	2.142149

    As expected, more than the target 1 megawatt of power is produced during the winter and less than 1 megawatt during the summer.  This creates a potential problem if communities were to become reliant on this form of power.  Ocean Power Technologies claims that it is feasible to store the power transmitted to the shore as electricity in a battery, eliminating the problem of high and low periods of productivity.
 
 

back