1. Energy for the Lower East Side Alannah Bennie, James Davis, Andriy Goltsev, Bruno Pinto, Tracy Tran

2. Outline Introduction Motivation Methodology Results Impact

3. Problem We want to harness the power of tidal currents into energy that can be used as electricity How many turbines can we put into the East River around downtown Manhattan to power the Lower East Side?

4. Why Tidal Energy Tidal energy is a clean alternative that we can use efficiently without harm to the environment Highly reliable: Tides will always exist due to the gravitational forces exerted by the Moon, Sun, and the rotation of the Earth Predictable: The size and time of tides can be predicted very efficiently

5. What are tides? Tides – the alternate rising and falling of the sea, usually twice in each lunar day at a particular place, due to the attraction of the moon and sun Currents generated by tides

6. Tides Flood tide – tide propagates onshore High tide – water level reaches highest point Ebb tide – tide moves out to sea Low tide – water level reaches lowest point Slack tide – period of reversing wave (low current velocity)

7. The East River Not a river A tidal strait connecting the Atlantic Ocean to the Long Island Sound Semidiurnal tides Flow of the river What makes up velocity Direction

8. Background Our region is bounded by: (40.715 N,73.977 W) (40.707 N,73.997 W) (40.704 N,73.996 W) (40.708 N,73.976 W)

10. Background Video of Tidal Turbine Size of turbine Each turbine has a rotor diameter of 4 meters Type of turbine Modeled after turbines used by Verdant Power (2007) Efficiency We are looking at a turbine efficiency of around 40%

11. Methodology Data from the National Oceanic and Atmospheric Administration (NOAA) Tidal velocity Daily 2007-2011

12. Monthly Mean Tidal Velocities

13. Methodology Use polynomial interpolation to gather a velocity field Interpolation is a method of constructing new data points within the range of a discrete set of known data points. Polynomial interpolation is the interpolation of a given data set by a polynomial

14. Polynomial Interpolation Since we are working with four data points, we need to find a third degree polynomial of the form: Thus, given any set of coordinates in our region, (x,y), we can use this polynomial to determine the velocity at that point P(x,y) = a 0 + a 1 x+ a 2 y+ a 3 x 2 + a 4 xy+ a 5 y 2 + a 6 x 3 + a 7 x 2 y+ a 8 x y 2 + a 9 y 3

15. Polynomial Interpolation Because we know the velocities at our four collection points, we will use polynomial interpolation to find a set of polynomials which go exactly through these points

16. Polynomial Interpolation Begin by defining the matrix that will be used to create our interpolating polynomials The matrix is a 4 x 10 since there are 4 data points with coordinates and 10 terms in the polynomial that we are seeking

17. Polynomial Interpolation Now create a system of equations, so that we can solve for the coefficients of our interpolating polynomials Here is the average tidal velocity at

18. Polynomial Interpolation Finally, we have found our coefficients and therefore our interpolating polynomials Since we looked at the average tidal velocities (mps) per month over the course of 5 years, we have 12 separate polynomials (one for each month) We can use these polynomials to find the velocity at any location in any month

19. Our Polynomials P 1 [x,y] = 0.000299263 + 0.00984117 x + 0.362105 x 2 + 15.4992 x 3 + 0.0120129 y + 0.200942 x y + 0.679683 x 2 y + 0.366569 y 2 - 14.844 x y 2 + 5.37202 y 3 P 2 [x,y] = 0.000289367 + 0.00957213 x + 0.35658 x 2 + 15.4945 x 3 + 0.0115257 y + 0.191041 x y + 0.67966 x 2 y + 0.348566 y 2 - 14.8392 x y 2 + 5.37048 y 3 P 3 [x,y] = 0.000288423 + 0.00954475 x + 0.355857 x 2 + 15.4786 x 3 + 0.0114819 y + 0.190195 x y + 0.678976 x 2 y + 0.347027 y 2 - 14.8239 x y 2 + 5.36498 y 3 P 4 [x,y] = 0.000281853 + 0.00937133 x + 0.352788 x 2 +15.5226 x 3 + 0.01115 y + 0.183318 x y + 0.681046 x 2 y + 0.334526 y 2 - 14.8659 x y 2 + 5.38031 y 3 P 5 [x,y] = 0.00029242 + 0.00965699 x + 0.358498 x 2 + 15.5127 x 3 + 0.011673 y + 0.193988 x y + 0.680411 x 2 y + 0.353925 y 2 - 14.8568 x y 2 + 5.37678 y 3 P 6 [x,y] = 0.000297207 + 0.00978715 x + 0.361172 x 2 + 15.5152 x 3 + 0.0119087 y + 0.198776 x y + 0.680429 x 2 y + 0.362631 y 2 - 14.8593 x y 2 + 5.37758 y 3 P 7 [x,y] = 0.00029066 + 0.00960398 x + 0.356925 x 2 + 15.4654 x 3 + 0.0115946 y + 0.192525 x y + 0.678349 x 2 y + 0.351262 y 2 - 14.8114 x y 2 + 5.36038 y 3 P 8 [x,y] = 0.00029513 + 0.00971291 x + 0.35798 x 2 + 15.3541 x 3 + 0.0118348 y + 0.197724 x y + 0.673347 x 2 y + 0.360707 y 2 - 14.7051 x y 2 + 5.32176 y 3 P 9 [x,y] = 0.000282421 + 0.00938159 x + 0.352511 x 2 + 15.4761 x 3 + 0.0111863 y + 0.184186 x y + 0.67898 x 2 y + 0.336101 y 2 - 14.8214 x y 2 + 5.36418 y 3 P 10 [x,y] = 0.000279165 + 0.00929402 x + 0.350803 x 2 + 15.4833 x 3 + 0.0110244 y + 0.180872 x y + 0.679356 x 2 y + 0.330076 y 2 - 14.8281 x y 2 + 5.36669 y 3 P 11 [x,y] = 0.000291449 + 0.00963447 x + 0.358401 x 2 + 15.5473 x 3 + 0.0116189 y + 0.19279 x y + 0.681959 x 2 y + 0.351751 y 2 - 14.8898 x y 2 + 5.38879 y 3 P 12 [x,y] = 0.000292155 + 0.00965048 x + 0.358429 x 2 + 15.5188 x 3 + 0.0116588 y + 0.193682 x y + 0.680686 x 2 y + 0.35337 y 2 - 14.8626 x y 2 + 5.37891 y 3

20. Polynomial Interpolation Our polynomials appear similar which is due to the fact the tidal velocities have minimal seasonal change This was verified when we plotted our contour maps of the velocities and saw that they all looked the same

21. Tidal Velocity Contour (mps)

22. Polynomial Interpolation Pros No error at the data points Easy to program Able to determine an interpolating polynomial just given a set of points Cons It is only an approximation Accuracy dependent on the number of points you interpolate Not the best technique for multivariate interpolation

23. Placement of the Turbines Each Turbine needs to be approx. 9.8 – 24.4 meters (32-80 ft) apart (Verdant Power, 2007) 1 degree of latitude = 111047.863 meters (364330.26 ft) 1 degree of longitude = 84515.306 meters (277281.19 ft) We decided to place the turbines 12.2 meters (40 ft) apart

24. Placement of the Turbines Using Mathematica, given a min/max latitude and longitude we were able find all points that lie 40 feet apart from one another in a set area We then had to use basic mathematics to confine the points to our particular area

25. Placement of the Turbines Using the fact that the line thru pt1 and pt2 y = -5.80563 x + 310.327 line thru pt2 and pt3y = 0.327377 x + 60.6708 line thru pt3 and pt4 y = -5.70626 x + 306.265 line thru pt4 and pt1 y = 0.292453 x + 62.0709 We used these lines to constrain the points to our study area

27. Methodology In an optimal environment, the available power in water can be calculated from the following equation: = turbine efficiency = water density ( kg/m 3 ) A = turbine swept area ( m 2 ) V= water velocity ( m/s ) P = power (watts)

28. Facts Total number of homes in the Lower East Side: 1546 On average, a household in America uses 10,000 kWh per year Total energy needed: 15,460,000 kWh per year

29. Results Total number of turbines: 3794 Total energy from turbines: 21893.9 kWh Total power output in a year: 1.91791 × 10 8 kWh Total # of homes we could power in a year: 19179.1

30. Discussion Limiting parameters Velocity Turbine efficiency

31. Comparison Efficiency40%50%60%70%80%90% Power (kWh)21893.927367.432840.938314.343787.849261.3

32. Comparison Efficiency40%50%60%70%80%90% # of Homes19179.123973.828768.633563.338358.143152.9

33. Costs The turbines cost $2,000-$2,500 per kilowatt installed Total Cost for 3794 turbines: 44 - 54 million dollars Who pays: In 2010, conEd gained a revenue of 25.8 ¢ per kWh to residents and 20.4 ¢ per kWh for commercial and industrial. The average yearly revenue for residencies alone would be approximately 49 million dollars. conEd would start profiting from the turbines in about a year after they are installed.

34. Bibliography Hardisty, Jack. "The Analysis of Tidal Stream Power." West Sussex, UK: John Wiley & Sons, Ltd, 2009. 109-111. NOAA. Tidal Current Predictions. 25 1 2011.. Power, Verdant. The RITE Project.2007. 2011. Yun Seng Lim, Siong Lee Koh. "Analytical assessments on the potential of harnessing tidal currents for electricity generation in Malaysia." Renewable Energy (2010): 1024-1032.