Andy Philpott, Geoff Leyland Department of Engineering Science University of Auckland CULMS/CMCT Lecture, September 28, 2010 Kevin Biggar Jamie Fitzgerald History 1896 Harbo and Samuelson (Norway) 55 days (NY to Scilly Is) 1969 John Fairfax (UK) 180 days (to Florida) Canary Islands to Barbados - 4800 km (2600 nm) 1986 Sean Crowley and Mike Nestor (UK) 73 days 1997 Rob Hamill and Phil Stubbs (NZ) 41d 2:55 2001 Matt Goodman and Steve Westlake (NZ) 42d 2:16 2001 Stephanie Brown and Jude Ellis (NZ) 50d 7:00 2003 Kevin Biggar and Jamie Fitzgerald (NZ) ……… Naval Lieutenant and Professor of Meteorology Wrote “The Physical Geography of the Sea” (1855) Charts in the book took 30 days off the trip from London to California Great Circle Path Favourable Winds & Currents Darwin’s cousin Invented fingerprinting and studied meteorology Proc. Royal Soc., Vol 21 (1873) (with thanks to Stuart Norris) F. Galton, Proc. Royal Soc., Vol 21 (1873) No one seems to know how fast ocean rowing boats go Propulsive efficiency: – Bakewell-White estimated 25% – Australian Institute of Sport estimates 60-80% We constructed a rowing speed model modified by currents and winds Model was then calibrated with 2001 data An isochrone is a curve made of points a fixed time to or from a destination F. Galton, Proc. Royal Soc., Vol 21 (1873) F. Galton, Proc. Royal Soc., Vol 21 (1873) Galtonʼs algorithm Wind Galtonʼs algorithm Wind F. Galton, Proc. Royal Soc., Vol 21 (1873) Barbados Use estimated rowing speeds and October wind rose data Stochastic dynamic program (SDP) solved in wait-and-see mode over grid Value function contoured using Matlab If you know the minimum time T(y) to row from point y to Barbados for all y locations ahead of you, then the minimum time to row from your current point x is T(x)=miny {t(x,y) + T(y)} Dynamic programming recursion Richard Bellman Destination Time to finish (Scenario 1) A (10) Wind A 3+10 = 13 B (8) B 2+8 = 10 C (7) C 5+7 = 12 D 8+8 = 16 D (8) E 12+10 = 22 E (10) Destination Time to finish Time to finish A (10) (Scenario 1) (Scenario 2) A 13 12+10 = 22 B (8) B 10 8+8 = 16 C (7) C 12 5+7 = 12 D 16 2+8 = 10 D (8) E 22 3+10 = 13 Wind E (10) Destination Time (Scenario 1) Time (Scenario 2) Expected Time A 13 22 17.5 B 10 16 13 C 12 12 12 D 16 10 13 E 22 13 17.5 Min 10 10 10 \ 12 (to C) R.E.Bellman, Eye of the Hurricane, p182 In 1873, Galton identified the dual problem (using isochrones) Galton defined a state-feedback control policy using isochrones Galton identified a recursive procedure for computing optimal policy – starting from the final destination Galton appears to have misunderstood the exchange of expectation and minimization One big chart and six smaller charts on plastic laminate Compass rose printed on reinforced transparency Transparency pens GPS to give boat velocity Holiday Shoppe won in record time: 40 days, 5 hours and 31 minutes – (Nearly 1 day faster than previous record) Kevin Biggar: “The map was best piece of technology we had on the boat” The key ingredient in winning was using a policy rather than a fixed plan Holiday Shoppe row into headwinds Headwinds. CRC on sea anchor. CRC protested HS because “they sped up” inexplicably Our analysis and records of the race helped HS prove their innocence HS did not speed up, CRC slowed down “The panel concluded that the speed difference between the boats at the end of the race could be explained in a number of ways, including changes in rowing patterns, the steering mechanism, success in surfing the waves and the crew's condition.” (www.oceanrowing.com) .