The data shows the affects of current on boats of two different speeds. based on a tacking angle of 45 degrees the length of the upwind leg would be 2.5/COS 45 or 1.414 x 2.5 = 3.54 miles. I calculate the times for each boat to complete the course with their boat speed. Then using the PHRF ToT correction formula and ToD formula I calculate their corrected times. As can be clearly seen -- at Zero (0 ) current the race ends in a tie. Now as the current the boats are tacking against increases the advantage increases for the faster boat. Even using PHRF Time on Time. At one knot the faster boat has a 1.67 minute advantage ToD or 100 seconds. ToT has "recovered" some of this as the advantage is "only" 1.02 minutes. When the current and wind are opposite, the advantage shifts to the slower boat but only raching a maximum of .19 minutes or 11 seconds @ -.5 knots. At -1 kt the advantage has shifted BACK to the faster boat! **************************************************************************************** The effect of current on boats with different PHRF #'s By Roy H. Lewis barcode845@earthlink.net Version: PHRF4.EXE VERSION 1.0 3/27/2006 Boat speed based on 550 ToT factor used: 550 Average boatspeed = 3600/(PHRF + Wind Factor) Average boatspeed is based on a windward/leeward course so the PHRF speed must be greater because the upwind leg is = length/Cos 45. True boat speed 'over the water' = Average speed * ((1/Cos 45)+1)/2 C.T. = E.T. * (Ave. PHRF + ToT Factor)/(PHRF + ToT Factor) PHRF 180 FASTBOAT's Average & True speeds 4.93 5.95 PHRF 240 SLOWBOAT's Average & True speeds 4.56 5.50 Sec/Mile difference: 60 Time on Distance adjustment: 5.00 Minutes Distance buoy to buoy: 2.5 Race distance: 5 Fast boat=5.95 Kts. VMG=4.21 Slow boat=5.50 Kts. VMG=3.89 <-------------------Times -----------------------------------------------> CURRENT F-UP F-DN Total S-UP S-DN Total Delta Error 1.00 46.74 21.57 68.31 51.91 23.07 74.98 6.67 Using ToT 71.12 72.14 -1.02 +++++++ Even using ToT, not Using ToD 53.31 54.98 -1.67 enough adjustment to 0.75 43.36 22.38 65.74 47.78 24.00 71.77 6.03 overcome effect of current Using ToT 68.44 69.05 -0.61 Using ToD 50.74 51.77 -1.03 0.50 40.44 23.25 63.68 44.25 25.00 69.25 5.57 Using ToT 66.30 66.62 -0.32 Using ToD 48.68 49.25 -0.57 0.25 37.89 24.18 62.07 41.21 26.08 67.30 5.23 Using ToT 64.62 64.74 -0.12 Using ToD 47.07 47.30 -0.23 0.00 35.64 25.20 60.83 38.56 27.27 65.83 5.00 Using ToT 63.33 63.33 -0.00 ++++++ Zero current Using ToD 45.83 45.83 0.00 Tie race ToT & ToD ! -0.25 33.64 26.30 59.94 36.24 28.57 64.80 4.86 Using ToT 62.40 62.34 0.06 Current & wind in Using ToD 44.94 44.80 0.14 opposit directions -0.50 31.85 27.51 59.36 34.17 30.00 64.17 4.81 advantage shifts to Using ToT 61.80 61.73 0.07 "slower" boat. Using ToD 44.36 44.17 0.19 But not as much ...... -0.75 30.25 28.83 59.08 32.33 31.57 63.90 4.83 Using ToT 61.50 61.48 0.03 Using ToD 44.08 43.90 0.17 -1.00 28.79 30.29 59.08 30.68 33.33 64.01 4.92 Using ToT 61.51 61.57 -0.07 ++++++ Eventually Using ToD 44.08 44.01 0.08 advantage shifts back to faster boat. Note 1: - Current: Current & wind in opposite directions. Note 2: Upwind VMG = 0.707X speed. Tacking angle 45 degrees. Note 3: Course length: 5.00 Distance sailed over the water: 6.04 Note 4: All times are in MINUTES. Race Distance = 5 Note 5: F-UP Fast boat's upwind time. F-DN Fast Boat's downwind time. S-UP Slow boat's upwind time. S-DN Slow boat's downwind time. Note 6: Error is based on boats should have tied in all races. - Error is advantage 180 PHRF boat has over 240 PHRF boat. *************************************************************************** This next simulated race is 2.5 miles between bouys and ther is NO tacking. i.e. as if the wind was on the beam both up and down. The effect of current on boats with different PHRF #'s By Roy H. Lewis barcode845@earthlink.net Version: PHRF4.EXE VERSION 1.0 3/27/2006 Boat speed based on 550 ToT factor used: 550 Average boatspeed = 3600/(PHRF + Wind Factor) Average boatspeed is based on a windward/leeward course so the PHRF speed must be greater because the upwind leg is = length/Cos 45. True boat speed 'over the water' = Average speed * ((1/Cos 45)+1)/2 C.T. = E.T. * (Ave. PHRF + ToT Factor)/(PHRF + ToT Factor) PHRF 180 FASTBOAT's Average & True speeds 4.93 5.95 PHRF 240 SLOWBOAT's Average & True speeds 4.56 5.50 Sec/Mile difference: 60 Time on Distance adjustment: 5.00 Minutes Distance buoy to buoy: 2.5 Race distance: 5 Fast boat=5.95 Kts. VMG=5.95 Slow boat=5.50 Kts. VMG=5.50 CURRENT F-UP F-DN Total S-UP S-DN Total Delta Error 1.00 30.29 21.57 51.86 33.33 23.07 56.40 4.54 Using ToT 53.99 54.26 -0.27 Using ToD 36.86 36.40 0.46 0.75 28.83 22.38 51.21 31.57 24.00 55.57 4.36 Using ToT 53.31 53.46 -0.15 Using ToD 36.21 35.57 0.64 0.50 27.51 23.25 50.75 30.00 25.00 54.99 4.24 Using ToT 52.84 52.90 -0.06 Using ToD 35.75 34.99 0.76 0.25 26.30 24.18 50.49 28.57 26.08 54.65 4.17 Using ToT 52.56 52.58 -0.02 Using ToD 35.49 34.65 0.83 0.00 25.20 25.20 50.40 27.27 27.27 54.54 4.14 Using ToT 52.47 52.47 0.00 +++++++ ToT tie Using ToD 35.40 34.54 0.86 ToD Advantage SLOWER boat -0.25 24.18 26.30 50.49 26.08 28.57 54.65 4.17 Using ToT 52.56 52.58 -0.02 Using ToD 35.49 34.65 0.83 -0.50 23.25 27.51 50.75 25.00 30.00 54.99 4.24 Using ToT 52.84 52.90 -0.06 Using ToD 35.75 34.99 0.76 -0.75 22.38 28.83 51.21 24.00 31.57 55.57 4.36 Using ToT 53.31 53.46 -0.15 Using ToD 36.21 35.57 0.64 -1.00 21.57 30.29 51.86 23.07 33.33 56.40 4.54 Using ToT 53.99 54.26 -0.27 Using ToD 36.86 36.40 0.46 Note 1: - Current: Current & wind in opposite directions. Note 2: Upwind VMG = 1.000X speed. Tacking angle 0 degrees. Note 3: Course length: 5.00 Distance sailed over the water: 5.00 Note 4: All times are in minutes. Race Distance = 5 Note 5: F-UP Fast boat's upwind time. F-DN Fast Boat's downwind time. S-UP Slow boat's upwind time. S-DN Slow boat's downwind time. Note 6: Error is based on boats should have tied in all races. - Error is advantage 180 PHRF boat has over 240 PHRF boat. This exercise shows the effect of current on boats with PHRF # 60 seconds appart. Using Time on distance, the adjustment given by ToD would be 5 minutes in ALL cases. The boat speeds are calculated using PHRF's formulas which seem to be extremely optomistic. Slower speeds and wider PHRF spreads exagerate the problem