Science Of Sailing

Laser VPP  briefly outlines the cycle of calculations from an initial guess of Boatspeed. Here are the numbers for the first cycle of calculations TWA = 45° and TWS =8kn BS =5kn for the starting value, which triggers calculations for AWA = 28.1° and AWS = 12.0kn Individual drags are calculated: Hull Friction = 3.2kg Hull Wave = 3.4 Board Friction = 0.8 Sail Induced = 2.1 Windage = 0.9 Sum of Drag  = 8.3 Thrust  =5.6  The net force on the boat is Force = Thrust - Drag = 2.7kg Acceleration = Force/Mass  - Newton's 2nd law New BS = Old BS + Acceleration x timestep = 4.97 RM = 72kgm and HM = 49kgm are compared, the crew is moved inboard -0.15m to reduce RM 2nd cycle AWA = 28.2° and AWS = 11.9kn Individual drags are calculated: Hull Friction = 3.2kg Hull Wave = 3.3 Board Friction = 0.8 Sail Induced = 2.1 Windage = 0.9 Sum of Drag  = 8.1 Thrust  =6.1  Net force = 2kg New BS = 4.95 RM = 57kgm and HM = 54kgm are compa...

Download link here Polar A polar table can be constructed by entering the TWAs listed in the blue cells as the TWA. BS, VMG, Leeway will be collected automatically and the polar is drawn for this Camber and TWS. Note this is dynamic and will be overwritten whenever a TWA is entered out of order. This is a limitation of writing for Excel Online. Data can be saved or expanded by duplicating the worksheet and having 1 sheet for each TWS, for example. Or copying the table to another sheet or workbook. But I'm leaving this up to you. Similarly Camber and Board Length can be explored: Depending on TWS, it is better to flatten the sail before maximum hiking is reached. This is reducing the sail profile drag by more than the lift is reduced, I guess. Feel free to contact on accuracy, errors, questions, improvements, requests.

A previous post outlined the  basic forces  on a yacht - Righting Moment, Heeling Moment, sideforce, friction drag, induced drag. It is an essential introduction to the work here. Download or run online  "VPP Laser & dinghy v2c.xlsx" To calculate the speed of a yacht is both simple and complex. Simply find the speed where the forward thrust from the sails is equal to the aftwards drag of the yacht. When these two forces are balanced the yacht is at a steady speed. At the same time, find the heel angle or hiking position or sail twist/flatness where the Righting Moment balances the Heeling Moment. The first Velocity Prediction Program VPP was written in about 1970 by Kerwin. The link above is a VPP spreadsheet that can be run online without Excel and links the forces and moments together to calculate speed. The process of balancing them is precise. However, modelling the forces is less exact and is simplified in various ways: Thrust The forward ...

Righting Moment is the rotation force that keeps a yacht from heeling further. It acts against Heeling Moment due to the sail and daggerboard forces. When  RM = HM heel angle is constant. The distance between the centre of sail forces and centre of daggerboard forces is called Heeling Arm HM divided by HA equals the Sideforce produced by the sails and wind, which is exactly reacted in the water by a combination of daggerboard area, leeway angle and boatspeed. An important point is that the HM can't be greater than RM. To increase Sideforce, the Heeling Arm must be reduced by twisting and/or flattening the top of the sails. Here is a simple calculator for RM of a dinghy that is being sailed upright. Enter boat, crew, sail dimensions and calculate the RM and Sideforce. Enter boatspeed, TWS and TWA and it estimates drag forces for friction, lift-induced drag, windage. Righting Moment - Sideforce   (Read the Manual page for instructions) Currently the...

A simple calculator in Excel, Enter: Boatspeed, True Wind Speed, True Wind Angle Results are: Apparent Wind Angle (the angle of the wind pennant) Apparent Wind Speed (what you feel on your face) Velocity Made Good into the wind direction Wind Triangle - Excel Trivial Notes: - Uses named ranges (Ctrl-F3) for ease of reading and error-checking - AWA uses MOD function to keep angle between 0 and 180