Laser & dinghy boatspeed - VPP

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 thrust from the sails is calculated using lift coefficients found in wind tunnel experiments. Lift varies with AWA and flatness, and the force varies with AWS^2.

Drag
Drag of the boat is the sum of several different components:

• keel & hull friction - varies with BS^2
• wave drag - varies with BS^3; weight
• windage - varies with AWS^2
• keel lift-induced drag - varies with sideforce^2 and BS^2
• sail lift-induced drag - varies with twist, sideforce^2 and AWS^2

It's easy to see how it's not possible to predict BS simply, it needs a calculation to link the various contributions together.

Interconnections between parameters:







How does it work?

The user specifies a TWA and TWS, and it starts with a guessed BS, then calculates as follows;

AWA, AWS (=28°, 12kn).
Drags of hydro parts are calculated for BS
Windage is calc'd with AWS
Thrust is calculated from AWS, AWA and sail area.

The net force on the boat is Thrust - Drag. If Thrust > Drag, the boat accelerates.

Acceleration = Net Force/Mass

New BS = Old BS + Acceleration x timestep (0.1secs)

The program repeats many times and in each cycle, BS, Heel, Twist, Hiking are altered towards correctness until the error is small.

At the same time RM and HM are compared and the crew is moved in or outboard to match RM to HM

In stronger winds, the crew moves outboard to their maximum hike, then the sail is twisted to reduce the Heeling Arm to balance RM & HM.

Normally a VPP searches for the sail flatness and twist to give best performance. However in this spreadsheet the user has to specify sail camber between 6-16%.

Quick Start

If you are using a Desktop version of Excel: 

File menu – Options Formulas – Automatic Calculation & Enable Iterative Calc

Max Iterations = 500 or more, Max Change = .01

Running Online 
If you don't have Excel it can still be run online. Download to your OneDrive account, and then open. Click on "Edit in Browser" 

"Laser" tab uses hull drag data for a Laser. You can edit rig dimensions for a Radial etc.
"Dinghy" tab uses wave drag data for a Laser, but all other calculations are based on your entered data. The main effect is Wetted Surface Area which is used for Friction Drag of the hull. 
Let me know how the model it is for your dinghy. I expect it will be reasonable for Opti through to 470 and 49er in light winds.

Pink cells are for user-entered data 

Enter TWS=10, TWA 45, sail camber 12%

Enter 1 in Cell H1 to switch to auto mode 

Change TWA or TWS, new estimates of hiking, twist, BS, Leeway

Try changing crew weight, Sail Camber, board depth, windage, rig height

Because each solution is based on the previous it is possible to crash if there is too big a step in TWS or TWA. See below for how to deal with errors.

Validity
Crew weight between 70-90kg
Sail camber between 6% and 16%. (Note sail camber is approximate. I've converted ORC Flat parameter into more intuitive camber)
At about TWS 20 there will be errors because the sail twist is maximum - it needs traveller eased but this is not included here. Bear in mind this is an educational toy.
There is no by-the-lee sail data available.

How accurate is it?
Well it doesn't predict BS of 0.5kn or 50kn, so that's a start.
There are about 12 forces and measurements to estimate. They will all have errors because we are not calculating every molecule around the yacht. (There is not enough RAM in the world to do so!)
Some measured data is available of unknown quality and it is roughly 0.5kn different.
When leeway is high - say >7° - accuracy will drop off.

If you sail a Laser with GPS logging, let me know how it compares for your weight and hiking ability.

Excel details
This is unusual in that there is no VBA programming so it will run in Excel Online without owning Excel. I guess this means it will run on a Mac.

A cell is allowed to refer to itself, and the sheet is automatically recalculated until the maximum number of iterations is reached or the new result is close enough to the previous result.

Eg "BS = BS + BS_difference" accelerates or decelerates to balance drag & thrust.

Errors

Because the answer depends on the previous cycle you can crash the calcs by entering a large step in TWS or TWA.
If errors: Enter 0 in Cell H1. Reduce camber or TWS, then Enter 1 to restart Automatic calcs.

16% sail camber results in errors above about 15kn upwind, whereas 6% camber will go to low 20s.

This can be easily modified to any other conventional yacht, with hull drag data.

Feel free to contact on accuracy, errors, questions, improvements, requests.