# Windsurf sail lift/drag vs Alpha

Discussion in 'Sailboats' started by windsomniac, Feb 8, 2009.

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### windsomniacJunior Member

Does anyone have any windsurf sail lift/drag vs alpha data?
I am developing a math model. Even data that is not that great
would be helpful. My math model is severely limited using generic
Cl, Cd sail data from Marchaj. My model does show some promise
giving some reasonable results for velocity prediction, planing,
and optimal trim and heel.
I'd prefer not to get into deriving Cl and Cd purely from theory as
this is difficult in 3-d without some type of check.
Thanks

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### daiquiriEngineering and Design

That will be a tough task.
Windsurf sails are not just about static lift and drag - you will also need to consider the aeroelasticity and dynamic aerodynamics. Well ok, you can also neglect these, but then the whole discussion we've seen about loose leeches will not be considered by your model, for example.
What is the numerical model you're using for the analysis?

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### windsomniacJunior Member

The loose leach thread was great! Just because my model is steady state doesn't mean it ignores sail twist. In fact thats why I would like to see some windsurf plan form lift and drag data.
The model: simple mechanics really, force balances, aero hydro of the components, sail, board, and fin etc. No solving unsteady navier-stokes here. It is an interesting problem because of
the free moving sail. How the sail can produce vertical lift with negative heel effectively reducing the kit's weight. Also intersting is how much the wetted surface of the board changes as a function of speed reducing drag. How the planing hull acts much like a wing skimming across the water than a boat pushing through the water. The model is steady state, using pretty much constant Cd, Cl for the components. There is some minor coupling changes in the coefficents and coupling with the hull and fin components.
Input: kit characteristics, wind strength, sailor weight, point of sail (gamma)
Output: max velocity at gamma, system is under constrained, so it finds max velocity by determining optimal values of leeway angle, board pitch, negative sail heel, and sail trim, while maintaining stabilty. The model is more geometry and iteration than calculus and elagance.

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### Hansen AerosprtJunior Member

Windsomniac:
Not sure how useful this is given the advances in board, sail and fin design but Dr.Peter I Somlo did a similar investigation a number of years ago.
- Bill Hansen

Board Speed vs. Wind Velocity

Contributed by Dr.Peter I Somlo

A theoretical solution of the numerous parametric equations which determine speed as a function of course and wind velocity is of great interest to the technical windsurfing enthusiast. Dr. Peter Somlo has developed such a solution utilizing the aeodynamic and fluid dynamic relatonships for lift and drag of the sail, fin and board over a range of courses to the true wind and at two wind velocities. Peter's solution is presented below for true winds of 12 and 15 knots and a sail size of 7.0 sqm.

Method

The calculation was performed for the board-speed (vector) as follows:

1. Set up the equations for sail-lift, sail & board-drag as functions of air temperature, air pressure, sail size, wind-velocity and board-velocity. Here we must remember that sail-lift and sail-drag depend on the velocity of the apparent wind (which we don't know yet because it depends on the board-speed) and the board-drag depends on the board-speed (not known).

2. Set up an equation for the apparent wind, which is a vectorial subtraction of the wind vector minus the board-speed vector. (The faster the board, the more the apparent wind comes from the front.) To make the vectorial calculations simple, all vectors were represented as complex numbers (which have magnitudes and angles).

3. Assume a sheeting-in angle which will be used to modify the angle of the sail-lift.

4. Assume that the sail-lift is at right angles to the sail direction.

5. Break this sail-lift force into two components: in the direction of the board and right angles to it.

6. Chose a direction of board-movement (relative to the true wind direction).

7. Realising that when moving at a steady speed, the forward-force must equal the backward drag (otherwise the board would be speeding up or slowing down), solve the equation(s) for the board-velocity vector - for the condition of the net forward-force to be zero - yielding the board-velocity vector, and so all the forces will become known.

------------

Notes:

a. Although the computation was carried out in SI units, speeds were converted to knots (from m/s) and forces were converted in results to kilogram-force (from N) - more familiar units.

b. An artificial function was devised to increase the hull-drag smoothly by a factor of 3 at the planing transition as the board-speed drops from 12 to 10 knots . (The choice of 11 knots was the result of a calculated hull-speed-limit of a commonly used board.) The factor of 3 came from estimating the reduction of the wetted surface when planing properly - or not.

c. The 'Forces' diagram shows the total sail-lift. The fin-lift is the component which is at right angles to the board, and the forward-force is the component in the forward direction. We see that most of the sail-lift is transferred to the fin (which is preventing the board going sideways), and the forward-force is a fraction of the sail lift only. For a 7m^2 sail, reaching in a 15 knot wind, the sail-lift is about 68 kgf (so you can hang most of your weight on the sail), but the force that makes you go forward is only about 11 kgf. The curves are not quite applicable for sailing downwind (square running at 180 degrees) because the transfer of lifting force to drag force only at square running is unknown, i.e. there is no sail-lift, only drag.

d. The Cartesian graph for board-speed shows two wind-speeds 12 and 15 knots, for a 7m^2 sail. Note the 'kinks' in the curves indicating the transition to planing above 12 knots.

e. The polar plot is the curve re-plotted for the 15 knots case, with laser-gun measurements by Ken Winner, technical editor of American Windsurfer magazine superimposed. It can be seen that the curves are very similar, differing mainly in scale (Ken suggested to reduce the drag coefficients.) However, at close-hauled sailing there may be another reason for the difference. If a competitor is asked to see how fast can he/she sail up-wind, they will bear off first to get on the plane, and then sail upwind. The computer program does not accomodate this behaviour. In the 10 to 12 knots regime the results are multi-valued, and one can chose which root to find: the planing one or the non-planing one. Below 11 knots the non-planing one was chosen.

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### daiquiriEngineering and Design

@Hansen:

Hi, just two questions:
1) how did you calculate the total aerodynamic forces on sail? You must have had the experimental Cl-alpha and Cd-Cl curves at hand, I guess. That was also the original info windsomniac was looking for, and would be very interesting for the rest of us if you could post the graphs.
2) same for the board drag - did you have some experimental data for actual surf boards and if you did, is it possible for you to share it with others here?

Thanks.

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### windsomniacJunior Member

Hi Bill, thats alot to take in. I would love to see Dr.Peter I Somlo's model! What sail coefficents is he using?
My model is similar, but a little different...
from memory...
1. i set up force balances in 3-d
for longitudinal direction
sail drive = sail drag + board and fin drag + parasitic drag of sailor
for lateral direction:
sail heel force = fin lateral lift
Vertical force balance:
board lift (buoancy + hydrodynamic) = sailor weight + kit weight - vertical lift from sail neg heel
2. relations with apparent wind, true wind and board speed are an integral part of system. i don't use complex numbers just

Va and beta.
3. i don't assume a sheeting angle, i iterate a solution find an optimal sheeting angle for max speed at any given point of

sail.
4. i don't know why he would assume sail lift is at right angle to the sail chord? the sail lift is perpendicular to the

apparent wind. as sail drag is parallelel to the apparent wind. the lift and drag will be functions of the angle of attack

the apparent wind acts on the sail. which depends on the apparent wind direction and trim angle.
5. the sail lift and drag vectors are then resolved according to the sail trim angle into longtidinal (drive), lateral

(heel), and a vertical component (which effectively reduces the wieght of the sailor and kit.
My model optimizes the sail trim and also negative sail heel for max speed.
6. yes my model you choose a direction you want to travel with repsect to the wind (gamma).
7. force balance see 1.
8. I think my model may go beyond the doctor in that it considers
a. the leeway angle (must be a variable in model, effects drag and lateral force balance)
b. negative heel of the sail
c. stability - this is the biggest factor in limiting speed upwind
Notes:
a.
b. i don't need an artifical function for the board drag. My model is based on a vertical force balance and updates the

wetted surfce and the board AoA to the water during iterations. in other words,at slow speeds there is little hydrodynamic

lift. lift is from bouyancy the wetted surface is large. at fast speeds (planing) vertical lift is from hydrodynamic lift. The model adjusts to satisfy the vertical foce balance.

More over, at any speed, there is an optimal combination of wetted length and AoA of the board that minimizes drag.

Model uses that combination.
c. for any solution all forces balnces must be satisfied.

Basically you enter wind speed, all your kit info sail size, fin depth, cavg, board dimensions, sailor weight, sailor height,

mast size, harness length, weight of all components.
The model will determine the max speed for the direction you want to travel (gamma). Also output all the other variables

including board wetted length, board AoaA to water, avg wwtted board width, leeway angle optimal, neg heel optimal, AoA

(Alpha) for sail optimal, Cl & Cd for sail at AoA, adjusted Alpha and Va for sail neg heel, board speed, V apparent,

Vapparent angle, Vmg, trim angle, sail lift, sail drag, board drag incl'd fin, parasitic drag from the sailor's fat ***,

epsilon for sail and board, force balance delta's, Fheel, Sail vertical, board vert lift, hydrodyn lift, hydrostaic lift, stabilty, and on and on.

Sorry this is so messy. My model is young I've only been working on a few months. If you are interested I will send you some

results.
The results have been promising (actually surprisingly realistic for a rough draft). But its still a work in progress.

Thats why I need better values of Cl and Cd for a windsurf sail.

I will have to post my polar diagrams...soon

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### windsomniacJunior Member

Bill, thanks for the tip on Dr. Peter Somlo. Sorry say I think he has passed away.

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### Hansen AerosprtJunior Member

Daiquiri:
Peter Somlo did this work and was kind enough to allow me to post it on my old website. Unfortunately, I can't tell you how or where he got his data.

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### BoatprideBoatpride

Hi guys,

I am looking for some mainsail draft diagrams to be used in an article I would like to write. Can anyone point me in the right direction? The article revolves around the position of the draft in relation to wind speed (of course)

Chris

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