Drag Angles vs VPP

[Peaky]

Hi, I am trying to put together a VPP for a simple unarig dinghy (Laser) and am getting some curious, and presumably wrong, results.
Given a true wind angle (to heading) and a true wind speed, the VPP calculates the boat speed and leeway angle to achieve equilibrium. And the sums show that the net thrust and side force (in the axis aligned with course) are zero. So all good, except that the apparent wind angle (to course) that results does not equal the sum of the aero and hydro drag angles (the aero one being set by a fixed angle of attack and the hydro one dropping out of the leeway equilibrium calc). The difference between the sum of the drag angles and the wind triangle derived apparent wind angle is consistently about 0.6 degrees, which doesn’t sound much but is physically impossible and has a significant impact on VMG. Any ideas?

 

[Doug Halsey]

My suspicion is that there's an inconsistency in using the leeway angle. You say "true wind angle (to heading)" and "apparent wind angle (to course)," but they should both be "to course."

Your leeway angle is probably fairly small, making it tricky to spot errors. It could help to input some data that results in a very large leeway angle and see if things become more obvious.

In any case, you shouldn't be assuming that the aero angle of attack is constant. On an actual boat, it can vary quite a lot. You need something like a loop on sail-trim angle to pick the best one in any given condition.

 

[Peaky]

Thanks Doug. The true wind to heading is just an input, all the calcs then take leeway into account so that apparent wind angle is against course.

I feel I must have mucked up with leeway somewhere but I can’t for the life of me see where, so I wondered if I had overconstrained the problem some how? By limiting the problem to a single set of aero figures, so that the aero drag angle is fixed and known, the hydro drag angle should just be AWA - aero drag angle. But the equilibrium point to balance heel and drive does not result in a hydro drag angle that equals AWA - aero drag angle.

 

[Peaky]

I decided to recode it from scratch after failing to find the problem... and it now works!

 

[Doug Halsey]

I decided to recode it from scratch after failing to find the problem... and it now works!

Isn't programming fun!

What are using using for your aero & hydro input data?

 

[Peaky]

Aero data at the moment is simply a Cl of 1.35 and a Cd of 0.3 (L/D of 4.5), which I have taken from a hybrid of data from Marchaj, Fosatti, Day, Pennanen and ORC low lift data. Hydro data for unappended hull is from Pennanen, appendages added and with downwash and wake over the rudder. The hard bit seems to be data for the increased drag from the hull at leeway angles, which increases much more rapidly than simply the lift induced drag so I have tuned this against what little data I could find. But if anyone knows of papers regarding hull resistance vs leeway angle that would be great.

 

[Doug Halsey]

You could simplify the leeway problem by pretending that Lasers have gybing boards, angled to make the hull go straight through the water. In that case, you could ignore the increment in hull drag due to side force. (There would still be an asymmetry in pressures on the hull, but that would probably have only a small effect on the drag.) I'll bet the errors due to all these simplifications of the leeway effects will be nothing compared to uncertainties in the rest of the input data.

A much more significant matter is that, to be realistic, you also need to balance the heeling moments & righting moments. You know that Lasers are overpowered much of the time, so you are going to have to allow Cl to vary. (Input a curve of Cd vs Cl, not just a single point on the curve.)

I know it's getting more complicated, but it's still doable. The hard part is always going to be finding good enough data to input.

Good luck.

 

[Peaky]

You’re right Doug. Last night I added HMmax as a constraint and Cl is varied to stay within the limit, but the L/D ratio is assumed constant. Today’s task is to fix that by adding an aero polar plot. The available data seems to vary quite wildly though, so not sure of the best source. I’d like to get to a point where the sail is split into 3 or 4 sections with the camber and twist at each section defined and control the overall lift and drag that way, much like applying sail controls. After that I want to include the effect of heel on resistance, righting moment, induced drags and rudder angle. Something to ponder.

I very much want to include leeway effects on the hull. The best I can find is a paper by Pennanen looking at the resistance of a Laser with and without leeway at one speed and have used the difference between that and the calculated sum of appended hull without yaw + induced drag of appendages to estimate an efficiency factor for the hull drag due to leeway. But that is very crude, not least because only small leeway angles were considered by Pennanen. It occurs to me that waterline length is shortening with leeway so there may be some mileage in exploring changes to wavemaking resistance but I’ve not gone there yet. At present the bare hull resistance is just that measured from tank tests, so isn’t broken down into constituent parts.

What my results do show is that the boat sails at leeway angles far below the optimum hydro L/D (assuming my hull leeway drag method is in the right ball park). Typical leeway angles upwind are about 4 degrees but highest side force/resistance is nearer 10 degrees.

 

[Doug Halsey]

...What my results do show is that the boat sails at leeway angles far below the optimum hydro L/D (assuming my hull leeway drag method is in the right ball park). Typical leeway angles upwind are about 4 degrees but highest side force/resistance is nearer 10 degrees.

That is the typical situation (in light air, at least). It's why adding sail area (or trimming the sail to Cl values higher than the one that maximizes the aero L/D) increases the speed.

In trying to minimize the sum of the aero and hydro drag angles, it will be very rare that each of those angles will be minimum. Maybe only for the ideal iceboat case (zero hydro drag) should the aero drag angle be a minimum.

 

[Peaky]

Isn’t that indicative that the daggerboard is too big and the chord could be cut? It might hurt during manoeuvres but a price worth paying?

 

[Doug Halsey]

Isn’t that indicative that the daggerboard is too big and the chord could be cut? It might hurt during manoeuvres but a price worth paying?

It's too big at that instant, under those exact conditions, but that could change at any moment. Daggerboards have to be designed to allow for worse conditions, but at least they can be raised when they aren't needed as much.

Every aspect of the boat's geometry is a compromise and will fail to be optimum almost all the time. Too bad we can't morph from one shape to another to continually have the best one for the ever-changing conditions.

 

[Peaky]

Well, I guess it’s something to investigate in the VPP... gives me a reason to play!

 

[Dolfiman]

I am also developing an home made VPP on a spreadsheet Framework, so I can share my thoughts with you.

To my understanding and what I am doing myself, all the data and computation are carried out with reference to the boat "to course" line as said Doug in his first quote, meaning the twa, the awa, … are computed with this reference, that the drag components formulations are computed and supposed consistent with this reference (friction drag, residuary drag, heeled extra drag, induced drag, aero drag), etc ....

The equilibrium is based on 2 equalities : thrust = drag and righting moment = heeling moment, obtained through iterations on two data : boat speed, heel angle. The VMG is then just boat speed * Cos(twa).

No need of any leeway angle conjecture in this process : it is like your floating object, moving in a "on course" line making with the real wind an angle called twa, has an axis of geometrical symmetry which makes with the "on course" line an angle called the leeway angle.

An important parameter to take into account when simulating an upwind sailing with VPP : the "Flat" parameter, reflecting the sailor ability to flatten the sail. Its introduction in the sail formulations is very simple :
CL = CLmax * Flat , CLmax being yours ~ 1,35 (mine is 1,5) one can consider constant when upwind (for awa around 27°)
CD = CDo + CL^2 / (pi * AR) , CDo being ~ 0,02 and AR the aspect ratio of the sail when assimilated to a wing

When the sail has its maximum "natural" camber (when by light winds, when downwind), Flat = 1
When the sail is flattened, Flat < 1 but of course with a limit, numerically (in the VPPs) it is usually 0,5 , in the real life it depends of the quality of the sail and/or the ability of the sailor to flatten it.

Although Flat reduce the aero lift force, it also reduces a lot (CL being at square) the aero drag force : the resulting force rotates forward and the side force is reduced (so less heel angle), and all that happens to be beneficial for the VMG to a certain point (i.e. for a certain combination Flat, twa)
>>> So upwind with a VPP, to maximise the VMG, you should play with 2 additionnal parameters : twa, Flat.
Some VPPs consider various twa (for example, 35°, 39°, 42°, 45°, 50°) and automatically optimise the Flat (in addition to iterations on boat speed and heel angle) to optimise the VMG. Often use to draw a speed polar.
Some others VPPs did automatically the dual optimisation and output a combination (twa, Flat) which gives the maximum VMG for each given wind force. Typical order of magnitude with a sailing yacht :
With wind 6 knots : Flat is still 1 and the twa is about 48° to 50°
With wind 16-20 Knots : Flat is ~ 0,5 and the twa can be around 42°
Your VPP should be consistent with this usual trend : if when upwind, by playing with twa and Flat, you cannot observe a maximum VMG, that means you have something wrong in your modelisation.

 

[Peaky]

Hi Dolfiman, thanks for sharing. How do you account for the induced drag of the keel etc if you assume no leeway?

I’ve now added Flat and ease (no twist) but so far only as a single entity rather than as sections up the mast. Currently adding in the effects of heel on righting moment, yaw balance etc and then hope to add jib and asymmetric spinnaker details but not too sure yet about how best to cope with the interaction between sails. Oh, and drag of crew which I currently ignore but which isn’t negligible for small boats.

 

[Doug Halsey]

...The equilibrium is based on 2 equalities : thrust = drag and righting moment = heeling moment, obtained through iterations on two data : boat speed, heel angle. The VMG is then just boat speed * Cos(twa).

There's also a 3rd equality : (hydro side force) = -(aero side force)