Drag Angles vs VPP

Technically there are three force balances and three moment balances, but a full 6DoF is a bit tough without a lot more data than is easily available!

 

Because the data problems and the sailing conditions vary so much with the type of boat, I've made separate codes for specific configurations: 1) conventional monohulls, 2) conventional catamarans, 3) V-foil trimarans like my Broomstick, and 4) bifoilers like Moths.

The conventional VPPs just use the 2 force balances & 1 moment balance, but the foiler VPPs use all 3 force balances, and 2 of the 3 moment balances (yawing moment being ignored).

 

Surely you can’t ignore the yaw balance in a moth will all that windward heel?

 

The skipper can't ignore it, but the program can

 

You are right, there is also this 3rd equality, I should mentioned it. I forgot it because she is actually integrated in the set of formulations, exactly in the induced drag one which, assuming the hull and its appendages as a wing and using the lifting line theory, use the hydro side force at square and so directly the aero side force at square.
Based on sources here attached (authors Peter van Oossanen and Andrew Claughton), I presently adopt a simple formulation directly in line with Claughton one :
Di = Fy^2 / [½ ρ V^2 cos (θ) π (1,2 T^2+ 0,8 (T – Th)^2)]
where ,
Di : the induced drag
Fy : the aero side force
V : the boat speed
θ : the heel angle
T : the draft overall (tip of the keel wing / water surface)
Th : the hull body draft
(here attached my working paper detailing the approach leading to this proposition.)
In Claughton formula, (1,2 T^2+ 0,8 (T – Th)^2) is 2 Teff^2 where Teff is called an "effective" draft, itself needing an expression and coefficients to be determined, the hull + keel design complexity is concentrated in the Teff estimation.
In my reformulation, I keep only the drafts consideration for just a VPP purpose consistent with possible design iteration on drafts, but of course not helpful for hull/keel wing more refined design iteration.
The advantage is that it reacts consistently with drafts, that one can illustrate with the dinghy case and two extreme configurations : daggerboard fully deployed, daggerboard fully retracted.
Order of magnitude with assuming T=1 m and Th = 0,1 m :
** Daggerboard deployed >>> (1,2 T^2+ 0,8 (T – Th)^2) = 1,848 m2 (= 2 Teff^2 , so as if Teff = 0,96 m)
, and Di = (…......) / 1,848
** Daggerboard retracted, T = Th = 0,1 m >>> (1,2 Th^2+ 0,8 (Th – Th)^2) = 0,012 m2 (= 2 Teff^2 , so as if Teff = 0,077 m)
, and Di = (…......) / 0,012 , so 154 more drag !
It is easy to understand (and can be easy to experiment in situ) that the speed and moreover the VMG will be quasi nul in this configuration daggerboard retracted, and that a VPP with using such formulation can be able to reflect that trend.

Still a simplified approach though : is the calibration lying in the 1,2 0,8 coefficients stable enough or fluctuant from one case to another ?

 

Looks like your formulation don't take rudder into account when daggerboard is retracted. Hobie 14 relies mostly on the rudder's lift when going to windward, and they are good upwind performer. Oossanen formulation is theoretical but looks good to me.

 

Here is a very simple Laser VPP in Excel in case it is useful. Laser & dinghy boatspeed - VPP http://scienceofsailing.blogspot.com/2018/06/laser-boatspeed-vpp.html
It was made for learning but the results seem plausible up to about 10kn.
The HM&RM, sideforces, thrust & drag are balanced for a given camber by adjusting hiking and twist.
It runs without Solver so there is no built-in optimisation, but it's usable without owning Excel. Instead the iterative calcs rely on the previous solution which will cause errors if a large change in TWS or TWA. The resultant large change in forces overwhelms the balancing formulae. RTM

Always interested if you find suggestions for improvements or questions.
Mike

 

As Dolfiman points out, I neglected to say that the Heel angle is fixed to zero. This is reasonable for a performance dinghy I feel.
I made a similar keelboat VPP which searches for the correct heel angle, but with twist as an input.

 

Good stuff Mike, thanks a lot for sharing. Lasers do use up to about 6 degrees of heel (gives about 10% more RM in exchange for losses from rig and appendages) but the difference in VMG is very small.

 

As a teaching tool, it's meant to be the simplest VPP that can run without even owning Excel. My emphasis in the interface was on the aero induced drag/sail twist tradeoff.
I also use it for an old dinghy that sails with >10 deg heel by fudging RM with an increased MaxHike. Not that I have heeled drag data.

It's too easy for me to get carried away with adding complexity than the basic force models justify. It's been good for my learning though!