I think it's awesome you're taking this on SWS!
I have been toying with the same idea for COAS and have seen the comments/considerations on transitioning POTC capabilities/aspects into COAS. After looking at the COAS code, I have the same level of dissatisfaction you expressed with POTC sailing realism.
There are just SO many things to take into consideration with hydrodynamics and air coefficients applied to weight and sail area. I know that we are talking about games here and I think you have taken the best 1st step in looking at historical commentary with regards to ship handling characteristics and speed.
Have you gone beyond this, or just using best guesswork? If you have I would LOVE to see your calculations! :will
Please don't take the following as gospel or something I'm trying to sell you on. I just want you to think about it. Many boat builders still argue about formulas and best shape and sail area to this day and I think this is largely due to it being almost as much a matter of art as it is science. A lot of expert boat builders use the axiom that if the boat "looks right" it will handle and sail well.
So much depends a lot on bottom shape and length. I can sail my agile 24 footer all day long and still be passed by, by less agile, heavier 36 footers. How can that be? I am lighter and take up less displacement. There are three things (formulas) I think we need to try to eventually model to truly get at accurate historical ship handling. First being easiest and last being hardest. I think they need to be built seperately so that if we fail to do a good job on the second or third we still have something decent in play.
1. Length and drag/resistence
2. Displacement, hull shape/form and wetted surface (will influence the first)
3. Wind coefficient vs sail area ratios to weight and shape/type of rig (we might even model a little hull lift here as well especially with smaller craft in good wind) (this formula will influence first and second),
1. Length and drag: Length of the hull at the waterline translates into more speed over smaller craft and goes the opposite direction in the curve after a while. Now my lumbering 2nd rater cannot catch my frigate even thought she is longer and carries more canvas.
Boat speed in knots (V) is compared to hull waterline length in feet (L) where V divided by the square root of L = the speed/length ratio or S/LR.
By way of example a boat 30 feet on the waterline at 6 knots has a S/LR of: 6 / 5.48 = 1.095. At 10 knots her S/LR 10/5.48) = 1.82. Whereas, a 400 foot ferry at 15 knots has a S/LR (15 / 20) = .75.
This rule allows us to categorise hull lengths which will suit a particular speed for a displacement vessel. For our purposes there are 3 categories to consider:
LOW SPEED - up to a S/LR of around 1.5
MEDIUM SPEED - with a S/LR between 1.5 to 3.0
HIGH SPEED - having a S/LR above 3.0
It will be seen that a 30 foot motor boat on the waterline at 20 knots has a S/LR of 3.6 (high speed) but that a 300 footer at the same 20 knot speed with a S/LR of 1.15 is classed as a low speed vessel. For the 300 footer to be considered high speed she would have to be traveling (work formula backwards) V = 3 x 17.3 = 52 knots or more.
2. Displacement and Hull Form: After we have determined the displacement and the weight of a given hull, we select the hull form from a table we build and assign values to hull types. The type will determine the resistance of the vessel through the water, and each hull form's resistance figure affects the power needed to reach the vessel's speed. This will also effect how fast it attains that speed. Some rather large ships could attain some impressive speeds with a following wind abaft, but it might take them quite a little while to build up that momentum and just as you've said it would take em longer to slow as well. These hull forms could include:
Deep Displacement-- High capacity hulls suitable for large merchant ships, Galleons, Indiamen, etc. However, they require more power to reach and sustain a given speed than other displacement hull types. A large percentage of a fully loaded deep displacement vessel's hull would be below the water line. This would also mean it would heel at much less of an angle in turns.
Parallel Displacement-- Both sides of a parallel displacement hull run roughly parallel to each other except at the bow and stern. Although simpler in form and to build, this hull form has higher drag than a curved displacement hull. Many smaller merchantmen like Packets and Colliers used parallel displacement hulls.
Curved Displacement-- This is the hull form used for many warship types: Frigates, Razees, Corvettes, Brigs, etc. The hull begins with a sharper bow and gently curves around the widest part of the hull, then tapers into the stern. The displaced fluid flows more efficiently with less drag around a curved hull. A vessel with a curved displacement hull will travel at a higher speed than a parallel displacement hull using the same amount of sail power.
3. Wind coefficient vs sail area ratios to weight and shape/type of rig
In COAS the formula is close but not quite right especially with regards to attaining the speed. The math relies more on sail handling ability of the captain and experience/size of crew than physics and that's not necessarily a bad thing. It definately needs to be a big part of the game. A simple formula for Sail Power (The power generated by wind on sails determined in a standard atmosphere):
1. Multiply the wind velocity in kilometers per hour by 0.28 to convert the wind velocity to meters per second.
2. Calculate the power available in watts with this formula. P = {[(1286)S]V} 0.1
Where P = power in watts
Where S = sail area
Where V = wind velocity in meters per second
Beyond that simple power consideration, a lot has been written on this subject and there is a lot of disagreement with regards to Wind Pressure Coefficient applied to righting and heeling based on size and shape of rig.
Francis Kinney gives a couple of methods (page 292 to 299 in Skene's Elements of Yacht Design) to compare
Heeling Moment to Righting Moment. Method #1 is called the "Wind Pressure Coefficient."
The equation is:
"Wind Pressure Coefficient = Righting Moment @ 20 degrees Heel, over Heeling Moment @ 20 degrees of Heel
R.M. @ 20degrees = Pounds Displacement x Righting Arm @ 20degrees Heel
Righting Arm @ 20degrees = GM x sine 20degrees
H.M. @ 20degrees = Sail Area x Heeling Arm x cos2 20degrees x Wind Pressure
Wind Pressure in Pounds per Sq. Ft. = .0053 x Wind Speed Knots2
For comparing boats, a wind pressure of 1 pound per sq. ft. (equal to almost 14 knots) is
assumed.
With the assumed heel angle of 20° we observe that sine 20° equals 0.342 and that cos2 20°
equals 0.883. The Heeling Arm is taken as being the vertical distance from the sails' C.E. to the
hull's C.L.R. at zero heel (thus the correction for cos2 20°).
A Wind Pressure Coefficient greater than "one" shows that he boat has reserve stability given
the assumed Heeling Moment. In other words, a number greater than one means the boat
would not heel to 20° in 14 knots of wind.
A graph of acceptable values is on page 295 in Skene's . A WPC of less than one reveals that
the Heeling Moment is greater than the Righting Moment and the boat will heel more than 20°
in 14 knots of wind.
- A small boat may have a WPC of less than one.
- For a medium size keel boat the WPC should be in the range of, say 1.1 to 1.2.
- A large boat should have a larger margin, say up to a WPC of around 1.5 or 1.6."
We might also want to consider hydronymic lift especially for smaller agile craft: L=0.5*p*v^2*A*CL guesswork would be required on the numbers we would apply for lift and used density of water for p.
As we say in my field all the time "what's good enough?" We want it to be good, realistic, and historically accurate, but not make the game less fun. This is one of those areas where we might want the toggles Pieter has brought up in the past that we plan on putting into COAS RTBL.
If you get this right SWS I will definately be playing with toggles on and your effort is tempting me back to playing POTC a little more.
If you have some numbers I'd love to see them. I'm willing to assist you in testing as well. Good hunting.
MK
And I knew she was playing with some fairly incomplicated values. However given the formulas I'm suggesting here we could at least get the BEST values possible plugged in even if we didn't build additional physics strings into the code. Just taking each ship through a set of analog tables on paper with pencil and extracting our best guesses - now we have both history and physics on our side as we tune the old wagon wheel/stone knife.
