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Poyraz

Feedback on Game Model of Sailing

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The alpha stage currently going on and having more time until the beta, I would like to give my feedback on the game model of "Naval Action" here. It will be mostly on game physics and ship behavior based on some formulas, theory crafting, some other sailing games like PotBS and real life data.

 

Sailing Dynamics, Physics, Maths and Game Modeling

 

Given the fact that, “Naval Action” already contains pretty and detailed ship models besides the close to real wave patterns and ocean; one also expects the game having close to real sailing physics and sailing model.

 

First of all I must remark that, the modeling work for ship sailing in reality as well as their behavior in contact with the environment is a grueling task due to the immense amount of variables and many independed dynamic factors defining their motion. Generally, the more variables the sailing model includes the more real the results will feel. However, this also brings major complexity alongside. At this point, the developers have to decide the target of the game, balancing the weight between realistic behavior and complexity, in other words simplicity or lean production.

 

As for now, the game model allows ships to sail in a direct and straight course, unless ships try to maneuver. The sailing model is about the control of the straightforward motion of the ship and turning around z axis with the help of rudder. The lateral forces causing sway and the leeway on lateral axis are not included extensively. Nonetheless, the effect of lateral force on the ship causing heeling is included artificially. This general conception for the sailing model in NA ensures basic and steady controls over the ship, whereas, it also slightly pull apart some of the realism. However, in the end this must be the optimal point for the developers between realism and simplicity. At this point, I think this approach is pretty much acceptable, if there are no intentions to make the game simulation-like instead of as a detailed MMORPG game.

 

Conception Model: Equibirilium

 

The motion of ships with the physic rules in the romantic age of sail were actually no different than today. They were floating over the waves in the ocean, while their sails provide the propulsion for them to sail forward instead of the current propellers of the modern ships. The resistant part against this motion were also similar; the water resistance against the movement of the hull inside water along with some of minor air resistance for the ship above the waterline.

 

The movement of the ship occurs between the balance of those two main forces; sails trying to push the hull forward and the water resistance forcing against this motion.

 

As we know, NA sailing model do not include lateral forces causing the leeway motion, sway, the swim-, course- and leeway angles which result in lean and simple motion and controls. Regarding this simple approach, the free body diagram of a sailing ship is as follows:

 

FBD.png

 

The movement of the ship occurs according to the battle between aerodynamic forces through sails and the hydrodynamic forces through the wetted surface of the hull underwater.

 

Setting sails at the very first seconds of the moving off, there is close to no drag affecting on ship in the first phase. On the other hand the sails filling with the blowing air will convey big amounts of impulsive force to the ship’s hull through the masts.

 

Now the ship gaining speed, the impulsive force of the wind on the sail drops exponentially in second phase. Meanwhile, the hydrodynamic drag force of water increases with the square of the ship’s speed exponentially. Those changes result in a decrease in ships acceleration compared to the first phase. The ship still gains speed, however, with incrementally smaller boosts.

 

In phase 3, the increasing drag and the decreasing propulsion of the sails come to equilibrium at one stage. That means the force on the sails and the drag on ships hull are equal concluding the total force on the ship is zero. This is also called steady-state, where the sum of all force vectors on the ship is equal to zero. At this point, the ship has arrived its maximum speed and will continue sailing with this constant speed with no acceleration.

 

Ultimately, we will consider the ship neutralizing its sails and dropping them, which would result in slowing down in phase 4. Assuming the sails are diverted parallel to the wind and also furled, the sail force would converge to zero. While sailing with maximum speed, we would only have the hydrodynamic water drag affecting on ship, which would decelerate the ship over time eventually until a full stop. However, since drag also builds up exponentially with increasing speeds, this means, the speed first would fall off of the maximum speed range drastically, however, over time the slowdown of the ship would be slower and slower just until the standstill.

 

Maximum Ship Speed: Froude Number

 

"Froude had observed that when a ship or model was at its so called "Hull speed" the wave pattern of the transverse waves (the waves along the hull) have a wavelength equal to the length of the waterline. This means that the ship’s bow was riding on one wave crest and so was its stern. This is often called the hull speed and is a function of the length of the ship:

 

debe7ac296f4be93d2afae178fa37969.png

 

with,

V Hull = Hull Speed

LWL = Length at Waterline

 

Observing this, Froude realized that the ship resistance problem had to be broken into two different parts: residuary resistance (mainly wave making resistance) and frictional resistance. To get the proper residuary resistance, it was necessary to recreate the wave train created by the ship in the model tests. He found for any ship and geometrically similar model towed at the suitable speed that:

 

There is a frictional drag that is given by the shear due to the viscosity. This can result in 50% of the total resistance in fast ship designs and 80% of the total resistance in slower ship designs."

 

The froude number gives the physical limit value for ship speed.

 

According to this formula, the maximum hull speed of

  • HMS Victory is 9,7 m/s (18,8 knots)
  • USS Constitution  9,1 m/s (17,7 knots)
  • Lynx is 5,9 m/s (11,4 knots)

So, the ship Lynx ingame sailing with 16 knots at beam reach is actually exceeding its theoretical hull speed limit of 11,4 knots.

 

Sailing Variables

 

The aerodynamic forces on sails, and the hydrodynamic drag force around ships hull below waterline can be expressed with the drag formula below:

 

99a6015b6a230860c9b1517b238e5de9.png

 

where;

 

Density, ϱ:                Water 998 kg/m3; Air 1,2 kg/m3                  

Sail Area, A:             44400 m2 (eg. for HMS Victory)

CD Sails:                   1,2

CB Hull:                     Block coefficient of the ship below waterline

VAir:                          Wind scale according to Beaufort level between 0 – 14 m/s

Projection Area, A:   Underwater area perpendicular to the water flow

Cd Hull:                     Hydrodynamic Hull factor

VShip:                        Speed of ship in m/s

Mass:                       Total mass of the ship

Acceleration:            The change of speed in m/s2

 

With the help of those parameters, the sailing characteristics of a ship can be interpreted.

 

Table.png

 

Most of the variables here, can be calculated or estimated roughly, but the drag coefficient of the hull, Cd. This coefficient depends on the shape of the hull, the surface roughness, the Reynolds number, Mach number and Froude number, and thus, is a dynamic value, which is very hard to define for every condition.

 

The block coefficient of hull also gives some info for interpreting and comparing the total drag coefficient of the ship. Below are some coefficients of rated ships, calculated with the molded models of the relevant ships in this paper.

 

Block.png

 

 

Sails as propulsion

 

We have the drag formula for the pushing force at sails and according the variables above,

 

99a6015b6a230860c9b1517b238e5de9.png

 

The force at sails of Victory in the phase of setting sails at a moderate breeze is: FD = 141487 N.

 

Considering the 3300 tonnes mass of HMS Victory, the initial acceleration would be a = 0,04 m/s2.

 

All variables but v2 and Cd are constant parameters here. Cd is the most dynamic and unpredictable one.

 

The v2 speed factor is depended on wind speed as well as the ship’s current speed. It is the square of the difference of wind speed and ship speed. The faster the ship sails, the less the v2 factor will be. In other words, a ship gaining speed would lose its acceleration slowly. But the ship getting closer to wind speed is not the only obstacle here.

 

The drag comes into play with the increasing ship speed.

 

Drag as an obstacle

 

The same formula is valid for the drag force at ships hull underwater (=wetted area);

 

At a moderate breeze, the HMS Victory will roughly have the following drag force at its ship's hull: Fd = 36772 N

 

Assuming there is no current at the sea and water mass standing still, the v2 variable depends only on the ship speed.

 

So, the faster the ship sails, the bigger the v2 factor will be, and therefore, the water drag would increase exponentially. The equibirilium of sail and drag force of HMS Victory would result in a 2,9 m/s maximum speed at a moderate breeze.

 

Ship speed and acceleration

 

The excel table determining the sail and drag force incrementally for every 0,1 m/s speed change is as below. The sum of propulsion and drag gives us the total force effecting on the ship.

 

Victory_6_Table.png

 

 

According to the table, the speed - acceleration (force) curve of the HMS Victory at a wind speed of 6 m/s is as follows

 

Victory_6.png

Having found the values for the total force on the ship, we can divide this value with the mass of the ship to find out the acceleration of the ship for any given speed.

 

864f9723bd47b6bacfaf1764847f7aad.png

 

Now, we have determined the acceleration of the ship for any speed value. We would move from acceleration – speed (F – v) graph to the time domain with the help of the numerical euler integration.

 

Formula.png

Here, it can be seen that HMS Victory needs 9000 seconds, approximately 2,5 hours to reach its maximum speed. As a game modeling perspective, this time frame surely has to be compressed. As long as the characteristics of the curves and the ratio of the curves witch eachother is stable, it can be scaled to a reasonable range to make the game playable as well as still feeling realistic. Below we can compare the speed - time curve of NA and PotBS.

 

HMS Victory in NA reaches its top speed in around 90 seconds, and a first rate in PotBS attains the max speed in 180 seconds. Comparing those with the theoretical 9000 seconds, we can say that NA compresses the time 100x, while PotBS compresses it 50x in sailing instances.

 

Comparing the curves above and below, USS Constitution right now has a relative high acceleration. Comparing its mass and sail area, it should have a characteristic more similar like HMS Victory. However, as seen in graph below, it is much more agile like Lynx right now.

 

Comparison_Pot_BS.png

 

 

 

Deceleration and Slowing Down

 

The deceleration corresponds the phase 4, where the only force acting on the ship is the water drag. Assuming the sails set paralel to wind and/or furled, the ship would lose speed immediately with a big rate of speed loss. Due to hull shape, surface roughness and other factors which raise the drag coefficient for HMS Victory, now those factors help her to decelerate faster than Constitution and Lynx. To lose speed until 0,5 m/s, HMS Victory needs roughly half of the time Lynx needs to slow down and to reach that speed.

 

Decel_Theory.png

 

To measure and record the deceleration process in NA, I neutralized and furled the sails at the same time. So, the first 5-10 seconds can be ignored because of this reason. Now if we look the values, it can be seen that there are some inconsistency with HMS Victory's characteristics. The graph below says that the the drag on HMS Victory is quite low compared to Lynx and Constitution, as a result it slows down in a longer period than the smaller ships.

 

However, this should not be the case. Dropped or neutralized the sails, HMS Victory should decelerate much faster than those two ships. I think, in late alpha and beta stages those saling parameters should be optimezed further for modeling the sailing better and for a realistic feel.

 

 

Decel_NA.png

In conclusion, I would say that, right now the game model in general does realise the straight-forward sailing motion quite good. My personel opinion is that, the time compression in battle instances could be decreased from 100x to 75x maybe. So, the fast acceleration of big ships in around 90 seconds to their maximum speeds would be around 120 seconds. That would also effect the small ships. To be fair, the Yacht and Lynx like ships react and sail too quick at the moment. They accelerate, turn and move really fast like remote control cars. Decreasing the time compression would also make those small ships to move a little bit slower.

 

Other than that, the maximum hull speed according to the Froude number might be considered for small ships to limit their top speeds realisticly.

 

In conjuction with this issue, different/changing wind speeds could be also a good addition to the current sailing mechanics. Like in Beufort scale, in a light breeze wind around 3 m/s, the top speed and acceleration of all ships would be decreased, whereas, in a fresh gale with 20 m/s wind speed, the acceleration and max speed of ships would be much higher altering the battle instance to be played in fast-paced environment. So, the changing wind speed might add another dimension to the battle instances determining the instance played slow-paced like chess or fast-paced like an action game.

 

I have only checked the three ships above, but as a thumb rule, (having smilar sail/mass ratios) a fast accelerating ship should decelerate slower and vice versa. HMS Victory should be worked on a little bit.

 

The game model and physics currently are pretty satisfying. This was all I would say for the straight forward motion for now. I will try to continue my feedback for modeling the turning and lateral forces later.

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For the convenience of devs and readers, I've taken the liberty of pulling out the main parts of the post that can be used as actual gameplay recommendations:

 

 

The graph below says that the the drag on HMS Victory is quite low compared to Lynx and Constitution, as a result it slows down in a longer period than the smaller ships.

 

However, this should not be the case. Dropped or neutralized the sails, HMS Victory should decelerate much faster than those two ships. I think, in late alpha and beta stages those saling parameters should be optimezed further for modeling the sailing better and for a realistic feel.

 

....

 

However, since drag also builds up exponentially with increasing speeds, this means, the speed first would fall off of the maximum speed range drastically, however, over time the slowdown of the ship would be slower and slower just until the standstill.

Here's one I've been calling for over the past few months. At high speeds, deceleration is also fast, becoming exponentially slower.

 

 

 

My personel opinion is that, the time compression in battle instances could be decreased from 100x to 75x maybe. So, the fast acceleration of big ships in around 90 seconds to their maximum speeds would be around 120 seconds. That would also effect the small ships. To be fair, the Yacht and Lynx like ships react and sail too quick at the moment. They accelerate, turn and move really fast like remote control cars. Decreasing the time compression would also make those small ships to move a little bit slower.

No argument there. The longer it takes to achieve top speed, the more your ability to plan ahead matters.

 

 

 

I don't think Lynx should get any slower, though. If she is based on the modern schooner, than a hull speed of 11 knots might be accurate. But the historical Baltimore clippers, including the original Lynx, were the fastest warships in history up to that point. The cutter and yacht probably do need a speed cut.

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Froude number and hull speed doesn't give a "maximum speed" it merely gives a speed of similar dynamics, and one particularly associated with an approximate value for a particular wave pattern.

It is "typically" a practical maximum due to limited sail area or mechanical propulsion compared to hull drag, but it can not be considered a true maximum as it is quite possible to design a vessel which carries sufficient sail or machinery to overcome the increased wave making drag consistent with Froude numbers of 0.9 to 1.34. Above this the "increment" of wave drag begins to decline again, although total drag is still rising due to skin friction and hull form. There are plenty of recorded speeds above the vessels' "hull speed", although it does require something other than a "cod-head, mackrel tail" design.

While the smaller ships have to do more to overcome their wave drag, sooner, they also carry significantly more sail area for their size, and have more suitable high speed underwater hull forms..

It should be noted that the paper referred didn't have any parameters directly related to hull drag ~ the KM(t) and KM(l) figures are stability 'heights' of the metacentre above the keel, transversely and longitudinally.
Block coefficient affects the form and relative scale of the resistance (both from wetted area skin friction and form resistance, and from the wave making drag), but the relationships are complex, and a fuller form can provide lower resistances at slow speeds (less skin area for a given displacement).

 

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There is some good stuff in here, some of which may be good information for development.  As it wasn't a suggestion, but rather feedback on the current Sea Trials build, I've moved it to the Sea Trials forum so it can receive the attention it deserves.

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While a large ship of the line has a wetted area around 3x that of a large frigate, and thus a resistance also roughly in proportion to 3x, it has nearly 3x the inertia as well, so it will only lose speed slightly slower than the frigate if the wind ceases to apply a driving or retarding force.

As the frigate carries a larger sail area for her wetted area, she will be able to back her sails more effectively in appropriate conditions, but again the differences are minor.

Upper speed in calm conditions (where weatherliness, sheer size compared to seas and strength of yards/spars aren't factors) the very slight edge in all of wetted area/displacement and sail area/wetted area in favour of the smaller ship permits a higher speed.

For these larger vessels speeds are away from the significant wave making regime.

As sizes get smaller, the wetted area/displacement becomes more favourable (due to differences in hull form, not scale effects) and sail area/wetted area increases markedly.
Cutters appear to trade wetted area against wetted area for safer operation (albeit at slower speeds) in inshore areas, and particularly on lee shores, and may be noticeably quicker to slow (both because of this unfavourable ratio and their likely operation in unfavourable Froude numbers (at or above "hull speed").

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Froude number and hull speed doesn't give a "maximum speed" it merely gives a speed of similar dynamics, and one particularly associated with an approximate value for a particular wave pattern.

It is "typically" a practical maximum due to limited sail area or mechanical propulsion compared to hull drag, but it can not be considered a true maximum as it is quite possible to design a vessel which carries sufficient sail or machinery to overcome the increased wave making drag consistent with Froude numbers of 0.9 to 1.34. Above this the "increment" of wave drag begins to decline again, although total drag is still rising due to skin friction and hull form. There are plenty of recorded speeds above the vessels' "hull speed", although it does require something other than a "cod-head, mackrel tail" design.

While the smaller ships have to do more to overcome their wave drag, sooner, they also carry significantly more sail area for their size, and have more suitable high speed underwater hull forms.

 

That is right, as long as there is enough propulsion to overcome the total resistance on the hull, be it wind or the engine, a ship can exceed its theoretical hull speed. Being at hull speed means, the hull needs a significant more amount of force ie. energy to go beyond this speed. That is correct for displacement hulls.

 

There are plenty of modern vessels with semi-displacement or planing hulls, which frequently exceed their hull speed.

 

If we go back to the age of sail, for many sailboats, this is not possible because the lack of adequate power to do so.

 

However, if there is historical data for Lynx stating that she did sail with 15 knots, maybe she does not have a displacement hull.

 

Speed-length_vs_weight-resistance.gif

 

It should be noted that the paper referred didn't have any parameters directly related to hull drag ~ the KM(t) and KM(l) figures are stability 'heights' of the metacentre above the keel, transversely and longitudinally.

Block coefficient affects the form and relative scale of the resistance (both from wetted area skin friction and form resistance, and from the wave making drag), but the relationships are complex, and a fuller form can provide lower resistances at slow speeds (less skin area for a given displacement).

 

 

The hull drag coefficient CD is mostly determined experimentally or calculated computationally. As said before this coefficient depends on many parameters and also is characteristic for every unique ship hull. The firm way to define it is according to the empirical model tests. If this is not the case, as in the simple model, those can be assigned by devs in correlation with other spesific hydrodynamic coefficients of ships for the sake of simplicity (eg. correlation between Cb of Wigley Hull and Series60)

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Very interesting post. The thought occurs to me that it could be a nice twist if the devs modelled length of time at sea and bottom fouling into the acceleration and deceleration model too so that in the open world if you went too long between slipping and scrapping the hull you lost acceleration and top speed and gained deceleration.  

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Very interesting post. The thought occurs to me that it could be a nice twist if the devs modelled length of time at sea and bottom fouling into the acceleration and deceleration model too so that in the open world if you went too long between slipping and scrapping the hull you lost acceleration and top speed and gained deceleration.  

LOL, if it gets too realistic they will have to start paying us to sail and maintain these ships...

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Awfully good stuff.....clearly someone either has too much time on their hands or is a bit of a sailing/hydrodynamics/physics geek (this is not necessarily a bad thing), nicely done Sir!

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Poyraz.. can you write the similar analysis on turning? 

particularly on sustained turning (when kiting)

In the same post 

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I would love to see more on the turning bit; especially eyeballing HMS Bellona: she's just too sweet a ship to be quiet true.

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Will the amount of sail area you should use in different weather ever be modelled? Carrying full sail in a storm would be asking for real trouble but is perfectly ok in the sea trials.

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Turning Dynamics

 

Having said that the modeling of the straight forward (sway) motion of a ship is too complex for our case; one should multiply this complexity many times for the modeling of the turning of a sailboat. That is why nowadays, even with computational calculations there are many trials and tests for determining the response of a ship in a turning maneuver.

 

Now, if we go back to the Naval Action, the target is to create a simple sailing model close as possible to the reality without adding much complexity both code- and gameplay-wise. To realize this, one should check the reality first.

 

What Happens while Turning

 

In general, to turn a ship in a desired direction the rudder is deflected against the flow, which creates a drag and a lift force. The drag here slows down the ship, whereas the lift force creates the turning force and thus, the needed moment to initiate the turning via the ships hull. Although the rudder seems to have the leading role here, the force and moments created by the ships hull is the other main actor. The turning moment via the ship's hull is created due to the drift angle, which is created by the rudder force.

 

Now lets assume a ship sailing with its maximum, constant speed and then the command is given to turn the rudder by 35 degrees.

 

Right before the rudder is turned, the resistance has already balanced the sail thrust in longitudinal direction. According to the simple model, in phase 1 there are no lateral forces acting on ships hull, because the flow field is symmetrical in lateral direction that the hydrodynamic pressures on the hull surface in port and starboard side balance each other.

 

The manoeuvring phase extends from the moment when the rudder is deflected until the blade reaches the angle desired. The flow field near ship stern and rudder changes by the movement of the rudder. The lift force on rudder creates a rotational moment to turn the ship’s hull slightly in phase 2. Now the hull has a drift angle to the main flow and the hull itself, acting as a foil, creates a lateral force and thus a moment. This is the varying phase when the rudder-deflection angle remains constant but the dynamic equilibrium among all the forces acting on the vessel has not been reached yet.

 

When all of the hydrodynamic forces, moments, inertial forces balance in phase 3, which takes a while depending on those forces, the ship reaches its steady state turning condition and turns with a constant turn rate, if the sail thrust and rudder conditions under which the evolution is undertaken are not altered.

 

Turning.jpg

 

Looking further into those 3 phases:

 

1. First phase is the time from the moment of the rudder deflection until the moment when the ship starts turning. Rudder force is the result of the rudder deflection by an angle α. One of its components is undesirable because it increases the ship’s resistance and slows down the ship, while the other component creates a transverse force on the ship’s longitudinal axis along with a simultaneous moment with regard to the current position of the pivot point. Before the ship starts turning, the mentioned moment induced by rudder force action must overcome the inertial moment due to the ship’s own mass and the added mass. Before it overcomes the mass moment of inertia, the effect of the transverse component manifests only in moving the entire ship sideways, in a direction perpendicular to the ship’s longitudinal axis. The first phase lasts a short period of time, and the movement is greater on the stern than it is on the bow. Thus, immediately after the rudder deflection, the ship’s motion is at first opposite from the desired one.

 

Turning_Graph.jpg

delta R = Rudder angle; r = turn rate, yaw rate;  ˙r  = turning acceleration

 

2. The second phase begins with the turning of the ship’s bow in the desired direction, at the moment when the rudder force moment overcomes the intertial moment due to the ship’s own mass and the added mass. During the second phase, ship speed decreases, the rate of turn increases, and the radius of the turning circle decreases. The ship continues to turn in a curve, the curvature radius of which decreases, and during the turning, the bow is always closer to the centre of the circle than the stern.

 

3. The third phase begins at the moment when all the forces and moments (ship’s resistance force, propulsion force, rudder’s moment of force, inertial forces and moments) are balanced. Then the ship starts turning with a constant speed in a circle of a constant radius. The bow continues to turn in a circle of a shorter radius than that of the stern. This phase of ship turning usually begins after the ship changed its course by 100° to 120°.

 

After all those phases, the ship starts to turn with a constant turn rate which results in a fixed turning radius in a fixed turning circle. The path described by a vessel’s centre of gravity when turned whilst keeping a constant speed and rudder angle is called the turning circle. Graphic representations of such circles for different speeds and rudder angles are called turning diagrams and provide an excellent overview of the vessel’s behaviour, allowing the ship’s handler to forecast the path the vessel will follow under the specific conditions affecting it.

 

Parameters Affecting the Turning Circle

 

The following conclusions may be drawn from a study of the turning circles for different types of vessels:

 

1. Advance and transfer

The advance for a 90° turn is considerably greater than the transfer. For rudder-deflection angles of 35°, the range varies between 3 and 5 ship lengths; it diminishes when increasing the rudder angle deflected and increases with vessel speed. Transfer at 90° turn for that same rudder-deflection angle generally varies between 2 and 3 ship lengths; it diminishes when increasing the rudder angle deflected.

 

2. Tactical and steady turning diameter

Both diameters diminish for one given velocity and water depth when the rudder angle deflected increases. These diameters vary little for the same depth of water and blade deflection for different speeds provided the latter are sufficient to guarantee good steering effectiveness from the rudder.

 

3. Influence of the hull form

The underwater hull form affects the dimensions of the turning circle. Two vessels similar length and draught, the one with the finer underwater hull needs more area to turn than that with fuller forms. The same happens with a relatively longer vessel, other general features being equal.

 

4. Influence of draught and load condition

Differences in a vessel’s draught affect its maneuvering conditions. Generally, loaded ships have a larger turning circle than in ballast. Trim also has an appreciable effect on the turning qualities of a vessel, with the tactical diameter increasing when the vessel is trimmed by the stern and diminishing when trimmed by then bow. Therefore, the effect of trim is to move the pivot point position to the end with larger draught.

 

5. Turning time

For a given rudder-deflection angle, the duration of turning diminishes when speed increases. For the same speed, the time diminishes when increasing the rudder angle. Full deflection angle of the rudder and maximum speed must be used to complete a turn in the shorter time possible.

 

6. Linear speed

A gradual loss of speed occurs with respect to the seabed through the effect of rudder resistance and the drift angle the vessel acquires during the first 90° turn, despite the propellers continuing to rotate at the same number of revolutions per minute as before commencing the evolution because the vessel moves with a certain drift angle and doesn’t take advantage of the hydrodynamic lines of its underwater hull. The amount or proportion by which linear speed is reduced greatly varies for different types of vessel and depends on the initial speed and rudder angle deflected.

 

When turning with the rudder fully deflected, most vessels lose between 1/3 and 1/2 of their speed when they have turned about 90º and their final speed which they keep steady may be between 1/3 and 2/3 of their initial speed.

 

7. Angular speed

The angular turning speed, which was zero when beginning to turn, reaches its maximum value before the bow has turned 90° and then slightly falls off becoming constant in the final steady turning period. It may vary between one and three degrees per second with the rudder fully deflected in very deep water, depending on the type of vessel.

 

8. Drift angle

This increases with the rudder-deflection angle and depth of water available but is practically independent from speed. The drift angle at the vessel’s centre of gravity for 35° rudder-deflection angles and very deep water generally varies between 5° and 10º, but may exceptionally reach values of 15° to 20°.

 

9. Stern swing in turning

When maneuvering in restricted waters and in the vicinity of obstacles, shallow waters or other vessels, it is very important to take that motion, called stern swing into accounts well as that that end of the vessel sweeps the water more outwards of the turning circle the smaller the tactical diameter is, measured in number of ship lengths.

 

10. Wind effects on the turning circle

The wind deforms the typical turning circle and the modification it undergoes depends on the wind force and direction with respect to the vessel’s initial heading before commencing to turn. The shape of the resulting curve varies according to the type of vessel being considered and the intensity and direction of the wind action, because of the fact that the leeway and transfer are not uniform during the whole turning and, therefore, the vessel’s angular turning speed accelerates or slows down according to the wind’s angle of incidence with respect to the centerline plane.

 

11. Current

Similar to wind, the current also deforms the turning circle.

 

Effects of Turning on the Ship

 

Getting into a turning maneveur and being affected by the relevant forces results in:

 

  • Speed loss of the ship: About 30-50% ship's speed is lost as of the steady state turning. The drag force against the flow is defined as the a factor of fluid density, square of flow velocity, cross-section against the flow and the drag coefficient. When the ship's hull turns relative to the flow direction, both the underwater cross-section and the drag coefficient increases. The disturbance in flow lines in phase 3 explains the increase of drag coefficient.

1329940531.jpg

 

 

Cross.jpg

  • Heeling of the ship: The centrifugal force during the turning results in heeling of the ship in direction to the outside of the turning curve.

4.JPG

  • Increase of the force on the helm: When turning the rudder with the helm, the force at rudder increases with the growing rudder angle. Like a spring, a 35 degree turned rudder will release its energy when it is left loose.

FR = Constant x Density x AR . v2 . sin (α)

 

Right now, turning the rudder and releasing it happens at same speed in the game model. However, releasing the rudder should be faster than turning it in a maneveur. (Considering lack of gears in age of sail)

 

Estimation of Turn (Yaw) Rate

 

For the sake of a simple model and considering all those parameters, a table of emprical values would be much more suitable for determinig the turn rates. Here comes the rudder factor into play. The rudder factor gives the correlation between ship's lateral area and the rudder blade area according to the block coefficient and the rudder angle. With the help of the data of HMS Victory, we can make an estimation about the turn rate of the ship.

 

Rudder.png

 

Emprik.png

 

Such diagrams are generally drawn up on the basis of very precise, complete tests performed with the first vessel of a class, before being commissioned. Those data rooting from modern vessels, one can expect the turning radius of an age of sail ship being more or less larger than those values read from the graphs for any given specifications. Despite this, there might be many differences even between similar vessels.

 

The yaw rate is the quotient of ship's speed with the turning radius. We have to define the turning radius according the graph above and the the turning speed is estimated 0,7 times the maximum ship speed.

 

US20030172728A1-20030918-M00016.png

 

Looking to the values of HMS Victory, the turning radius might be around 3x of the ships length which is around 170 meters. Assuming that the ship loses 30% of its speed, the yaw rate which is calculated with the help of the speed and turning radius would be than around 0,022 radians per seconds. This corresponds around 1,3 degrees per second for HMS Victory, while sailing with 5,2 m/s in a fresh breeze just before the turning maneveur.

 

Table.png

 

I have been out of town for business lately and could not have the time for more details. But I will try to add more information on turning and also the sources whenever I have more time in my hands.

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Trim also has an appreciable effect on the turning qualities of a vessel, with the tactical diameter increasing when the vessel is trimmed by the stern and diminishing when trimmed by the stem.

Typo here.

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Thank you for the summary. I can't help but notice you've neglect to mention lift, which is essential to fore-and-aft rigging, and, I assume, important to square-rigged ships when beating into the wind. Can you elaborate on whether lift is a contributing force in square rigged ships?

 

The aerodynamic forces on sails, and the hydrodynamic drag force around ships hull below waterline can be expressed with the drag formula below:

 

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Lift applies to any sail when you are beating upwind. A square sail can behave exactly the same as a fore-and-aft lugsail if you brace it up sharp enough.

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this feedback will pale in complexity compared to the main posts on here, but I have one request for a mechanics edit. add the spanker to the list of sails that are lowered/depowered when the user hits 'T'.

the intension behind this is to try and make box-hauling actually work. I've tried it repeatedly, and no matter what I do with yard angles, I can never actually get myself angled downwind further than a beam reach sailing astern. even with 3 masts of square sails backed, and everything else depowered, the spanker brings me to a stop as I reverse into a beam reach. this may also be a momentum issue, but I think lowering the spanker may be enough.

 

As the Naval Action team has had "Correct tacking, boxhauling, clubhauling and other elements of the age of sail sailing are possible." on their website since the beginning, I'm surprised that it's not actually possible. clubhauling is also not possible (no anchors), but that one is harder to fix.

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I would like to update this feedback after quite some time.
 
As for now the acceleration and deceleration of the ships look like on the right track. Furthermore, I have observed around 20% speed loss during constant turning while sailing a 3rd rate as well.
 
There were many other parameters mentioned in this thread, however, in my opinion a specific one should be further worked, which is turning of the ships.
 
Need for Turning Acceleration
Turning acceleration is what we are lacking right now. This is the exact reason why turning ships in Naval Action feels arcadish.
 
This can be compared with linear acceleration to understand the relation between turning speed and turning acceleration. When you set sais, it will take some time like 40-50 seconds to achieve the maximum speed depending on the acceleration of the ship. As in linear motion, it is similar in angular motion. So, when you begin your turn, it would take some time up until you reach your maximum turn rate.
 

331249.image4.png

 
 
Currently in game, when you inititate a turning with A or D keys, the ship waits like 1 second and then suddenly reaches its maximum turn rate. This is the same for all ships from Cutter to Santisima.
 
In real life, it would take some time as shown in the graph below to reach a constant turning rate( r ), which is phase 3. During the phase 1 and 2, the turn rate increases for a definite amount of time.
 
The dh graph here is the rudder angle. The turning behavior currently ingame, represents actually the change of rudder angle. As you can see from the graph, you won't reach to your maximum turning rate, as soon as the rudder is turned to its maximum angle. Some period of time had to pass by, until the ship responses on the deflected rudder angle.
 

zewpTij.jpg
 
Finally, I would like to add a comparison between the current turning behavior and the suggested one. As you can see, the ship on right builds slowly its turn rate and after some time it begin to turn with a constant turn rate. On the other hand, the ship on the left begin to turn with constant turn rate slightly after the start of the turn, which is current state in NA.
 
Turning acceleration feature if added, would add:

  • much more realistic ship behavior while sailing and turning
  • much more variety to the ships, and each ship will have its own characteristics for turning.
  • a gain/loss factor for all ships, for instance a ship of line would bring more gun power in return of slower turning, whereas, frigates and smaller ships would act more agile and nimble in return of less armor and guns.

d5dDziz.gif

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