IRL: big ships go faster than little ships!

[Thomas Cochrane]

I’ve noticed that the relative speeds of ships is often discussed, most recently in the Feb 25 patch thread.

I wanted to explain something which maybe some people don’t know : the maximum speed of a mono-hull displacement craft (so all the naval action ships) is limited by its length. The shorter the vessel the lower its maximum speed. The longer the vessel the higher its maximum speed.

The formula is like this:
Maximum speed (in knots) = 1.333 times the square root of the waterline length (in feet).

So a vessel with an 81 feet waterline length is limited to a maximum speed of 12 knots but a 16 foot vessel could only manage about 5 and a half knots.

If you are interested about why this is then see this link.

Vessel cannot normally exceed their hull speed which means that generally longer ships are faster than smaller ships (not the other way around!). Exceeding hull length does happen sometimes by planing (lifting the prow out of the water like a speed boat) or surfing (like a .. dolphin or surfer). If a naval action ship starts surfing or planing this likely to be very bad news. It happens sometimes when you are running from heavy weather and so ships have sea anchors (drogues) to slow you down to hull speed to prevent damage to the boat.

Now, maximum speed through water doesn’t mean it will go that fast. And it doesn’t necessarily mean that this longer ship will be faster than that shorter ship because it depends on conditions, points of sail, ship design, crew skill, quality of sails etc. But it does mean that the top speed it can physically be propelled through the water is higher - whether under sail or with a diesel engine. So if two ships have roughly the same profile and same rigging but one is twice as long as another it will be roughly twice as fast. And, in fact, this is one of the factors used to group ships for racing.

It is important also to note the difference between speed through water and speed over land. Ships can, and do often, exceed their maximum speed over land because they are helped along by tides or current, but they will never exceed their maximum speed through water.

I don’t know whether speed in game is speed through water (like sailing away from the knotted rope, or the little propeller under modern sail ships) or speed over land (like a GPS). In the day the knotted rope measured speed through the water but the daily fixes measured speed over land. I suspect that its speed over land.

If the in game speed was speed through water then you could have a situation where your speed was showing 2 knots east but you were actually moving 2 knots west (-2 knots east) over land because of a 4 knots current and I don't think that's the case.

And finally, remember that there are points of sail where smaller ships do better, either be faster or be more manoeuvrable, but this would be because of this rig. For example fore and aft rigs can get closer to the wind than square rigged. In the case the length is irrelevant because one ship is, for example, not receiving any drive from the sails at all.

TLDR: the longer the ship, the faster its top speed.

Edited February 28, 2015 by Thomas Cochrane

[Brigand]

Some while back I did some calculation on this (historic data):

		      LWL	Hull speed 	Actual	   C	   % of Hull speed
Lady Washington       58 ft     10.2            9.5        1.25    93.09%
USS Niagara           111 ft    14.1            15         1.42    106.25%
HMS Surprise          114 ft    14.3            12         1.12    83.87%
USS Constitution      175 ft    17.7            13.5       1.02    76.16%
HMS Victory           196 ft    18.8            11         0.79    58.64%

There is more to this whole discussion than just length of the waterline. As you can see, the fastest vessel in reality turns out to be the USS Niagara, she is almost 4 knots faster than the USS Constitution which has a significantly larger length at the waterline.

I wondered for some time where the differences in C come from, they are quite important and, as shown, most often not 1.33 as suggested on wikipedia.

 

~Brigand

Edit:

I thought it would be a good idea to post this quote from @admin earlier today:

(...)

2) speed is relative - please don't look at the knots on the indicator as real life knots - those are numbers showing certain number of unity meters in relation to game time. Those numbers will be readjusted eventually to match real life speed (after all balancing is done). When judging speed at this stage you should be mostly concerned with feel - how this speed feels gameplay wise.

[Grim DeGrim]

In general... Tl;Dr... Small ships accel faster to top speed, big sail have a faster top speed. Generally, for comparative best points of sail.

Did I get it right?

Edited February 26, 2015 by Grim DeGrim

[Axralis]

I’ve noticed that the relative speeds of ships is often discussed, most recently in the Feb 25 patch thread.

 

I wanted to explain something which maybe some people don’t know : the maximum speed of a mono-hull displacement craft (so all the naval action ships) is limited by its length. The shorter the vessel the lower its maximum speed. The longer the vessel the higher its maximum speed.

 

The formula is like this:

Maximum speed (in knots) = 1.333 times waterline length (in feet).

 

So a vessel with an 81 feet waterline length is limited to a maximum speed of 12 knots but a 16 foot vessel could only manage about 5 and a half knots.

 

If you are interested about why this is then see this link.

 

Vessel cannot normally exceed their hull speed which means that generally longer ships are faster than smaller ships (not the other way around!). Exceeding hull length does happen sometimes by planing (lifting the prow out of the water like a speed boat) or surfing (like a .. dolphin or surfer). If a naval action ship starts surfing or planing this likely to be very bad news. It happens sometimes when you are running from heavy weather and so ships have sea anchors (drogues) to slow you down to hull speed to prevent damage to the boat.

 

Now, maximum speed through water doesn’t mean it will go that fast. And it doesn’t necessarily mean that this longer ship will be faster than that shorter ship because it depends on conditions, points of sail, ship design, crew skill, quality of sails etc. But it does mean that the top speed it can physically be propelled through the water is higher - whether under sail or with a diesel engine. So if two ships have roughly the same profile and same rigging but one is twice as long as another it will be roughly twice as fast. And, in fact, this is one of the factors used to group ships for racing.

 

It is important also to note the difference between speed through water and speed over land. Ships can, and do often, exceed their maximum speed over land because they are helped along by tides or current, but they will never exceed their maximum speed through water.

 

I don’t know whether speed in game is speed through water (like sailing away from the knotted rope, or the little propeller under modern sail ships) or speed over land (like a GPS).  In the day the knotted rope measured speed over land but the daily fixes measured speed over land. I suspect that its speed over land.

 

If the in game speed was speed through water then you could have a situation where your speed was showing 2 knots east but you were actually moving 2 knots west (-2 knots east) over land because of a 4 knots current and I don't think that's the case.

 

And finally, remember that there are points of sail where smaller ships do better, either be faster or be more manoeuvrable, but this would be because of this rig. For example fore and aft rigs can get closer to the wind than square rigged. In the case the length is irrelevant because one ship is, for example, not receiving any drive from the sails at all. 

 

TLDR: the longer the ship, the faster its top speed.

 

So you are saying that Santisima is 1.5x-2x faster then the Trin ? She is that time longer in length, she is  square rigged with 3 masts and same sail configuration ?

[Hethwill]

Does displacement mass get considered ? Ship nominal mass plus full storage.

Edited February 26, 2015 by Hethwill_Khan

[Brigand]

The actual formula should be:

I guess the OP should be edited?

~Brigand

[Ned Loe]

I already mentioned this to the dev team. Acceleration and speed they don't feel right. Ships accelerate too fast and when you turn you drift and slide, especially on little boats. 

 

I suggested Potbs formulas from this thread:

 

http://forums.burningsea.com/forum/archive/retired-forums/discussion-topics/ships-ship-combat-ship-skills/93869-ship-acceleration-turning-turning-acceleration-and-turning-decel

 

Linear Acceleration

At full sails and sailing in a straight line, this is fairly well established more or less to follow the formula

a = A ( 1 - v^2 / V^2 )

where
a is acceleration at that moment
A is maximum acceleration (the value in the ship stats sheet)
v is the linear speed at that moment
V is the max speed at that wind angle.

[Yankee jack]

This is all good stuff.

 

 One of the biggest factors affecting the speed of these ships in their day was the "box" coefficient of the hull.  These were, in general, "boxy" warships that were designed and built to fight now and sail later.  Anyone who has seen the Santis and Vics lumbering about can see this in action.

 

Compare these to the clippers and big steel sq riggers of the later years.  They could do 15 to 20kts in a gale and keep it up for weeks.  They were fine lined and built to go fast.

[GreatScott]

When it comes to the game I don't want a realistic game with terrible game play.  Although I find this discussion interesting, to me the most important thing is that the game is fun while being as realistic as possible.

Edited February 26, 2015 by GreatScott

[Kngsbrg]

One aspect not mentioned yet is heavy sea. Some ships can maintain a somewhat decent speed even in heavy sea, others are completely crippled by it.

 

Other than that, ship lenght is in no way the go to criteria for a high max. speed!

[maturin]

 

One aspect not mentioned yet is heavy sea. Some ships can maintain a somewhat decent speed even in heavy sea, others are completely crippled by it.

 

Other than that, ship lenght is in no way the go to criteria for a high max. speed!

Of course, heavy seas will almost always favor the heavier (thus longer) vessel.

 

 

 In the day the knotted rope measured speed over land but the daily fixes measured speed over land. I suspect that its speed over land.

Just pointing out a typo here, although I think we know what you mean.

[DeRuyter]

I think it is important to point out as the OP noted that "hull speed" is the potential maximum speed and just guessing I would say that many ships in the 18th c. rarely ever attained it. Just looking at the chart you will note that the USS Niagara is the only ship listed with a sharp clipper style hull shape, although I would still question how she exceeded hull speed with a displacement hull (ie not a modern racing dingy designed to plane on a reach).  Be that as it may I'd rather be onboard one of the other ships in heavy weather on the open ocean.

[admin]

I already mentioned this to the dev team. Acceleration and speed they don't feel right. Ships accelerate too fast and when you turn you drift and slide, especially on little boats.

I suggested Potbs formulas from this thread:

]

Ships slide and drift sometimes in real life even with no sails.

Overall - brigand shown that OP formula is incorrect.

Ship speed depended on dozens of factors including ballast placement, trims, mast placement, and captains skill.

+

We are not making an encyclopedia. Our goal is to make every ship useful and usable in combat.

90% of ships in potbs were useless. References from potbs will be accepted, but with 90% discount.

[Prater]

I think the Brig and Navy brig would be useful if it was as fast as the Cerb.  I think the speed they had before was fine, maybe even a touch too fast but making them the same speed as the Cerb or even slightly faster is a lot better than what it is now where it is the 2nd fastest ship in the game and only the Trincomalee can outrun it on broadreach. 

 

The brigs just needed a touchup on the waterline, maneuverability, armor and the addition of 24lb carronades, and the ship would be useful in a decent role.  Such a brig adds needed firepower to a light ship fleet without having to make the concession of speed you would make with the snow.  It can also chase down merchant ships and be a merchant ship.  It is a cheap and well used tool that you get more than your monies worth out of if used right, but it isn't the heavy machinery that might be able to do the job better but cost a fortune to buy and maintain.

 

By making the brigs so fast, you completely ruin the advantages of the fore-and-aft craft.  Now the only thing they are useful for are running away close hauled.  There is no longer any point to the fore-and-aft craft, nor the Cerberus and maybe even the Surprise.  Same with the Snow.  The Brigs can easily solo any of those ships now.

Edited February 26, 2015 by Prater

[Magnum]

I agree with Prater - putting a HEMI in the Brig and navy Brig did no favors to anyone - please dial them back like they were or close.

 

And to the OP - this isn't IRL - it's a game and it has to be fun or no one will play.

Edited February 26, 2015 by ampaholic

[Brigand]

I'm not sure if it is a pattern that would hold up with more samples (more ships in the list) but it may be intersting to note that in this list, the for the bluf-bowed vessels, the smaller ones manage to get closer to their theoretical maximum.

 

		      LWL	Hull speed      Actual	   C	   % of Hull speed
Lady Washington       58 ft     10.2            9.5        1.25    93.09%
HMS Surprise          114 ft    14.3            12         1.12    83.87%
USS Constitution      175 ft    17.7            13.5       1.02    76.16%
HMS Victory           196 ft    18.8            11         0.79    58.64%

I wonder if this has any relation to the reference that most of the 'fast' vessels in the age of sail where relatively small (luggers, etc).

~Brigand

[Brigand]

There are some metric that give a "feel" for the effect of fullness, displacement and sail quantity. They are only 'rough' metrics and shouldn't be used to directly compare very different rig/hull form, but can give reasonable correspondence with relative performance of 'similar' forms in different scale (or qualitative variations between two ships of the same size but different form).

Sail Area to Displacement (ft^2)/(ft^3)

SailArea/(Disp (ton) * 35)^0.667

Displacement Length (tons)/(ft @ wl)

Disp(ton) / (WL/100)^3)

Thanks, interesting. It is a bit problematic however that, for ship from the age of sail, the displacement is rarely know/available. In those times, they specified size/volume in ton burthen (cargo capacity) and even then, there are so many different methods (Carpenters formula, Builder's Tonnage, Builder's measurement, Builder's old measurement, Old Custom House Measurement) and none are too precise (estimating depth-in-hold as being equal to beam, etc). Most confusingly, those method's names are mixed up a lot in modern references.

In 1678 Thames shipbuilders used a method where displacement was calculated by multiplying length × beam × draught × block coefficient (0.62), all divided by 35 ft³ per ton of seawater. But I guess that too simplistic an estimate to be of any use.

Are there any modern methods that estimate the displacement based on ship dimensions (other than just modelling the hull in a cat program)?

~Brigand

[maturin]

I wonder what the criteria for sail area is.

[Brigand]

I'm having a bit of difficulty reading the columns / figuring out the column headers:

+--------------+-----------------------+---------------+-------------------+----------------+----------+----------+------------+-------------+-----------+------------------+
| Vessel       | Length (ft.)          |               | Gun port Height   | Burthen        | Displacement (tons) | Sail Area  | Waterline Area (sq.ft.) | absolute berthen |
| type         | Gun Deck | Water Line | Beam (ft.)    | above Load WL     | nominal (tuns) | Launched | Load     | (sq.ft.)   | Launched    | Load      | (Load-Launch)    |
+--------------+----------+------------+---------------+-------------------+----------------+----------+----------+------------+-------------+-----------+------------------+
| 120 gun      | 205.5    | 205.3      | 54.5          | 5.5               | 2808           | 2400     | 4720     | 25619      | 8440        | 10012     | 2320 tons        |
| 84 gun       | 195.6    | 195.8      | 51.44         | 5.5               | 2279           | 1848     | 3840     | 26724      | 7176        |  8960     | 1992 tons        |
| 76 gun       | 182      | 182        | 49            | 5.5               | 1925           | 1784     | 3102     | 24226      |             |           |                  |
| 74 gun       | 176      | 176        | 47.5          | 5.667             | 1741           | 1600     | 3028     | 23027      |             |           |                  |
| 74 gun razee | 176      | 175.3      | 47.5          | 8.667             | 1741           | 1420     | 2402     | 24374      |             |           |                  |
| 74 gun       | 168      | 168.3      | 46.92         | 5.333             | 1614           | 1384     | 2624     | 23027      |             |           |                  |
| 74 gun razee | 168      | 168        | 46.92         | 7.333             | 1614           | 1220     | 2616     | 24374      |             |           |                  |
| 60 gun       | 172.8    | 173.5      | 43.67         | 8                 | 1474           | 1040     | 2140     | 23072      |             |           |                  |
| 46 gun       | 151.8    | 153        | 39.92         | 6                 | 1073           |  760     | 1592     | 16651      |             |           |                  |
| 42 gun       | 145      | 145.3      | 38.17         | 7                 | 943            |  728     | 1460     | 16107      | 3760        |  4776     | 732 tons         |
| 28 gun       | 113.7    | 115        | 31.5          | 4.75              | 499            |  405     |  768     | 10152      |             |           |                  |
| 28 gun (fir) | 113.7    | 115        | 31.5          | 4.75              | 499            |  264     |  668     | 10152      |             |           |                  |
| 18 gun       | 109.5    | 106.8      | 30.5          | 4.5               | 429            |  232     |  506     |  9605      |             |           |                  |
| 18 gun       | 100      | 97.25      | 30.5          | 4.5               | 382            |  178     |  444     |  9277      |             |           |                  |
| 10 gun       | 90       | 87.17      | 24.5          | 4.167             | 235            |  135     |  291     |  6246      |             |           |                  |
| cutter       | 70.7     | 66         | 24            | 4.125             | 160            |  84      |  176     |  4825      |             |           |                  |
| cutter       | 60.75    | 57         | 20.333        | 3.5               | 108            |  63      |  109     |  3502      |             |           |                  |
+--------------+----------+------------+---------------+-------------------+----------------+----------+----------+------------+-------------+-----------+------------------+

Would the above be correct?

 

What does GD stand for?

 

~Brigand

[Brigand]

Ah, that makes sense, I've updated the table. The displacement values listed, are they from actual displacement figures (as in: did somebody model the hull shape to do the calculations?) or are they estimates?

What is the unit for the ton used? Imperial (long ton) or Metric (short ton)?

~Brigand

[Barberouge]

For approximations I had noted from various sources:

• block coeff 0.6-0.7 for merchants and 0.5-0.6 for warships
• displacement/tonnage 1.3 to 1.5 for warships
• hull weight/loaded displacement 0.5 for warships, 0.35 to 0.45 for merchants

Which seem to fit the values.

 

Also the resistance curves look like this:

 

 

Wave-making resistance (which determine the hull speed) is part of the residual resistance. If for example the sails would provide 10 tons, the max speed would be 20 knots instead of the 25 knots hull speed.

 

BTW just for the fun, there was a university student project about the maneuverability of Trafalgar ships, using a 1:40 model and a wind tunnel: article and figures. The Victory could move at up to 9.5 knots, but couldn't sail closer than 110° with squares set.

[maturin]

 

The Victory could move at up to 9.5 knots, but couldn't sail closer than 110° with squares set.

I hope he acknowledged that as only the theoretical prediction of his model.

[Dharus]

While I don't disagree with larger ships (really Frigates), being the fastest ships on paper and usually reality.  The calculation of hull speed is one thing but reality of sailing is that there are lots of variables.  Smaller ships have a advantage in that they don't need as much wind to reach close to their hull speed.  Thus on light wind days the smaller, lighter ships could easily outrun larger ships.  That's one reason the lighter ships served as scouts, couriers, etc.  Problem with game mechanics and gameplay is that light wind sailing isn't thrilling (its like a slow trainwreck).

[maturin]

in this case the area of each regular sized staysail, course, topsail, t'gallant, jib and spanker. This is different from the effective sail area, makes no distinction for height above surface or attitude. It would be lower with storm sails, and could be higher if studding sails were set on.

Yeah, but where do you stop? What about royals? If you include every jib, you have to include the royals. And including every staysail just makes the stat meaningless because staysails vary in proportion a lot depending on the vessel, yet will almost never be flown in their entirety.

 

I assume that the numbers give the surface area of 'all plain sail,' but what constitutes plain sail varies by country and decade.

[Thomas Cochrane]

The actual formula should be:

I guess the OP should be edited?

~Brigand

 

Thanks fixed. I forgot to say "the square root of", but the calculations were right so hopefully it was understood. 

Edited February 28, 2015 by Thomas Cochrane