Advanced Ship Mechanics

Introduction

The word Ship will be interchangeably used to refer to 1) Sail Ships, 2) Steam Ships and 3) Airships; if something only applies to a single type of Ship then it will be explicitly referred to such.

Terms

• Movement Speed
• Cargo Capacity
• Cargo Slowdown
• Loading Speed

Ship Properties

Trade Ships

		Speed			Slots		Cargo			Loading
Name	Type	Min (kn)	Max (kn)	Session (%)	Item	Cargo	Full Factor	Threshold (%)	Slowdown (%)	Speed (%)
Schooner	Sail	4.4	15.8	1	1	2	0.5	0.5	1	1
Clipper	Sail	5.5	19.8	1	1	4	0.5	0.5	1	1
Cargo Ship	Steam	10.4	-	1	2	6	0.8	0.5	1	1
Extravaganza	Steam	10.4	-	1	3	6	0.8	0.5	1	1
Great Eastern	Steam	11	-	1	3	8	0.8	0.5	1	1
World-Class Reefer	Steam	11	-	2	1	6	0.8	0.5	1	1
Harpy	Air	27	51	0.9	1	2	0.4	0.5	1	0.2
Manticore	Air	20.8	41.6	0.8	2	3	0.5	0.5	1	0.2
Hermes	Air	19.2	36	1	2	3	0.6	0.5	1	1.2
Pegasus	Air	16.5	30.8	1.3	3	5	0.7	0.5	1	0.5
Zephyr	Air	14	26	1.7	2	8	0.8	0.5	1	0.9
Boreas	Air	9.4	32.8	1	2	4	0.5	0.5	1	0.5

• Name
• Type
• Speed
  • Min (kn): The minimum speed (in knots) given Wind for Sail Ships and Airships, Steam Ships are unaffected by Wind.
  • Max (kn): The maximum speed (in knots) given Wind for Sail Ships and Airships. Since Steam Ships are unaffected by Wind; their maximum and minimum speed are the same.
  • Session (%): The modifier applied to determine a ship's speed while traveling between sessions.
• Slots
  • Item: Number of Item Slots that a Ship can equip.
  • Cargo: Number of Cargo Slots that a ship has; each Cargo Slot can hold a maximum of 50 tonnes (t).
• Cargo
  • Full Factor: Multiplier used to calculate the impact on the ship's total speed given how full it is. More on this later.
  • Threshold (%): How much of the ship's maximum Cargo Capacity needs to be filled before it starts experiencing Cargo Slowdown.
  • Slowdown (%): Base Cargo Slowdown modifier prior to any positive or negative boosting items.
• Loading
  • Speed (%)

Basic Movement Speed

Summary

Every single ship has a minimum and maximum movement speed which can be affected by internal factors such as:

• Items
• How full the Cargo Hold is

But also by external factors such as:

• Influence boosts
• Arctic Gas Chambers Buff
• How many Hitpoints the Ship has remaining
• In which direction and how strong the Wind is blowing (Sail Ship and Airship only)

Without looking at how Movement Speed is affected by Cargo Capacity and Slowdown; the basic formula is

$Speed_{f}=Speed_{b}\times (1+s_{1}+s_{2}\cdots +s_{n})$

• Final Speed: $Speed_{f}$
• Base Speed: $Speed_{b}$
• Speed Modifier N: $s_n$ (where n refers to each modifier applied)

Example

	Sail Ship	Steam Ship	Airship
Name	Clipper	Cargo Ship	Hermes
Modifiers	Trade Influence (Broker Effect): +7% Fore-and-Aft Rig Sails: +15%	Trade Influence (Broker Effect): +7% Controllable-Pitch Propeller: +15% One-Turn Screw Propeller: +10%	Trade Influence (Broker Effect): +7% Sports Gondola: +15%
Min Speed	$Speed_{b}=5.5kn$$s_{1}=0.07$ $s_{2}=0.15$ $Speed_{\min }=5.5kn\times (1+0.07+0.15)$ $Speed_{\min }=5.5kn\times (1.22)$ $Speed_{\min }=6.71kn$ $Speed_{\min }=6.7kn$(Rounded)	$Speed_{b}=10.4kn$$s_{1}=0.07$ $s_{2}=0.15$ $s_{3}=0.10$ $Speed_{\min }=10.4kn\times (1+0.07+0.15+0.10)$ $Speed_{\min }=10.4kn\times (1.32)$ $Speed_{\min }=13.728kn$ $Speed_{\min }=13.7kn$(Rounded)	$Speed_{b}=19.2kn$$s_{1}=0.07$ $s_{2}=0.15$ $Speed_{\min }=19.2kn\times (1+0.07+0.15)$ $Speed_{\min }=19.2kn\times (1.22)$ $Speed_{\min }=23.424kn$ $Speed_{\min }=23.4kn$(Rounded)
Max Speed	$Speed_{b}=19.8kn$$s_{1}=0.07$ $s_{2}=0.15$ $Speed_{\max }=19.8kn\times (1+0.07+0.15)$ $Speed_{\max }=19.8kn\times (1.22)$ $Speed_{\max }=24.2kn$ $Speed_{\max }=24.2kn$(Rounded)	$Speed_{\max }=Speed_{\min }$$Speed_{\max }=13.7kn$	$Speed_{b}=36.0kn$$s_{1}=0.07$ $s_{2}=0.15$ $Speed_{\max }=36.0kn\times (1+0.07+0.15)$ $Speed_{\max }=36.0kn\times (1.22)$ $Speed_{\max }=43.92kn$ $Speed_{\max }=43.9kn$(Rounded)

These are the minimum and maximum potential speeds for Ships without taking into consideration any factors that may induce Slowdown as a result of Damage or Cargo.

Cargo Capacity and Cargo Threshold

Cargo Capacity is the total capacity that a ship can hold.

$MaxShipCargoCapacity=CargoSlots\times CargoSlotCapacity_{\max }$

• Maximum Ship Cargo Capacity in tonnes (t): $MaxShipCargoCapacity$
• Number of Cargo Slots the Ship has: $CargoSlots$
• Maximum Capacity of each Cargo Slot in tonnes (t): $CargoSlotCapacity_{\max }$(50t by default unless using mods)

Example

	Steam Ship
Name	Cargo Ship
	$CargoSlots=6$$CargoSlotCapacity_{\max }=50t$ $MaxShipCargoCapacity=6\times 50t$ $MaxShipCargoCapacity=300t$

This means that a Cargo Ship can carry up to 300 tonnes (t) of Goods.

Cargo Threshold refers to the point where a ship will start to experience Slowdown as a result of carrying too much goods. In the case of all Ships (Sail, Steam and Airships); that Cargo Threshold Percentage starts when the ship is carrying more than 50% of its Maximum Ship Cargo Capacity. In the case of the Cargo Ship; it will start experiencing Cargo Slowdown once it has 51% (151t) of it's Cargo Capacity filled. As a ship's Cargo Hold is filled; it will experience greater Slowdown effects to it's Movement Speed.

Cargo Slowdown

As mentioned, it is the impact on the minimum and maximum speed of a ship as a result of having its Cargo Hold filled with Golds.

Example

A Cargo Ship has Base Movement Speed of 10.4 knots (kn) and a maximum Cargo Capacity of 300 tonnes (t); assuming that there are no other Movement Speed modifiers in place; we can calculate the the Final Movement Speed of the Ship as follows:

$CurrentShipCargoCapacity=275t$ (The Cargo Ship is carrying 275 tonnes (t) of Goods in its Cargo Hold)

Step	Formula	Math	Result
1 - Calculate how much the Cargo Hold is.	$CurrentShipCargoCapacity\div MaxShipCargoCapacity$	$275t\div 300t=$	$0.9167$or $91.67\%$
2 - Given that the Threshold is 50%; calculate how much of the Cargo Hold Capacity affected by the Slowdown is filled.	$(0.9167-CargoThreshold)\div CargoThreshold=$	$(0.9167-0.5)\div 0.5=$	$0.8333$or $83.33\%$
3 - Calculate the Cargo Slowdown.	$CargoFullFactor=0.8$ $Speed_{\text{slow}}=(Speed_{\text{base}}-(Speed_{\text{base}}\times CargoFullFactor))\times 0.8333$	$Speed_{\text{slow}}=(10.4kn-(10.4kn\times 0.8))\times 0.8333$$Speed_{\text{slow}}=(10.4kn-(8.32kn))\times 0.8333$$Speed_{\text{slow}}=2.08kn\times 0.8333$ $Speed_{\text{slow}}=1.7332kn$	$Speed_{\text{slow}}=1.7kn$(Rounded)
4 - Calculate the Final Movement Speed based on the Cargo Slowdown.	$Speed_{\text{final}}=Speed_{\text{base}}-Speed_{\text{slow}}$	$Speed_{\text{final}}=10.4kn-1.7kn$	$Speed_{\text{final}}=8.7kn$

The takeaway here is how Cargo Modifiers will impact the Movement Speed of the Ship. But wait, what about when there are both Movement Speed modifiers and Cargo Modifiers? Well, that's where things get interesting and where we will deep dive into the formula that the game uses behind the scenes to determine your Ship's Final Movement Speed.

Before we move onto the final point tho; let's just remember the following:

• Cargo Slowdown is an effect that slows down the ship based on the number of loaded Goods.
• This effect is triggered when more than 50% of the Ships capacity is filled and results in a calculated penalty to the Ships Movement Speed.
• Each ship has its own Penalty called the Cargo Full Factor in the table above.
• Items do NOT count as Cargo and will thus not trigger the Cargo Slowdown penalty.
• The Cargo Slowdown effect can be completely mitigated by equipping appropriate items.
• Cargo Slowdown is capped between 0% and 100%; with each Ship starting at 100%.

Advanced Movement Speed - A Working Example

We're going to take a look at a Ships Final Movement Speed given everything we've learned so far while taking into consideration Movement Speed Modifiers and Cargo Slowdown Modifiers.

Reference (from table above):

• Name: Cargo Ship
• Cargo Load: 275 tonnes (t) - This is how many goods we've loaded onto our ship.
• $CargoSlots=6$
• $CargoSlotCapacity_{\max }=50t$
• $MaxShipCargoCapacity=300t$
• $Speed_{\text{base}}=10.4kn$
• Effects:
  • Trade Influence (Broker Effect):
    • +7% Movement Speed
  • Controllable-Pitch Propeller:
    • +15% Movement Speed
    • -50% Cargo Slowdown
  • One-Turn Screw Propeller:
    • +10% Movement Speed
    • -25% Cargo Slowdown
• Effects Summary:
  • $Speed_{\text{modifier}}=0.32$ or 32%
  • $CargoSlowdown_{\text{modifier}}=-0.75$ or -75%
• $CargoSlowdown_{\text{base}}=1$or 100%
• $CargoFullFactor=0.8$or 80%
• $CargoFullThreshold=0.5$ or 50%

Step 1) Calculate how full the Cargo Hold is in relation to the total capacity.

1. $CurrentShipCargoCapacity\div MaxShipCargoCapacity=$
2. $275t\div 300t=$
3. $0.9167$or $91.67\%$

Step 2) Given that the $CargoFullThreshold=0.5$; we need to calculate how much we've over.

1. $(0.9167-CargoFullThreshold)\div CargoFullThreshold=$
2. $(0.9167-0.5)\div 0.5=$
3. $0.8333$or $83.33\%$

Step 3) Calculate the Cargo Slowdown given that $CargoFullFactor=0.8$.

1. $Speed_{\text{slow}}=(Speed_{\text{base}}-(Speed_{\text{base}}\times CargoFullFactor))\times 0.8333$
2. $Speed_{\text{slow}}=(10.4kn-(10.4kn\times 0.8))\times 0.8333$
3. $Speed_{\text{slow}}=(10.4kn-(8.32kn))\times 0.8333$
4. $Speed_{\text{slow}}=2.08kn\times 0.8333$
5. $Speed_{\text{slow}}=1.7332kn$

Step 4) Calculate the Cargo Slowdown given that $CargoSlowdown_{\text{base}}=1$.

1. $CargoSlowdown=CargoSlowdown_{\text{base}}+CargoSlowdown_{\text{modifier}}$
2. $CargoSlowdown=1+(-0.75)$
3. $CargoSlowdown=1-0.75$
4. $CargoSlowdown=0.25$ or $25\%$
5. IMPORTANT:
   1. The minimum value for $CargoSlowdown_{\text{min}}=0$ or $0\%$; this means that having -200% Cargo Slowdown from Items will grant the same effect as -100% (assuming there are no other modifiers in play).
   2. The maximum value for $CargoSlowdown_{\text{max}}=1$ or $100\%$; this means that any Items which increase the Cargo Slowdown effect will not be able to decrease the Movement Speed past 100%.

Step 5) Calculate the adjusted Cargo Slowdown given that $CargoSlowdown=0.25$ and $Speed_{\text{slow}}=1.7332kn$.

1. $Speed_{\text{slow}}=Speed_{\text{slow}}\times CargoSlowdown$
2. $Speed_{\text{slow}}=1.7332kn\times 0.25$
3. $Speed_{\text{slow}}=0.4333kn$

Step 6) Calculate the bonus Movement Speed given that $Speed_{\text{base}}=10.4kn$ and $Speed_{\text{modifier}}=0.32$

1. $Speed_{\text{bonus}}=Speed_{\text{base}}\times (1+s_{1}+s_{2}\cdots +s_{n})$ or $Speed_{\text{final}}=Speed_{\text{base}}\times (1+Speed_{\text{modifier}})$
2. $Speed_{\text{bonus}}=10.4kn\times (1+0.32)$
3. $Speed_{\text{bonus}}=10.4kn\times (1.32)$
4. $Speed_{\text{bonus}}=13.728kn$

Step 7) Calculate the Final Movement Speed given that the Bonus Movement Speed and Penalty from Cargo Slowdown.

1. $Speed_{\text{final}}=Speed_{\text{bonus}}-Speed_{\text{slow}}$
2. $Speed_{\text{final}}=13.728kn-0.4333kn$
3. $Speed_{\text{final}}=13.2947kn$
4. $Speed_{\text{final}}=13.3kn$(Rounded)

Formula Summary

• $Speed_{\text{final}}=Speed_{\text{bonus}}-Speed_{\text{slow}}$
• $Speed_{\text{bonus}}=(Speed_{\text{base}}\times (1+s_{1}+s_{2}\cdots +s_{n}))$
• $Speed_{\text{slow}}=(((Speed_{\text{base}}-(Speed_{\text{base}}\times Cargo_{\text{factor}}))\times (((Cargo_{\text{load}}\div Cargo_{\text{capacity}})-Cargo_{\text{threshold}})\div Cargo_{\text{threshold}}))\times (CargoSlowdown_{\text{base}}+CargoSlowdown_{\text{modifier}}))$

Loading Speed

Loading Speed reflects the speed at which tons are exchanged between a ship and the kontor/pier. Both the Level 1 kontor and the standard pier have a loading speed of 2 tons per second. This increases to 3 tons per second and 5 tons per second for the Level 2 and 3 Kontor respectively whilst the pier can be upgraded to an Advanced Pier with a loading speed of 4 tons per second, given that the player owns the Land of Lions DLC. The minimum time to exchange goods is always 5 seconds even though you might only be trading one ton. When trading with third parties such as Archibald Blake, Eli Bleakworth, Kahina, (Ketema) or the Pirates at their harbour, the loading speed is an astonishing 10 tons per second.

When considering how items effect loading speed. It is important to distinguish between items that effect ships and items that effect harbour buildings. The latter will work as following: If a player was to use Hogarth the Harbourmaster who provides +100% loading speed to standard piers and the basic kontor, the base rate of goods exchanged would be 2*(100%+100%(Hogarth)) = 4 tons per second on each pier/kontor effected by the item. Following the same template, a level 2 kontor would load at 6 tons per second and the level 3 at 10 tons per second before interacting with ships that have items to further increase the loading speed .

Items that effect ships on the other hand scale with the base value of the building's loading speed. If we were to socket the item "Salima the Shipping Operator" which provides +60% loading speed and we would trade with a level 1 kontor that would result in: 2*(100%+60%(Salima)) = 3.2 tons per second. If we would trade with the same ship at the kontor with Hogarth equipped mentioned above we would get: 4*(100%+60%)= 6.4 tons per second.

Thus we see that loading speed changes depending on whether first of all, the kontor/pier has items effecting it (and thus the base rate has changed), and secondly the ship trading has items effecting it. It is worth noting that the airship loads at exactly half the speed calculated due to a hidden attribute(This needs verification when the factor actually applies).