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Here you can find information about how OpenTTD calculates in-game figures.

You always wanted to know how the station-rating was built up? How goods-distribution works? Here you can find it!

Company rating

Each part of the company rating is a linear function, ie. earning 50% of the target for a component will give 50% of the points allocated for that component. Where components involve monetary amounts, these are converted to the currency of the current game; internally these amounts are stored as the pound amount.

Component Target Points (min) Points (max) Percentage
Number of company-owned vehicles that turned profit last year >=120 0 points for 0 vehicles 100 points for at least 120 vehicles 0 to 10%
Number of recently-served station parts company owns >=80 0 points for 0 parts 100 points for at least 80 parts 0 to 10%
Lowest profit of vehicles at least two years old >=£10,000 0 points for loss or £0 100 points for at least £10,000 0 to 10%
Lowest quarterly revenue earned in past 3 years >=£50k 0 points for £0 50 points for at least £50k 0 to 5%
Highest quarterly revenue earned in past 3 years >=£100k 0 points for £0 100 points for at least £100k 0 to 10%
Units of cargo delivered in past year >=40,000 0 points for 0 units 400 points for at least 40,000 units 0 to 40%
Number of types of cargo delivered in past quarter >=8 0 points for 0 cargo-types 50 points for at least 8 cargo-types 0 to 5%
Current cash in bank >=£10m 0 points for £0 50 points for at least £10m 0 to 5%
Current loan from bank £0 0 points for >£250k 50 points for £0 0 to 5%
Totals 0 points 1000 points 0 to 100%
Company League Table ratings
Rating Title
0 to 127 Engineer
128 to 255 Traffic Manager
256 to 383 Transport Coordinator
384 to 511 Route Supervisor
512 to 639 Director
640 to 767 Chief Executive
768 to 895 Chairman
896 to 959 President
960 to 1000 Tycoon
2050 High Score ratings
Rating Title
320 to 447 Entrepreneur
448 to 575 Industrialist
576 to 703 Capitalist
704 to 831 Magnate
832 to 959 Mogul
960 to 1000 Tycoon of the Century

Station rating

This section shows the factors that affect the station rating. All calculations are done separately for each cargo type.

Factor Condition Rating points Rating %
Max speed of last vehicle to load cargo (to a max of 255 km/h)
Divide speed by 2 if it was a road vehicle.
Above 85 km/h (52 mph) (Speed (km/h) - 85) / 4 0% to 17%
Age in years of last vehicle to load cargo 2 10 4%
1 20 8%
0 33 13%
Days since last cargo pickup
Multiply days in "Condition" column by 4 if last vehicle was a ship.
(Note: If a vehicle was ready to pick up a cargo but there was no cargo, or if it was full, it is still regarded as a cargo pickup. This may be a bug.)
30 to 52.5 25 10%
15 to 30 50 20%
7.5 to 15 95 37%
less than 7.5 130 51%
Units of cargo waiting at station
Note: if cargo has been transferred to other stations, then the game MAY consider the maximum cargo waiting at any of those stations as the waiting cargo for the source station: TruncateCargo().

This is triggered when the game truncates cargo (waiting_changed = true), which occurs when any of the stations meet the following conditions:

• Cargo has not been picked up from any of those stations in 637.5 days. [1]
• Station has rating less than or equal to 25% AND has more than 200 units of cargo waiting. [2]
• Station has rating less than 50% AND more than 0 units of cargo waiting, happening with RANDOM PROBABILITY proportional to the station rating. I.E. if station rating is 49%, there is a ~1% chance, at 25% rating there is a ~50% chance, and at 0% stating rating there is a 100% chance. [3]
• Station has more than 4096 units of cargo waiting. [4].
More than 1500 -90 -35%
1001 to 1500 -35 -14%
601 to 1000 0 0%
301 to 600 10 4%
101 to 300 30 12%
less than 100 40 16%
Statue in town of station Built 26 10%
Event Condition Rating point change Rating % change
Small advertising campaign bought Station within 10 tiles of town center +64 +25pp
Medium advertising campaign bought Station within 15 tiles of town center +112 +44pp
Large advertising campaign bought Station within 20 tiles of town center +160 +63pp
Road vehicle crashed Station within 22 tiles of crash -160 -63pp
Train crashed Station within 30 tiles of crash -160 -63pp
Town bribe failed Station within town influence -255 -100pp

Divide the total rating points by 255 to get the percent rating. The maximum possible rating is 100%.

Every 2.5 days (185 ticks) station ratings are computed; ratings can't change by more than 2 points (0.78%) per cycle, except due to items under "Event". Events give an instant, temporary boost (or penalty) to ratings of nearby stations. The rating will gradually return to normal, following the 2 point per 2.5 days rule.

The amount of cargo that can be transported from an industry is fully reliant on the station rating. This means that if there is exactly one station serving an industry, on ticks when the industry produces cargo, exactly station rating % of the cargo will be moved to the station. So if the amount of cargo transported from an industry is low, it is probably because the station rating is low, too.

Note: The exact formula can be seen under "UpdateStationRating()" in station_cmd.cpp. This uses some values calculated in "LoadUnloadVehicle()" in economy.cpp.

Note: If the rating gets to be less than 50%, the station starts losing cargo.

Note: If the amount of cargo waiting is greater than 4096 units (or 4,096,000 liters), the station also starts losing cargo. There is a hard cap of 32,768 units of cargo that can be waiting at a station. Any more than that completely disappears every few days. [5]

Cargo delivery to stations

During each cycle of 2.5 days for each cargo type of the delivering industry a maximum of 2 stations can get cargo assigned. If there are more than 2 possible stations with the same maximum rating value for the current cargo type then it depends on internal ordering of the stations which ones get the cargo.

If there's only one possible station then the delivered amount is: produced_amount * station_rating_in_percent, rounded up to the next integer value.

For two possible stations the calculation is more complex. First the rating in points of station 2 is divided by 2 for the further local calculations. The amount available to station 1 is calculated as follows: (station_rating_in_points1 * (amount + 1)) / (station_rating_in_points1 + station_rating_in_points2); for similar ratings this is about 2/3 of the production, it increases for larger differences. The result is subject to the same calculation as in the single station case. This is delivered to station 1. If station 1 doesn't get the full amount available to it then that part won't be transported at all. The remaining amount of the production, if any, is subject to the same calculation as in the single station case and delivered to station 2.

Local authority rating

Ratings limit some player actions; they start at +500 and can change based on some actions.

Currently you can exploit the game by planting about 200 trees within a town's influence radius. You may need to clear an area first, in order to have somewhere to plant them, but planting 200 will raise even a minimum rating of -1000 to 220. If your rating is Mediocre or lower, planting 30 trees will approximately wipe out the rating penalty from building one station. Planting trees while at a rating of Very Good or better has no effect.

Rating points Rating
-1000 to -400 Atrocious
-399 to -200 Very Poor
-199 to 0 Poor
0 to 200 Mediocre
201 to 400 Good
401 to 600 Very Good
601 to 800 Excellent
801 to 1000 Outstanding
Player action Required rating* Effect on rating
Build a station -200 n/a
Destroy an 'edge' piece of road 16 / 64 / 112 -18, down to -100.
Destroy an 'inner' piece of road 16 / 64 / 112 -50, down to -100.
Destroy a city tunnel or bridge 144 / 208 / 400 -250, down to 0.
Destroy building** 40 to 300 -40 to -300
Plant tree on clear square n/a +7, up to 220.
Clear a tile with trees n/a -35
Successful bribe n/a +200, up to 800.
Unsuccessful bribe n/a Set to -50.

* "Required rating" is listed for the settings Permissive / Neutral / Hostile of
the difficulty option City council attitude towards area restructuring.
** For default buildings. NewGRFs can set this number from 0 to >1000,
which effectively makes the building unremovable.

Each month players' ratings automatically change:

• Rating goes up by 5 if it is less than 200.
• Rating goes up by 12 for each station that has transferred cargo in the last 50 days.
• Rating goes down by 15 for each station that has not transferred cargo in the last 50 days.

Example:
A player has a rating of -300, (Very Poor), 2 active stations and 1 inactive station at a town.
5pts + 2 * 12pts - 15pts = 14pts points gain per month.
(-200 - -300)pts / 14pts/mo = 8 months before the town will let him build another station.

Code for town ratings is in town.h, town_cmd.c, tree_cmd.c, and road_cmd.c.

Industry production

Here is how the game determines how much cargo an industry produces per month. Production of raw materials happens 8 or 9 times per month. (It happens every 256 ticks. There are 74 ticks in a day, and 28 to 31 days in a month (date_type.h). This means that only about 9% of industries will produce 9 times in a 28-day February, but about 96% of industries will produce 9 times in a 31-day month like March.) The production will always be a multiple of 8 or 9, unless the industry changed production during that month.

This table lists possible starting productions governed by the smooth economy patch. These numbers are multiples of 8. When the game generates a new map, each industry produced 8 times and had no production changes in the December before the game started.

Raw Material Industry Produced Cargo Initial production range
Coal Mine Coal 56 to 176
Forest Wood 48 to 152
Oil Rig Oil 56 to 176
Farm Grain and Livestock 40 to 112
Copper Ore Mine Copper Ore 56 to 112
Oil Wells Oil 48 to 152
Iron Ore Mine Iron Ore 40 to 112
Bank (temperate) Valuables 24 to 64
Gold Mine Gold 24 to 80
Diamond Mine Diamonds 24 to 80
Fruit Plantation Fruit 40 to 112
Rubber Plantation Rubber 40 to 112
Water Supply Water 48 to 152
Farm Maize 40 to 128
Lumber Mill Wood 180 or 225 (if trees available)
Candyfloss Forest Cotton Candy 48 to 152
Battery Farm Batteries 40 to 128
Cola Wells Cola 48 to 136
Plastic Fountains Plastic 56 to 160
Bubble Generator Bubbles 48 to 152
Toffee Quarry Toffee 40 to 112
Sugar Mine Sugar 40 to 128

(To calculate this table, look under _origin_industry_specs in table/build_industry.h for the industry and its cargo. The sugar mine has `CT_SUGAR, 11`, so the production starts at 11. Apply the formula from DoCreateNewIndustry() in industry_cmd.cpp: multiply the production by a random integer from 128 to 383, then divide by 256, rounding down. So 11 becomes 5 to 16. Finally, multiply it by 8 to get 40 to 128.)

Production change

Each month the game randomly changes some industry productions.

Default / TTD-like Economy Rules

For 256x256 tile maps there is one change per month possible (only 1 industry changes). Number scales nicely with map size since the introduction of "Daily production changes" function in trunk (r14332).

• As with smooth economy, industries produce cargo 8 or 9 times per month.

However - productions are limited to 6 production levels: lowest, lower, normal (with a new game started or a new industry built), higher, 2x higher and the highest. Production changes between these levels are either a 50% decrease (half) or a 100% increase (double).

• Examples:
• A Coal Mine: lowest (32 or 40 t per month), lower (64 or 72), normal (120 or 135), higher (240 or 270), 2x higher (480 or 540) and the highest (960 or 1080).
• A Forest: lowest (32 or 64 t per month), lower (35 or 70), normal (78 or 117), higher (208 or 260), 2x higher (416 or 468) and the highest (832 or 936).
• A Gold Mine: lowest (12 or 18 bags/month), lower (32 or 40), normal (56 or 63), higher (112 or 126), 2x higher (224 or 252) and the highest (448 or 504).

To make things simple, let's look what are the chances for 256x256 maps (max. 1 change per month = max. 1 industry per month changes production):

• The chance for a production change each month is:
• 50% for `only_decrease` industry to decrease (currently only Temperate terrain Oil Wells) or
• 50% for 1/3 chance (=16.7%) that other industry (non `only_decrease`) changes production.

• If a production change does occur (~16.7% chance per month):
• For an industry that has poor or no service (less than 60% of its cargo is transported): 33% chance of increase, 67% chance of decrease.
• For an industry that has good (greater than 60%) service: 67% chance of increase, 33% chance of decrease.
• There is no bonus for excellent service with default economy.

• To calculate the chance for a particular change, i.e. 50% * 1/3 * 33% = 5.56%:
• Poor service: 5.56% that 1 possible change per month is an increase and 11.12% that 1 possible change per month is a decrease.
• Good service: 11.12% that 1 possible change per month is an increase and 5.56% that 1 possible change per month is a decrease.

Smooth Economy Rules

• The chance for a production change each month is 4.5%, i.e. 4.5% of producing industries from industry list change production.

• If a production change does occur:
• For an `only_decrease` industry (currently only Temperate terrain Oil Wells) 0% chance of increase, 100% chance of decrease.
• For an industry that has poor or no service (less than 60% of its cargo is transported): 33% chance of increase, 67% chance of decrease.
• For an industry that has good (greater than 60%) service: 67% chance of increase, 33% chance of decrease.
• For an industry that has excellent (greater than 80%) service: 83% chance of increase, 17% chance of decrease.

• These two are multiplied together, i.e. 4.5% * 33% = 1.5%:
• `only_decrease` industry: 0% chance to increase and 4.5% chance to decrease
• Poor service: 1.5% chance to increase and 3.0% chance to decrease
• Good service: 3.0% chance to increase and 1.5% chance to decrease
• Excellent service: 3.75% chance to increase and 0.75% chance to decrease

• With the smooth economy option enabled, production changes per month are between 3% and 23%
• Industries with very low productions, (ie. 12-40 tonnes per month) will have higher changes.
• Primary industries produce cargo 8 or 9 times a month. Monthly production is an industries 'base value' multiplied times 8 or 9. For example, the base value for a coal mine is 15 tons, so the monthly production is 120 or 135 tons. This base value is capped at 255, so the maximum possible monthly production for any industry is 2040 or 2295. Ref
Special Cases
• Oil Rig passenger production is limited to 16 passengers per production event, meaning a maximum of 144 or 128 passengers per month. [6]
• Lumber Mill is technically not a producing industry and is classified as a secondary industry in the code. Four or five times a month it will search outward in a 40 by 40 area in a spiral pattern looking for a fully-grown tree to cut down. If it finds one, the tile will be demolished and 45 tons of wood will be output. This means it has a maximum production of 225 or 180 tons of wood per month, solely dependent on the availability of trees.[7]
• Temperate climate Banks never change production (except due to the 8 vs 9 production events per month).

Examples

If a coal mine has 70% of its output transported, there is a 3% chance (4.5% * 67%) of a production increase from 3-23% and a 1.5% chance (4.5% * 33%) of a production decrease from 3-23% (but 13% on average).

(1 + (0.03 - 0.015) * 0.13) ^12 - 1 = 0.0237 or 2.37%

The coal mine will grow an average of 2.37% on average after the first year.
(1.0237 ^20) - 1 = 59.6% after twenty years
(1.0237 ^50) - 1 = 321.8% or 3.22x after fifty years
(1.0237 ^100) - 1 = 10.35x after one hundred years

For an industry with rating of more than 80%, there is a 3.75% chance of increase and 0.75% chance of decrease:
(1 + (0.0375 - 0.0075) * 0.13) ^12 - 1 = 0.0478 or 4.78%

The industry will grow approximately 4.78% on average after the first year.
(1.0478 ^20) - 1 = 2.54x after twenty years
(1.0478 ^50) - 1 = 10.32x after fifty years
(1.0478 ^100) - 1 = 106.62x after one hundred years

For an industry with the `only_decrease` flag set (currently Temperate Oil Wells), there is only a 4.5% chance of decrease:
(1 + (0 - 0.045) * 0.13) ^12 - 1 = (0.99415) ^12 -1 = -0.068 or -6.8%

The industry will shrink on average by approximately 6.8% after the first year.
(0.9320 ^20) = 24.46% of initial production after twenty years
(0.9320 ^50) = 2.96% of initial production after fifty years

ln(0.5) / ln(0.99415) = 118.1 months or 9.84 years is the half life of an `only_decrease` industry.
ln(8 / 48) / ln(0.99415) = 305.9 months or 25.4 years is the mean lifetime of a temperate Oil Wells (starting at 48 oil/month).
ln(8 / 152) / ln(0.99415) = 501.8 months or 41.8 years is the mean lifetime of a temperate Oil Wells (starting at 152 oil/month).

For good service, it takes 29.6 years on average to double; with excellent service, it takes 14.8 years. If in the game's time a day is 2.36 seconds, then the doubling time with good service is 7.1 hours; with excellent service, the doubling time is 3.6 hours. For production to go from near bottom of 100 to near maximum of 2040 or 2295 takes 130 years with good service and 65 years with excellent service.

However, in game you will find industries changing their production rate very randomly. It must be stressed the above examples are only true when observing many industries over the long-term; individual industries may greatly deviate from these averages. Statistically speaking, 6 out of 10 industries will not go from 100 to 2040-2295 even with the best service during 65 years. About 1 out of 9 industries will even lower their production when being served at 60-80% cargo transported for 50 years.

For more responsiveness from industries, adapt the number of wagons to industry production (for the lowest production, you should use two wagons). [Full Load] orders are usually used for such cargo trains.

Note: The exact formula can be seen under "ChangeIndustryProduction()" in industry_cmd.cpp.

Delivery payment rates

The amount you get paid for delivering cargo is based on 4 factors: the amount of cargo you deliver, the value of the cargo, the distance you deliver it, and how on-time you deliver it.

Cargo Units Early Delivery
Time (days)
Late Delivery
Time (days)
Initial cargo
payment (pounds)
Passengers Immediate 24 £39
Valuables Bags 1 32 £91
Livestock Items 4 18 £53
Grain Tons 4 40 £58
Goods Crates 5 28 £75
Coal Tons 7 None £72
Steel Tons 7 None £69
Iron Ore Tons 9 None £62
Wood Tons 15 None £61
Oil Kiloliters 25 None £54
Mail Bags 20 90 £55
Arctic specific
Wheat Tons 4 40 £58
Paper Tons 7 60 £66
Gold Bags 10 40 £71
Food Tons Immediate 30 £69
Tropical specific
Rubber Kiloliters 2 20 £54
Fruit Tons Immediate 15 £51
Maize Tons 4 40 £53
Tropical Wood Tons 15 None £97
Copper Ore Tons 12 None £59
Water Kiloliters 20 80 £57
Diamonds Bags 10 None £71
Toyland specific
Sugar Tons 20 None £54
Toys 25 None £68
Batteries 2 30 £53
Sweets Tons 8 40 £75
Toffee Tons 14 60 £58
Cola Kiloliters 5 75 £59
Candyfloss Tons 10 25 £61
Bubbles 20 80 £62
Plastic Kiloliters 30 None £54
Fizzy Drinks 30 50 £76

Initial cargo payment values are for delivering 100 pieces of cargo 1 tile. Payment goes up with inflation as the game progresses.

Late delivery penalties:

• For each day after the Early Delivery time that you deliver the cargo, you are penalized 0.4%.
• For each day after the Late Delivery time that you deliver the cargo, you are penalized an additional 0.4%.
• Maximum penalty is 88%.

Examples (no inflation):
Deliver 200,000 liters of oil 20 squares in 10 days:
2 * £54 * 20 squares * 100% = £2160

Deliver 100 bags of mail 100 squares in 100 days:
£55 * 100 squares * (1 - 80*0.004 - 10*0.004) = £3520

HINT calculate easy:
Income = cargo units * cargo value * 0,4
cargo value comes from the Y-axis on the specific transported goods graph in-game
measure your real delivery time in days and plot on x-axis This result will give you an easy estimation of your income with 5% deviation

Notes:

• The exact formula is much more complicated and slightly more accurate, due to rounding error when converting from larger discrete values. See economy.cpp (GetTransportedGoodsIncome) and Cargo income.
• Distance is measured between the name-labeled tiles of the stations, not from the industries or by vehicle distance traveled. It is computed by adding the differences in x and y tiles (manhattan distance), not straight-line distance.
• Each cargo has a characteristic time at which payment is maximized, assuming you can keep it moving away from the source station at a constant speed. For a cargo with a "late delivery" penalty, this time is typically around 70 days; for one without, this is typically around 130 days.

Vehicle speeds

Internally OpenTTD works with a unit called "km-ish/h", which is equal to "mph/1.6". The conversion factor from km-ish/h to km/h is 1.00584, and the conversion factor from km-ish/h to mph is 1.6.

A tile is, for vehicle speed purposes 664.(216) km-ish, 668 km or 415 miles long. This is based on the following facts:

• A tile has 16 sub locations per X/Y axis.
• A vehicle has stores remainder of tile movement in a byte called subspeed, thus has 256 different values.
• The vehicle's (raw) speed is added to subspeed. The resulting number is divided by 256, the remainder is stored in subspeed and the vehicle is moved quotient sub locations forward. For trains and aircraft the raw speed is in km-ish/h, for road vehicles/ships in 0.5 km-ish/h. For trains and aircraft this step is done twice a tick, whereas ships and road vehicles do it once a tick.
• A day contains 74 ticks, and takes 24 hours.

Now assume a vehicle going 1 km-ish/hour: (1 * 16 * 256) / (74 * 2) * 24 = 664.(216).

The net result is that 100 km/hour is ~3.6 tiles/day.

Aircraft

• By default aircraft fly at a quarter of their listed speed (this can be changed in advanced settings).
• Aircraft acceleration varies per aircraft, between 144 km-ish/h/day and 400 km-ish/h/day.
• Broken down planes fly at 320 km-ish/h.
• Airport taxi speed is 150 km-ish/h.

• Road vehicles accelerate at 37 km-ish/h/day.
• Road vehicles go around corners at half their max speed.
• When going uphill, road vehicles slow down 10% 4 times per tile. This balances out with acceleration at 34-ish km/h for all road vehicles.

(Note: This does not apply when using the improved road vehicle acceleration model.)

Ships

• Ships accelerate at 37 km-ish/h/day.
• A "stopped" ship resumes its last speed instantly.

Trains

(with the realistic train acceleration patch)

• Trains are not affected going up or down hills if they are powerful enough.
• Trains are limited to entering and exiting a depot and making 90° turns at 61 km/h.
• Trains can make one 45° turn or two 45° turns in opposite directions at a time without slowing down.
• When making two or more 45° turns in the same direction, the max speed is limited as follows:
Curvature Max speed (km/h)
0 (90° turn) 61 91 121
1 (2x45° turn) 88 132 176
2 111 166 221
3 132 198 264
4 151 226 301
5 168 252 336
6 183 274 365
7 196 294 392
8 207 310 413
9 216 324 432
10 223 334 445
11 228 342 456
12+ 231 346 461
Curvature Max speed (mph)
0 37 56 75
1 54 82 109
2 68 103 137
3 82 123 164
4 93 140 187
5 104 156 208
6 113 170 226
7 121 182 243
8 128 192 256
9 134 201 268
10 138 207 276
11 141 212 283
12+ 143 214 286

"Curvature" means the average number of wagons of the train between turns. However, very sharp turns (curvatures 0 and 1) are not averaged out in longer trains.

• New railtypes can specify custom maximum curve speeds in the same steps as the three default types in the table.
• Tilting train gain an additional bonus of 20% on the maximum speed.
• Train acceleration and max speed are affected by engine power, maximum tractive effort (all engines and powered wagons combined), current speed, air drag, total train mass, and wagons/engines on slopes.
• Non maglev train Acceleration spreadsheet can be found on tt-forums: tt-forums
• Braking is twice acceleration except when entering a depot or a station.

See ground_vehicle.cpp, aircraft_cmd.cpp, roadveh_cmd.cpp, ship_cmd.cpp, train_cmd.cpp, vechicle.cpp for code.

As of OpenTTD 1.6.1, given power in hp, max tractive effort in kN, total weight of the train in tonnes, the number train parts (engines and wagons), the air drag value of the first engine in the train (NewGRF setting, defaults to `min(192,max(1,floor(2048/max_speed)))`, meaning faster trains are built more aerodynamically), the combined weight of any train parts (engines or wagons) currently on an up-slope, the combined weight of any train parts (engines or wagons) currently on a down-slope, the slope steepness (game setting [1-10], default 3), and the current speed of the train in km/h, the acceleration of a non-maglev train can be calculated as follows:

force = min((max_te * 1000), floor((power * 746) / (current_speed * 5/18))) [N]
slope_force = weight_on_upslope * slope_steepness * 100 - weight_on_downslope * slope_steepness * 100 [N]
axle_friction = total_weight * 10 [N]
rolling_friction = total_weight * 15 * (1 + floor(current_speed / 512)) [N]
air_drag_coefficient = 14 * floor(air_drag_value * (1 + number_of_parts * 3/20)) / 1000
air_drag = floor(air_drag_coefficient * current_speed^2) [N]
acceleration = (force - (slope_force + axle_friction + rolling_friction + air_drag)) / (total_weight * 4) [256th of a km/h per half-tick]

Note: air_drag_coefficient is twice that if any part of the train is in a tunnel

Given the same values, the equilibrium speed, eg the speed the train would eventually settle on if the same conditions continued indefinitely, can be calculated as follows [Assuming a constant `rolling_friction` (ie the speed stays below 512 km/h), and ignoring the flooring of `force` and `air_drag` to an integral value]:

p = (slope_force + axle_friction + rolling_friction) / air_drag_coefficient
q = (-power * 746 * 18/5) / air_drag_coefficient
C = (27/2*q + ((27/2*q)^2 + 27*p^3)^(1/2))^(1/3)
equilibrium = min(max_speed, p/C - C/3, max(0, max_te * 1000 / air_drag_coefficient - p)^(1/2))