Archive for the Vector movement Category

Vector movement game units

Posted in Intercept, Other vector movemet systems, Rules, Science, Traveller, Vector movement on July 16, 2019 by Anders Backman

When you create your own vector movement system, as I am sure everyone does, you need to determine what map scale, turn length and acceleration units are. There is an obvious formula from school that most seem to use and but will argue for why this is wrong and why one should instead use another formula, also from school.

Plotting example

Mapscale

Typically one decide on the map scale first (how large will the hexes, squares, inches or centimeters be?). Deciding on scale is mainly about what you want in your maps, do you want planets to be one unit or less in scale? Do want to show Earth and the moon on the same map? Do you want to fit the inner solar system on your map, like Triplanetary? And so on.

Some examples:

  • Intercept 10 000 km per square, 15 minute turns, 1G per square.
  • Intercept large scale 100 000 km per square, 60 minute turns, 1G per square.
  • Traveller LBB 1000 km per inch, 5 minute turns, 1G per inch.
  • Mayday by GDW 300 000 km per hex, 100 minute turns, 1G per hex.
  • Triplanetary ~10 million km per hex, 1 day per turn, ? G per hex.

Intercept let you play using two different scales and switch back and forth as you like, there’s even a smaller scale in the works if I can iron out the problems with planets taking up large parts of the map, that scale will be 1 000 km, 4 minute turns and 1G per square as usual.

We will later calculate what acceleration Triplanetary is likely using based on the distance and time scales and formulas learned.

Formulas

High school math teaches us two formulas for determining distance traveled, one for when applying constant acceleration from a standstill and another when having constant speed.

The two formulas are:

Formula one and two

Notice how formula 2b is the same as formula 1 but without the 1/2 multiplier. Distances traveled become twice as far in formula 2 so one of them must be wrong, right?

Not so fast! The formula from high school actually looks like this:

Formuila one with prior speed

Formula (3) also take the velocity from the previous turn into account (the v0 term). As v equals a multiplied by t we get our beloved formula (2b) as the first term, or something similar at least.Why is the first term twice as big as the second term? Well, the the first term assumes the speed is constant through the time segment t while the second term treat is as increasing, the distance traveled can be seen as areas in graphs with speed plotted versus time, like this:

Formula and area

If we use formula (3) to determine total distance traveled while t keeping t as the turn length and v as v (n-1) where n is the number of turns we’ll see that as the number of turns increase the grey area will more and more resemble a rectangle (the triangle of the last turn will contribute less and less of a fraction of distance traveled).

Formula graph

The grey area is the distance traveled. If we call one rectangle as 1.0 and one triangle as 0.5 we get the following distances:

  • Turn 1: 1 triangle plus 0 rectangles = 0.5
  • Turn 2: 2 triangles plus 1 rectangle = 2.0
  • Turn 3: 3 triangles plus 3 rectangles = 4.5
  • Turn 4: 4 triangles plus 6 rectangles = 8.0

and so forth…

You see that as the number of turns increases the number of rectangles increases faster than the number of triangles. So, as the number of turns increase the the number of rectangles will outstrip the number of triangles.

In the vector movement systems of Triplanetary, Mayday, Traveller, Intercept etc we use a vector that both represent velocity and acceleration however. So we either decide that one unit length should be correct for acceleration from a standstill but wrong for drifting or accelerating with a prior velocity (1) or we decide that one unit length should be correct for drifting and approach correct when handling prior velocity (2).

Too much theoretical bullshit you say? OK, let’s do a practical example.

Let’s travel from a standstill to the moon as see which of formula (1) or (2) most closely fit (3). We ignore braking at the moon just go to the moon as fast as possible. The average distance between the earth and the moon is 380 000 km so let’s go with that.

Units for formula (1)

  • A = 10 m/s^2
  • T = 1000 s
  • S = 5000 km

Distance earth – moon will be 76 squares.

Traveling 76 squares with 1 unit acceleration will be

1+2+3+4+5+6+7+8+9+10+11+12 = 78 units after 12 turns (12 000 s) = 3 h 20 m
(We overshot the moon by 2 squares but this is the closest we could get)

Units for formula (2)

  • A = 10 m/s^2
  • T = 1000 s
  • S = 5000 km

Distance earth – moon will be 38 squares.

1+2+3+4+5+6+7+8+9+10 = 46 units after 10 turns (10 000 s) = 2 h 45 m
(We overshot the moon by 8 squares but this is the closest we could get)

The correct value using formula (3) and setting v0 to zero is (8 718 s) = 2 h 25 m

 

Sorry about the long winded explanation but for some reason most vector systems get this wrong. Doesn’t matter when you play of course but say you want to travel from earth to the moon using actual mapboard movement you’d find that the travel time would not match the calculated value.

Apollo 11 50 years anniversary July 16 1969

Yes, 50 years ago today a couple of Americans started their travel from earth to the moon , certainly not under constant 1 G acceleration and they made damned sure their velocity was as close to zero as possible before they hit the moon. Apollo 11 did the trip in about half a week.

Apollo_11_Flight

 

Traveller day

Posted in Boardgames, Computer games, Elite Dangerous, Films and TV, Other vector movemet systems, Traveller, Vector movement on May 1, 2019 by Anders Backman

Mayday

Today is Traveller day.
Just read what’s written on the box and you’ll get it.

Traveller was the first science fiction rpg ever published, it came out the same year as Star Wars but before the movie was released, a happy coincidence. Traveller was a strong influence for the Elite computers games as well as the Firefly and Expanse TV series, Traveller has also influenced Intercept which of course is eminently usable as a space combat system for the Traveller rpg.

Oh, and Traveller used vector movement for its starships instead of some lame-ass Trek thing…

Marc Miller, the creator of the game just started a Kickstarter for his new edition of Traveller today:
https://www.kickstarter.com/projects/traveller5/traveller-fifth-edition/description

Countersheet done

Posted in Boardgames, Intercept, Vector movement with tags , , , , on April 13, 2019 by Anders Backman

The Intercept countersheet with all 176 double sided counters has been sent to the printer (the Comic sans use is POD and not mine, cross my heart and hope to die).

The counters and map tiles may or may not be available for purchase with a printed rulebook and some plotting pages, we’ll see. Intercept is of course completely playable without these.

Intercept movement tutorial

Posted in Intercept, Vector movement on July 29, 2017 by Mr Backman

Vector movement, a scary term to some, is the way ships and missiles move in Intercept, it is also happens to be the way real spaceships move. Movement in Intercept is done in three simple steps; Drift, Turn and Thrust. Drift can be done in any order as it is entirely automatic, Turn and Thrust are done in reverse initiative order ie the ship with the worst initiative goes first and then the second worst and so on. Untracked ships do Drift, Turn and Thrust in secret, after all tracked ships are done.

Facings closeup smaller

Directions and facings

A ship is always facing in one of 8 directions. Draw the ship as a pointed arrow in the direction of its nose, typically but not always in the direction it thrusted. The direction it is moving has no effect on the direction its nose faces.

Movement sequence

Initiative is based on higher steps of turn from the Pilot task
Turn and thrust is done one ship at a time, reverse Initiative
You may only thrust to your forward facing arc
Rolling cost 3 steps of turn
The movement sequence consist of Drift, Turn and Thrust. Do Drift for all Tracked ships and missiles before Turn and Thrust. Turn and thrust is done in reverse Initiative order, worst Initiative goes first, best goes last, declare any missile launches when your ship moves. After all ships have Turned and Thrusted its time to do missiles, in reverse Initiative order too. Missiles ignore turning as they can thrust in any direction.

aMove0
Drift
Look at your ships last move and repeat it, draw a small cross where the new position would be. This is called your Drift square and if done right your Current position should be exactly midway between your Drift and your Past (except for gravity effects, see page 16). Perform drift on all tracked ships at the same time, before any turning or thrusting, there are no choices involved so the order doesn’t matter. A stationary ship would have its drift, present and past in the same square. Take care to keep the ships facing when doing the drift as facing and movement direction are totally independent in Intercept. Aerobraking is done at the end of Drift, see page 18-19 for details.

aMove2
Turn
How many steps of turning a ship can do depends on the Pilot task result but Untracked ships can turn up to 4 steps without a Pilot roll. Turn your ship up to the number of steps, left or right, or spend 3 steps to roll the ship. Look at the firing sector diagram in the combat section to bring your weapons to bear on the enemy.

aMove3
Thrust
Each ship does its Thrust right after turning and can only thrust into squares in its forward facing arc as show in the picture above, there is no strafe thrust or reverse thrust. A ship may also elect to drift and not thrust at all. Drifting makes a ship easier to hit but also better at defending itself.

aMove complete

Completed movement
This is what your completed move will look like, the thin x marks your drift position. After moving around with a ship for a while it will become second nature to you, it’s much easier than it seems. Ships that are Untracked may assume that they always have 4 steps of turning to use ie they can turn in any direction and they don’t need to roll a Pilot task to do so.

Well, that’s all folks, fly safe.

Cinematic movement

Posted in Films and TV, Intercept, Vector movement on April 1, 2017 by Mr Backman

I have recently come to the conclusion that not many people find Vector movement to be neccessary or even preferrable for a space combat system. Less and less people read actual Science Fiction, ie something not based on films, games or comics, so it gets harder and harder to sell the idea that vector movement is how spaceships move and they should therefore like it.

So, today I have decided to go with the flow and embrace the more cinematic style of space combat. Battles from SciFi universes such as Star Wars and Star Trek could run battles using the Intercept rules with double blind hidden movement, fully deterministic, logarithmic values etc without foregoing their popular cinematic movement style.

What then IS a proper cinematic movement system? I have decided to break down the two most popular settings, Star wars and Star Trek and see how we could emulate that in our game:

Star Trek
I have complained about the various scientific inaccuracies of Star Trek but failed to mention its strengths; Star Trek shows us a positive and humanistic view of the future. Enterprise and its brave crew aren’t on a mission to subjugate planets and aliens, they are there to explore and help and always keeping in mind the prime directive, never interfere destructively. Star Trek also gave us the female perspective with Lt Uhura as a near equal on the bridge yet still able to express her female side with her short hemlines and sensuality. Star Trek also stress how important emotions are to us humans, always trumping cold logic. Kirk wins by persevering over staggering odds despite Spocks logic telling him his efforts are futile. We can learn something from this as politics is often too much ruled by logic and hard facts ignoring the very thing that makes us unique in the world; our emtions.

Star Trek ships use subspace warpdrives to quickly move from system to system. There are cases when they have battled during warp but this is too different to regular combat and will be covered in a future post. Star Trek ships always move with the nose in their forward direction. Some kind of drag seems to be in effect as ships with damaged impulse drives tend to slow down and ultimately stop. Top speed vary little between capital ships as is eveident from their inability to outrun each other. The Wrath of Kahn end battle has Kirk using thick clouds of a Nebula to turn the tides on Kahn instead of merely outrun him. The ability to turn seem more or less the same, regardless of speed and ship size.

Star Wars
I have often critizesed Star Wars for being a fantasy story disguised as Science Fiction. This may or may not be true as all Science Fiction is really nothing but some other literary genre in disguise (Blade runner is crime fiction, Barbarella and Zardoz is soft-porn etc). What Star Wars did to Science Fiction is to put religion as center stage. Many know me as a fervent atheist but what is atheism exactly, if nothing but a different faith? All humans need to believe in something and to hold something higher than himself, to serve and strive for. Star Wars also show us that not everything can be settled by a majority vote; there are issues and questions that must be handled by wise and spiritual elites, far better at judging changes in tradition and culture. Jedi knights show us a solution to the problems facing todays democracies; the lack of spirituality and disregard for tradition.

Star Wars ship jump between solar systems very much like the Traveller jump drives but no combat seems to occur while in jump space. Star Wars ship seems to have vastly different top speeds depending on size where smaller ships outrun bigger ones. Star Wars ships turn slower the faster they go as is evident if one analyze the dogfights in Star Wars Episove IV.

Star Trek cinematic movement rules
Use as much of the Deterministic optional rules as possible to get the feeling of Kirk and Klingon in a battle of the minds. It is especially important to use the deterministic ruls of Initiative where the Initiative goes to the ship which ‘skipped’ more steps, see the Deterministic combat rules for details on this.

Ships should note their speed and can move to any square in their forward arc. Turning is done anywhere during movement.

All ships can turn 4 steps each turn regardless of size, -1 step if Hull or Crew has Light damage, -3 if Hull or Crew has Severe damage. No turning if Hull or Crew has Critical damage.

Ships can increase or decrease speed by Acc, top speed is 6 regardless of Size, Acc etc. Ships lacking thrust reduce speed by 1 each turn until stopped.

Star Wars cinematic movement rules
Do not use the deterministic rules as Star Wars portray battles as individual skill rolls. Give your hero characters lots of skill bonus.

Ships should note their speed and can move to any square in their forward arc. Turning is done anywhere during movement.

Ships roll Pilot tasks vs Size as usual noting the steps of turning. Reduce turning steps by one for each full multiple of Acc in speed. Ships moving at top speed cannot turn at all.

Ships can increase or decrease speed by Acc, top speed is Acc * 4. Ships lacking thrust reduce speed by 1 each turn until stopped.

Well, that is all folks, get out and enjoy this beautiful April fools day!

Goodbye Vectors, hello April fools!

Posted in Boardgames, Films and TV, Intercept, Rules, Science fiction, Vector movement on April 1, 2013 by Mr Backman

I have recently come to the conclusion that not many people find Vector movement to be neccessary or even preferrable for a space combat system. Less and less people read actual Science Fiction, ie something not based on films, games or comics, so it gets harder and harder to sell the idea that vector movement is how spaceships move and they should therefore like it.

So, today I have decided to go with the flow and embrace the more cinematic style of space combat. Battles from SciFi universes such as Star Wars and Star Trek could run battles using the Intercept rules with double blind hidden movement, fully deterministic, logarithmic values etc without foregoing their popular cinematic movement style.

What then IS a proper cinematic movement system? I have decided to break down the two most popular settings, Star wars and Star Trek and see how we could emulate that in our game:

Star Trek

I have complained about the various scientific inaccuracies of Star Trek but failed to mention its strengths; Star Trek shows us a positive and humanistic view of the future. Enterprise and its brave crew aren’t on a mission to subjugate planets and aliens, they are there to explore and help and always keeping in mind the prime directive, never interfere destructively. Star Trek also gave us the female perspective with Lt Uhura as a near equal on the bridge yet still able to express her female side with her short hemlines and sensuality. Star Trek also stress how important emotions are to us humans, always trumping cold logic. Kirk wins by persevering over staggering odds despite Spocks logic telling him his efforts are futile. We can learn something from this as politics is often too much ruled by logic and hard facts ignoring the very thing that makes us unique in the world; our emtions.

Star Trek ships use subspace warpdrives to quickly move from system to system. There are cases when they have battled during warp but this is too different to regular combat and will be covered in a future post. Star Trek ships always move with the nose in their forward direction. Some kind of drag seems to be in effect as ships with damaged impulse drives tend to slow down and ultimately stop. Top speed vary little between capital ships as is eveident from their inability to outrun each other. The Wrath of Kahn end battle has Kirk using thick clouds of a Nebula to turn the tides on Kahn instead of merely outrun him. The ability to turn seem more or less the same, regardless of speed and ship size.

Star Wars

I have often critizesed Star Wars for being a fantasy story disguised as Science Fiction. This may or may not be true as all Science Fiction is really nothing but some other literary genre in disguise (Blade runner is crime fiction, Barbarella and Zardoz is soft-porn etc). What Star Wars did to Science Fiction is to put religion as center stage. Many know me as a fervent atheist but what is atheism exactly, if nothing but a different faith? All humans need to believe in something and to hold something higher than himself, to serve and strive for. Star Wars also show us that not everything can be settled by a majority vote; there are issues and questions that must be handled by wise and spiritual elites, far better at judging changes in tradition and culture. Jedi knights show us a solution to the problems facing todays democracies; the lack of spirituality and disregard for tradition.

Star Wars ship jump between solar systems very much like the Traveller jump drives but no combat seems to occur while in jump space. Star Wars ship seems to have vastly different top speeds depending on size where smaller ships outrun bigger ones. Star Wars ships turn slower the faster they go as is evident if one analyze the dogfights in Star Wars Episove IV.

Star Trek cinematic movement rules

Use as much of the Deterministic optional rules as possible to get the feeling of Kirk and Klingon in a battle of the minds. It is especially important to use the deterministic ruls of Initiative where the Initiative goes to the ship which ‘skipped’ more steps, see the Deterministic combat rules for details on this.

Ships should note their speed and can move to any square in their forward arc. Turning is done anywhere during movement.

All ships can turn 4 steps each turn regardless of size, -1 step if Hull or Crew has Light damage, -3 if Hull or Crew has Severe damage. No turning if Hull or Crew has Critical damage.

Ships can increase or decrease speed by Acc, top speed is 6 regardless of Size, Acc etc. Ships lacking thrust reduce speed by 1 each turn until stopped.

Star Wars cinematic movement rules

Do not use the deterministic rules as Star Wars portray battles as individual skill rolls. Give your hero characters lots of skill bonus.

Ships should note their speed and can move to any square in their forward arc. Turning is done anywhere during movement.

Ships roll Pilot tasks vs Size as usual noting the steps of turning. Reduce turning steps by one for each full multiple of Acc in speed. Ships moving at top speed cannot turn at all.

Ships can increase or decrease speed by Acc, top speed is Acc * 4. Ships lacking thrust reduce speed by 1 each turn until stopped.

Well, that is all folks, get out and enjoy this beautiful April fools day!

Large counters and maps

Posted in Intercept, Rules, Vector movement on October 9, 2010 by Mr Backman

Why has there been no updates you ask? Well I’ve been busy working mostly but I have also spent some time preparing counters for the game.

Large scale maps and counters

When a ship has been spotted in Intercept one can keep playing on the small maps, drawing with pencils as usual but one could also put all the spotted ships onto a larger map with real counters and do the fight there. As the counters depict the position and vector on the map you still get the same feel for how the ships move as on the smaller map. The larger map is split into 9 separate pages to print out, making a 3 x 3 sheet larger map. Each square on the map as well as the counters are 15 mm wide. The map download contains both black space with white lines (better looking) and white space with black lines (saves on toner and ink).

Each ship or missile volley is represented by three counters, Present, Past and Last. One can get away with using only two counters per ship but then you wouldn’t be able to see how much a ship has accelerated by the counters alone and I believe very strongly that as much information as possible should be shown on the map itself

Ship and missile counters; Present, Past and Last

Present represents where your ship is located but also in what direction it faces. It depicts a solid ship or missile volley. The counters are double-sided so one can show that a ship is rolled by flipping its counters over. The Present counter is moved by gravity based on the Past counters position relative to the planet.

Past represents your ship’s position and facing in the last turn. It depicts an outline of a ship or missile volley. The position of the Past counter vs the planet determines how the Present counter will be moved by gravity.

Last represents your ship’s position and facing two turns ago. It depicts a dashed outline of a ship or missile volley.

Last, Past and Present counters moving north

Movement procedure

Movement in Intercept is done in two stages; drift and thrust. First we drift all ships and missile volleys and this can be done in any order as there are no choices to be made. They blindly follow the laws laid out by Mr Isaac Newton. The next step is done in reverse Initiative order with the worst Initiative moving first before the second worst Initiative, and so on until all ships have moved. Missile volleys are then moved but the order which this is done doesn’t matter as missiles cannot attack missiles.

Drift is performed by moving the Last counter to the Past, moving the Past counter to the Present and then finally repeating the Last to Past move again for the Present. If done right the three counters will lie along a line with Past at its center. The final step of the Drift phase is to adjust for gravity. If the Past counter is inside the central planet’s (if any) gravity field note what arc it lies in visavi the planet. Move the Present one square in the same direction, be careful to keep the facing. Do the same for all ships and all missile volleys and then the Drift phase is over.

Thrust is performed in reverse Initiative with lowest Initiative going first. Each ship may turn up to its turn limit and then thrust in the new direction. Rolling the ship costs 4 turn and is shown by flipping the counter over to its Rolled side. Optionally, a ship can turn after thrust but all turns and thrust will then cost double.

Making your own counters

You can download the countersheet here and print it out. The shipcounters with Rolled printed on them should be on the flip side of each ship counter. Missiles don’t roll so they have no flip side artwork. I printed them out on regular paper and the glued them onto cardboard, one can also buy 15 mm octagonal plastic pieces from here and glue the paper counters on, which makes for nice and sturdy counters. I’ll post pictures the plastic ones when I am ready with them. Each ship comes with four volleys of missiles with roman numerals to separate them. You can download the 9 mapsheets here (both the black and the white versions are included) to print out.

In space, nobody can hear you scream – except yourself, really loud, when you scream inside your helmet, and everyone else on your radio channel.