Ship Velocity Question

[chrome_gnome]

I've got a couple of velocity related questions.

Is there a maximum velocity for starships? The maneuver drives are rated by the acceleration 1G, 2G and so on. So according to simple kinematics formulas

v^2 = 2*a*d

You basically take 2 times accel times distance and then take the square root of it to get velocity. Therefore a starship given a few million kilometers could accelerate to fairly impressive speeds. In something around 1/10 a parsec it could reach the speed of light with a 1G constant acceleration, granted it would take a year of time. So is there a limit?

Second question regarding velocity.
When ships encounter each other on the strategic map how do you determine their initial speeds? IT seems like they could be wildly different. Depending on if the ship has just jumped into the system, is accelerating to the outer orbits, etc. I know I can make my own system, which I don't mind doing, but I want to know if there is a widely accepted way to do it or even an official system that I am missing.

A third and final velocity question.
The advanced starship combat section says that moving at your current speed is a free action that must be done first. Ok if it is a free action in typical d20 rules you can take two move actions on your turn. Does that mean I can move once as a free action then do 2 more moves at the current speed? Or the required move as a free action and then 2 move actions of accleration? Just need some clarification on this.

 

[kaladorn]

Two comments:

Speed Limit: The speed of light
Speed Limiter: Relativity (mass increases as you approach significant fractions of the speed of light, thus slowing future acceleration until it gets (for all practical purposes) asymptotic).

That's the 'absolute limiter'. The actual shorter limits will be:
Fuel (depends on how much you have)
Sensors and manouver Gs.

That is to say, if you can only apply say 1/4 of your thrust sideways (well, okay, even if you can rotate 90 and push with your full 1 G).... there will come a speed where your sensors will not be able to see far enough in advance to allow you to dodge any obstacles. That should be the practical limit of speed for anyone without a real deathwish. Otherwise, one unseen comet or rock and blammo.... ship smithereens.

Now, how far can sensors see? In MT, numbers between the small thousands of km and 2 AUs were bandied about. So, once your speed starts to get close to covering (IMO) about 25% of that distance in one game turn, that's a good place to cap your speed.

Of course, the more Gs you can put out, the more you can alter course to dodge things. So a 6G ship has a far faster maximum speed than a 1G ship for just that reason alone. It can dodge far faster.

Plus, from a political/military/legal PoV, coming in towards a planet or space station or orbital city at high vee may be contraindicated. It may be contraindicated by the fact that the local system defence forces may pop a cap in your keister if you try it! They may have a 'speed limit' and 'controlled space'. In those areas around the ports or satellites or entering standard orbits, I'd be surprised if the vectors you'd be authorized to take wouldn't be dictated by SPA traffic control... (this assumes a populated moderate tech planet with a decent starport... on the fringes you can be as loony as you want).

 

[BetterThanLife]

Originally posted by chrome_gnome:
I've got a couple of velocity related questions.

Is there a maximum velocity for starships? The maneuver drives are rated by the acceleration 1G, 2G and so on. So according to simple kinematics formulas

v^2 = 2*a*d

You basically take 2 times accel times distance and then take the square root of it to get velocity. Therefore a starship given a few million kilometers could accelerate to fairly impressive speeds. In something around 1/10 a parsec it could reach the speed of light with a 1G constant acceleration, granted it would take a year of time. So is there a limit?

There is a limit. The Speed of light, it isn't just a good idea it is the speed limit.

On a more practical level, you will run out of fuel before you get close to that. Since these questions seem to be leading to the use in combat, there is one other point. Absolute velocity, in space, doesn't really matter, relative velocity does matter. Relative vectors matters even more.

Second question regarding velocity.
When ships encounter each other on the strategic map how do you determine their initial speeds? IT seems like they could be wildly different. Depending on if the ship has just jumped into the system, is accelerating to the outer orbits, etc. I know I can make my own system, which I don't mind doing, but I want to know if there is a widely accepted way to do it or even an official system that I am missing.

Hmmmm. Now you have me looking.

Obviously they are on converging vectors or there would be no encounter. Exactly how to apply that...

After consulting, LBB2, LBB5, MT Referee's manual, Mayday and the THB, I have come to the following conclusions. In all, except LBB5, you are dealing with vectors and relative velocity. In none of them does it give you a base vector at the start of an encounter. So because there are a variety of possibilities as to what a ship is doing when encountered, the rule would have to be Referee's discretion. However, one thing to keep in mind with Advanced combat and T20, if they leave the map, combat is over. So a relative vector that won't let them leave the map in the first two turns might be a good choice.

A third and final velocity question.
The advanced starship combat section says that moving at your current speed is a free action that must be done first. Ok if it is a free action in typical d20 rules you can take two move actions on your turn. Does that mean I can move once as a free action then do 2 more moves at the current speed? Or the required move as a free action and then 2 move actions of accleration? Just need some clarification on this.

I would require you to take the free action, then a move action to accellerate, and a second move action to accellerate again, though the total accelleration must not exceed the accelleration rating of the engine. (For example a Scout Ship accellerates 1G in direction 1 and then 1G in direction 2.) But you aren't going to get to take the free action more than once per turn. (And you are going to be required to take it once per turn.) Law of conservation of momentum.

 

[chrome_gnome]

Ok the speed of light as a limit is what I was thinking and the relativity theory is a good explanation.

Now regarding the other things. I have a mathematical problem with how the maneuver drives are rated in G's. They say each drive lets you accelerate 1G per G rating of the drive so between 1-6G. The book goes on to provide formulas and a time chart for getting to certain distances at various accelerations. The formulas they list are written in an odd format, at least from what I remember from engineering school, and I am pretty sure the first one is wrong. So I pulled out my engineering mechanics book and got the proper equations for linear motion with constant acceleration. Plugging in the various G ratings and the distances listed, also assuming the acclerate 1/2 way and decelerate the last 1/2 of the way note, I get the same answers they did.

10,000km in 33 minutes at 1G of acceleration

Now that made sense and I went on to the advanced starship combat section and read that a tactical hex is 750km across, a tactical round is 60 seconds and the G rating of the drive lets you accelerate or decelerate by that many hexes every turn. So if your speed is measured in hexes then the slowest you can move is 1 hex per round. That means you move 750km in 60 sec for a velocity of 12.5km per second. Ok this still makes sense. Now the part about accelerating one hex for every G rating of the drive is where things seem to break down.

If you are traveling at 1 hex per round (12.5km/s) and have a 1G drive it says your new speed will be two hexes per turn. Now if your new speed is 2 hexes per turn it means you are travelling at 1500km in 60 seconds. That equates to 25km/s. Well using the simple formula of (Vf-Vo)/t = a, where Vf is final velocity in m/s, Vo is initial velocity , t is time in sec and a is acceleration in m/s^2 you get the following:

25000m/s -12500m/s = 12500m/s
12500m/s / 60 seconds = 208.3 m/s^2
208m/s^2 = 21G

So in order to change velocity from 1 hex per round to 2 hexes per round on the tactical scale would require an acceleration of 21G not 1G. If you plug in 1G for 60 seconds, assuming you accelrate your whole round, your velocity only goes from 12.5km/s to 13km/s

Now I know this is nit picky and I may be making a math mistake, feel free to double check me its been 7 years since I got my Mechanical Engineering degree, but it seems odd how it works out. The book goes to the trouble of rating maneuver drives in G's, calculates travel times using those G ratings as 9.81m/s^2(10m/s^2 if you round) but then seemingly throws them out the window when measuring combat speeds. Now I could easily just say a 1G maneuver drive actually produces 21G's of acceleration which would make their combat rules correct but then I would need to rework their travel time chart. Alternatively I could assume their drives really are 1G, 2G and so on and alter the combat rules. The problem with the second option is 1G and 2G type drives will not change the velocity enough on a tactical scale to even be refelcted over several minutes of combat. At 1G it would take me 21 minutes(21 tactical rounds( to accelerate from 12.5km/s (1hex per round) to 25km/s (2 hexes per round). At that rate it seems it would be better to ignore acceleration in tactical combat which seems to ruin the fun of it.

So I am leaning towards re-speccing the G rating of the drives to reflect the actual math results. It would mean travelling to a safe jump point would take alot less time but at least to me the accelerations and speeds would be accurate and scale properly between any hex map you care to use. Also making the G ratings actual represent a higher actual G for acceleration maintains the 6:1 ratio of the fastest to slowest acceleration drives. A 6G drive would still be able to leave tactical combat with a 1 or 2G drive almost at will, as it should be.

So feel free to check my math or comment on my points. Here is a link to a site with a good explanation of each of the simple equations written in normal form.

http://physics.about.com/cs/acceleration/a/060703.htm

I know this may seem overboard but it just appears that a game that is supposed to be based on real science, that goes so far as to publish equations and results of those equations should be consistant in their application of it. I did a little research and found that the NASA space shuttle when orbiting at 300km is travelling at about 8km/s. This seems to jive pretty well with the slowest combat speed being 12.5 km/s.

 

[kaladorn]

Maybe some of the Brilliant Lances crowd will speak up. It had a more hard-sci feel to it.

Generally, after having looked at this under a number of systems, once you reach interplanetary speeds (for some sort of expedient trips), two things become apparent:
1) Your residual vector is what matters. You can alter it a wee bit on short timescales, but really not that much.
2) Two ships that do not have *darn near identical* vectors are going to get one jousting pass and that is it, *if* they can even manage that. Real space intercepts of fast moving ships are tough without *ludicrous* accelerations.

To my mind, the answer is in having 5, 10, or 15 minute combat turns.

For instance, we have a ship moving 750km in one 5 minute turn. That means he's clipping along at 9000 kph, which is fairly snappy in some senses, though slow for interplanetary space.

In this case, we want to figure out his velocity after a turn of acceleration directly along his prior vector[1].

So, v(+5 min) = v(0) + at
t = 15 * 60 = 300 seconds
a = 1G (9.81 m/s^2)
v(0) = 9000 kph = 2500 m/s

v(+5 min) = 2500 + 2943 = 5443 m/s
= 19594.8 kph.

So, we find with a 5 minute timescale, that we can accelerate from moving 1 hex per turn to moving essentially two hexes per turn with 1G (about twice as fast, in broadly rounded figures).

--------- DIGRESSION -----------
Note however that almost every game breaks in this aspect:
A rating of X for thrust over a turn usually lets you move X the next turn and you usually move X units doing it, instead of moving 0.5 X units.
--------- DIGRESSION -----------

So, with a 5 minute time frame, 1G lets you add 1 hex/turn. Thus 6Gs would let you add 6 hexes/turn.

I think I'd rather go to a five minute time frame for the game (which in space combat might well be sensible... it may have a lot more in common with sub warfare than any other kind...) than break all the speed/travel assumptions of ye olde game.

 

[kaladorn]

Forgot my footnote:
[1] Acceleration not along that vector will have reduced effect, and will lead to the joys of resultant vectors and vector addition. The inevitable result will be the sounds of non-gearhead or non-mathgeek heads exploding, and that can be quite messy in your living room.

 

[kaladorn]

And if you go to vector movement, you can do like Full Thrust (and presumably PP:E) do -- you can do the turn as:
1) Drift your vector
2) Then apply all modifiers for a turns worth of thrusting

Due to the commutative property of vector addition (if I reall my geek lingo), the final position you end up with will be okay. The new post-acceleration vector can be calculated using TrigBoy(TM) super-powers, or else the simple expedient of tracking start and endpoints on the table and measuring distance and direction between. Note, facing quickly ceases to match the direction of the ship's vector.

The problem with this of course then becomes that the endpoint is right, but *points in the middle are not*. That is to say, you can add all the thrust at the end, it is simple, but then you really only know start and endpoints. You can't really accurately judge the intermediary locations. This mostly matters when trying to orbit planets, avoid collisions with objects, or when flying through a fictional supradense Star-Wars asteroid field. Otherwise, that idiosycracy isn't problematic.

Note however that if you want more accurate results, you have to 'phase' the movements into discrete phases, using a sort of numerical-methods like approximation technique for each part of the movement. This gets SFB-like. If you don't know why this might be a bad thing, I suggest you are an ideal candidate to recheck every table in each version of Fire, Fusion and Steel yourself (by hand, no mechanical or electronic aides please!).

So, wherein lies a good compromise between playable and real? Good question, when it comes to vector movement. Answers: Many. Right Answer: TBD.

 

[chrome_gnome]

Vector math gives me dynamics flashbacks of a horrible sort

I like the idea of a 5 minute tactical turn because the math works out. 1,632km is close enough to 1,500km (2 hexes) for me.

 

[BetterThanLife]

I think it all depends on a question of scale. Mayday, was 300,000KM hexes and 100 minute turns. Now back then I was na engineering student and I recall doing the math and finding that it worked. But I might be wrong and I certainly don't have the math anymore. Does the THB Strategic, 20 minutes and 15,000km work?

 

[kaladorn]

Originally posted by chrome_gnome:
Vector math gives me dynamics flashbacks of a horrible sort

Is there any other sort?

Between Hamiltonian Transforms, Laplace Transforms, Eigenspaces, Ring Theory, Queue Theory, Number Theory, Graph Theory, Quantum Mechanics, and Statistical Mechanics... I'll never be the same.

 

[TheEngineer]

Hi !

Bhoins is quite right.
Its all just a matter of scale.
As long as the hex scale unit relates correctly to time scale unit everything should work (at least good enough for gaming purpose).

hex diameter = velocity change * time scale unit
->
hex scale unit = 10 * (time scale unit ^ 2)

Thats ok for 20 min turn and 15000 km hex, but 750 km hex and 1 minute turns are completely out of bounds.
A 1 minute turn would result in a 36 km hex scale, or the other way around you might need a 274 second turn to keep the 750 km scale working.

Regards,

Mert

 

[kaladorn]

My five minutes for the 750km hex was a 'first order approximation' of the actual answer of 274 seconds.

Nice work Mert. I think those formulae are actually kind of useful.

 

[aramis]

The simple way to track current turn end position and vector gain is with a three marker system, and hexes half the size of a turn's accumulated vector:

Marker 1: This Turn Start Position. (TTSP)
Marker 2: This Turn End Position, aka Next Turn Start Position. (TTEP aka NTSP)
Marker 3: Next Turn End Position (NTEP)

Process: when you maneuver the ship, for each burn move the TTEP 1 hex in the desired direction, and the NTEP 2 hexes in that same direction.
At end of turn, everyone picks up marker 1, and puts it under the marker 2.
Then they pick up marker 2, and place it under marker 3.
Finally, marker three is placed the same distance and bearing from marker 2 as 2 is from one.
Firing should be done from the TTEP, IMO.

 

[mike wightman]

Altenatively use the Triplanetary/LBB2 system of drawing the vector arrows - this isn't as difficult as it sounds.

A laminated sheet and a drywipe pen are all you need.

 

[kaladorn]

I prefer 'hexless' gameboards, and it is even simpler there, though the method is quite similar.

 

[chrome_gnome]

Battle Fleet Gothic used a "hexless" board and it did a fair job of representing the momentum of the massive capital ships. I played Warhammer Fantasy, 40 and BFG and got tired of measuring. For ship combat I like the scaleability of hex maps, like how T20 uses different "zooms" of maps.

 

[chrome_gnome]

I found this nifty write up that explores Full Thrust and a couple of other games and how well they model physics. It breaks down the game systems' by how well they handle velocity, distance and implied acceleration via total distance.

I found it interesting in light of this discusion.

http://www.smallcuts.net/articles/vector.jsp

 

[kaladorn]

chrome_gnome, where be the link?

 

[aramis]

THe method I described KEEPS the realism of non-full distance on turn of vector accumulation. It's a fix to BL/mayday.

BL and Mayday actually move the ship further than it should for the acceleration this turn.

using a three counter system works even better on a mapless board.

 

[mike wightman]

A "simple" add on for a hex based system, like Triplanetary or Mayday, is to make 2 hexes the equivalent of a 1G velocity change (rather than the 1 hex for 1G it is now).
On the turn the acceleration is applied the ship only adds one hex to its vector, and on the second turn this goes up to 2 hexes.
The ship can accelerate on this second turn so a further 1 hex can be added...

Here's another thought. If each player has a laminated sheet, hidden from his opponent, the turns can be plotted in secret and then applied at the same time to get simultaneous movement.

Firing can then be at the discretion of the player at any point during the movement.