Maths / Intercept question

[Matt123]

A question for someone with better maths than I.

Given a merchant exiting jump on or near the 100d limit of a large GG (say GG radius 90,000 km) and a raider on or near the 100d limit at a point 'blah' (1).

The merchant from a 0 velocity start, engages its 2G MD and angles away from the raider towards the GG to start skimming. The raider starts from a 0 velocity start and heads straight for the merchant at 4G to engage in combat.

The question is; How long will the merchant be under fire from the raider?

Cheers
Matt

(1) There must be a word for this... If the merchant is considered to be on the 0-180 degree line running through the centre of the GG, the raider is on the 90-270 degree line. The raider is halfway between the merchant and the 'other side' of the planet. Or the raider is a quarter the way around the circumphrance of the GG.

***** Thread Summary 25 Jan 2010 *****

First, thanks to the contributors.

The answer is the raider will bee line for the GG and place his ship between the merchant & the GG, intercepting the merchant whilst it is still 1-2 hours out from the GG. Once refueled, the merchant will likely head for the 10d line, at a constant 2g reaching it in 3 hours 40 min before jumping away with a high risk of mis-jump.

The combat time line is then
1-2 hours before the GG
2 hours 20 min for the merchant to refuel
3 hours 40 min to escape to the 10d limit. Total 7-8 hours or 21-24 HG combat turns.

This will apply regardless of where on the 100d limit the merchant & the raider start assuming the merchant is detected.

 

[Lycanorukke]

The question is; How long will the merchant be under fire from the raider?

Okay - the GG is radius 90,000, so diameter is 180,000
100 Diameter = 1,800,000km
The raider is at 90 degrees, merchant at 0 degrees initially (both equidistant from the centre of the GG)

So this is is basic trig - c^2 = a^2 +b^2
Where a and b = 1,800,000 - 90,000
So a and b = 1,710,000km
So C (distance between initially) = 2,418,305km or about 8 light seconds apart.

Now here is the catch for which more info is required...

Which ruleset do you want to use - this defines the 'range bands' of lasers and missiles. For example a range band of extreme is 500,000+ km using certain rules means the pirate could get a lucky shot in even at this distance. So what would you consider a 'firing distance'?

Also, will the merchant try to slow down before it hits the GG (velocity 0), and will the raider try to match the merchant speed? Or will the merchant plow into the GG at maximum velocity? Will the raider want to match speeds or just get in range to shoot his M-drive out and then take his time to match velocity? (I am assuming the merchant is not going to evade, but just try to run to the GG).

On edit:
If they just power in at maximum accelleration (2G)...

equation: d = 1/2at^2

1,170,000km = 1,170,000,000 m
1,170,000,000 = (a * t^2) /2
2,340,000,000,= a * t^2
a = 19.6 m/s^2 (2G)
119387755 = t^2
t = 10926 s
t = 182 min
t = 3 hrs to reach the GG (6 combat turns of 30 mins)

Mind you they will hit the GG at about V = 214km/s

 

[Tellon]

And another thing that wasn't really discussed -- something that I deal with

How fast was that Merchant going in direction A --

Thus, if merchant was going direction A -- the same amount of thrust & burn would be needed to "stop" going in that direction -- to reverse couse away towards the GG

Thus -- if direction A took 1 hour of 1 G thrust -- then 2 full combat turns (1 hour) will be needed to "stop" and go back towards the GG

----

Also with the Pirate -- how fast was he going -- or was he just sitting out there "dead" in space -- peering at his PEMS and watching for some suitable prey?

if A) he was headed somewhere -- then thrust/burn issues occur

if B) then he can fire up his thrusters and head for the merchant who is still trying to "stop" and head for the GG --

-- now issue C brought up in the above post -- the distances are gonna be REAL BIG, even with a BIG PEMS, 10 hexes is 300,000 km -- so extreme would be 1.2 M km -- obviously the merchant would be picked up easily at that range -- but weapons fire? .. still iffy

so for me -- the merchant uses 1 hour to slow to a dead stop -- and head for the GG -- the Pirate is heading at the merchant -- we'll say he's doing 4 G, so the distance THEN between the 2 is a lot less

so after an hour, the Pirate could easily overtake the merchant (doing that 4G), the merchant now at 0G but heading for the GG -- so both are "heading" for the GG -- where SDB's are lying in wait for a tasty snack .. lol

===

*note: I use realistic thruster rules -- so no grav stuff/handwavium in MTU --

 

[Matt123]

Great stuff Tellon.

I use CT & HG, but I'm not sure what the range of starship weapons are, a quick search last night didn't turn up anything. If someone could help out here that would be great. I am many interested in HG short & long range bands (the trig calcs help establish how long the HG combat may last).

The starting positions chosen were intended to average out the two main variables, positions related to each other & relative velocities in relation to the GG. I am looking for a finger in the wind guide to how long the merchant in this situation will take fire.

The calcs shown are great, with luck (& google) I should be able to use these again.

My first observtion is that at the distances shown, under LBB bk2 the raider is out of sensor range, IIRC 6 light seconds (not a slight on your help, just one of those things that come to light when you ask the right question!) I'll assume for this exercise, remote sensors are in play.

Hopefully someone will help with CT weapon ranges. But assume the merchant stays at 2G throughout the run, whilst the raider closes to short range and then matches velocity. How long at long range is needed as well.

In CT/HG 20 minute turns we have 3 hours (9 turns) in & out plus 7 20 minute turns filling the jump tanks. Total 8 hours, 20 minutes or 25 HG turns.

Cheers, very interesting stuff!

 

[far-trader]

It's not exactly spelled out that I recall (though it may be in Mayday, I'd have to check, later if I get a chance). What I recall doing was interpretive. Taking the CT detection ranges and tracking range, and applying them to the HG short, long, and reserve ranges.

CT gives non-military sensors a detection range of 150,000km. So I set that as the HG short range limit. i.e. Contact to 150,000km is short range.

CT gives military sensors a detection range of 600,000km. So I set that as the HG long range limit. i.e. 150,000km to 600,000km is long range.

CT allows tracking of a ship, once detected, up to 900,000km. I mention this only in passing as the likely range for the Reserve in HG combat. Beyond detection range (and outside weapons range) but within tracking range so ships from the line that retreat to the reserve can still be tracked, but not targeted.

Also don't forget the effects of running silent and planetary/gg masses interfering with sensors.

 

[far-trader]

Had a quick look through Mayday and didn't see anything for weapons ranges, beyond the expanded missile rules.

My old solution (post above) is quick and dirty and made more to fit the game than reality. It basically makes missiles into semi-guided artillery. They strike the turn of (at short) or after (at long), being fired. They don't maneuver (much, a little terminal guidance to kick the warhead the right way). I find it hard to credit much more into a small, light (50kg) package, even at high TLs.

Larger missiles, what I call torpedoes in MTU, do behave more like the maneuvering missiles CT intended. But they are just barely usable from turrets (1 torpedo in the place of 3 missiles per launcher) and strictly speaking a military item. And of course they are the normal load for missile bays. Torpedoes have the capability to chase targets beyond the detection range, as long as tracking is maintained.

 

[Shonner]

I figure missiles are in range (still in play) until the gunner decides they are no longer controllable on his end. Planets and stars can block sight, sensor/target locks, and communication with ships and missiles.

Uncontrolled missiles can either continue off the game map or the gunner can have them detonate after a time or at some pre-determined distance he thinks is close enough to an enemy ship.

 

[Whipsnade]

Dan,

The best estimate I've seen involved a three-step HG2 to Mayday to LBB:2 conversion and even that falls apart.

• HG2 has Short and Long range bands.
• Those bands convert to 0-5 Mayday hexes and 6-15 Mayday hexes respectively.
• A Mayday hex is said to be approximately one light second or 300,000 km.

That is where the conversion starts to break down. You'll notice that HG2 are routinely detecting and targeting each other at Long range or upwards of 15 light seconds. It then gets screwier because Mayday penalizes attacks for each hex of range and uses a roll under system as opposed to HG2's and LBB:2's "roll over" system.

In Mayday a ship is hit on a roll of 4 or less. If all the offensive and defensive DMs cancel out, a laser attack of over 9 hexes or 9 light seconds is impossible. (Detection limits constrain this though.) Contrast that to HG2 where laser attacks up to 15 hexes or 15 light seconds are possible and anything more distant impossible. LBB:2 then adds to the problem as laser attacks over 5,000mm or 1.67 light seconds use a -5 DM are thus impossible without applying a beneficial DM.

Detection ranges only add to the fun. There's no apparent detection range in Mayday and in HG2 you can detect vessels out to at least 15 light seconds. While LBB:2 gives us a fist full of numbers, they don't mesh well with the rest. Commercial starships can only detect other vessels at one-half of a light second or one-half of a Mayday hex. Warships aren't much better, they can detect out to two light seconds or two Mayday hexes. Once detection is accomplished, both can maintain detection out to three light seconds or three Mayday hexes.

Just how to blend all this together is up to a GM and each GM will prefer a different blend.


Regards,
Bill

 

[Matt123]

Hmmm, at least I don't feel so bad for not being able to find the range info myself.

I'll go with Dan's interpretation for now, I like the logic used.

Just realised I credited Tallon with both early posts, thanks [FONT=arial,helvetica]Lycanorukke for the calculations & explanation.

So using Dans 150,000 k's for short range, 600,000 k's for long range. How does that change things?
[/FONT]

 

[Lycanorukke]

So using Dans 150,000 k's for short range, 600,000 k's for long range. How does that change things?
[/SIZE][/FONT]

Just to make sure of the premises.

So we'll go with both ships starting from a 'standing start'.
The merchant will accellerate at 2G all the way to the GG.
The pirate will move to intercept and match vectors.
The pirate has military grade sensors and can start shooting at 600,000km distance from the merchie, with better odds at 150,000km.
The pirate wants to match vectors so he can rob the merchie.
I'll assume it takes 2 combat turns (40 minutes) to board, rob and run away once velocities are matched.
From the initial equations - the pirate must intercept or shoot out the mechie drive inside 9 combat turns, 7 if he wants to board and rob.

Assuming this is right ( I hope), I have a rough idea of the sums - but want to avoid calculus so I'll crunch the numbers when I get a chance.

 

[Tekrat04]

@ Lycanorukke:
Right formulas wrong numbers.

Distance between ships: Both ship are 18,000,000km from the GG not 1,800,000 and 90,000. The real distance between ships is 25,245,844km or just over 84 light seconds.

The merchant will take 11h54m17s to reach the planet with a final velocity of 840km/s.
The raider will take 8h26m22s to reach the planet with a final velocity of 1191km/s.
Both of thoes velocities are way to much to do more than just a fly by.

@Matt123
For a strait intercept (no matching vectors) with both ship starting 100 diameters out from the GG at 90 degree to one another, will take 8h49m16s with a closing velocity of just under 1500km/s (vectors taken into account here).

 

[Matt123]

@ Lycanorukke:
Right formulas wrong numbers.

Distance between ships: Both ship are 18,000,000km from the GG not 1,800,000 and 90,000.

I read that as being 100 diameters from the surface of the GG, 18,000,000 km plus the distance from the GG surface to its centre 90,000. ???

---

I'm replicating a commerce raider, its role is to catch up & damage/destroy the merchant, rather than board it.

Cheers!

 

[Tekrat04]

I read that as being 100 diameters from the surface of the GG, 18,000,000 km plus the distance from the GG surface to its centre 90,000. ???

---

I'm replicating a commerce raider, its role is to catch up & damage/destroy the merchant, rather than board it.

Cheers!

Your right.

I'll redo the math.

 

[Whipsnade]

Matt,

Your "Time To Weapons Interception" is going to depend greatly on with weapon ranges you choose.

Going from longest to shortest:

• HG2 - Weapon range is 15 light-seconds
• Mayday - Weapon range is 9 light-seconds
• LBB:2 - Weapon range is 1.67 light-seconds

Using the ~8 light-second separation previously calculated, at HG2 and Mayday weapon ranges, the raider can begin firing as soon as the merchant is detected. Because the raider needs to "see" the merchant before it can begin the chase or open fire, we need look at detection ranges too.

Again, going from longest to shortest:

• Mayday - No detection range stated.
• HG2 - No detection range stated, but weapon range suggests at least 15 light-seconds.
• LBB:2 - Initial detection is either 1/2 or 2 light-seconds, tracking after detection is 3 light-seconds.

If we're using Mayday and HG2 the raider can both see and begin shooting at the merchant as soon as it arrives, so no chase is necessary. If we're using LBB:2, the raider never sees the merchant, so no chase ever begins.

The marked disparity between detection and weapons ranges in the three CT space combat rule sets makes inferring many things about the "real" nature of space combat in the setting impossible. We can work out the broader brushstrokes, but anything more specific than that starts precluding one rule set in favor of another. These differences even produce different warship designs.

Let's look at your example and imagine the gas giant is a clock. The merchant arrived at the 12:00 postions while the raider was at 3:00.

Using HG2/Mayday, the raider at 3:00 can both see and fire at any merchant which arrives at positions between 12:00 and 6:00. Among other things, that means, with he ranges involved, as few as two ships can picket the giant and detect every ship - either a merchant or a raider - which crosses the 100D limit.

Using LBB:2, however, results in a very different picture. The raider at 3:00 never sees the merchant at 12:00 because of the ~8 light-second range in involved. Instead of having as few as two ships each covering an entire hemisphere of the jump limit sphere, we'd need many more vessels covering the jump limit sphere in patchwork of 1.67 weapons and/or 2 detection light-second radius "chunks".

You can see just how different numbers, designs, tactics, and the rest become when shifting between these two scenarios.

Everyone must make their own choices here. My choice has been HG2 ranges with Mayday movement because I tilt towards the "Limited Stealth" model for space combat.


Regards,
Bill

 

[Tekrat04]

Snip...

Using the ~8 light-second separation previously calculated,

...Snip

Bill,
You basing your logic on an incorrect number, the initial contact is not 8 light seconds but 85 light seconds. Lycanorukke made a mistake in his calculations, he use 10 diameter out minus the radius of the GG, not the 100 diameters plus radius.

Steph

 

[Tellon]

100 diameters plus radius.

with that kind of distance -- it makes an attack by the raider on the merchant a non-issue -- The merchant can easily turn around, turn on it's thrusters to slow down -- then head towards the GG, kick on it's thrusters at 1G and get there to radio the SDB's for the raider in the area

the raider captain would easily calculate the distance and time to intercept (even going 4G) -- realize he WILL have SDB's in the area -- and see the raid aint worth it

edit: Now as I re-read the OP - I see the merchant was going 0 km/hr when it spotted the raider -- THUS, the merchant doesn't even have to slow down -- all the mechant does it angle towards the GG @ 1G and calls for SDB help. The merchant would probably skim for say 2 or 3 hours -- and watch its PEMS closely to see where the raider goes -- as the SDB's will also be watching closely...

All while our raider is heading to wards the GG @ 4G???

Like I said before -- it's a non-issue -- all due to the 100d distance the raider has to go.

--

To be sneaky -- I would have the merchant by closely escorted by the SDB to the 100d line -- so as to confuse the raiders sensors (as at that distance, it shoudl confuse the raiders sensors, as the raider all of a sudden would see a large signature heading his way, instead of the merchant -- thus the raider would have to serious ponder on "seeing" what this large signature is.)

 

[Whipsnade]

You basing your logic on an incorrect number...

Tek,

That doesn't matter. Whether it's eight light-seconds or 85 light-seconds, the lesson remains the same.

Because my raiders or pickets can detect/engage a target at Mayday's 9 or HG2's 15 light-seconds distance, I'll need far fewer raiders and pickets to cover the 100D limit sphere than if the detection/engagement range was LBB's 1.67 or 2 light-seconds.

While both sets of detection/engagement ranges belong to CT, the consequences of those differing ranges lead to different ship designs, different ship deployments, and even different navies.


Regards,
Bill

 

[Tellon]

when I take a look at my TNE book -- pg 225 on the 100 diameters Travel Time chart --

Burn G-hours -- .9 -- for an "average" LGG -- 78.7 hours, and from the mention of 90,000 km for a diameter -- I am certain we're dealing with an LGG

so for our raider -- going at 4G -- we're looking at 78.7/4 -- so ~19.8 hours -- and that is a straightline advance -- for a flyby -- not even time to turn around, and re-do 4G's to slow down.

-- now for the LS question -- looking at the TNE book on pg 227 at the Interplanetary Speed chart .. the time to go 1 LS for a 1G thrust is 142 minutes, while our raider going 4G is 35 min/LS

so then -- how many LS are we dealing with here?

The distance from Orbit 0 to Orbit 1 is 100 LS --and were taking planetary orbits -- see the Interplanetary Distance Matrix chart on pg 226 (TNE)

So (from pg 195 of the TNE book) the difference is .2 AU to .4 Au -- or .2 AU for those 100 LS -- or roughly 29.9 M km

(from pg 188 to double check the diameter of our average LGG) -- Then we see what the distance those 100d is in M km (100 x 90,000) or 9 M km

so then if 100 LS = 29.9 M km, and we have 9 M km, then we get 9/29.9 = .3010033 -- then we 100 x .301033 = 30.10033 LS (according to TNE)

SO THEN -- we need times!!!

for our raider doing that 1 hr of 4G burn -- 30.10033x35min = 1053.5115 min or 17.558525 hrs -- less than our "proposed 19.8 hrs up top, but close enough --and this is a fly-by (not even a "turn & burn" to slow down -- cause you would add 1 hr of 4G to get to 0 km/s -- thus our total time = ~18.56 hrs)

-- SO ULTIMATELY -- Is this raid worth it? -- [and AEMS (pg 51 of FF&S) 480,000 km is tops -- so extreme = 3.84 M km for an active search, and PEMS is 1/2 that (pg 52 FF&S) 240,000 km = 1.92 M km for extreme range.]

No, the raider is too far away for an effective sensor lock -- thus the chances of a strike are Nil.

 

[Tekrat04]

with that kind of distance -- it makes an attack by the raider on the merchant a non-issue -- The merchant can easily turn around, turn on it's thrusters to slow down -- then head towards the GG, kick on it's thrusters at 1G and get there to radio the SDB's for the raider in the area

the raider captain would easily calculate the distance and time to intercept (even going 4G) -- realize he WILL have SDB's in the area -- and see the raid aint worth it

edit: Now as I re-read the OP - I see the merchant was going 0 km/hr when it spotted the raider -- THUS, the merchant doesn't even have to slow down -- all the mechant does it angle towards the GG @ 1G and calls for SDB help. The merchant would probably skim for say 2 or 3 hours -- and watch its PEMS closely to see where the raider goes -- as the SDB's will also be watching closely...

All while our raider is heading to wards the GG @ 4G???

Like I said before -- it's a non-issue -- all due to the 100d distance the raider has to go.

--

To be sneaky -- I would have the merchant by closely escorted by the SDB to the 100d line -- so as to confuse the raiders sensors (as at that distance, it shoudl confuse the raiders sensors, as the raider all of a sudden would see a large signature heading his way, instead of the merchant -- thus the raider would have to serious ponder on "seeing" what this large signature is.)

Actualy the intrecept I calculated occures just over 8 million km short of the GG if the merchant heads strait for orbit and the raider heads strait for an interception. And yes the raider will have to travel more than 100 diameters to make the interception.

The time and speed to the planet is just for an example of the time needed to get to the planet without deceleration.

 

[Tellon]

And yes the raider will have to travel more than 100 diameters to make the interception..

100d is STILL 9 M km (and the raider to go that distance @ 4G is still ~17.56 hrs) -- like I mentioned above using both AEMS and PEMS -- the distances are too great for sensor locks -- thus, the chance for a strike are Nil.