large escorts raider trap - math help please

[Matt123]

Ok, parameters for a raider trap at our large GG (90,000 km radius).

The bait is the merchant approaching the GG to refuel. Shadowing the merchant is a large escort MD-6, perhaps a destroyer, sitting say 1LS (300,000 km) behind & waiting to see if anything bites at the bait.

The goal is to see if the escort can catch the raider before the raider hides in the GG. Does the raider get to shoot at the merchant before he runs or must he break off immediaely he spots the escort.

The raiders priority is escape over damaging the merchant. Preferably by jump otherwise by hiding. The Escorts priority is to damage or destroy the raider.

When the raider hides in the GG, the distance between the raider & the Escort at that point, will be of use in a future thread.

*** step 1. raiders vs merchant
The raider (or the ships boats on the other side) spots the merchant at 150,000 km's at right angles to the raider relative to the GG. The merchant is 150,000 km away from the GG (GG radius 90,000 km). The raider is 150,000 km from the GG in orbit (GG radius 90,000 km). For the purposes of keeping this simple & reletively generic tho' we will say the raider is stationary (MD-4).

The merchant (MD-2) when spotted is on the final phase of its approach to the GG. It is decelerating at 2g aiming to stop on the GG 150,000 km away.

So the merchant is decelerating at a constant 2g. Raider is covering the same distance point to point at 4g. The raider (for simplicities sake) will aim to reach the GG first & move to intercept the merchant before the merchant gets to the GG.

The merchant will be able to spot the raider at 75,000 km & broadcast for help, that will be at some point before the raider gets into a blocking position.

Q. How much time does the raider get to shoot the merchant, before the merchant reaches the top of the GG atmosphere?

Q. How long before combat starts is the raider is spotted by the merchant at 75,000 km away?

*** Step 2. large escort vs raider
The escort starts 300,000 km behind the merchant and is decelerating at 2g toward the GG (mirroring the merchants movement) when it gets the SOS call. The raider at this point is 75,000 km away from the merchant and converging on it.

The raider is intent on getting the merchant and we will assume the large escort does not respond to the merchant until the raider spots it, in other words the escort will run silent. At 300,000 km the raider will spot the escort.

Q. In relation to the raider vs merchant intercept, at what point (in time) does the raider know of the escort?

Q. At that point, how far away is the GG for the raider?

Q. Can the raider risk a turn of combat (20 min & 1 turn vs a merchant should be quite nasty) and still escape into the GG before the escort intercepts?

 

[sabredog]

Can't we just roll 8+ with positive DM's for Commo skill and Computer Model?

 

[Matt123]

Obviously too big a job to rely on charity help! The offer of a die roll was kind tho'...

Having spent a couple of evenings googling & playing with formula's, I think I'm ready to give this a go. If you are up to it, please check my math.

Just to be obvious, I use CT/HG.

Positioning of the Raider to cover the Large GG (90,000 km radius)
The Commerce Raider (in this scenario Government owned) & its ships boat both have military sensors. The range of military sensors (CT) is 600,000 km. Positioning each ship on opposite sides of the GG will optimise coverage, in practise no doubt they will be offset to ensure LoS comms.

Positioning the two sensor platforms 240,000 km from the GG (330,000 km from the centre of the GG) gives a distance (d) between sensors of 660,000 km. The GG is midpoint on the chord joining the intersection of the two sensor circles (R & r each = 600,000 km).

The chord formulae is;
[FONT=Times New Roman, serif]a = (1/d)*sqrt(4*d^2*R^2 – (d^2-r^2+R^2)^2)[/FONT]
[FONT=Times New Roman, serif]a = 1,002,198[/FONT]

[FONT=Times New Roman, serif]Half the chord is 500,00 km, which is the smallest distance from the centre of the GG covered by sensors. The maximum distance is (600,000 + 330,000) 930,000 km. I will use the mid-point of these two results as the detection range or 715,000 km or[/FONT] 625,000 km from the GG surface.

Raider Intercepts Merchant
The Merchant. We have distance (625,000,000 m) & acceleration (actually deceleration at 2g constant = 19.6 m/s), we are looking for time. t = sqrt(2d/a)
t = 2 hour 13.2 minutes
So when detected, the merchant is roughly 2 hours 20 minutes away from the GG.

The Raider. As we are starting at right angles and aiming for the point the merchant reaches the GG, the raider will "cut the angle". The angle sides are 330,000 km to the GG centre and 90,000 km.
c^2 = 330,000^2 + 90,000^2
c = 342,053 km

So again we have distance (342,053,000 m) & acceleration (point to point, accelerate at 4g to midpoint, then decelerate at 4g. 4g = 39.2 m/s), we are looking for time. t = 2*sqrt(d/a)
t = 1 hour 38.4 minutes or roughly 1 hour 40 minutes.

The Raider arrives at the GG surface 40 minutes before the Merchant.

Perhaps more interesting tho' is the question...

When does the Shooting Start?
Using bk2 detection ranges as a HG range substitute, we have .5 LS for close range & 2 LS for long range. 1 LS = 300,000 km, making long range 600,000 km. Shooting can start from (HG) turn 2, at long range.

Close range is achieved (optionally for the Raider, whom may choose to hang back), from turn 4 (no formulae, iterated the numbers).

The Merchants Gauntlet of Fire
Turn 1. The Merchant is spotted at 715,000 km, well within the 10d jump limit of the GG (1,800,000 km). To jump away is almost certain catastrophic mis-jump. The merchant is caught between a rock & a hard place and does not yet know of the risk. The Raider moves to intercept.
Turn 2. The Raider may choose to open fire. If so, the range is long and the Raider is automatically spotted by the Merchant.
Turn 3. Long range
Turn 4. The Raider may optionally move to Short range, if so the Raider is automatically spotted, if it hasn't already been.
Turn 5. The Merchant reaches the GG.
Turn 6-12. The Merchant scoops for fuel (no doubt still under fire)
Turn 13. The Merchant leaves the GG and accelerates for the 10d limit at a constant 2g. t = sqrt(2d/a) d = 1,800,000,000 m a = 39.6m/s ergo t = 3 hours 45.6 minutes or 11 turns.
Turn 23. The Merchant reaches the 10d limit.
Turn 24. The Merchant jumps away, risking mis-jump.

Summary
In most cases, the merchant will not last beyond the first 3 or 4 turns. This perhaps serves merely to illustrate the scale of the Merchants problem. A single Raider can watch the entire Large GG and fire upon the merchant well before it can get to safety whether by hiding in GG clouds or reaching the 10d limit.

Smaller GG's and planets only add to the merchants difficulties. The point of detection does not change, the Raider can fire on the Merchant 4 turns before the surface is reached, still beat the Merchant to the surface - preventing the Merchant easily hiding and the Merchants need to refuel is still present. Only the escape to a much smaller 10d limit improves, but Turns 1 to 13 sill have to be suffered.

(eg: A size 8 planet (Earth) has a 10d limit 160,000 km away from the surface, taking 4 Turns to reach arriving in Turn 16, jumping away in Turn 17.)

Thoughts, feedback or my calcs are wrong !!??!!

Cheers
Matt

 

[Whipsnade]

Matt123,

Your math is fine.

Your assumptions are all messed up however.

You've got detection and weapon ranges from three different rule sets all snarled around each. You've got the raider using HG2 detection ranges and LBB:2 weapon ranges for example. You can't cherry pick like that because both types of ranges are integral parts of their respective rule sets. The assumptions within each rule set only work within that set, they're not modular, and you can't disassemble and reassemble them into whatever shape pleases you.

Until you use the assumptions in one rule set alone, the results of your exercise will be gibberish.

Let's return to the beginning and examining the three rule sets in turn:

In two of CT's three space combat rule sets, LBB:2 and HG2, detection range and weapon range are essentially the same. Once a vessel can detect another vessel it can open fire. In only one space combat rule set, Mayday, are detection and weapon ranges substantially different, however Mayday is not a good choice for your intercept exercise as I'll explain below.

LBB:2

• Detection: Explicitly stated, 1/2 or 2 light-seconds
• Tracking: Explicitly stated, 3 light-seconds
• Weapons: Inferred through combat DMs, 1.67 light-seconds

HG2

• Detection: Inferred through combat rules, 15 light-seconds
• Tracking: Inferred through combat rules, 15 light-seconds
• Weapons: Explicitly stated, 15 light-seconds

Mayday

• Detection: Assumed as infinite
• Tracking: Assumed as infinite
• Weapons: Capped at 9 light-seconds via DMs

As you can see, in two of CT's three space combat rule sets, LBB:2 and HG2, detection range and weapon range are essentially the same. Once a vessel can detect another vessel it can open fire and that means there is no interception to be calculated unless a third vessel is acting as a spotter.

In only one space combat rule set, Mayday, are detection and weapon ranges substantially different. However Mayday is not a good choice for your interception exception because the vessels in question will always see each other and the merchant can choose not to place itself in harm's way.

You need to recast your exercise. Choose either LBB:2 or HG2 and use those rules as a unit. Next, place the merchant, the raider, and a spotter working for the raider. Finally, calculate the amount of time will elapse between the spotter detecting the merchant and the raider moving into within weapon range.

As I wrote earlier in another thread, knowing which question to ask is more important than asking a question.


Regards,
Bill

 

[Matt123]

Interesting. (& I'm pleased about the math)

Can you give a page referances for HG2's inferred weapon range.

I've just spotted "Defender DM's" for Laser fire, in LBB bk2, which are worth pondering on and can perhaps be translated as;

Short Range... Up to 250,000 km
Long Range... Up to 500,000 km
Extreme Range... Up to the limits of detection 900,000 km

Concur?

I'm not phased by "blending" the rules systems, after all I'm using a vector system to establish game length for a theoretical HG scenario.

But I appreciate the new info. Let me know the HG2 page referance.

Cheers!

 

[Matt123]

As an aside, I tried to find the math to establish the size of the blind spot when you have only one sensor platform orbiting a GG.

Its obviously a "google the right question" sort of thing. Any ideas?

 

[aramis]

As an aside, I tried to find the math to establish the size of the blind spot when you have only one sensor platform orbiting a GG.

Its obviously a "google the right question" sort of thing. Any ideas?

Take the diameter of the world as the base of an isosceles triangle, the distance of the platform as the height. apply normal traingular trig.

 

[Whipsnade]

Can you give a page referances for HG2's inferred weapon range.

Matt123,

Sure. It's on Page 12 of Mayday in the High Guard section:

Two ships which have matched course are considered to be at boarding range. Otherwise, all ships within five hexes of each other are at short range. Ships separated by more than five hexes are at long range. Ships beyond fifteen hexes are out of range, and cannot fire.

I'm not phased by "blending" the rules systems, after all I'm using a vector system to establish game length for a theoretical HG scenario.

Whether you're fazed or not is of no consequence. The fact that you're blending rule systems limits the lessons that can be learned from this exercise because the way you've decided to blend the various sensor and weapon ranges is entirely subjective. The lessons thus "learned" are predicated on the choices you made of what to keep in an what to keep out. Others can and will make other choices, choices that will produce results very different from yours.

You're claiming to be "using a vector system to establish game length for a theoretical HG scenario". If that is so, you should use High Guard and not rope in non-High Guard elements as you see fit. The rules are not modular and are meant to be used as a unit.

When I can crack open LBB:2, I'll look at those defensive fire ranges you posted.

In the earlier thread I wrote of another "tweak" you might find interesting. One of several problems with the HG2/Mayday "fusion" Mayday so briefly touches upon is how to mesh Mayday's essentially infinite detection range with HG2's weapons range. After comparing LBB:2's 1.67 light-second weapon range against it's 2 light-second detection range, I house-ruled a 15 hex weapon range and 18 hex detection range for my HG2/Mayday "fusion".


Regards,
Bill

 

[Tellon]

Ok, parameters for a raider trap at our large GG (90,000 km radius).

The bait is the merchant approaching the GG to refuel. Shadowing the merchant is a large escort MD-6, perhaps a destroyer, sitting say 1LS (300,000 km) behind & waiting to see if anything bites at the bait.

*** step 1. raiders vs merchant
The raider (or the ships boats on the other side) spots the merchant at 150,000 km's at right angles to the raider relative to the GG. The merchant is 150,000 km away from the GG (GG radius 90,000 km). The raider is 150,000 km from the GG in orbit (GG radius 90,000 km). For the purposes of keeping this simple & reletively generic tho' we will say the raider is stationary (MD-4).

Q. How much time does the raider get to shoot the merchant, before the merchant reaches the top of the GG atmosphere?

Q. How long before combat starts is the raider is spotted by the merchant at 75,000 km away?

*** Step 2. large escort vs raider
The escort starts 300,000 km behind the merchant and is decelerating at 2g toward the GG (mirroring the merchants movement) when it gets the SOS call. The raider at this point is 75,000 km away from the merchant and converging on it.

The raider is intent on getting the merchant and we will assume the large escort does not respond to the merchant until the raider spots it, in other words the escort will run silent. At 300,000 km the raider will spot the escort.

Q. In relation to the raider vs merchant intercept, at what point (in time) does the raider know of the escort?

Q. At that point, how far away is the GG for the raider?

Q. Can the raider risk a turn of combat (20 min & 1 turn vs a merchant should be quite nasty) and still escape into the GG before the escort intercepts?

using TNE stuff here -- so
using 1 LS = 299,000 km (rounded to 300k for discussion)

Q1: Immediately -- depending on sensors and "short range" -- usually it is 10 hexes or 300,000 km. The merchat is decelerating -- so turn 1 is 2G -- thus according to TNE, pg 227 the time for 2G is 71min/LS

so at 2G straight to GG, it would take 35.5 min -- if the merchant used 4G burn straight to GG -- it would be 17.5 to go the 150k km. I doubt the merchant would continue to decel to get to a stable GG orbit, and then procede slowly to the LO -- his life is on the line -- he will get to the GG atmosphere FAST!

So for arguments sake, we can say it would take easily 1 turn + change at the 2G speed

Q2: Most AEMS/PEMS is pretty good -- even a TL 9 HRT/Radar can spot the raider at 75,000 km -- so the merchant will spot it immediately!! And for TL 9+, your looking at short range for those sensors.

Q3: The raider will know of the sensor if the escort is using any kind of thrust - so will light up like a bright ball of fire and be spotted very fast. If the escort is just floating with the thrusters off & cold -- there are a few other factors but at that range, I would think the escort is seen

Q4: As soon as the raider turns on his thrusters and heads for the merchant -- being spotted is immediate!! -- and at that point all 3 ships know of each other and crews will see tangents and target velocities and angles of attack -- so the 3 captains WILL know who is going where.

Q5: The escort is a military ship -- the MFD's will be 300,000 km @ short range -- so the extra distance will only be good for MAYBE 1 turn, after that, the escort WILL BE firing at short range --

Summary:

The Raider has 1 turn at BEST -- after that, the escort will be calling in all SDB's and any other escorts in the GG's immediate area -- in order words -- the raider will have attracted a whole bunch of trouble. And the escorts will pummple the raiders hull and puncture it so as the raider heads into the GG's deep atmosphere -- eventually, the raider will be crushed by the pressure.

-- at 90,000 km rad (were looking at a dia of 180,000 km or a 1.25 J dia), the GG will have a basicly HUGE GG --

here are the stats for our 180,000 diam GG
J Mass = 5 x jupiter (5 jupiters)
J Dia = 1.25 (as Jupiter has a diameter of 142,984 km)
Surf Grav in G's = 8.2

ok, now folks -- do you honestly have 8.2 G's and more to escape out of it's grasp?? If not -- then your in deep doo doo.

-- Even a J-sized GG -- with a .95 J-Mass, J-diam of 1.0, the G's are 2.5: Thus, we need basically 3G's to escape.

-- Which is why IMTU -- GG skimming occurs on small SGG's with less than 1G.

Take a look at the article on Freelance Traveller called 'Gas Giants' by Ken Pick for an in-depth look at why skimmin on LGG's+ can be very dangerous.

 

[Matt123]

Matt123,

Sure. It's on Page 12 of Mayday in the High Guard section:

Two ships which have matched course are considered to be at boarding range. Otherwise, all ships within five hexes of each other are at short range. Ships separated by more than five hexes are at long range. Ships beyond fifteen hexes are out of range, and cannot fire.

You stated earlier "[FONT=arial,helvetica]Weapons: Explicitly stated, 15 light-seconds" in relation to HG2. I assumed you had a HG2 referance.[/FONT]

Whether you're fazed or not is of no consequence. The fact that you're blending rule systems limits the lessons that can be learned from this exercise because the way you've decided to blend the various sensor and weapon ranges is entirely subjective. The lessons thus "learned" are predicated on the choices you made of what to keep in an what to keep out. Others can and will make other choices, choices that will produce results very different from yours.

You're claiming to be "using a vector system to establish game length for a theoretical HG scenario". If that is so, you should use High Guard and not rope in non-High Guard elements as you see fit. The rules are not modular and are meant to be used as a unit.

Cobblers. HG2 does not allow me to answer this type of specific question. LBB bk2 does.

You are getting a little precious Bill. If others find my musings of use then great, otherwise I'm sure this will fade into background static.

What makes it funny tho' is that you are advocating I blend three systems, rather than two whilst berating me for "roping in non-High Guard elements as I see fit." Not to mention you carry on to describe your HG/Mayday "fusion". I suspect this is more about me making differant choices to you, than a guenuine dig at me making choices.

Having said that, I am interested and I'm sure you won't mind if I "fusion" the ideas I like and discard the rest.

In the earlier thread I wrote of another "tweak" you might find interesting. One of several problems with the HG2/Mayday "fusion" Mayday so briefly touches upon is how to mesh Mayday's essentially infinite detection range with HG2's weapons range. After comparing LBB:2's 1.67 light-second weapon range against it's 2 light-second detection range, I house-ruled a 15 hex weapon range and 18 hex detection range for my HG2/Mayday "fusion".

Makes sense. I prefer the LBB bk2 detection ranges, but thats just a preferance for shorter ranges and much greater unknown space.

 

[Matt123]

Take a look at the article on Freelance Traveller called 'Gas Giants' by Ken Pick for an in-depth look at why skimmin on LGG's+ can be very dangerous.

Will do that. I focused on a LGG after a recent thread discussing the difficulties of getting sensor coverage around a LGG. I was surprised after that discussion how easy it is to watch all the approaches to a LGG and with only two sensor platforms. And thats using LBB bk2 sensor ranges which I'm picking are the shortest of all the editions.

Ta for the TNE example.