Maths / Intercept question

[Lycanorukke]

Thanks Tekrat04 for picking up my stupid error
Bloody dropped a zero - throwing the calculations right out and looking like an idiot.

I fed the results into a spreadsheet, and checked again - breaking it down into 20min combat turns. Comparing it against the intercept time you calculated (which I'm more likely to trust) it matches for the most part this time (I suspect the variation is due to cumulative rounding by the spreadsheet).

The absolute earliest the raider can intercept at 4G is turn 26, with a separtation of 929,462km at start of the turn. On the start of turn 27, the raider will have overshot by 874,413.

Turn: 26
Minutes: 520
Seconds: 31200
Hours: 8.67
Merch Distance to reach GG: 8,550,288 km
Raider has to travel to intercept: 20,008,886 km
Raider travels at 4G: 19,079,424 km
Distance apart: 929,462km at start of turn

Turn 27
Minutes: 540
Seconds: 32400
Hours: 9.00
Merch distance to reach GG: 7,802,352 km
Raider has to travel to intercept: 19,700,883 km
Raider travels at 4G: 20,575,296km
Distance apart: -874,413 km (overshoot) at start of turn

So depending on how one interprets the rules, the raider should get at least one shot in assuming he doesn't slow down. And also assuming I got the numbers right this time.

 

[Whipsnade]

The absolute earliest the raider can intercept...

Lycanorukke,

Two silly questions on my part.

A) By interception are you referring to physical interception or the point when the raider's weapon range intercepts the merchant?

2) Which of the three CT detection ranges are you using?


Regards,
Bill

 

[Lycanorukke]

A) By interception are you referring to physical interception or the point when the raider's weapon range intercepts the merchant?

Physically only. I did the sums for each turn until the merchie reached the GG - adding the 'fireing sphere' scared me off.

2) Which of the three CT detection ranges are you using?

Ah, I didn't worry about detection ranges as there seesm to be disagreance. But taking these from earlier in the thread...

LBB:2 - Initial detection is either 1/2 or 2 light-seconds, tracking after detection is 3 light-seconds. Assuming stays on the same intercept track to hit turn 26. Working with rough sums (caveat emptor from my past screw up )...

With 1/2 LS detection he can only detect during turns 26 & maybe 27
With 2 LS detection he can detect during turns 26, 27 and maybe 25
With 3 LS tracking, they can track until turn 28
If they try and intercept earlier (say turn 24), they wont get any locks as the separation is to great.

The 15 LS HG is a lot more messy due to the size of the 'detect and shoot sphere', will have to work on it. Or ask Tekrat04 who seems better at it.

I am also assuming that if at any time during a turn ships separation distance gets close enough it is a target, even the distance may have been too great at the start of the turn (due to the speed they are moving).

 

[Whipsnade]

Physically only. I did the sums for each turn until the merchie reached the GG - adding the 'fireing sphere' scared me off.

Lycanrukke,

Well, we're only looking at this is two dimensions so it's only a firing circle. If you add firing ranges to the problem, you're intercept will take place earlier.

However, earlier or later doesn't matter because the intercept won't happen at all if the raider doesn't know that the merchant has arrived.

Ah, I didn't worry about detection ranges as there seesm to be disagreance. But taking these from earlier in the thread...

Oh there's a disagreeance all right.

The merchant and raider are roughly 85 light-seconds apart when the scenario begins, so according to:

Mayday, which seemingly has an unlimited detection range, the raider will spot the merchant and begin to shape an interception course.

HG2, which has a detection range of 15 light-seconds, the raider will not spot the merchant, never move in response, and no interception will occur.

LBB:2, which has a detection range of 2 light-seconds, the raider will not spot the merchant, never move in response, and no interception will occur.

Out of the three rule sets, the raider will only detect the merchant in Mayday and even then the capability is more of an omission on the designers' part then any actual ability.

My point is that, in the case of two rule sets with both a detection range and weapon range, HG2 and LBB:2, those two ranges are essentially identical, 15 ls to detect and 15 ls to shoot for HG2 and 2 ls to detect and 1.67 ls to shoot for LBB:2. A raider who sees the merchant can also shoot at the merchant, making interception courses more a matter of maneuvering to keep the merchant in weapons range rather than maneuvering to place the merchant in weapons range.

The only time an interception of the type you're modeling occurs is when Mayday is used and it's lack of a stated detection range is taken literally.


Regards,
Bill

 

[Lycanorukke]

Ah, my bad (again)

I was working under the assumption of a remote sensor or the like as mentioned somewhere upwards in the thread. Though thinking on that, if the merchant is 'running legal' then he is doing the next best thing to using remote sensors - the transponder broadcast.

If he is running that then it seems more than likely that the raider will detect it even at quite a few light seconds. And if they simply track the source they can calculate it's accelleration and then plot an intercept. It also kindly says "Hi, I'm a big fat mechant, rob me please". As the raider runs silent, the first the merchie will know is when his tail is shot off. Unless of course the point radio source suddenly switches to "I'm a war cruiser, time to rumble" when the reaider get close enough for a scan/lock,

 

[Hal]

Ok, now I'm a bit confused...

Page 2 of MAYDAY gives us game scale for use with MAYDAY itself, suggesting that each turn is 100 minutes, or equal to FIVE turns in HIGH GUARD's 20 minute turns.

Page 12 of High GUARD suggests the following:

Short range is 5 hexes or less
Long range is 6 to 15 hexes
Extreme range (and out of weapons range) is 16+ hexes

It is suggested, that when playing HIGH GUARD using the MAYDAY movement rules, that one should use the combat system from HIGH GUARD, not MAYDAY.

Which brings me to the next point. I don't see anywhere, where "sensor ranges" are suggested, only that weapon targeting sensors may not operate beyond 15 hexes.

Per the rules in HIGH GUARD prior to combat, ships can be detected sufficiently well enough that the general size can be determined, as well as where the ships are - prior to the ships starting off at Long range for the first round of combat. Put another way, round ZERO begins at extreme range where weapon's can't fire and hit their targets, and range is automatically long range where ships can finally fire at each other.

So what precisely are the ranges for sensors in High Guard? Is it concievable that sensor ranges are a bit more long ranged than 15 light seconds, and that only targeting sensors are limited to a range of 15 light seconds?

 

[Whipsnade]

Which brings me to the next point. I don't see anywhere, where "sensor ranges" are suggested, only that weapon targeting sensors may not operate beyond 15 hexes.

Hal,

Your confusion is my fault. It's due to the composition of my posts and not your ability in reading my posts.

As you point, there's nothing suggesting that HG2 sensors don't operate beyond 15 light-seconds/hexes. I acknowledged that as I wrote in my first post:

HG2 - No detection range stated, but weapon range suggests at least 15 light-seconds.

(emphasis added)

I simply hadn't been adding the "at least" qualifier since that first post.

Per the rules in HIGH GUARD prior to combat, ships can be detected sufficiently well enough that the general size can be determined, as well as where the ships are - prior to the ships starting off at Long range for the first round of combat.

HG2 is so stylized that I've been long hesitant to infer much of anything regarding 57th Century space combat beyond that of weapons performance. Among many other things, the Line & Reserve mechanism cannot be replicated in game which use a map, HG2 missiles somehow cross 15 light-seconds in 20 minutes regardless of the vectors involved, and the launch of small craft is constrained.

The last, especially, strongly indicates that there is no "Round Zero". As I've pointed out in other threads on other HG2 topics, the game is strictly a tactical one. There are no operational components in the game, no "pre" or "post" battle" steps beyond those of the most basic record keeping, nothing for us to examine and derive inferences from.

So what precisely are the ranges for sensors in High Guard? Is it concievable that sensor ranges are a bit more long ranged than 15 light seconds, and that only targeting sensors are limited to a range of 15 light seconds?

Sure, it's conceivable. The question now becomes what are those ranges? Twenty? Twenty five? Eighty five? How many additional light-seconds do you want? Should the range be the infinite one Mayday seems to suggest? There's LBB:2's example to consider also. In it detection and weapon ranges are almost the same; 2 light-seconds for detection versus 1.67 light-seconds for weapons.

Using LBB:2's example, HG2 detection range is 18 light-seconds which still isn't enough to cover the ~85 light-second distance between the starting position of the merchant and raider in Matt's scenario.

In my games I used the 18 light-second figure. That was a house rule, however, so I didn't raise it here. I believe the 18 number strikes a nice balance. Among other things, it extends sensors, but not too much, it allows some form of "stealth", but not too much, and it creates a nice role for small craft too.

We can finagle HG2's sensor ranges, but not everyone will buy into the number(s) we select. That's why I kept writing about the one range we do know for certain; the 15 light-second weapons range.


Regards,
Bill

 

[Whipsnade]

I was working under the assumption of a remote sensor or the like as mentioned somewhere upwards in the thread. Though thinking on that, if the merchant is 'running legal' then he is doing the next best thing to using remote sensors - the transponder broadcast.

Lycanorukke,

Yes, a transponder aboard the merchant will make the detection job somewhat trivial. Of course, the raider isn't going to begin plotting an intercept course immediately. Remember, the two vessels are ~85 light-seconds apart.

The questions now becomes 1) "Why is the merchant running a transponder during wartime?" and B) "Can the raider trust the transponder signal?"


Regards,
Bill

 

[Matt123]

The questions now becomes....

Hi Bill,

You have hi-jacked my question, which relates purely to the math incolved on a theoretical intercept. Detection is not the issue I am looking for help with.

Additionally, it is with great difficulty I refrain from commenting on your assertions with regards HG abstractions. Those may be your opinions, but again they do not relate to the question I am seeking help on. I will happily engage you in a differant thread on those opinions, as I'm pretty sure we have already.

Can you help with the math?

 

[Matt123]

Hi Lycanorukke,

By my reckoning (using LBB bk2 tables pg10), it takes roughly 15 hours for our trusty 2g merchant to travel the 18,000,000 km trip from the 100 d limit to the surface, assuming a standing start & a stop at the surface. (1)

Starting from 90 degrees the pirate would at worst, be at the planet in half the time & sit there waiting.

In a nutshell, Lycanorukke your calc makes sence (intercepting at 8 hours) Can you adjust it so the raider is capable of matching speed & course with the merchant? That will probably add several hours to the intercept time.

I may be looking to steal your spreadsheet after this!

Cheers
Matt


1. I am obviously ignoring a whole bunch on important variables, like height of the hydrogen clouds, speed gain from the GG's gravity, etc, etc. Please humour me! Having said that, if you have easy answers that can be incorporated into this calc, I'm all ears errr eyes errr....

 

[Whipsnade]

You have hi-jacked my question...

Matt,

My apologies.

Sometimes knowing which question to ask is more important than asking a question.

Can you help with the math?

The math has been answered. It's a straightforward exercise in trig.


Regards,
Bill

 

[Lycanorukke]

Can you adjust it so the raider is capable of matching speed[/SIZE][/FONT] & course with the merchant? That will probably add several hours to the intercept time.

At a preliminary guesstimate - the raider can't match.

Burning at 4G to the halfway point, turning around and then burning again to slow down will cover exactly the same distance as a constant 2G burn. (the difference being one is at 0 velocity while the other screams past). So as the raider hits the mechies 'line of travel' the merchie is entering the GG atmosphere. So you need 5+ G just to match before he escapes.

The big catch is, the raider _also_ has to expend 2G (or a time based equivilant) to "keep pace" with the mechant, and this 2G is at a 90 degree angle to the "travel line". With a 6G raider drive (2 pacing 4 intercept) they would match vectors just as the merchie hit the atmosphere. So you would need at least 7G's of thrust.

(Note: this is very very simplified - the actual path would be a curving arc looping in behind the mechant with the exact thrust vectors changing all the time but I think its a good approximation)

Assuming this is roughly right (fingers crossed ) - at 7G (2G pacing, 5G intercept) they would match at around turn 32 (10.6 hours) and would have about an hour to board & rob (3 turns) before entering the GG.

Sometimes knowing which question to ask is more important than asking a question.

I found the side track very interesting - esp with regard to various sensor rules/ranges I knew nothing about.

To have any sort planetary defence systems would have to make extensive use of remote buoys or massive "deep space" detection arrays. It also aptly illustrates that pirates have no chance in hell of catching anything but stardust unless they work in extensive 'wolfpacks', have inside info, operate very close to planets/choke points, or have an infinite improbability drive.

 

[Whipsnade]

I found the side track very interesting - esp with regard to various sensor rules/ranges I knew nothing about.

Lycanorukke,

It is interesting, but it's not the topic under discussion.

I've a well deserved reputation for hijacking threads, purely unconsciously mind you, but it is something I do far too often and must really work on.

If you'd like to start a new thread, I'll be happy to discuss the various points you raised concerning planetary defenses, sensor buoys, and all the rest...

... until I hijack that thread too.


Regards,
Bill

 

[Matt123]

lol, thanks for the humour Bill. I may start that thread myself on detection problems, the size of the GG I started with kinda begs somes exploration in that direction.

*****

Lycanorukke, I follow what you are saying regards 2g constant = 4g point to point.

Just thinking this through, after 8 hours you have the merchant & the raider at the same spot (on/near the GG), the merchant has 8 hours of 2g accumulated (16g/hours), the raider has no velocity (0g/hours).

To catch up at 4g, the raider accumulates velocity at twice the rate of the merchant. After 6 hours (hour 14), the raider has 24g/hours vs the merchants 28g/hours. After 8 hours (hour 16) the raider has 32g/hours vs the merchants 32g/hours.

Obviously I'm out of my depth a little, but I figure the raider will at the least catch up matching velocities at the 100d limit. This assumes the merchant maintains a constant 2g acceleration throughout and somehow manages to refuel at the GG on the way through (a 2 hour 20 minute operation in the GG atmosphere).

The other extreme is both merchant and raider travelling point to point to the GG, with the raider getting there in half the time.

Am I making sense???

 

[Tekrat04]

By my reckoning (using LBB bk2 tables pg10), it takes roughly 15 hours for our trusty 2g merchant to travel the 18,000,000 km trip from the 100 d limit to the surface, assuming a standing start & a stop at the surface. (1)

Starting from 90 degrees the pirate would at worst, be at the planet in half the time & sit there waiting.

The tables in LLB2 may be a bit off. By my calculation the merchant will take 16h50m to make it to orbit of the GG.

The pirate will not make it to the planet in half the time. For the same time period doubling the accel will double the distance traveled. For the same distance travel doubling the accel will not halve the time. It's going to take the pirate 11h54m to make it to orbit around the planet.

Still, for the pirate the best bet would be to head strait for the planet and make the intercept in orbit.

 

[Matt123]

The tables in LLB2 may be a bit off. By my calculation the merchant will take 16h50m to make it to orbit of the GG.

I was extrapolating between 10,000,000 ks & 40,000,000 ks, your figure is no doubt more correct.

The pirate will not make it to the planet in half the time. For the same time period doubling the accel will double the distance traveled. For the same distance travel doubling the accel will not halve the time. It's going to take the pirate 11h54m to make it to orbit around the planet.

& you are no doubt correct here as well. Looking again at the bk2 tables, the 2g vs 4g results don't match my assumptions. 4g results are 'roughly' 3/4 of the 2g results, not half as I'd assumed.

Still, for the pirate the best bet would be to head strait for the planet and make the intercept in orbit.

So, assuming detection, the best bet is for the raider is to get to the GG first and adopt a a blocking position, perhaps an hour or two out from the refueling point.

In HG terms, say 4-6 20 minute combat turns before the merchant gets to start refueling, with range controlled by the raider unless the merchant chooses to forgo refueling for x turns. Followed by 7 20 minute turns refueling and then a run for the jump point or at a minimum the 10d limit at 2g all the way.

In the unlikely event of Merchant survival after refueling (surviving 11-13 turns or 3.66 - 4.33 hours), how long to get to the 10d limit 1,800,000 ks at a constant 2g?

Cheers!

 

[Tekrat04]

In the unlikely event of Merchant survival after refueling (surviving 11-13 turns or 3.66 - 4.33 hours), how long to get to the 10d limit 1,800,000 ks at a constant 2g?[\QUOTE]
It would take 3h46.

 

[Matt123]

Thanks Tekrat, Lycanorukke & everyone else that contributed. Very much appreciated.

So to summarise, we have 1-2 hours of combat before the GG, 2 hours 20 min at the GG whilst the Merchant attempts refueling (whilst dodging) and a further 3 hours 40 minutes to get away with a high risk of mis-jump.

Thats a total of 7-8 hours or 21-24 HG turns. Thats the minimum period an escort or picket at a large GG needs to fend off raiders for. Quite an ask. I'll use this info in the other thread "How cheap can you make a raider?"

Cheers & thanks again!

 

[rancke]

That's a total of 7-8 hours or 21-24 HG turns. That's the minimum period an escort or picket at a large GG needs to fend off raiders for. Quite an ask. I'll use this info in the other thread "How cheap can you make a raider?"

If the defender is accompanying the merchant, the raider will have to come inside his weapon range in order to have any chance of damaging the merchant. So if the defender is stronger than the raider, he can deal with it by damaging or destroying it.


Hans