Range Bands how do they work?

[DanHeidel]

I was looking at space combat cheat sheets to prep for my game and came across this one: https://d1vzi28wh99zvq.cloudfront.net/pdf_previews/193820-sample.pdf

I wanted to combine that sheet with another one with better graphic design and immediately ran headlong into the question: Mother effing magnets range bands, how do they work?

Specifically, how are the values for the number of rounds required to traverse a range band calculated? I'm using the assumption that a round in space combat is 360 seconds and each level of M-drive amounts to 10 m/s^2 of acceleration. Plugging those into a spreadsheet, I was able to faithfully reproduce the transit times shown in the table on page 163 of the 2022 core book. However, when I compared my numbers with ship movement table on page 166, things do not line up at all. I've tried ignoring the the adjacent and close range bands since those are calculated on 6 second intervals and that helped some of the lower range bands line up a little bit better but once you hit the long range band, the two tables wildly diverge from each other. Is there something obvious I'm missing that would explain why the distance values used in these two tables are so different?

I assume it's to account for the effects of random maneuvering or something. Ultimately it doesn't matter since M and J drives are just space magic and Mongoose can implement them however they want. However, does anyone know what equation or tweaks they are using to generate that table on pace 166? That cheat sheet looks to just be using linear interpolation between the data points but now that I've been beating my head against this problem, I'm feeling stubborn and want to know the exact algorithm Mongoose is using so I can make an accurate version of the cheat sheet.

Also, I'm scratching my head over why the equations on page 163 for distance vs acceleration and time use the equation d = at^2/4 instead of d = at^2/2. I know my calculus is rusty but I can't see where that 4 is coming from.

 

[AnotherDilbert]

I wanted to combine that sheet with another one with better graphic design and immediately ran headlong into the question: Mother effing magnets range bands, how do they work?

Synthetic simplification to remove vectors from the gameplay.

Specifically, how are the values for the number of rounds required to traverse a range band calculated? I'm using the assumption that a round in space combat is 360 seconds and each level of M-drive amounts to 10 m/s^2 of acceleration. Plugging those into a spreadsheet, I was able to faithfully reproduce the transit times shown in the table on page 163 of the 2022 core book. However, when I compared my numbers with ship movement table on page 166, things do not line up at all. I've tried ignoring the the adjacent and close range bands since those are calculated on 6 second intervals and that helped some of the lower range bands line up a little bit better but once you hit the long range band, the two tables wildly diverge from each other. Is there something obvious I'm missing that would explain why the distance values used in these two tables are so different?

It's just a game representing two experienced pilots manoeuvring against each other in 4D space.

It's intended to be simple and fast to play, not represent reality all that well.

Also, I'm scratching my head over why the equations on page 163 for distance vs acceleration and time use the equation d = at^2/4 instead of d = at^2/2. I know my calculus is rusty but I can't see where that 4 is coming from.

Accelerate to midpoint, turn over, decelerate to a stop.
It's two accelerations.

 

[AnotherDilbert]

There is a simplified one-dimensional vector movement system in the Companion.


The underlying physics is standard, M-drives are just producing thrust, ships obey F=ma, as you can see in the Travel Time table. Ship combat and missile movement is highly simplified in order to be able to play it in an afternoon.

 

[DanHeidel]

It's just a game representing two experienced pilots manoeuvring against each other in 4D space.

I figured as much. It's just confusing to me that the bieest discrepancies are at longer distances where there's not going to be any maneuvering. Once you're past a few hundred km, it's a drag race.

Accelerate to midpoint, turn over, decelerate to a stop.
It's two accelerations.

Right, I forgot it finishes at rest to the original frame of reference.