Quote from: estar on February 21, 2022, 12:37:52 AMIt pegs Earth to Mars as a 4 day trip as a 1G Brachistochrone trajectory.

The problem with that table is that getting from the Earth's orbit to the Martian orbit in 4 days is only helpful is Mars is there when you arrive. And that still requires Earth and Mars to be in a precise alignment which only happens once every 26 months. So you'll still need some math to determine how long it takes for the other 25 months out of every Earth/Mars cycle. At that point you've just using charts to calculate travel times and the map becomes useless.

Although, I do like the idea of Earth/Mars traffic being concentrated on a once in two years cycle, where a whole fleet of ships launch at the same time and, effectively, travel together. Sort of a wagon train to the stars but with the potential that they might not all be friendly with one another. This is a game scenario that really doesn't occur in any other genre since you can normally just leave whenever you want if traveling by horse, ship, or aircraft.

Quote from: estar on February 21, 2022, 10:04:50 AM
You are right that I misread it so in that case I recommend the following

Code Select Expand


.3 G = 1 days per burn
1 G = 1/2 day per burn
7 G = 1/6 day per burn
12 G = 1/8 day per burn


The show doesn't deal with speeds at all, beyond the occasional "here comes the juice" moment to tell you they're burning hard. But the books deal with speeds all the time and it's pretty consistent. For reference:

• 0.1g is slow, a stately pace when you've got nowhere to go.
• 0.3g is a standard, sustainable pace that most travel takes place in, unless you have a reason to go slower.
• 1g is a moderate burn, can be uncomfortable for those used to lower gravities, but can be kept up for hours at a time, with breaks at a lower speed when the crew need to eat and change stations. People can still move around the ship at 1g.
• Anything over 3g is a "hard burn" which requires everyone in acceleration couches and pharmacology to reduce the risk of people stroking out and such. When Eros sped up to 4g and didn't look like it would have any trouble keeping that speed indefinitely, trying to keep pace with it for more than a brief period was a potential death sentence. 3-4g is the standard speed for hard maneuvers in combat.
• The Tachi left the belly of the Donnager at 12g to escape the blast radius of the self-destruct, but that was for a few minutes and everyone passed out until the ship slowed down.

Quote from: hedgehobbit on February 21, 2022, 10:40:05 AM

Quote from: estar on February 21, 2022, 12:37:52 AMIt pegs Earth to Mars as a 4 day trip as a 1G Brachistochrone trajectory.

The problem with that table is that getting from the Earth's orbit to the Martian orbit in 4 days is only helpful is Mars is there when you arrive. And that still requires Earth and Mars to be in a precise alignment which only happens once every 26 months. So you'll still need some math to determine how long it takes for the other 25 months out of every Earth/Mars cycle. At that point you've just using charts to calculate travel times and the map becomes useless.

Although, I do like the idea of Earth/Mars traffic being concentrated on a once in two years cycle, where a whole fleet of ships launch at the same time and, effectively, travel together. Sort of a wagon train to the stars but with the potential that they might not all be friendly with one another. This is a game scenario that really doesn't occur in any other genre since you can normally just leave whenever you want if traveling by horse, ship, or aircraft.

See this comment by the designer
https://boardgamegeek.com/thread/868735/why-are-planets-static-high-frontier

This is the relevant reason for the Expanse.

QuoteA fourth reason is, for high ISP rockets (including most of the ones in the game) the difference in energy between the worse and best synodic positions is less than 15%. Only in low specific impulse rockets with miniscule delta-v (i.e. all NASA missions until Dawn) do such celestial billiards become significant.

And that leads to the question why bother with a map at all then? Well you bother with a map if you want to include a way for the players to change destination midway through the journey. Which a cross index table of distance values doesn't handle well. Also a energy map illustrates natural way points around which stations will be positioned notably the lagrange points.

Quote from: estar on February 21, 2022, 11:16:21 AMThis is the relevant reason for the Expanse.

QuoteA fourth reason is, for high ISP rockets (including most of the ones in the game) the difference in energy between the worse and best synodic positions is less than 15%. Only in low specific impulse rockets with miniscule delta-v (i.e. all NASA missions until Dawn) do such celestial billiards become significant.

All these energy calculations require that the target (i.e. Mars) be in the exact perfect spot of the elliptical orbit the ship is traveling. Which is a safe assumption since waiting for a proper alignment launch window takes no energy. In High Frontier, you're abstracting a two-year launch window in one-year turns. But, IMO, it completely breaks down when using turns of 1 day or 1 hour when your launch window is one day out of 700.

QuoteAnd that leads to the question why bother with a map at all then? Well you bother with a map if you want to include a way for the players to change destination midway through the journey.

If you want your space travel to be anywhere approaching realistic, then you're going to need an app to calculate position and travel times. But, I can see why that may not matter.

Quote from: hedgehobbit on February 21, 2022, 11:59:50 AM
All these energy calculations require that the target (i.e. Mars) be in the exact perfect spot of the elliptical orbit the ship is traveling. Which is a safe assumption since waiting for a proper alignment launch window takes no energy. In High Frontier, you're abstracting a two-year launch window in one-year turns. But, IMO, it completely breaks down when using turns of 1 day or 1 hour when your launch window is one day out of 700.

Again there is a difference but it inconsequential when talking about torch drives which is what I am focusing on. If we are talking chemical rockets with limited delta-vee budgets then we need to have turns that span a year just like the High Frontier game to marginalize the difference that windows make. And the Expanse uses torch drives.

I am well aware of what required and how it works. And programmed ships that were capable of continuous thrust like Traveller's Type-S Scout. It not a case of just point straight at the destination and go but it also doesn't require hitting a window every two years either.  What it takes is point in the RIGHT direction which is usually off angle from the target. Sometimes a dogleg is required. The more Gs you can put out the more you can ignore the effects of gravity. A Free Trader with a 1G drive has to often take a counter initutive approach to reach a destination that I can best describe as a spiral and it is NOT a hohman transfer.  Where a speeder ship capable of pulling 6G can almost but not quite just point at where needs to be and just go.

https://www.ibiblio.org/mscorbit/

Quote from: hedgehobbit on February 21, 2022, 11:59:50 AM

If you want your space travel to be anywhere approaching realistic, then you're going to need an app to calculate position and travel times. But, I can see why that may not matter.

Only if your delta-vee budget is limited.

Quote from: estar on February 21, 2022, 11:16:21 AM

Quote from: hedgehobbit on February 21, 2022, 10:40:05 AM

Quote from: estar on February 21, 2022, 12:37:52 AMIt pegs Earth to Mars as a 4 day trip as a 1G Brachistochrone trajectory.

The problem with that table is that getting from the Earth's orbit to the Martian orbit in 4 days is only helpful is Mars is there when you arrive. And that still requires Earth and Mars to be in a precise alignment which only happens once every 26 months. So you'll still need some math to determine how long it takes for the other 25 months out of every Earth/Mars cycle. At that point you've just using charts to calculate travel times and the map becomes useless.

Although, I do like the idea of Earth/Mars traffic being concentrated on a once in two years cycle, where a whole fleet of ships launch at the same time and, effectively, travel together. Sort of a wagon train to the stars but with the potential that they might not all be friendly with one another. This is a game scenario that really doesn't occur in any other genre since you can normally just leave whenever you want if traveling by horse, ship, or aircraft.

See this comment by the designer
https://boardgamegeek.com/thread/868735/why-are-planets-static-high-frontier

This is the relevant reason for the Expanse.

QuoteA fourth reason is, for high ISP rockets (including most of the ones in the game) the difference in energy between the worse and best synodic positions is less than 15%. Only in low specific impulse rockets with miniscule delta-v (i.e. all NASA missions until Dawn) do such celestial billiards become significant.

And that leads to the question why bother with a map at all then? Well you bother with a map if you want to include a way for the players to change destination midway through the journey. Which a cross index table of distance values doesn't handle well. Also a energy map illustrates natural way points around which stations will be positioned notably the lagrange points.

What about time, though? It will take less time at the same acceleration when two worlds are at closest approach then if those two worlds were at furthest distance.

In terms of energy (delta V), changing destinations mid-voyage may require a huge expenditure of energy to allow a rendezvous with a new destination. Those pesky belters and their torchships have a huge advantage with their drives in that area..

Quote from: jeff37923 on February 21, 2022, 03:06:56 PM
What about time, though? It will take less time at the same acceleration when two worlds are at closest approach then if those two worlds were at furthest distance.

As the author said the difference between the two amount to 15%. I am being handwaving it away in favor of playability.

Quote from: jeff37923 on February 21, 2022, 03:06:56 PM
In terms of energy (delta V), changing destinations mid-voyage may require a huge expenditure of energy to allow a rendezvous with a new destination. Those pesky belters and their torchships have a huge advantage with their drives in that area..

Any intersection is a hohmann pivot and you can change to another orbit at a cost of two burns or one day of travel at 1 G. Remember the map is a ENERGY map. Not a position map.

Also in the Expanse the Belters don't have any inherent advantage as everybody has access to torch drives and Epstein Drives.

Quote from: estar on February 21, 2022, 03:20:03 PM

Quote from: jeff37923 on February 21, 2022, 03:06:56 PM
What about time, though? It will take less time at the same acceleration when two worlds are at closest approach then if those two worlds were at furthest distance.

As the author said the difference between the two amount to 15%. I am being handwaving it away in favor of playability.

Something about that doesn't sound right.  So you're saying the travel time between Earth and Mars is only 15% different between the cases when they're at closest approach versus the case where they're at opposite sides of the sun?

Quote from: Mishihari on February 21, 2022, 07:24:48 PM

Quote from: estar on February 21, 2022, 03:20:03 PM

Quote from: jeff37923 on February 21, 2022, 03:06:56 PM
What about time, though? It will take less time at the same acceleration when two worlds are at closest approach then if those two worlds were at furthest distance.

As the author said the difference between the two amount to 15%. I am being handwaving it away in favor of playability.

Something about that doesn't sound right.  So you're saying the travel time between Earth and Mars is only 15% different between the cases when they're at closest approach versus the case where they're at opposite sides of the sun?

When using magically efficient rockets...

Something the books tease at, but never really deal with is what happens to munitions that miss. Newton's First Law still applies, after all, so railgun and PDC rounds that don't hit something carry on travelling.

Railgun rounds are probably something you can discount because there are so few of them. But PDC rounds are fired off at thousands at a time, lethal clouds spraying off each time they're used. All sorts you could do with that creating some unexpected hazard nowhere near the site of the original fight.

Quote from: Mishihari on February 21, 2022, 07:24:48 PM

Quote from: estar on February 21, 2022, 03:20:03 PM

Quote from: jeff37923 on February 21, 2022, 03:06:56 PM
What about time, though? It will take less time at the same acceleration when two worlds are at closest approach then if those two worlds were at furthest distance.

As the author said the difference between the two amount to 15%. I am being handwaving it away in favor of playability.

Something about that doesn't sound right.  So you're saying the travel time between Earth and Mars is only 15% different between the cases when they're at closest approach versus the case where they're at opposite sides of the sun?

Something was lost in the conversation there. Technically, that information (with the 15% difference) is based on the Hohmann transfer formula and the delta-v required to successfully make the transfer. The idea is that it takes a certain amount of energy to accelerate the craft to sufficient velocity to be at the target body in order to make a capture. There's windows where it just doesn't work, although generally speaking, when talking about transfer orbits you can just ramp up the delta-v until you make whatever happen that you want to. The actual time required for a Hohmann transfer is ALWAYS 1/2 the period of the semi-major axis; you're either in the transfer or you're not. For Mars, this is about 259 days.

In the case of Expanse mechanics, where constant-thrust is a thing, you're really using Brachistochrone transfers (even at low thrust) which mean you're just boosting halfway and then decelerating the other half. Your target point isn't where the object IS, but instead where it's going to be (meaning you'll be captured in its gravity well). The calculation is pretty simple, since bodies have a uniform rate of movement in their orbits.

If you're talking about high-thrust applications (anything in the 1g+ range) you're only looking at days of travel time, so the planet won't move much during the transfer. At lower g applications (by that I mean in the .05g range) you might have to give it some lead time. The difference in travel time isn't much even at those levels though; for instance a 1g Brachistochrone transfer at perihelion would only take 29 hours, while at aphelion it would take 79 hours (assuming you fly through the Sun; a detour would add some time to that), while at .05g the perihelion B-stone transfer would be 132 hours, while an aphelion transfer would be 355 hours (about 14 days).

In the latter case, you'd want to shift your point of aim, since Mars has an orbital velocity of 29km/s; over the course of the longest passage the position of the planet would have shifted by 37 million km (about 7 degrees of its orbit). Again, it's a simple calculation to figure out what that point is and aim for it though.

All of that takes place in the easy areas of physics though, the reason orbital mechanics get hard is when you're talking about the seriously optimized minimum-energy transfers that are required for modern engineering. As HappyDaze said, if you have any kind of magical efficiency that leads to constant thrust, you're golden.

Quote from: Panzerkraken on February 28, 2022, 07:44:45 PM
If you're talking about high-thrust applications (anything in the 1g+ range) you're only looking at days of travel time, so the planet won't move much during the transfer.

The problem I found that unless we are talking Traveller style 6G drive. Is that the Brachistochrone trajectory is still impacted by gravity. The issue is not the amount of delta-vee you have, but the amount of time it takes to apply that delta-vee.

For example today's ion drives are capable of continuous thrust with a very high total delta-vee. But they are so low thrust they that have to take a spiral out of Earth orbit.  For a 1 G the problem is not as bad but the issue still exist. This means some Brachistochrone trajectories being more optimal in terms of travel time than others. It gets better until at 6G you can basically ignore the local gravity fields.

I tried this in physics simulators like Orbiter Space Simulator with crafts that emulated Traveller style ships from 1G to 6G thrust. Played with the numbers until I got the thrust to mass ratio right and fussed with the ISP value until the on-board fuel could last 30 days at full thrust.

Honestly, three body problems are beyond the scope of RPGs. It's possible to plan ahead for things like making sure you're in excess of v=sqrt(GM/r^2) when you pass near a body, but while I'd be fine with playing in that game (math isn't a four letter word to me..) I've probably only played with a couple people in my entire life  that would agree that it sounds like something they'd want to do.

Quote from: Panzerkraken on March 01, 2022, 04:14:18 PM
Honestly, three body problems are beyond the scope of RPGs. It's possible to plan ahead for things like making sure you're in excess of v=sqrt(GM/r^2) when you pass near a body, but while I'd be fine with playing in that game (math isn't a four letter word to me..) I've probably only played with a couple people in my entire life  that would agree that it sounds like something they'd want to do.

Which goes back to why the map is a map of energy costs not one that show physical position.

For all that people say The Expanse is hard sci-fi, the books are much harder than the TV show. It strikes me the licensed RPG, from my cursory reading of it, is calibrated for the show's level of grittiness, not the books.