Space drives.

[Sir Ofeelya]

Been looking through lots of oldl threads on this topic and found some cool stuff.

For my Space Opera Hero game I want a star drive using instantaneous jumps (ala Mote in God's Eye). I am putting a limitation on jump drives that will not allow them to work within xAU of the central star, depending on type.

 

What I want is normal space drives that take, depending on how good the astrogation is, anywhere from days to weeks to transit from planet to jump point (and vice versa).

 

I have looked at the SH sample space ships and cannot get my head around how long trips would take with, say for instance, the merchant ship example.

[L. Marcus]

Re: Space drives.

 

Just use the ship's listed Move as it's maximum acceleration, then work out the distance traveled over time from there.

 

We take the Merchant Ship as an example. It has a pretty hefty NCM of 240" and a SPD of 3, which gives the vehicle a total of 720"/turn. This translates to an acceleration of 120 m/s^2! That's over 12 Gs! And without any protective inertial compensators! The crew is paste!

 

Anyway, let's say you want to travel a AU under constant acceleration. That's about 150,000,000,000 meters. Since s = s(0) + v(0)t + at^2/2, and assuming that s(0) and v(0) are zero, then t = (2s/a)^(1/2). Entering the numbers, we get that the Merchant Ship reaches one AU after 50,000 seconds, or just under 14 hours.

 

But if the crew don't wanna become paste, they use the ship's Combat Movement of 60", which translates to an acceleration of 30 m/s^2. Then the same trip will take 100,000 seconds, or just under 28 hours.

[shadowcat1313]

Re: Space drives.

 

marcus has the simplest idea, other thing you could do is look around for transit time tables in various rules sets, Traveller or GURPS for one, I dont have Star Hero handy atm to see if theres one there

[Nyrath]

Re: Space drives.

 

Now, you have two distances: [a] the distance between the planet and its sun, and the distance between the jump point and its sun.

 

The "superior" object is the one farthest from its sun. The "inferior" object is the one closest to its sun.

 

The question is: how far is it from the planet to the jump point? This will of course vary as the planet moves in its orbit.

 

The planet and the jump point are at their closest when both are on the same side of the sun. The distance between is equal to SuperiorDistance minus InferiorDistance.

 

The planet and the jump point are at their farthest when they are on opposite sides of the sun, with the sun inbetween. The distance between is equal to SuperiorDistance plus InferiorDistance. (actually a bit more, since you have to zig-zag around the sun).

 

The average distance between is the average of these two distances. As it turns out, the average distance is equal to SuperiorDistance.

[Cancer]

Re: Space drives.

 

It could be also that instead of "jump point" it's "jump surface" ... if jump is impossible within some distance of a star, but that's the only limitation on jumping, then the "jump point" is actually a sphere around the star whose radius is that minimum distance. Then rather than travel to a specific place, all a ship has to do get far enough away from the star, so the distance it must go is always (copping Nyrath's terminology above) SuperiorDistance minus InferiorDistance. You can complicate it with real orbital mechanics considerations in the low-energy regime of real-space ship drives, but that's much messier and harder to do.

[matrix3]

Re: Space drives.

 

Has anyone churned the math to let their players save fuel by using the gravity wells of intervening planets to navigate?

[L. Marcus]

Re: Space drives.

 

. . . Oooo . . . Y'know, I'd just handwave that as a Combat Piloting roll, so the ship can change course without using much fuel.

[Sir Ofeelya]

Re: Space drives.

 

Just use the ship's listed Move as it's maximum acceleration, then work out the distance traveled over time from there.

 

We take the Merchant Ship as an example. It has a pretty hefty NCM of 240" and a SPD of 3, which gives the vehicle a total of 720"/turn. This translates to an acceleration of 120 m/s^2! That's over 12 Gs! And without any protective inertial compensators! The crew is paste!

 

Anyway, let's say you want to travel a AU under constant acceleration. That's about 150,000,000,000 meters. Since s = s(0) + v(0)t + at^2/2, and assuming that s(0) and v(0) are zero, then t = (2s/a)^(1/2). Entering the numbers, we get that the Merchant Ship reaches one AU after 50,000 seconds, or just under 14 hours.

 

But if the crew don't wanna become paste, they use the ship's Combat Movement of 60", which translates to an acceleration of 30 m/s^2. Then the same trip will take 100,000 seconds, or just under 28 hours.

 

 

Thanks - just one thing.

 

What are the variables in the equation above.

 

v = velocity? t = time? a = acceleration? what is s? distance?

[Manic Typist]

Re: Space drives.

 

Don't forget: if you decide physics requires worrying about acceleration, it also requires you worry about DEacceleration. That'll slow down your speed, since you generally won't be able to travel at max speed and then just stop. At least, and let everyone off intact.

[L. Marcus]

Re: Space drives.

 

Thanks - just one thing.

 

What are the variables in the equation above.

 

v = velocity? t = time? a = acceleration? what is s? distance?

Yeah, sorry. You got it. When I think about it, I don't know the English standard symbol for distance. s is short for sträcka.

[Nyrath]

Re: Space drives.

 

Don't forget: if you decide physics requires worrying about acceleration' date=' it also requires you worry about DEacceleration. That'll slow down your speed, since you generally won't be able to travel at max speed and then just stop. At least, and let everyone off intact.[/quote']

The equation Marcus supplied is for a Brachistochrone trajectory.

This is where the ship accelerates constantly until it reaches the midpoint, then it decelerates constantly until it arrives at rest with respect to the destination.

 

If you want to accelerate to a point, coast a while, then decelerate to the destination, I have the equation here:

http://www.projectrho.com/rocket/rocket3i.html

[Nyrath]

Re: Space drives.

 

Yeah' date=' sorry. You got it. When I think about it, I don't know the English standard symbol for distance. s is short for [i']sträcka[/i].

I dunno, I'm in the United States, and I am used to seeing "s" as the variable for distance.

[Cancer]

Re: Space drives.

 

Has anyone churned the math to let their players save fuel by using the gravity wells of intervening planets to navigate?

 

That led me to look for observational constraints on the population of free-floating planetary mass objects in the Galaxy. Microlensing surveys are about our only way to get at that situation. One paper I found is here but that is about planets found in orbit around stars which cause lensing events ... that in itself is interesting: the opening of that paper's abstract says

Thirteen exo-planets have been discovered using the gravitational microlensing technique (out of which 7 have been published). These planets already demonstrate that super-Earths (with mass up to ~10 Earth masses) beyond the snow line are common and multiple planet systems are not rare.

Other papers are bit more readable, but it looks like this question is in the stage of "we can see how to do this, but it'll take money and 3 to 5 years before solid statistics come out". While the lensing event made by a star lasts days to weeks, that of a planet is hours. The lensing surveys now operating were designed for stellar-mass lensers, and they work OK for that, but they don't have the real-time reaction ability needed to do planetary mass lensing search well.

[matrix3]

Re: Space drives.

 

That led me to look for observational constraints on the population of free-floating planetary mass objects in the Galaxy. Microlensing surveys are about our only way to get at that situation. One paper I found is here but that is about planets found in orbit around stars which cause lensing events ... that in itself is interesting: the opening of that paper's abstract says

Other papers are bit more readable, but it looks like this question is in the stage of "we can see how to do this, but it'll take money and 3 to 5 years before solid statistics come out". While the lensing event made by a star lasts days to weeks, that of a planet is hours. The lensing surveys now operating were designed for stellar-mass lensers, and they work OK for that, but they don't have the real-time reaction ability needed to do planetary mass lensing search well.

 

 

I don't think I stated that very well. I meant, instead of having your PC's just go from point A to point B, you let them plot out a path that used the gravity of intermediary planets to aid in acceleration, thus saving fuel. The calculations would be pretty complex, I believe, and you'd have to keep records on where all the planets are in their respective orbits.

 

I think NASA does this with probes, to put as little fuel as possible on board.

[Nyrath]

Re: Space drives.

 

I don't think I stated that very well. I meant, instead of having your PC's just go from point A to point B, you let them plot out a path that used the gravity of intermediary planets to aid in acceleration, thus saving fuel. The calculations would be pretty complex, I believe, and you'd have to keep records on where all the planets are in their respective orbits.

 

I think NASA does this with probes, to put as little fuel as possible on board.

Yes, this is actually done with two separate techniques:

 

Gravity Assist

Oberth Effect

 

You appear to be talking about Gravity Assist.

 

Keep in mind that once you have a rocket powerful enough to do prolonged accelerations, gravity assist is not really worth it.

 

However, if you were in a crippled rocket, a survivor of a pirate raid, making an astrogation skill roll to perform a gravity assist maneuver could be the difference between life and death.

[Cancer]

Re: Space drives.

 

 

I don't think I stated that very well. I meant, instead of having your PC's just go from point A to point B, you let them plot out a path that used the gravity of intermediary planets to aid in acceleration, thus saving fuel. The calculations would be pretty complex, I believe, and you'd have to keep records on where all the planets are in their respective orbits.

 

I think NASA does this with probes, to put as little fuel as possible on board.

S'ok. I kind of figured you meant that, but the other alternative intrigued me enough to read up about it. No harm done.

[Basil]

Re: Space drives.

 

The equation Marcus supplied is for a Brachistochrone trajectory.

This is where the ship accelerates constantly until it reaches the midpoint, then it decelerates constantly until it arrives at rest with respect to the destination.

 

Actually, it isn't. It's the equation for a constant-acceleration "fly-by"--- t=sqrt(2d/a)

 

for a Brachistochrone trip, it's t=2*sqrt(d/a)

 

{In the above, "sqrt(x)" means the square-root of x, and "d" is distance.}

 

 

BTW, for a trip involving acceleration, coasting, and deceleration:

D is the total distance,

t' is the time spent accelerating (= the time spent decelerating)

a is acceleration.

 

Total time=(2D/at')+(t'/2)

 

 

One thing to remember about all these formulae: They are meant for situations where acceleration is constant and in a straight line, and the ship is not effected by any force other than it's own acceleration. When you throw in varying acceleration and gravity effects...well, it become rocket science.

[Dr. Anomaly]

Re: Space drives.

 

You could simplify things a bit if you took a book out of FASA's page re: JumpShip travel in Battletech.

 

There, it was easiest to make the calculations for destination if you always jumped to a point where the gravitational forces (speaking solely in terms of distance here) tended to have a known average value; for most star systems, this would be a point directly "above" or "below" the star, at right angles to the plane of the orbits of the planets. Since planets (at least ones habitable by our kind of life) tend to follow orbits that don't tend to deviate too far from a good approximation of a circle, that means the distance between planet and jump point tends to, on average, change very little over the course of the planet's orbit.

 

Since the distance between planets and jump points varies by a relatively small percentage during the planet's year, this means the planet's gravitational influence on the jump point tends to be pretty stable, too, making the jump calc about as easy as they're going to get.

 

This also means the transit time from jump point to a given planet will be pretty standardized, too. So once you've worked out your tables for a given system, the transit time from that system's jump point to each of that system's planets will remain pretty close to constant for any standardized acceleration you chose as your "benchmark".

 

You don't have to worry about where the planet is in its orbit, what time of year it is, or whatever; if they jump into that system, you'll know that for X acceleration the transit time will be Y time units.

 

Of course, this does lead to a disadvantage as well: if the zenith and nadiar jump points are so easy (relatively) to calculate for any system, then if Ship A is known to be going to System B, there are only two relatively small areas of space where an enemy would have to put a ship to be pretty much guaranteed to intercept Ship A when it arrives in System B. Sort of the way that a strait or canal between oceans or the mouth of a fjord make natural choke points for water ship travel, and hence ideal ambush points.

 

Of course, from the perspective of a GM, you get a massive bonus for that kind of restriction, and I don't mean making it easy to ambush the PC's ship. Under a set-up as described above, FASA also mentioned "pirate points" -- points of temporary gravitationally flat areas that form, change, and vanish as time passes and the planets move in their orbits, because such points are formed by the interactions of the various planets and the star of the system. Such points are usually MUCH closer to the planets, so transit time from them would be MUCH shorter than transit times from the zenith or nadiar points; on the other hand, without VERY precise data on the bodies of the system and their movements, it wouldn't take much to calculate and jump to a jump point that doesn't in fact exist...

 

In other words, it gives the PCs an exceedingly dangerous, nail-biting way of cutting off crucial time to beat someone to a destination, or to avoid waiting interceptors by avoiding the common jump points; and, as we all know, if you give players a risky way to do something, they will try it, sooner or later (and probably sooner) because they'll rationalize they "have no choice" or "the risk is worth it" or whatever. If it works, great... they've got the thrill of taking a huge gamble and having it pay off! If it doesn't work, then you get the fun of running them through what happens when a ship misjumps... a result that, according to common lore, no ship has ever returned from...

 

And, of course, if you need to surprise the PCs earlier than the enemy could possibly show up, the enemy could choose to risk a "pirate point" jump...

[Vulcan]

Re: Space drives.

 

For that matter, somewhere in the Battletech/Mechwarrior suplements there is an actual chart of how long it takes to get from the jump points to a planet, based on the accelleration of the ship (in G's) and the stellar class of the star. (Although I make no claims about how accurate they might be...)

 

I would guess that the number assumes the planet is right in the middle of the habitable zone around the star (the equivalent of 1 AU for Sol), so some fudging could be done for hot planets being a little closer, and cold planets being a little farther. Habitable moons of a gas giant would likely be signficatly farther out, and asteroid bases could be quite a long ways away from 'normal' planetary location...

 

Of course, BT sets the jump points where they are because of the technology of their jump drive, and their method of recharging it. The ships can likely jump a bit father in, but the 'jump points' are really just the volume of space where the gravity of the sun is balanced by the effect of the solar wind on the huuuuuge solar panels the JumpShips deploy to recharge their jump drives.

 

I might still have this stuff somewhere, PM me if you're interested and I'll go looking for it.