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Old 04-20-2015, 01:18 AM   #41
Mailanka
 
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Default Re: GURPS Space GURPS Math

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Originally Posted by Warden View Post
What about the Rocket Equation on page 31 of 'Space'?

I don't understand any of that
I'll jump in and add to the chorus.

First: What is that equation?

The rocket equation is how rockets work. Every action has an equal and opposite reaction, right? That means to go forward in space you have to throw something back. So if you wanted to travel, you'd have to throw, say, a baseball away from you in the opposite direction of where you wanted to go. I'm sure you've seen that image somewhere. It's a fairly common one. Doing so would accelerate you ever so slightly. If you had a great bag of baseballs, you could keep accelerating! But you'd also have to accelerate the baseballs. That is, if you have 50 baseballs, the momentum gained from throwing one baseball would be spread across you and the remaining 49 baseballs. If you threw another, the momentum gained from that one would be spread across you and the remaining 48, and so on. That means that each throw would actually accelerate you slightly more than the previous. That equation is a mathematical representation of that fact.

We just call it ΔV, or "delta-v."

Okay, so why do I need it?

Because it defines how rocket ships move in space. That's a real-world equation. You're looking at actual rocket-science there, my man.

But how would I use it in a game?

You wouldn't. Well, you wouldn't have to. All it would really tell you is how much fuel you would need to get to, say, Mars in a week. Now, what if you don't care about that little detail? Then you would just say "Your ship gets to Mars in a week." Star Trek doesn't use delta-V, nor does Star Wars. They just show up where they want to be. I suspect Interstellar used delta-V, but it wasn't nearly as pertinent to the plot as the effects of gravity on the flow of time.

So you don't need it.

But you could use it. I might use it to understand what sort of technologies are necessary to achieve certain things. See, different fuels and engines have different levels of efficiency. Our old rockets aren't nearly as fast as our current "ion drives," which won't get you into orbit, but are much more efficient in the long-run for getting us to distant worlds. Check out the New Horizon that's arriving at Pluto in June:

Quote:
New Horizons has both spin-stabilized (cruise) and three-axis stabilized (science) modes controlled entirely with hydrazine monopropellant. Additional post launch delta-v of over 290 m/s (1,000 km/h; 650 mph) is provided by a 77 kg (170 lb) internal tank.
Oooo, there it is again, delta-v. They're saying that it has enough fuel and fuel-efficiency to reach a speed of 290 meters per second (pretty fast!).

But what if we wanted to get there even faster than that? What if we envisioned a sci-fi setting where you could reach Pluto in 2 weeks? What kind of speeds would be necessary then?

Atomic Rockets has a list of speculative drives and, using our rocket-science, we could try to figure that out. OR! We could dig out GURPS Spaceships and flip to the Space Travel section. It turns out Pluto is about 40 AU away, and on page 39 we see that we'd need to move at a constant acceleration of 1 G to get there in ~3 weeks. What does that mean? That means our constant acceleration would generate the equivalent forces to standing on the Earth. You wouldn't need artificial gravity. You could simply stand on the ship while it pushed beneath you.

How much delta V would be required for 40 AU worth of 1G acceleration? Page 38 states that it would require: (the square-root of (Distance in AU/ Acceleration in G)) x 1,482 x acceleration in G. Well, we can simply plug in "40" into the distance in AU and "1" into our acceleration, so that gives us

(square root of (40/1)) x 1,482 x 1
(square root of 40) x 1,482
~6.325 x 1,482 = ~9375

Is there anything in the GURPS Spaceships book that will give us those kinds of engines? It turns out, there are!
Page 23: The Total Conversion Torch is gives 1 G and each fuel tank gives us 10,000 mps delta-v. So, we could certainly, casually, get to Pluto in 2 weeks with a TL 12 super-science engine, but that's hardly surprising (a total conversion torch is probably a pretty good candidate for an interstellar sub-light drive). An Antimatter Plasma Torch also provides the necessary acceleration and at TL 11, each tank of fuel gives us 360 mps of delta-v, three of which will get us to Pluto in ~2.9 weeks (if our ship is mostly rocket fuel). So, we can do it with TL 11 super-science. Of course, with super-science, a basic Hot Reactionless drive will also get us there in 2.9 weeks without fussing with fuel. If we don't want super-science, then our options become more limited: A fusion rocket or an advanced fusion pulse drive will both give us the necessary delta-v at TL 11-12 (if our ship is mostly rocket-fuel), but have much slower acceleration than 1G, which will slow our journey down. The antimatter pion has more than enough delta-v (three tanks would do it), but also has a very slow acceleration.

So our back-of-the-envelop calculations tell us that if we want a civilization that gets to Pluto in two to three weeks (from Earth), we see that this is not realistic. We either need a judicious dose of super-science, or we need to accept slower acceleration and extremely high technology. Either way, a civilization that can reach Pluto in ~2 weeks doesn't look much like ours. That is, if we wanted to be consistent.

That sort of thought process is the only reason to use the equations. It lets you fuss around and figure out greater implications. If you like that, keep at it. We'll certainly help, I think, If you don't want that, then don't worry about the equations.
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Old 04-20-2015, 01:24 AM   #42
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Default Re: GURPS Space GURPS Math

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Originally Posted by scc View Post
Log functions are related to squares (As I understand things). Logx(y) is you asking what power do I have to raise x to to get y
Pretty much, with the caveat that in mathematics log(y) is always taken to mean log10(y) and ln(y) is taken to mean loge(y) (natural log of y), because log10 and loge are so common in mathematics that they get special treatment.
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Old 04-20-2015, 01:40 AM   #43
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Default Re: GURPS Space GURPS Math

This is precisely the type of thing I was talking about in my first post.

I've learned though that apparently none of it is required for play, so it's just ignored.
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Old 04-20-2015, 01:46 AM   #44
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Default Re: GURPS Space GURPS Math

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Originally Posted by Warden View Post
This is precisely the type of thing I was talking about in my first post.

I've learned though that apparently none of it is required for play, so it's just ignored.
All GURPS really requires is 3d6. Check out the Roll-and-Shout side-bar in the GURPS core books. GURPS provides lots of resources if you want to figure things out or make them internally consistent. If you want to work out the felt recoil of a portable railgun, or what a realistic, physically accurate interstellar starship might look like, or if you read about some cool exoplanet and you want to plug it exactly into GURPS Space and see what it might be like as a gaming location, then you have the resources to do that. But you don't need them.

They're like the digging rules or the ladder-climbing speeds. People who dislike GURPS love to poke at them and say "Wow, this is crazy! You guys actually have rules for digging speeds! Hilarious!" but you don't need them. I've never used them. I just don't care. But if I did care, they'd be there for me.

That's how most of the GURPS rules (especially the math-heavy ones) work. They're all optional. Only use them if you want them, if they add to your game.

GURPS is a toolkit. You use the tools you need for the job and ignore the rest.
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Old 04-20-2015, 01:51 AM   #45
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Default Re: GURPS Space GURPS Math

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Originally Posted by Mailanka View Post
GURPS is a toolkit. You use the tools you need for the job and ignore the rest.
I've known this for the longest time but it's only recently that it's hit me and I've realised that this really is the case.

I love GURPS, I love the crunch and can use about 90% of the rules now, thanks to the good folk on this forum
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Old 04-20-2015, 02:12 AM   #46
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Default Re: GURPS Space GURPS Math

The Rocket Equation measures increasing fuel efficiency as weight decreases. Imagine two cars with the same engine, one weighing a ton and the other half a ton, the half ton car will go twice as far per unit of fuel as the one ton car. Now imagine if the half ton car was simply the one ton car with basically an empty fuel tank.

So now our car sets out with a full tank of fuel and it weighs a ton, as it travels it uses fuel and gets lighter and each unit of fuel will propel it further, the Rocket Equation is a bit math magic that allows us to know how far that half ton tank of fuel will take use without having to calculate fuel efficiency every pound (Or kilo more likely as our car is a metaphor for a spaceship and astronautics works pretty much excursively in metric to make the math easier)
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Old 04-20-2015, 03:01 AM   #47
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Default Re: GURPS Space GURPS Math

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Originally Posted by Warden View Post
What about the Rocket Equation on page 31 of 'Space'?

I don't understand any of that
Ignore the fact that it's there; it's not a rule you need and is explicitly marked as such. It's also not a GURPS rule - it's a reference to real-life laws of physics and, as such, can have more math than an actual games-rule would prefer.
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Old 04-20-2015, 03:08 AM   #48
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Default Re: GURPS Space GURPS Math

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Originally Posted by ericbsmith View Post
Pretty much, with the caveat that in mathematics log(y) is always taken to mean log10(y) and ln(y) is taken to mean loge(y) (natural log of y), because log10 and loge are so common in mathematics that they get special treatment.
That's incorrect. What log(y) means depends entirely upon the author; in various textbooks I've seen it mean 'log base 10', 'log base e', and 'log base 2'. Log base 10 is probably the most common, but log base e is also pretty common. Log base 2 I've only seen once, in a computer science textbook.

There is no common standard in regards to what 'log(y)' means and you shouldn't assume it's any one thing without being aware that your assumption could be very wrong.
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Old 04-20-2015, 03:13 AM   #49
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Default Re: GURPS Space GURPS Math

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But also, when I create a character, I have a clear concept of what the starting point, "a human being," is like, and how I want to modify it to get what I'm aiming at. I don't have a clear concept of what "a spaceship" is like, generically. I don't have a clear sense for "it has this part that does this, and this part that does that," the way I have the idea that a character either has eyes, or is blind and may need a ranged sense; either has hands, or has other manipulators, or can't manipulate; and so on. I could figure all that out with the comparatively physical descriptions in Vehicles. The very handwavy descriptions in Spaceships leave me nowhere.
One thing you need to understand about Spaceships is that it's very free-form and can represent a lot of different things. The Spaceships rules can be used to stat up a normal terrestrial van, a bunker complex built into the side of a mountain, a high-rise skyscraper, a space station, a sea barge, a fighter jet, a fighter space craft, a block of solid metal, or even a spaceship like the Enterprise from Star Trek. That was not an exhaustive list.

Spaceships doesn't assume just about anything, except that the object that you're creating is of the mass that you select.
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Old 04-20-2015, 08:10 AM   #50
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Default Re: GURPS Space GURPS Math

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Originally Posted by dataweaver View Post

If anything, my only complaint about the system is that it sometimes oversimplifies. It assumes that your mass never changes; but every fuel tank or cargo module is a potential 5% decrease in effective mass when it's empty. That's not a problem when you only have one or two such modules; but what about when you have fifteen of them, and your empty mass is a quarter of your loaded mass? .
This is addressed by the table in the fuel Tank section. That makes ships with many fuel tanks more efficient than ones with few tanks. this refects the larger mass change in such ships.

It's just that (like many things in Spaceships) that t is handled behind then curtain or in some other indirect fashion..
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