04-20-2015, 01:18 AM | #41 | ||
Join Date: Dec 2006
Location: Eindhoven, the Netherlands
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Re: GURPS Space GURPS Math
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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:
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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My Blog: Mailanka's Musing. Currently Playing: Psi-Wars, a step-by-step exploration of building your own Space Opera setting, inspired by Star Wars. |
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04-20-2015, 01:24 AM | #42 |
Join Date: Aug 2004
Location: Binghamton, NY, USA. Near the river Styx in the 5th Circle.
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Re: GURPS Space GURPS Math
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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Eric B. Smith GURPS Data File Coordinator GURPSLand I shall pull the pin from this healing grenade and... Kaboom-baya. Last edited by ericbsmith; 04-20-2015 at 01:28 AM. |
04-20-2015, 01:40 AM | #43 |
Join Date: Jul 2010
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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. |
04-20-2015, 01:46 AM | #44 | |
Join Date: Dec 2006
Location: Eindhoven, the Netherlands
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Re: GURPS Space GURPS Math
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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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My Blog: Mailanka's Musing. Currently Playing: Psi-Wars, a step-by-step exploration of building your own Space Opera setting, inspired by Star Wars. |
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04-20-2015, 01:51 AM | #45 | |
Join Date: Jul 2010
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Re: GURPS Space GURPS Math
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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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04-20-2015, 02:12 AM | #46 |
Join Date: Mar 2013
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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) |
04-20-2015, 03:01 AM | #47 |
Join Date: May 2008
Location: CA
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Re: GURPS Space GURPS Math
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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04-20-2015, 03:08 AM | #48 | |
Join Date: May 2008
Location: CA
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Re: GURPS Space GURPS Math
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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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04-20-2015, 03:13 AM | #49 | |
Join Date: May 2008
Location: CA
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Re: GURPS Space GURPS Math
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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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04-20-2015, 08:10 AM | #50 | |
Join Date: Aug 2007
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Re: GURPS Space GURPS Math
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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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