Question regarding GURPS SPACESHIPS formulas

[hal]

Hello Folks,
Was working on some space craft for my Cyberpunk campaign - thinking I'd give GURPS SPACESHIPS a whirl to see what it could do. Knowing that my buddy doesn't much like dealing with Math during gaming, I thought I'd put together a spreadsheet that has all of the Formulas from the first book GURPS SPACESHIPS on it, and I'd simply enter the values as necessary.

Under "Space Travel with Reaction Drives" page 37, it talks about deltaV and moving between Mars and Earth. More specifically, it talks about accelerating for a bit, and then having to drop down to a final velocity of 2.1 miles per second to reach orbit around Earth.

But my question is this:

The ship starts off with a velocity equal to that required to escape the Mar's velocity (or .93 MPS). If it accelerates to 25 MPS, it would have needed an additional 25 MPS (its target speed) less that it already had, or 24.07 MPS.

So, in the example given - shouldn't the formula have been working of off the 24.07 MPS rather than 25? Likewise, if the ship needs to slow down to 2.1 MPS, it requires a delta V change of 25-2.1 or 22.9 MPS which would require its own calculation?

"Example: Since Princess of Helium has an acceleration of 0.5G and wants to reach 25 mps, it spends 25 x 0.0455/0.5 = 2.3 hours accelerating to cruising speed near Mars. In the process, the occupants experience a gentle one- half of an Earth gravity acceleration. The ship will need to decelerate for the same time at the other end of its trip."

Just checking to insure that I'm doing this right, which is why I'm following the examples given in the book - step by step so that my answers agree with what is in the book.

Thanks.

Hal

[Ulzgoroth]

Well, the reality is more complicated than that, since Earth and Mars are in motion relative to one another, and the ship will pick up some extra speed as it drops from martian to terrestrial orbit...

But if you're treating the planets as stationary, as the book seems to, what you're saying seems to make sense. There is an additional consideration of gravitational acceleration and deceleration when near the planets, but if you can do your burns close enough to periapsis it won't much matter.

[hal]

So, I should essentially be adding the orbital velocities of the staring planet and the ending planet to the equation?

[MrTim]

That assumes that the planets are moving straight toward each other, though, which requires very carefully planned (and very small) launch windows.

[Fred Brackin]

Originally Posted by hal

So, I should essentially be adding the orbital velocities of the staring planet and the ending planet to the equation?

If you care that much about absolute accuracy. For a ship with 50 miles per second or more of Delta-V it's not critically important. If the ship had only 5 mps of Delta-V or so it would be more important.

[Anthony]

In general the rules on SS37 should only be used for ships with enough delta-V that escape velocity is a rounding error; the actual interaction between planetary escape velocity and transfer velocity is complex and dependent on the acceleration of the craft (for example, to go from low earth orbit to escape velocity actually ranges from about 2.1 to 4.9 mps delta-V, depending on thrust).

[hal]

Originally Posted by Anthony

In general the rules on SS37 should only be used for ships with enough delta-V that escape velocity is a rounding error; the actual interaction between planetary escape velocity and transfer velocity is complex and dependent on the acceleration of the craft (for example, to go from low earth orbit to escape velocity actually ranges from about 2.1 to 4.9 mps delta-V, depending on thrust).

Oddly enough, this only started as a "create a spreadsheet and make sure it matches the concepts and numbers". If the example says one thing, and the concept says another, then I question it a little.

I guess that's why I'm going to look at the Halfway to Anywhere article, as it has a bit more to the formula than is in GURPS SPACESHIPS. Originally, I had considered the prospect of simply using GURPS TRANSHUMAN SPACE ship building rules, but thought "hey, I paid the money for the rules, I should at least give it a whirl!".

Thanks Folks.

[Mike Wightman]

Perhaps what's needed is another Spaceships supplement book for very hard sci fi where all of this is explained and put into game terms. With diagrams, lots and lots of diagrams :)

[Anthony]

it's worth remembering that this stuff is rocket science, all but the simplest problems are impractical to do by hand, or with the level of math it's practical to put into a spreadsheet.

[cvannrederode]

Originally Posted by Anthony

it's worth remembering that this stuff is rocket science, all but the simplest problems are impractical to do by hand, or with the level of math it's practical to put into a spreadsheet.

Yup, this is the heart of the matter. As a somewhat avid player of Kerbal Space Program, I can say transfer orbits are very much beyond a simple spreadsheet. Just to give you a hint:

In addition to the orbital/escape velocities of Mars and Earth, you need to take into consideration their own orbital velocities around the sun. (14.9 and 18.5 mps respectively). A spacecraft on a minimum energy Hohmann transfer orbit from Earth to Mars will actually arrive at Mars with a slower orbital velocity (around the Sun) than Mars. You start off with a greater velocity than Earth, but as you climb out of the Suns gravity well, you slow down. Doing a quick Google search claims that to get to a transfer orbit to Mars from Earth escape is about 0.3 mps, which will put you at 18.8 mps. You'll then need 0.6 mps to make a capture orbit at Mars, so you'll be going 14.3 mps when you get there. The climb to Mar's orbit cost you 4.5 mps, which you'll have to pay no matter how directly or indirectly you get there. It doesn't come from your Delta-v in low energy transfers, since you already had it from Earth's orbit. But if you wait for minimum distance and burn straight "up" to Mars, you'll notice it.

The ultimate (for a Reactionless system) would be to thrust towards Mars until you reach your suicide burn distance, then doing a suicide burn on approach. (A suicide burn is a deceleration burn at maximum that brings you just to zero velocity at the target). (Generally speaking, in order to just burn at the target, then suicide burn to slow down, you must be able to thrust to overcome the gravitational attraction of the Sun at your distance. At 1 AU this is 0.0006 G or so, so it doesn't take much, but low thrust designs won't be able to cut it.)

How long that takes can vary widely. The distance between Mars and Earth varies from about 40 million to 250 million miles depending on where they are in their orbits. And as you're thrusting towards Mars, it's still zipping along at almost 15 mps in it's orbit, so you'll have to make an Artillery roll (not Gunnery ;-) )

Note that this all glosses over plane changes (Mars orbits in a different plane than Earth. If you don't start at a node where they cross, you need to spend delta-v to haul yourself into the proper plane), and things like the Oberth effect (you get more delta-V from your reaction mass the closer to Earth you are), interactions with other bodies--either in passing or for assists-- and some other things I'm probably forgetting.