GURPS Spaceships and a beanstock

[bkkat]

I hopeing that someone with a better Physics and Math background then I can help me with this one. I need a formula to find the Delta-V of a spaceship that has been launched from a beanstock. the height of the launch as well as the wolrd that the beanstock is on are veriable.
Thanks for reading.

[ericbsmith]

That depends on how the beanstalk is built. Most designs involve parking a large mass (such as an Asteroid) in geosynchronous orbit as an anchor. You then building the beanstalk down to the planets surface. In this case the center of mass of the tether/asteroid is not going to be significantly beyond the geosynchronous orbital speed of the planet - about 1.91 mi/s for Earth. This is about 90% of the escape velocity for the Earth.

OTOH, you could build a tether which isn't anchored, but instead continues stretching beyond geosynchronous orbit. Using this method the total length of the tether grows exponentially. Some quick reading suggests that the speeds at the end of this 144,000 km tether would be able to launch a vehicle at around 6.8 mi/s safely, or faster if you don't mind risking damaging the tether.

[malloyd]

Originally Posted by bkkat

I hopeing that someone with a better Physics and Math background then I can help me with this one. I need a formula to find the Delta-V of a spaceship that has been launched from a beanstock. the height of the launch as well as the wolrd that the beanstock is on are veriable.
Thanks for reading.

A beanstalk moves synchronously with the planet, so it provides an "eastward" boost just like launching in the direction of the planet's rotation does (though unlike eastward launch, you have to build the beanstalk on the equator). Since it is synchronous speed is fairly simple 2 x pi x (radius of planet + height above the surface) / (length of day). Example if you are 50,000 miles above a 4000 mile radius planet with a 30 hour day, speed is 2 x pi x (50,000 + 4000) / 30 = 11310 miles/hour = 5.1 km/s

[bkkat]

Thanks everyone! That was just what I was looking for.

[Agemegos]

Originally Posted by bkkat

I hopeing that someone with a better Physics and Math background then I can help me with this one. I need a formula to find the Delta-V of a spaceship that has been launched from a beanstock. the height of the launch as well as the wolrd that the beanstock is on are veriable.
Thanks for reading.

Where the planet has radius 'r', and daylength 'p', and if you haul a payload up a beanstalk to height 'h' above the surface, then the velocity of of the payload is obviously

v = 2 * pi * (r + h) / p

Be careful to use consistent units. Ie. if you want v in miles per second, give r and h in miles and p in seconds.

If the planet has mass 'm', then the well known result is that escape velocity at height 'h' above the surface is

v_esc = SQRT { 2 * G * m / (r+h)}

Therefore the delta-v that a ship will need to reach escape velocity having been hauled up a beanstalk to height 'h' is

v_def = SQRT { 2 * G * m / (r+h)} - {2 * pi * (r + h) / p}

Where 'G' is the universal gravitational constant (6.67 * 10^-11 m^3/kg/s^2). I strongly suggest that you calculate this in SI units and then convert to US Customary medieval measures if that is what you want to use.

Read about beanstalks in the Wikipedia article on orbital elevators.

[rogersd]

I'm not a math guy, but I read the wikipedia article and it made sense. I had no idea that there was that volume of work done toward the construction and development of Space Elevators.

Would a space elevator be TL9?

[Crakkerjakk]

I'd put it at 10 or (maybe)11. The materials technology required is somewhat tricky, as I understand it. There's been a lot of fuss over space elevators recently, but despite the press I'm not sure that the technology is really ready at the scale needed for a megastructure level project.

[Verjigorm]

I disagree with KJ and say that a beanstalk is mature TL9. We're just now branchign itno TL9 as it is(HE lasers, Railguns, Radical Stealth, Neural netowrks, Cyberware, etc).

[Crakkerjakk]

According to UT, you're right, Verjigorm. TL 9.

[Peter Knutsen]

Originally Posted by Verjigorm

I disagree with KJ and say that a beanstalk is mature TL9. We're just now branchign itno TL9 as it is(HE lasers, Railguns, Radical Stealth, Neural netowrks, Cyberware, etc).

If an Earth beanstalk is mature TL9, what about a Mars or Lunar beanstalk? Could that be doable at TL8? Or early TL9? Or late TL8?