Calc Cyberpunk: Near Orbit calcs

The Cyberpunk tabletop games also have some considerable feats which compliment the game and the anime, so why not have a look at them? All of these (as far as I recall) are taken from Cyberpunk: Near Orbit, which is set in 2013 of the Cyberpunk timeline.

Railguns use powerful magnets to hurl projectiles at hypersonic speeds. The projectile can be metal or plastic with a metal "skirt" to grip the magnetic field.

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Railguns can shoot projectiles at hypersonic speeds, or mach 5. What's more, we can also determine the speed of the spacecrafts to climb from Earth to low orbit, given we are outright given both a distance and a timeframe.

It is assumed in these rules that spacecraft move at 100 miles (150km) per FNFF combat phase (3.2 seconds). This would mean that a delta would take about 10 phases (320 seconds/5.3 minutes) to climb from Earth to LEO, get a lock on and shoot.

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In general, an object in low orbit will be orbiting at @2,000 (3,200km) miles above the Earth.

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T = 3200km/320s
= 10000/340.29
= Mach 29.3866996

Quite close to the escape velocity of Earth. Interesting enough, it also says spaceships can move 150km per combat phase (3.2 seconds). This may be gameplay mechanic (or given that 320 seconds is 10 combat phases, it may be a misnomer for 32 seconds). In anycase it's worth looking into.

(Low end)
T = 150km/32s
= 4687.5/340.29
= Mach 13.7750154

(High end)
T = 150km/3.2s
= 46875/340.29
= Mach 137.750154

Mass Drivers
These are magnetic "rocket sleds" which hurl a capsule into Low Earth orbit. A massdriver handles cargo of up to ten tons, usually in huge storage containers. They cannot be used for passengers as the G-shock is too high. There is one massdriver on Earth, running up Mt. Kilimanjaro in Africa - it is controlled by the EuroSpace Agency. There are massdrivers of larger sizes in Tycho and Copernicus craters; both are used to send materials back to Earth or the L-Zones.

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Mass drivers can launch materials into space (as used on Earth and the Moon), and can handle cargo of up to 10 tons (10,000kg). Even if I can't find a value for speed, this means that at minimum, the ones fired from Kilimanjaro would have to reach the escape velocity of Earth, that being 11.19km/s (or 11190m/s).

KE = (0.5)mv^2
= (0.5) X 10000 X 11190^2
= 626080500000 joules
= 149.636830783939 tons of TNT

It says that the mass drivers on the Moon are even bigger than the ones on Earth, so they should be just as powerful if not even more so. These mass drivers were weaponised at one point and used against the Earth.

Finally, let's get the size of the O'Neill Colonies.

The next step in the colonization of space is the half-completed O'Neill One colony. Built along the cylindrical plan, the colony, named after space colonization pioneer Dr. Gerard K. O'Neill, is a titanic twenty miles (30km) long and five miles (8km) wide at the cross section.

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Final Results
Railgun projectiles = Mach 5
Spacecrafts fly from Earth to LEO = Mach 29.386
Spacecraft flight speed (low end) = Mach 13.775
Spacecraft flight speed (high end) = Mach Mach 137.750
Mass Drivers = 149.637 tons of TNT
O'Neill One's length = 30km