Calc The Dark Forest calcs, part 2

More calcs and numbers from The Dark Forest!

1. SFJC ships maximum acceleration

“Our spacecraft are incredibly powerful. Far more powerful than Trisolaran ships!”
“How is that possible?”
“Why wouldn’t it be? Put the superweapons aside and look purely at speed. They can reach fifteen percent of the speed of light! Tons faster than the Trisolarans!”

Click to expand...

Natural Selection was the flagship of the third squadron of the Asian Fleet, and in gross tonnage and performance it was second to none. Possessing the latest non-media fusion propulsion system, at full thrust it could accelerate to 15 percent of the speed of light, and its impeccable internal ecological systems could sustain a long-term voyage.

Click to expand...

Ships of the Solar Fleet Joint Conference have a maximum acceleration of 15% C.

2. SFJC railguns
On top of another reference to their spaceships being able to reach 15% the speed of light, there's also another impressive feat here...

“And the spacecraft that can reach fifteen percent of light speed?”
“Well, that’s true. When those warships mobilize, it’s like a tiny sun in the sky. And their space weapons—the day before yesterday I saw a newsreport on TV about an Asian Fleet exercise. A laser cannon swept a targetship as big as a carrier. Half of that iron guy evaporated like a chunk of ice, and the other half exploded like fireworks in a shower of sparkling molten steel. And there are railguns that can fire a hundred iron spheres a second, each the size of a football, at tens of kilometers per second. In a few minutes they can flatten a mountain on Mars.... So even though thereisn’t any of your perpetual motion, with these technologies, humanity is more than capable of putting down the Trisolaran Fleet.”

Click to expand...

The Solar Fleet Joint Conference (SFJC) has ships that fire football-sized iron balls at a rate of 10s of km a second with a hundred spheres fired a second, which can flatten a mountain in a few minutes. According to this link here, the average football has a volume of about 4800cm^3 (or 0.0048m^3). The spheres are made of iron, which weights 7873kg/m^3.

M = 0.0048 X 7873kg
= 37.7904kg

The speed at which it's launched is tens of kilometers a second, which given plural, is at least 20km a second.

T = 20km/1s
= 20000/340.29
= Mach 58.7733992


KE = (0.5)mv^2
= (0.5) X 37.7904 X 20000^2
= 7558080000 joules
= 1.806424474187 tons of TNT

And this is just one round out of a hundred a second!

E = 1.806424474187 tons of TNT X 100
= 180.642447 tons of TNT

Finally, this is not merely limited to short burst rounds, but can sustain firing for 'a few minutes' at least. A few implies more than a couple, so for now let's go with three minutes, or 180 seconds.

E = 180.642447 tons of TNT X 180
= 32515.6405 tons of TNT (32.5156405 kilotons)

The ship also possesses lasers that melted half a targetship, but unfortunately I have no reference for it's dimensions or mass (although it's the size of a carrier).

Final Results
SFJC Fleet ships maximum acceleration = 15% C
SFJC's Railgun firerate = Mach 58.773
SFJC's Railgun firepower (individual rounds) = 1.806 tons of TNT
SFJC's Railgun firepower (per second) = 180.642 tons of TNT
SFJC's Railgun firepower (several minute barrage) = 32.516 kilotons