Just Another Calculation.

[Shadow Archon]

Arcturus Mengsk's Capital Ship, the "White Star" tanking a suicide impact by another Battlecruiser.

Thought I would just put this here considering how long it took me.

First, for size, I'm going with my scaling of the Terran Battlecruiser by scaling from the Drop-Pod hatches based on this Heart of the Swarm cutscene. (Sorry Robear.)

So:





Second, the incident in question:

“On this, I will defy you down to my last breath, Father.”

“That can be arranged,” came Arcturus’s voice. “I’ve tried to be reasonable with—”

Another voice cut in abruptly. “Sir, this is Captain Roger Merriman of the Herakles. I regret to inform you that I am about to defy your orders.”

“What?” Valerian didn’t yelp, not quite, but his voice rose in pitch.

“Ha!” Arcturus sounded triumphant. “See there, Son? Your people are about to defect back over to the winning side.”

“No, Emperor Arcturus. We pledged our service to Prince Valerian, sir, and our lives. We know you planted tracking devices on his ship, and that’s how you’ve been able to follow our jumps. This ship is probably too badly damaged to make the jump—but we can buy the Heir Apparent time.”

“No,” cried Valerian, reasoning it out apparently at the same instant that Annabelle did. Her eyes widened in horror. “I forbid it. Fire on the White Star! If we cripple him, we can all—”

“No, sir,” Merriman’s voice continued. “This is the only way. Remember us to our families.”

Annabelle clasped her knees tight to control her sudden shaking. Tears stung her eyes. Nearly six thousand people were about to give their lives for Valerian, for Raynor, for the hope that Kerrigan held out.

“Sir, the Herakles is approaching the White Star at full speed,” someone said. “Time to impact . . . seven seconds.”

Instinctively, heedless of how it might be interpreted, Annabelle reached out and brushed the leg of the navigator, desperate for human contact. She expected him to pull back, but instead, a hand reached down and grasped hers. She clung to it, wordlessly, squeezing, and he—she didn’t even know his name—squeezed back.

Even from under the console, Annabelle could see the flashes of light that signaled the end of the suicide run.

There was a long, long pause. Then Valerian sighed. “It looks like it worked,” he said. “The White Star is taking heavy damage.”

“Damn, Valerian, you would have made a fine actor,” came Jim Raynor’s familiar drawl. “I think he bought it hook, line, and sinker.”

“How are my crewmen doing over there?”

“It makes for interesting people watching, but so far no fights have broken out. Gonna be a bit crowded with nearly three thousand more mouths to feed, but we’ll manage.”

“What?” The word escaped Annabelle’s mouth before she could stop it. The navigator scooted his chair back and peered down at her. A few seconds later, Valerian’s own visage appeared, the small ponytail slipping over his shoulder as he bent over.

“Ah, Miss Annabelle,” he said. “I’m afraid you were left out of the loop. My apologies.”

She blinked, looking at Valerian and the navigator, both of whom regarded her kindly. “I—it was a trick?”

“One that worked,” Valerian said. “We had just enough time to transfer the crew of the Herakles—which, sadly, had suffered great losses—to the Hyperion and the Bucephalus. We then had the captain speak from my personal suite about using the Herakles on a suicide run while the ship’s adjutant piloted it right into the White Star. Arcturus won’t be able to follow us for some time now, even if he eventually does discover where we are. The Herakles was in bad shape—but her crew is just fine.”

First, to determine the speed of the Battlecruiser, we'll look to Liberty's Crusade and Dark Templar Saga : Twilight:

The tech reached for his ear, then said, “Sir, we have anomalous readings.”

“Location?” snapped the colonel, turning away from Liberty.

“Zed-Two, Quadrant Five, one AU out. Numerous anomalies.”

“Bearing?”

“Working.” A pause, and then a defeated shrug crept into the tech’s words. “Heading for Mar Sara,
sir.”

Duke nodded. “Prepare to intercept anomalous readings. Launch fighters when in range.”

Mike spoke before he thought, “Are you crazy?”

Duke turned back to the reporter. “That was a rhetorical question, I hope, son.”

“We’re one ship.”

“We’re the only ship between them and Mar Sara. We will intercept.”

Mike almost said, “Easy for you, you’re in a hard-shelled battlesuit,” but caught himself. Whatever could
go through a planetary crust wouldn’t be stopped by a few layers of combat armor.

Instead Mike took a deep breath and just gripped the railing, as if he were hoping that this might ease
the eventual blow.

“Approaching visual,” said the tech. “Putting on screen.”

The main screen flickered to reveal a scattering of fireflies against the night sky. They looked almost
pretty against the darkness. Then Mike realized that there were hundreds of them, and that these were
only the main ships. Smaller gnats danced around them.

“Are we within launching range for the Wraiths?” the colonel asked.

“Mark at two minutes,” replied the tech.

“Launch as soon as possible.”

Tassadar gave the order to move to the sister planet of the one he had just destroyed. He kept his thoughts to himself, and Jake did not pry. Tassadar had been in the forefront arguing against the action he had just been ordered to take; it was to be expected that he would harbor regrets.

“Executor, we are detecting terran vessels.”

“I am not surprised, after what we have just done. Display.”

The crystal hummed and an image appeared before them.

“Vessel is identified as Norad II, Colonel Edmund Duke in command. It is a Behemoth-class ship….”

Jake paid little attention as the statistics of the terran vessel were described. The protoss had long kept a watchful eye on the terrans; the Dae’Uhl, the “Great Stewardship,” demanded it. The protoss had watched this young race grow and expand, marveling at how they managed to thrive despite almost constantly attacking one another. It was the Dae’Uhl that Tassadar had cited when he had been ordered to utterly destroy Chau Sara. The protoss knew a great deal about terrans, their weaponry and ships, and what they were capable of. And while the Norad II was a powerful ship by terran standards, it was but a single vessel, and posed no real threat at all. It was a buzzing insect, easily swatted away. Except Tassadar gave no order to do so.

“Executor?” queried the pilot. “Shall I destroy the terran ship?”

Jake watched both her friend and the vessel.

It was moving quickly to intercept. No doubt it would begin attacking them as soon as it was within range.

“There are no other ships. It comes to its doom,” Tassadar said. Jake felt Tassadar’s respect and sorrow wash over her. “They are…courageous, these humans.”

“Sir? They are almost within range.”

Tassadar’s next words stunned everyone. “Deploy the subwarp field and give the order to retreat.”

An Astronomical Unit, or AU, is 149,597,871 kilometers. That takes light about 8.31675 minutes to cover.

Well, it can't be going faster than light without them explicitly saying so, so it has to be slower than light, given I am using real physics in this analysis. Well, they are expected to be in range to launch fighters at two minutes and are considered "almost" in range by Protoss to start firing weapons , so minutes of travel are actually very significant to the time tables to Duke. (I guess the Liberty's Crusade author thought Battle-cruisers used real laser weapons and Blizzard just kind of went the Star Wars / oBSG route with "lasers", hmm?)

So, let's step back, and for sake of argument assume they can cover an AU in an hour, even if the implication is clearly that they can cross this distance much faster. That's 149,597,871 kilometers an hour.

So, we need to figure out the constant acceleration to get them to that speed.

Average Acceleration = 0 meters per second (V1) - 41,554,964.167 meters per second (V2) / 0 seconds (T1) - 3,600 seconds (T2)

That's 11,543.046 meters per second per second. In seven seconds, the Battlecruiser would be be going at 80,801.32 meters per second.

Now, we just need to figure out the mass of the Battle-cruiser.



Using 3DS max, I was able to figure out the Volume of the Cinematic Battlecruiser.

So, going with a length of 1392.4 meters, a Battlecruiser has a volume of 120,377,885 cubic meters, or 1.20377885 × 10e14 cubic centimeters. (120,377,885,000,000)

I will determine a mass amount by assuming an arbitrary percentage of the volume is taken up by NeoSteel. Neosteel, according to an old Marine Model kit, is 80% DU. Marine armor is Neosteel, as is Battlecruiser armor. Marines also are stated to weigh 1090 kilograms as well, so Neosteel indeed is heavy given an average human male weighs about ~70 kilograms (according to google anways...)

Moving on.

10%: 12,037,788,500,000 cubic centimeters x 19.1 = 229,921,760,350 kilograms x .8 = 183,937,408,280 kilograms

20%: 24,075,577,000,000 cubic centimeters x 19.1 = 459,843,520,700 kilograms x .8 = 367,874,816,560 kilograms

30%: 36,113,365,500,000 cubic centimeters x 19.1 = 689,765,281,050 kilograms x .8 = 551,812,224,840 kilograms.

Low-End (10%) : (.5) 183,937,408,280 x (80,801.32 x 80,801.32) = 600450178785033381773.536 joules. Or, 1.43511037 × 10e11 tons of TNT. Or 143 gigatons of TNT.

For the next tier, the middle, I will make additional assumptions about the speed and time.

We'll assume the Battlecruiser was already accelerating by the time Annabelle was freaking out about it. Assuming that time passed equivalent to the average adult reading speed, that's seventeen seconds plus the seven stated for a total of twenty-four seconds

We will also assume that the Norad 2 covered an AU in thirty minutes. (23,086.091 meters per second per second)

Middle (20%) : (.5) 367,874,816,560 x (554,006.184 x 554,066.184) = 56466822879849530325039.36768 joules. Or 1.34958946 × 10e13 tons of TNT. Or 13 teratons of TNT.

For the high-end, we'll assume the Battlecruiser was accelerating since the second time the captain of the Herakles spoke. That's fifty-one seconds + seven for fifty-eight seconds total, as well as assuming that the Norad 2 covered an AU in fifteen minutes. (46,172.18 meters per second per second)

High-End (30%) : (.5) 551,812,224,840 kilograms x (2,677,986.44 x 2,677,986.44) = 1978691413662894202341470.112 joules. Or 4.72918598 × 10e14 tons of TNT. Or 472 Teratons.

To note, in these calculations, I'm still missing the mass of whatever the other 90%/80%/70% is and the 20% of whatever else the Uranium is!

Conclusion:

The White Star is one tough son of a bitch.

It may take heavy damage in this scene, but by the end of the novel, it's still combat capable and takes two Yamato Cannon Strikes from the Hyperion without batting an eye!

[Telenil]

Nice! Though you should have used scientific notation, all those digits don't really matter. Note that relativistic effects increase the mass of the battlecruiser by a few percents, which is small but not negligible in that calculation.

I'll take the lowest hypothesis because I've always thought the battlecruiser in the cinematic was far too large for what it is supposed to be.

The Herakles accelerates at 1000 to 2000g, meaning the piloting adjutant has the equivalent of a herd of elephants resting on her head during the minute of acceleration - a clear giveaway that whatever guides the ship is not flesh and blood. If someone in the White Star is watching on visual, his eyes don't have time to send an image to the brain as the Herakles becomes visible, closes the distance and crashes into the White Star, delivering a thousand times the energy of every nuclear bomb ever detonated on Earth combined (this puts the shock in the range of asteroid impacts).

The White Star effectively hits a large asteroid at full speed, which instantly vaporizes a sizeable fraction of the ship. What's left of her is thrown backwards at thousands of kilometers per second, accelerating in a split second to a speed the Herakles could only reach in half a minute or more. Even if the White Star itself was indestructible, a fraction of this acceleration would still crush everyone into a thin layer of dust and fluids.

So the ship (and her crew) has effectively survived being hit by the entire Terran arsenal in the Koprulu Sector and then some. No wonder she took two Yamato hits and kept firing, it's not that she is tough, it is that she turns towards the laws of physics and says a hearty "fuck you".