By the numbers: The Adama maneuver

In season three of Battlestar Galactica, with our heroes’ backs against the wall, the eponymous ship carries out an incredibly risky maneuver that fans have called “the Adama maneuver.” She jumps into the atmosphere, launches fighter support for the people on the ground while falling like a rock, and jumps back out seconds before she would have hit the hard-deck. I was asked  to take a stab at the Galactica‘s altitude when she jumps out of the atmosphere. We can do that using the pinhole projection formula and some geometry; the answer is approximately 16,000′. Let’s work through the math and some questions.

Question 1: How far is Galactica from the camera?
The formula is x/f = X/d, “where x is the size of the object on the sensor, f is focal length of the lens, X is the size of the object, and d is distance from nodal point to the object.” Steve McNutt reports that BSG was shot using Sony F900 cameras (16.99mm sensor, apparently) and used 27mm, 72mm, and 112mm lenses depending on the application. For this kind of shot, it’s a safe bet that 27mm-lenses were used. That lets us plug in some initial values: x/27mm = 1445m/d.

In the picture on my iPad screen, the frame is 15.3mm diagonal and the Galactica is about 6.2mm, or 40.5228758% of the frame diagonal; so the width on the sensor is 40.5228758% of 16.99mm, i.e. 6.8848366mm. So now we have the equation: 6.8848366 / 27 = 1445000 / d, solve for d. It comes out to about 5666.81m

But because the ship isn’t directly above us, we’re not done yet.

Question 2: What is Galactica’s altitude?
Here’s where we have to settle with being as precise as is reasonably-possible—“within a fudge,” as I like to say. I set a protractor on the vertical of the scaffold to Tigh’s left with 90 degrees directly north along that axis; Galactica’s angle on that appears to be about 60 degrees. That gives us values for one angle (we can infer the other two) and the hypotenuse of a triangle. That yields an altitude of 4907.601m, or 16,101’, which feels plausible.

Question 3: What was the margin of error—how long before they were a smear on the hard-deck?
To know how fast the Galactica falls, we need to know her mass and (to calculate wind-resistance) surface-area. With her flight-pods retracted, Galactica has a beam of about 400m, so with her 1,445m length (excluding engine-bells), she presents a surface area of 578,000 m/2. Simplifying somewhat, she has an overall height of 200m. This give her an internal volume of 115,600,000 m/3.

It seems reasonable to suppose that her internal arrangements are much like that of any other aircraft-carrier, just on a larger scale. Let’s consider the conveniently-oblong USS Wasp. The Wasp displaces 40,532 long tons; she is 257m long, 32 meter beam, and keel to flight-deck, she’s about 33 meters tall, giving her an internal volume of 271,392 m/3. That makes the Galactica 425.95 times larger than the Wasp, and gives us a rough number of 17,264,691.7 long tons for her mass.

On these figures, we can calculate the Galactica‘s terminal velocity at 995.7 m/s. From an altitude of 4907.601m, she is just over 4.92 seconds above the hard-deck when she jumps out.

Question 4: So—I mean… Clio; just how big are Adama’s brass ones?
Big. They’re very big.

Question 5: Do these numbers tally with “99,000”?
When we cut to the CIC, Cpt. Kelly announces that the Galactica is at an altitude of “99,000, falling like a rock.” No unit is specified, as is the show’s way. The ship then falls for ~24.5 seconds before executing the jump into orbit, and because we can assume that she has already reached terminal velocity by the time Kelly announces 99k, we can say that the Galactica is at that moment at an altitude of 29,302.251m or 96,135′. This is so close to Kelly’s 99,000 number that we can rationalize the difference away under at least two plausible explanations (timeline compression or unit variation) and say that the calculated numbers do square with what is on screen.

Question 6: What would have happened had the Galactica not jumped out in time?
Everyone would have died. The impact of a massive object (17.5 billion kg) traveling at just short of a thousand meters per second would yield 8,695,601,022,417KJ, the equivalent of a 2.07-megaton nuclear bomb. Adama would have died; Tigh and Tyrol would have died; the Cylons would have died; the people on the ground—all of them—would have died. To see what a weapon of that yield would do to Caprica City, click here: http://nuclearsecrecy.com/nukemap/classic/…

So, to sum-up. The battlestar Galactica has a mass of just over 17 million long tons. She jumps into the atmosphere at an altitude above 100,000’. She swiftly accelerates to a terminal velocity of nearly a kilometer per second while launching vipers, and jumps away from an altitude of 16,000’ not five seconds before she would have hit the hard-deck causing an explosion that would have evaporated everything within half a mile and would have leveled and killed everything within two miles.