Well this is the new stuff that BigHairyMountonMan is up to. Tell me what you think of his numbers method.
Let us define:
Intensity: I
Power: P
Volumetric Energy Density: D You may think of this as the temperature of the bolt, or its intrinsic brightness per unit size.
Bolt Speed: V
Bolt Length: L
Bolt Width: W
Bolt Duration: T
Bolt Energy: E
Let k represent pi/4.
E=kDLW^2 Energy is proportional to the volume of the bolt times the energy density of the bolt.
T=L/V Bolt duration is equal to the length divided by the speed.
P=E/T=EV/L=kDVW^2 Power is equal to energy divided by time.
I=P/(kW^2)=DV Intensity equals power divided by area, i.e., the energy density times the speed.
Now, there are two models for turbolaser bolts. Curiously enough, unlike AT-ATs, the apparent intrinsic brightness/temperature of the bolt remains constant during all known firings, which simplifies matters somewhat.
First, the bolts are fired from the same weapon, in which case actual bolt diameter is held constant, and the apparent width is actually the result in intrinsic brightness in some sort of camera effect, i.e., energy density ~ apparent width. In this case, a 7.5 meter wide, 50 meter long bolt (e.g., such as those seen asteroid blasting in TESB with 5-500 terajoule energy) would have, relative to a 5 meter long, 0.5 meter wide bolt of the same speed, as seen striking the Falcon:
150 times the energy.
15 times the intensity.
15 times the power.
I.e., given an impact time of 1/15th-1/30th second (1-2 frame) impact for the 50 meter bolt (with, therefore, a 750-1500 m/s speed), the 5 meter long bolt would have a:
Yield equal to 7.85 to 785 tons of TNT.
5 terawatts to 1 petawatts' power.
Of course, we could consider it as the temperature of the bolt... in which case, thanks to the fourth power dependence of temperature and radiative energy, means a factor of 50,625, which would in turn mean that the Falcon was severely threatened by several megajoules of energy - i.e., much too low. It's much more generous to assume a bolt intensity relation directly to energy through an alternative mechanism of release than radiated thermal energy (which wouldn't fit anyway).
Now, if bolt diameter is actual bolt diameter, rather than brightness, then the 5 meter bolt would have:
1/2250th the energy - i.e., 2.2-220 gigajoules. Reasonably matches up with the observed range of fighter weapon energy yields, represents a 300-30,000 megajoule per cubic meter density.
The same intensity of 1.7-340 terawatts per square meter.
1/225th the power.
So what, then, of a 22.5 meter wide, 500 meter long bolt, with ten times the speed? Well, it would have, given an uncertain actual diameter no less than those of previous bolts:
30-90 times the energy - i.e., up to 4.5 petajoules, but at least 150 terajoules.
10-30 times the intensity.
30-90 times the power.
Notice anything? Bolt geometry supports remarkably similar conclusions to analyzing the ISD as a naval vessel with a role to fulfill.
Bolt geometry also suggests that if the same weapons are firing the 5m and 50m bolts, they consume dramatically different amounts of energy over time. Even the instantaneous power draw is dramatically different.
Is it impossible that these are the same weapons? No, just highly improbable that these all are the same grade of weapon... even if the bolts are fired from a similarly sized bore. And the model fits the existing evidence best when the TLs are different rather than identical in actual width, suggesting they were fired by different bore weapons.
Anticipated responses:
But the visible bolt doesn't indicate anything!
Ans #1: Actually, the persistent byproduct of an invisible bolt gun would be expected to maintain similarly close relations to the yield of the weapon.
Ans #2: The visible bolts are consistently described in both novelizations and screenplays/scripts to be what deals damage.
But the size doesn't have anything to do with anything!
Ans: Size has everything to do with it. The presumption that visible bolt brightness has something to do with the energy density is one thoroughly justified by the variation in brightness of AT-AT bolts when ordered to "maximum" as well as all other occurances of varying bolt brightnesses. This then leaves us with very simple analysis of bolts with the same apparent intrinsic brightness.
The apparent intrinsic brightness seems roughly constant over all ISD bolts.
But the ICS says they're all light turbolasers!
Ans: Light turbolasers with dramatically different behavior, apparently. Perhaps "light" in that particular case refers to "not being the heaviest weapon" in the same sense that I might describe secondary weapons on a battleship as "light" instead of the more useful term of "medium."
But the heavy weapons should be arbitrarily heavier!
Ans: Not really, no. There's nothing within the movies, novelizations, or screenplays that requires heavy weapons to be arbitrarily heavier. Very little even remotely suggests that.
But the Death Star...
...is a unique weapon system that operates entirely differently from ship-grade turbolasers, and is powered by an exotically different reactor, per ANH novelization's description of its remains' behavior vs the descriptions of every normal starship's destruction.
But what about the size of the weapons?
Ans: Bolt geometry suggests a difference of a factor of ~5,000-200,000 in yield per shot based on bolt sizes, with the mid-sized bolts used to blast asteroids in TESB falling near the geometric mean. This range is very similar to the range suggested by both contemporary naval examples and that suggested by the gun sizes themselves, as well as the use of thermonuclear weapons against SW capital ships, etc etc. It all fits in very nicely with heavy shots peaking into the low megaton range and having a power in the mid to high petawatt range during the actual shot.
This incidentally tells us that SW armor is made of rather normal materials, much as the destroyed tower suggests.
But how do TLs work anyway?
I can provide detailed models if necessary... but those aren't necessary for this analysis.
