In Die is Cast fleet destroys 30 % of planetary crust in single salvo (previously, we know that crust should be destroyed in 1 hour, and mantle within 5). Volume of crust could be around 1.5 x 10e10 km^3 or 1.5 x 10e19 m^3. We see 10 to 12 torpedoes and around 16 beams fired. 30% of crust equates 4.5 x 10e18 cubic meters.
Here is table of elements of crust, along with calculated volume of each element in area of crust melted in attack:
60.2 % silicium - 2.709 x 10e18 m^3
15.2 % aluminium - 6.84 x 10e17 m^3
5.5 % lime - 2.475 x 10e17 m^3
3.1 % magnesium - 1.395 x 10e17 m^3
3.8 % iron (II) oxide - 1.71 x 10e17 m^3
3 % sodium oxide - 1.35 x 10e17 m^3
2.8 % potassium oxide - 1.26 x 10e17 m^3
2.5 % iron (III) oxide - 1.125 x 10e17 m^3
1.4 % water - 6.3 x 10e16 m^3
1.2 % carbon dioxide - 5.4 x 10e16 m^3
0.7 % titanium oxide - 3.15 x 10e16 m^3
0.2 % phosphorus pentoxide - 9 x 10e15 m^3
So we now have exact volume of each of major elements of crust melted during attack. Now only thing needed to calculate exact firepower is to do 12 calculations for each element separately, then calculate sum of involved energy and calculate how much of energy is done by torpedoes and how much by energy weapons. That I will do at later time.
We know that they planned to melt both crust and mantle. Given that temperature of mantle is in range from 1400 to 3000 ° Celzius, we can assume temperature produced is at least 1400 ° C. Given that calcium oxide melts at 2572 ° C, temperatures in excess of 2600°C are possible. So temperatures produced are around 2600 ° C.
Silicium
Specific heat capacity of silicium is 1.547 J(cm^3 x K). Volume is 2.709x10e24 cm^3; that means that energy required to melt it is 1.08961398 x 10e28 J.
Aluminium
Specific heat capacity of aluminium is 2.422 J(cm^3 x K). Volume is 6.84 x 10e23 cm^3. So we have E = 4.3072848 x 10e27 J.
Magnesium
Specific heat capacity of magnesium is 1.773 J(cm^3 x K). Volume is 1.395 x 10e23 cm^3. So we have E = 6.430671 x 10e26 J .
Water
Specific heat capacity of water is 4.1796 J(cm^3 x K). Volume is 6.3 x 10e22 cm^3. So we have E = 6.8461848 x 10e26 J .
(unfinished)
I currently do not have specific heat capacities for remainder of elements, but so far we have 1.653 x 10e28 J or 3.95 exatons of firepower (3 950 000 000 gigatons). If we take torpedoes to be 5 times stronger than beams, then 1 beam has little less than 52 000 000 Gt of power and one torpedo has around 260 000 000 Gt of firepower (52 and 260 petatons).
NOTE: Some claim that visuals, which show no ejecta, no fire etc. contradict that, and that sensors were fooled by Dominion. However, such argument is nonsense. Dominion already had fleet lying in its trap, so fooling them to think attack was succeeding is actually contraproductive, since any false, over-inflated readings woud have warned Tain and his officers about Dominion plan - fleet was "manned by combat veterans", and any combat veteran would notice if destruction levels were so much out of scale. Yet, officer which read sensor report wasn't surprised at all until sensor showed no changes in lifeform readings, and only at that point they realized it was trap. And even if inflating readings was not actually contraproductive, they weren't exactly helpful - fleet was already in Dominion trap at that point. So that firepower is canon. About contradicting visuals - show did have budget after all. For other possibility look at Note 2 below.
Also, in "The Chase" one Klingon Bird of Prey can obliterate all life on a planet, to the point where no DNA would be recoverable from any of the remains. This is, to put it bluntly, impressive, however it is some sort of chain reaction. Not only that, but we know about Starfleet General Order 24 - order to destroy all life on planet. A last resort.
NOTE2: It is possible that petaton-range effective yield of weapons was not actually true yield of weapons, but rather included some form of chain reaction/NDF. Given evidence from "Chase" and visual evidence from episode, that seems most likely.
NOTE 3:
Enterprise season 3 episode 20 "the forgotten".
TUCKER: "HELL, it would take at least (he stops to think/calculate) a thousand starships like enterprise to blow up a entire planet".
Based on 1x10e29 J requirement for blowing up planet calculated by (someone) for Death Star, that quote would put firepower for each ship at 1x10e26 J or 23.9 petatons which fits with DE requirements for stated "Die is Cast" firepower.
petak, 20. kolovoza 2010.
četvrtak, 19. kolovoza 2010.
Federation warp drive
Warp speeds
Star trek ships have to “plot a course”; that implies that they use star charts to calculate route. It might also explain inconsistencies in speed – some parts of galaxy are more hazardous for navigation than other, plus in unexplored space they will have to use sensors to evade hazards (stars, planets etc) so that might be one of factors contributing to awfully low speeds in Star Trek : Voyager (75 years for 70 000 light years or 933 c) when compared to some other episodes. It is also possible that Voyager's usage of Bussard collectors to partially resupply during warp flight dictaded extremely low speed when compared to longer-range Galaxy class.
For example, in episode "The Chase" we have route that Professor Galen was expected to finish in few days to 6 weeks in shuttle.
According to TNG warp formula table here, warp 9 is 3.867 times faster than warp 6. That would give us warp 9 being 1 345 283.7 c in explored space and possibly under ideal conditions. That is why I tend to use Graham's idea of "warp highways" where ships travel faster than under "normal" conditions, where speeds are denoted by warp formula. Also, it is mentioned that usage of high warp "overextended" warp drive.
"Normal" warp speeds:
http://memory-alpha.org/wiki/Warp_factor
---------------------------------------------------------------------------------------------------
TNG, "Encounter at Farpoint":
At this time, top speed for the Enterprise-D is about warp 9.3. Warp 9.8 may be possible, but it may also destroy the ship.
TNG, "Where None Have Gone Before":
Maximum warp speed is about 9000c. (Data reports the distance as 2.7 million ly, and Geordi reports a 300+ year travel time.) As of the pilot, maximum warp is about 9.3.
TNG, "The Icarus Factor":
Riker claims that it would take months at high warp to get from the current location of the Enterprise to the Vega-Omicron sector, on the far side of Federation territory. Assuming the upper limit on distance is 8000 ly (per Star Trek: First Contact) and the lower limit on travel time is two months, the upper limit on speed is 48,000c. Actual speed is probably far lower.
TNG, "Q Who":
Data reports they are 7000 ly from Federation space, and it would take them 2 years and 7 months of travel to get there. This indicates that the maximum sustainable speed of the Enterprise-D is about 2700c.
TNG, "Up the Long Ladder":
The trip from the Bringloid system to NB2323 is 0.5 light-years and takes more than 18 hours at warp 5. This means that warp 5 is less than 244c.
TNG, "Bloodlines":
It would take 20 minutes to travel 300 billion km at warp 9; this would put warp 9 at 833c. This estimate is an outlier, being quite low compared to other TNG speed examples.
TNG, "Clues":
0.54 parsecs is about a day's travel at cruising speed. This would indicate a cruising speed of 644c.
TNG, "The Most Toys":
Kivas Fajo's merchant ship, with a maximum speed of warp 3, could have traveled no more than 0.102 light-years in 23 hours. This is about 39c.
VOY, "The Caretaker":
According to Janeway, at "maximum warp", Voyager's 70,000+ ly trip back to the Federation would take 75 years. This is about 1,000c. "Maximum warp" may represent the best speed they could sustain over that distance with their limited resources.
VOY, "The 37's":
According to Tom Paris, warp 9.9 is 4 billion miles per second, which is 21,473c.
VOY, "Unimatrix Zero":
Voyager travels 2 light years in 2 hours when responding to a distress call. This is about 8,766c.
VOY, "Maneuvers":
Harry Kim gives a current speed of 2 billion kilometers per second, about 6,667c.
VOY, "Scorpion":
Chakotay states that at Voyager's maximum warp, a 40 ly trip would take five days which is just under 3,000c.
VOY, "Hope and Fear":
It takes Voyager two days at high warp to travel 15 Light-years. This is approximately 2,740c.
VOY, "Equinox""
Using an exotic fuel, the USS Equinox supposedly traveled 10,000 ly in about 2 weeks, for a speed of 260,893c. It should be noted, however, that there is no actual evidence that USS Equinox achieved such speeds other than a statement from Captain Ransom, a known liar and murderer.
VOY, "Friendship One":
A 132 light-year side-trip to investigate a planet would require two months round-trip at "maximum warp". This equates to a speed of about 1584c.
VOY, "Critical Care":
When Janeway asks how quickly Paris can get Voyager to an asteroid 3 ly away, Paris replies 2 hours. This is approximately 13,149c. The "How fast can you get us there?" question suggests top speed.
ENT, "The Expanse":
The Enterprise (NX-01) took seven weeks to reach the Delphic Expanse. That is approximately 373c.
ENT, "Damage":
The Enterprise (NX-01) travelled 4 Light Years in 3 days. That is approximately 487c.
ENT, "Detained":
The Enterpise (NX-01) traveled 5.2 Light-years in 3 days. That is approximately 633c.
ENT, "Affliction":
The Enterprise (NX-01) has become capable of Warp 5.2.
TOS, "That Which Survives":
Spock predicts that the Enterprise can travel 990.7 ly in 11.33 hours at warp 8.4, for a speed of 766,503c.
TOS, "Obsession"
The Enterprise pursues an alien cloud creature to it's point of origin 1,000 light years away in the Tycho system. Kirk then notes that they must make a rendezvous with the starship Yorktown, coming back the 1,000 ly to make the rendezvous in 48 hours. Thus one day to get to the Tycho system and one day to come back for a speed of 365,000c
TOS, "The Squire of Gothos"
The Enterprise is 900 light-years from Earth. While this is not a specific speed versus distance quote, it does show that the Enterprise can travel in one week out into unexplored territory across nearly a thousand light years, then the next week be somewhere completely different for the events of "Arena".
TOS, "The Cage/The Menagerie"
Pike attempting to communicate with his Talosian captors "My name is Christopher Pike, commander of the space vehicle Enterprise from a stellar group at the other end of this galaxy". This implies travel on a galactic scale, and would require speed and knowledge unlike anything seen in all of Trek. Some have taken it to mean not the literal other opposite side of the Milky Way galaxy from where Earth would be located, but something much closer.
TOS, "Where No Man Has Gone Before"
The Enterprise seems capable of routine travel to the very literal edges of the galaxy where they are turned back by a mysterious energy barrier. This will not be the only time the ship travels this far and beyond in TOS; "By Any Other Name" and "Is There In Truth No Beauty?". Even if the ship is somehow heading "up" or "down" straight out of the Galaxy though the shortest distance possible, not going to the outer edges of the spiral arm disk, it still means the Enterprise has to traverse across thousands of light years, and all in a very short span of time.
TOS, "Bread and Circuses"
The Enterprise travels across one-sixteenth of a parsec in "seconds". This would equate to a speed of approximately 215,000c, assuming it took a full 30 seconds to get to the system, never mind the specific planet there.
Trekkies have difficulty explaining why Federation starships of the 24th century would be substantially slower than Federation starships of the 23rd century. Their response is that Warsies cherrypick modern Trek for the lowest showings, ignoring higher examples, such as the following:
TNG, "The Chase"
Picard's old professor Galen marks out a path on a map of the Milky Way galaxy that must be followed in order to put together an ancient puzzle. The line Galen traces subtends an impressive 40,000 lys. Galen then notes that with a shuttle or transport, the trip will require months to complete, but if he had access to a starship, then it would only be a matter of weeks. The minimum speed a starship would require to complete the journey as shown would require an average speed of 1 million c.
TNG, "The Best of Both Worlds, Part I and II"
The E-D chases the Borg cube back to Earth over the course of 6 days from the edges of Federation territory. Assuming the nearest edge of Federation space was just 1,000 ly away from Earth, it would require the E-D to maintain a speed of nearly 61,000 c.
DS9, "Valiant"
The cadets tell how the original mission of the Defiant-class USS Valiant was to circumnavigate the 8,000 ly Federation in 90 days. Assuming by that they ment the ship was to go straight out 8,000 lys and then come back to Earth with no stops along the way, then the ship would need a speed of 64,888c.
However, if "circumnavigate" means "circumvent", we have 2 x 4000 ly x pi or 25 000 light years in 90 days. That is 102 000 c.
-----------------------------------------------------------------------------------------------------------
Warp manouvering
Janeway: "Tom, what's the first thing they teach you about maneuvering at warp?"
Tom: "'Faster than light, no left or right.' When possible, maintain a linear trajectory. Course corrections could fracture the hull."
Janeway: "Exactly. We'd have to drop to impulse every time we made a course change."
That basically throws any possibility of radical warp manouvers out through window (it also explains why Dominion fleet was able to simply wait for Federation fleet to come to them - "hold a roadblock", as I put it on Factpile. Federation fleet did not want to lose time by taking longer route, and Dominion fleet blocked route they were going - after all, Dominion has sensors capable of detecting ships from way longer range than Federation can).
There are some examples of warp manouvering, as seen here. However, all these examples involve one to two ships at most; performing warp manouvers with entire fleet will be extremely difficult at best, especially if fleet has large number of older ships. Also, in TOS episode "The Ultimate Computer" we have clear and relatively rapid warp manouvering at warp 4.
On my site.
Star trek ships have to “plot a course”; that implies that they use star charts to calculate route. It might also explain inconsistencies in speed – some parts of galaxy are more hazardous for navigation than other, plus in unexplored space they will have to use sensors to evade hazards (stars, planets etc) so that might be one of factors contributing to awfully low speeds in Star Trek : Voyager (75 years for 70 000 light years or 933 c) when compared to some other episodes. It is also possible that Voyager's usage of Bussard collectors to partially resupply during warp flight dictaded extremely low speed when compared to longer-range Galaxy class.
For example, in episode "The Chase" we have route that Professor Galen was expected to finish in few days to 6 weeks in shuttle.
Our galaxy is light years in diameter, and route shown is approximately equal to 4/5ths of its radius, or 40 000 light years. Most TNG shuttles are able to achieve warp 6, so we have warp 6 being 347 857 c in explored space.
According to TNG warp formula table here, warp 9 is 3.867 times faster than warp 6. That would give us warp 9 being 1 345 283.7 c in explored space and possibly under ideal conditions. That is why I tend to use Graham's idea of "warp highways" where ships travel faster than under "normal" conditions, where speeds are denoted by warp formula. Also, it is mentioned that usage of high warp "overextended" warp drive.
"Normal" warp speeds:
http://memory-alpha.org/wiki/Warp_factor
---------------------------------------------------------------------------------------------------
TNG, "Encounter at Farpoint":
At this time, top speed for the Enterprise-D is about warp 9.3. Warp 9.8 may be possible, but it may also destroy the ship.
TNG, "Where None Have Gone Before":
Maximum warp speed is about 9000c. (Data reports the distance as 2.7 million ly, and Geordi reports a 300+ year travel time.) As of the pilot, maximum warp is about 9.3.
TNG, "The Icarus Factor":
Riker claims that it would take months at high warp to get from the current location of the Enterprise to the Vega-Omicron sector, on the far side of Federation territory. Assuming the upper limit on distance is 8000 ly (per Star Trek: First Contact) and the lower limit on travel time is two months, the upper limit on speed is 48,000c. Actual speed is probably far lower.
TNG, "Q Who":
Data reports they are 7000 ly from Federation space, and it would take them 2 years and 7 months of travel to get there. This indicates that the maximum sustainable speed of the Enterprise-D is about 2700c.
TNG, "Up the Long Ladder":
The trip from the Bringloid system to NB2323 is 0.5 light-years and takes more than 18 hours at warp 5. This means that warp 5 is less than 244c.
TNG, "Bloodlines":
It would take 20 minutes to travel 300 billion km at warp 9; this would put warp 9 at 833c. This estimate is an outlier, being quite low compared to other TNG speed examples.
TNG, "Clues":
0.54 parsecs is about a day's travel at cruising speed. This would indicate a cruising speed of 644c.
TNG, "The Most Toys":
Kivas Fajo's merchant ship, with a maximum speed of warp 3, could have traveled no more than 0.102 light-years in 23 hours. This is about 39c.
VOY, "The Caretaker":
According to Janeway, at "maximum warp", Voyager's 70,000+ ly trip back to the Federation would take 75 years. This is about 1,000c. "Maximum warp" may represent the best speed they could sustain over that distance with their limited resources.
VOY, "The 37's":
According to Tom Paris, warp 9.9 is 4 billion miles per second, which is 21,473c.
VOY, "Unimatrix Zero":
Voyager travels 2 light years in 2 hours when responding to a distress call. This is about 8,766c.
VOY, "Maneuvers":
Harry Kim gives a current speed of 2 billion kilometers per second, about 6,667c.
VOY, "Scorpion":
Chakotay states that at Voyager's maximum warp, a 40 ly trip would take five days which is just under 3,000c.
VOY, "Hope and Fear":
It takes Voyager two days at high warp to travel 15 Light-years. This is approximately 2,740c.
VOY, "Equinox""
Using an exotic fuel, the USS Equinox supposedly traveled 10,000 ly in about 2 weeks, for a speed of 260,893c. It should be noted, however, that there is no actual evidence that USS Equinox achieved such speeds other than a statement from Captain Ransom, a known liar and murderer.
VOY, "Friendship One":
A 132 light-year side-trip to investigate a planet would require two months round-trip at "maximum warp". This equates to a speed of about 1584c.
VOY, "Critical Care":
When Janeway asks how quickly Paris can get Voyager to an asteroid 3 ly away, Paris replies 2 hours. This is approximately 13,149c. The "How fast can you get us there?" question suggests top speed.
ENT, "The Expanse":
The Enterprise (NX-01) took seven weeks to reach the Delphic Expanse. That is approximately 373c.
ENT, "Damage":
The Enterprise (NX-01) travelled 4 Light Years in 3 days. That is approximately 487c.
ENT, "Detained":
The Enterpise (NX-01) traveled 5.2 Light-years in 3 days. That is approximately 633c.
ENT, "Affliction":
The Enterprise (NX-01) has become capable of Warp 5.2.
TOS, "That Which Survives":
Spock predicts that the Enterprise can travel 990.7 ly in 11.33 hours at warp 8.4, for a speed of 766,503c.
TOS, "Obsession"
The Enterprise pursues an alien cloud creature to it's point of origin 1,000 light years away in the Tycho system. Kirk then notes that they must make a rendezvous with the starship Yorktown, coming back the 1,000 ly to make the rendezvous in 48 hours. Thus one day to get to the Tycho system and one day to come back for a speed of 365,000c
TOS, "The Squire of Gothos"
The Enterprise is 900 light-years from Earth. While this is not a specific speed versus distance quote, it does show that the Enterprise can travel in one week out into unexplored territory across nearly a thousand light years, then the next week be somewhere completely different for the events of "Arena".
TOS, "The Cage/The Menagerie"
Pike attempting to communicate with his Talosian captors "My name is Christopher Pike, commander of the space vehicle Enterprise from a stellar group at the other end of this galaxy". This implies travel on a galactic scale, and would require speed and knowledge unlike anything seen in all of Trek. Some have taken it to mean not the literal other opposite side of the Milky Way galaxy from where Earth would be located, but something much closer.
TOS, "Where No Man Has Gone Before"
The Enterprise seems capable of routine travel to the very literal edges of the galaxy where they are turned back by a mysterious energy barrier. This will not be the only time the ship travels this far and beyond in TOS; "By Any Other Name" and "Is There In Truth No Beauty?". Even if the ship is somehow heading "up" or "down" straight out of the Galaxy though the shortest distance possible, not going to the outer edges of the spiral arm disk, it still means the Enterprise has to traverse across thousands of light years, and all in a very short span of time.
TOS, "Bread and Circuses"
The Enterprise travels across one-sixteenth of a parsec in "seconds". This would equate to a speed of approximately 215,000c, assuming it took a full 30 seconds to get to the system, never mind the specific planet there.
Trekkies have difficulty explaining why Federation starships of the 24th century would be substantially slower than Federation starships of the 23rd century. Their response is that Warsies cherrypick modern Trek for the lowest showings, ignoring higher examples, such as the following:
TNG, "The Chase"
Picard's old professor Galen marks out a path on a map of the Milky Way galaxy that must be followed in order to put together an ancient puzzle. The line Galen traces subtends an impressive 40,000 lys. Galen then notes that with a shuttle or transport, the trip will require months to complete, but if he had access to a starship, then it would only be a matter of weeks. The minimum speed a starship would require to complete the journey as shown would require an average speed of 1 million c.
TNG, "The Best of Both Worlds, Part I and II"
The E-D chases the Borg cube back to Earth over the course of 6 days from the edges of Federation territory. Assuming the nearest edge of Federation space was just 1,000 ly away from Earth, it would require the E-D to maintain a speed of nearly 61,000 c.
DS9, "Valiant"
The cadets tell how the original mission of the Defiant-class USS Valiant was to circumnavigate the 8,000 ly Federation in 90 days. Assuming by that they ment the ship was to go straight out 8,000 lys and then come back to Earth with no stops along the way, then the ship would need a speed of 64,888c.
However, if "circumnavigate" means "circumvent", we have 2 x 4000 ly x pi or 25 000 light years in 90 days. That is 102 000 c.
-----------------------------------------------------------------------------------------------------------
Warp manouvering
Janeway: "Tom, what's the first thing they teach you about maneuvering at warp?"
Tom: "'Faster than light, no left or right.' When possible, maintain a linear trajectory. Course corrections could fracture the hull."
Janeway: "Exactly. We'd have to drop to impulse every time we made a course change."
That basically throws any possibility of radical warp manouvers out through window (it also explains why Dominion fleet was able to simply wait for Federation fleet to come to them - "hold a roadblock", as I put it on Factpile. Federation fleet did not want to lose time by taking longer route, and Dominion fleet blocked route they were going - after all, Dominion has sensors capable of detecting ships from way longer range than Federation can).
There are some examples of warp manouvering, as seen here. However, all these examples involve one to two ships at most; performing warp manouvers with entire fleet will be extremely difficult at best, especially if fleet has large number of older ships. Also, in TOS episode "The Ultimate Computer" we have clear and relatively rapid warp manouvering at warp 4.
On my site.
utorak, 17. kolovoza 2010.
Shipboard phasers
"Masks"
In this episode we see Enterprise-D melting comet.
To make our comet boil, we need to do following things:
1) Raise temperature of ice to melting point (0°C or 273 K)
2) Melt ice ( E = 333.55 kJ/kg or 333 550 J/kg)
3) Raise temperature of water to boiling point (373 K)
4) Make water boil (2257 kJ/kg or 2 257 000 J/kg)
Heat capacity:
ice at -10°C : 1.938 J/(cm^3 x K)
water at 25 ° C : 1.938 J/(cm^3 x K)
water at 100 ° C : 4.2160 J/(cm^3 x K)
After ice/water have reached sufficient temperature to melt/boil (0°C for melting, 100°C for boiling), you need to add additional energy for melting/boiling to actually occur. To melt ice, that energy is 333 550 J/kg; to boil water, you need 2 257 000 J/kg. Density of water at 0°C is 999.8395 kg/m^3; density at 100°C is 958.4 kg/m^3.
Mass of comet is around 3.868474 x 10e13 kg.
So for step one we need 1.1394x10e19 J.
Step two requires 1.29x10e19 J.
Step three requires 8.17836 x 10e18 J.
Step four requires 8.73 x 10e19 J.
So energy required in total is 1.197838 x 10e20 J. Gigaton is 4.184 x 10e18 J. So total energy delivered is around 28.629 Gt over course of 10 seconds, on 10% power. Actually, it would be more like 25 Gt due to object inside, or 2.5 Gt per second at 10% power. NDF, if applied, might lower actual DET value somwhat (to around 0.25 Gt per second at 10% power).
Other examples
In "Who Watches the Watchers" Riker considered a 4.2 Gigawatt generator sufficient to power "a small phaser bank". In "The Mind's Eye" Data says a Type 3 phaser rifle was using energy at a rate of "one point oh five megajoules per second". In "A Matter of Time" Geordi cautions that it will be difficult to control the ship's phasers to within 0.06 Terawatts (60 Gigawatts). That would seem to confirm that shipboard phasers are in Terawatt range at least, possibly even in Petawatt range given that we're talking about 24th century.
Also, here we have very interesting theory about phaser output, by Graham Kennedy.
"So 5 GW hand phasers are reasonable, and even 73 GW is not impossible. "
This is my conclusion for Type-2 hand phasers output. If we reduce that to 50 MW, Type 10 would come as 5 PW. If my conclusion is correct, then Type-10 phaser would have output of 500 PW, or 0.119 Gt per second. If my Masks calculations are good, output would rise to 1.046 x 10e20 W or 10.46 exawatts.
During TNG, Enterprise D drilled hole 50 meters wide at minimum and 2800 km deep in 14 seconds. Phasers were specially modified to prevent tecton instabilities and earthquakes which would be caused by normal phaser beam. That is 5.5 billion cubic meters of rock melted. Granite has density of 2.7 g/cm^3 average. That gives us 1.48 x 10e16 grams of granite melted. Granite has heat capacity of 0.79 (kJ/kg K). Granite melts at 1215 to 1260 ° C. So delta t=1200 K. Energy is 1.4 x 10e19 J over 14 seconds or 1 x 10e18 J per second. That is 2.39 gigatons per second.
Conclusion: Phasers are 2.39 Gt per second minimum
Also, term phaser originally comes from photon maser, which suggests that phaser is primarly particle weapon using photons (hand phasers were described as particle weapons on several occasions), with NDF/chain reaction as optional extra (althought we don't know that for certain).
Generations incident
D 12 was able to destroy 1 058 968 052 to 2 117 936 103 cubic centimeters of Enterprise-D's hull with each shot, depending if only outer hull was damaged or inner too. Actual value is between these two. I will take that shots heated hull 15 000 K. So we have 4.76 x 10e18 to 1.143 x 10e19 joules per shot for our outdated D-12. That is 1.138 to 2.73 gigatons per shot.
Note: Special thanks to Starfleet Jedi forum for providing screenshot showing size of comet in relation to size of object buried iside (episode Masks).
22nd century phaser cannons
Designed as a starship-based version of the hand-held phase pistol, the phase cannon was rated for a maximum power output of 500 gigajoules (given occasional confusion of basic physical terms by Star Trek writers - which only worsened over time - it is quite possible that actual output is 500 GW, and not 500 GJ - for that, however, we have no confirmation. Still, given that shots from these cannons generally last for about 1 second, it is essentially same).
UPDATE: Output of warp core is calculated at 5.84x10e24 W. If phasers use 10% of core output, then we are talking about 5.84x10e23 W or 139.579 teratons per second as high end.
On other note, 4.2 GW is enough to power small phaser bank, presumably consisting of single emitter. I will take that to be shuttlepod emitter. Now, GCS emitters are certainly larger than those on shuttlepod, and I will take them as being 8 times more powerful.
Emitters are in two rows. 12.82 meters long segment has 9 emitters in one row.
Array is incomplete ellipse, with long axis being 321 and short one 214 meters. Array itself is 7/8 of length of ellipse, which gives array length of 749.875 meters. So total count of emitters is 526 in one row, and 1052 total. So total energy output of GCS main array is 35 347 GW high and 4 418 GW low end (low end is taking GCS emitters as being equal in power to those on shuttlepod - GCS certainly does not use "small" emitters, but it is useful as lower end).
Galaxy class hull
http://www.youtube.com/watch?v=fyNm8EWM5K0&NR=1
Here we se that hull thickness of Enterprise-D is 70 centimeters. Hull of galaxy class starship is made of tritanium, and was shown here to be able to absorb rather impressive damage.
Both from Q Who and Best of Both Worlds, Part II it is clear that Enterprise-D has inner and outer hull. That means that, while total hull thickness might be 70 centimeters, it is actually lower due to space between inner and outer hull plates, which is around 6 times thickness of single hull plate. So Galaxy class has double hull, with each hull being 12 centimeters thick.
"Hand phaser can put 100 megajoules of disintegration energy in a beam a centimeter wide, and yet can't even melt - let alone disintegrate - a tritanium plate a few centimeters thick? If 100 MJ/cm^2 were sufficient to punch a hole through several centimeters of tritanium, disintegrating several hundred square meters of tritanium cladding several tens of centimeters thick would require close to a gigaton." - from Starfleet Jedi
So it seems possible that GCS hull might be able to withstand kiloton- to megaton- level weaponry. Enterprise-D saucer was able to survive crash-landing without any apparent damage to hull - althought damage to inner parts was heavy, outer hull "shell" seemed intact.
That is reinforced by TNG episode "Wounded" - in that episode, both Galaxy-class USS Enterprise-D and Nebula class USS Phoenix were able to withstand hits from Cardassian warship's main beam weapons as result of unshielded attack - Enterprise D was hit while its shields were still down (with only damage reports being "minor damage to secondary hull" and "starboard power coupling down" reports by Worf and LaForge), and Phoenix was hit with its shields disabled. Also, explosion caused by warp core breach of "bug" that collided with USS Odissey produced relatively minor damage to secondary hull - however, due to sensitivity of that area, ship was destroyed by warp core breach. USS Galaxy, lead ship of class, withstood significant pounding in First battle of Chin'toka.
Analyzing Arsenal of Freedom
Hand phasers have 5 to 12 GW power output, with 73 GW high end. In "Arsenal of Freedom" Tasha Yar states that Federation weapons cannot melt centimeter thick plate of tritanium. If we take that hand phaser can melt 5 cm^3 of tritanium per second (tritanium is able to withstand 12 000 ° C without showing any signs of melting) then heat capacity of tritanium is around 300 000 J/(cm^3 x K) to 720 000 J/(cm^3 x K).
Generations incident
D 12 was able to destroy 1 058 968 052 to 2 117 936 103 cubic centimeters of Enterprise-D's hull with each shot, depending if only outer hull was damaged or inner too. Actual value is between these two. I will take that shots heated hull 15 000 K. So we have 4.76 x 10e18 to 1.143 x 10e19 joules per shot for our outdated D-12. That is 1.138 to 2.73 gigatons per shot.
Here we se that hull thickness of Enterprise-D is 70 centimeters. Hull of galaxy class starship is made of tritanium, and was shown here to be able to absorb rather impressive damage.
Both from Q Who and Best of Both Worlds, Part II it is clear that Enterprise-D has inner and outer hull. That means that, while total hull thickness might be 70 centimeters, it is actually lower due to space between inner and outer hull plates, which is around 6 times thickness of single hull plate. So Galaxy class has double hull, with each hull being 12 centimeters thick.
"Hand phaser can put 100 megajoules of disintegration energy in a beam a centimeter wide, and yet can't even melt - let alone disintegrate - a tritanium plate a few centimeters thick? If 100 MJ/cm^2 were sufficient to punch a hole through several centimeters of tritanium, disintegrating several hundred square meters of tritanium cladding several tens of centimeters thick would require close to a gigaton." - from Starfleet Jedi
So it seems possible that GCS hull might be able to withstand kiloton- to megaton- level weaponry. Enterprise-D saucer was able to survive crash-landing without any apparent damage to hull - althought damage to inner parts was heavy, outer hull "shell" seemed intact.
That is reinforced by TNG episode "Wounded" - in that episode, both Galaxy-class USS Enterprise-D and Nebula class USS Phoenix were able to withstand hits from Cardassian warship's main beam weapons as result of unshielded attack - Enterprise D was hit while its shields were still down (with only damage reports being "minor damage to secondary hull" and "starboard power coupling down" reports by Worf and LaForge), and Phoenix was hit with its shields disabled. Also, explosion caused by warp core breach of "bug" that collided with USS Odissey produced relatively minor damage to secondary hull - however, due to sensitivity of that area, ship was destroyed by warp core breach. USS Galaxy, lead ship of class, withstood significant pounding in First battle of Chin'toka.
Analyzing Arsenal of Freedom
Hand phasers have 5 to 12 GW power output, with 73 GW high end. In "Arsenal of Freedom" Tasha Yar states that Federation weapons cannot melt centimeter thick plate of tritanium. If we take that hand phaser can melt 5 cm^3 of tritanium per second (tritanium is able to withstand 12 000 ° C without showing any signs of melting) then heat capacity of tritanium is around 300 000 J/(cm^3 x K) to 720 000 J/(cm^3 x K).
Generations incident
D 12 was able to destroy 1 058 968 052 to 2 117 936 103 cubic centimeters of Enterprise-D's hull with each shot, depending if only outer hull was damaged or inner too. Actual value is between these two. I will take that shots heated hull 15 000 K. So we have 4.76 x 10e18 to 1.143 x 10e19 joules per shot for our outdated D-12. That is 1.138 to 2.73 gigatons per shot.
nedjelja, 15. kolovoza 2010.
Death Star sizes
Death Star I
Death star is 135 mm high and 141 mm wide in this shot. Equatorial trench is 0.9 to 1 mm high.
Now we have following shots:
Falcon is around 22.5 meters width. That gives width of bay to be 33.088 meters. Height of bay is 33 mm or 14.55 meters at rate of 44 centimeters per milimeter.
If we return to previous shots, we will see that larger depression Falcon is entering is around 15 times larger in height than bay alone. That gives us 218.25 meters. Trench itself is 3 times larger in height than that area, or 654.75 meters. That gives us rate of either 654.75 meters or 727.5 meters for one milimeter in first shot. That means that DSI is either 92 or 102.6 kilometers wide. Height would be either 88.4 or 98.2 kilometers.
However, I found another shot which could give us better scaling:
In this shot, trench is 1 mm high, with DS being 187 mm high and 204 mm wide. Using previus values of 654.75 meters and 727.5 meters for one milimeter, we can get following values of either 122 438 or 136 042.5 meters for DSI height and either 133 569 meters or 148 410 meters for DSI width.
Death Star II
In this shot trench is 0.9 mm high. From RotJ it is clear it is similar in size to DSI trench, which means that 1 mm here is either 727.5 or 808.3 meters. DSII is around 198 mm wide; I measured height of 200 mm but it could be 181.5 mm if we assume DS1 height-width ratio. That means that DSII is either 144 045 or 160 043 m wide; height could be 132 041, 146 706, 145 500 or 161 660 meters.
Conclusion
I will go with DSI being 122 438 meters high and 133 569 meters wide; for DSII I would take values of 160 043 meters wide and 146 706.5 meters high.
P.S. : I would like to thank Darkstar beacouse I used some screencaps from his "Death Star sizes" page. Work on scaling is completely mine, thought.
I would also like to warn enyone who wants to check my work that shots here are rescaled by webpage; if you want to do scaling yourself, open images in new tab or new window or download them to your computer.
Hand Phasers
ommenting on phaser firepower, Ronald D. Moore said: "The weapons are way too powerful to present them in any realistic kind of way. Given the real power of a hand phaser, we shouldn't be able to show ANY firefights on camera where the opponents are even in sight of each other, much less around the corner! It's annoying, but just one of those things that we tend to slide by in order to concentrate on telling a dramatic and interesting story." (AOL chat, 1997)
And he is right.
Level one: lowest setting, Light Stun, capable of stunning most base humanoids for approximately five minutes. According to Starfleet regulations all phasers must be stored at this setting. Possesses enough force to break large urns. (Star Trek: The Next Generation Technical Manual; TNG: "Aquiel"; TAS: "The Lorelei Signal")
Level seven: Capable of vaporizing noranium carbide alloy. (TNG: "The Vengeance Factor")
Level ten: Kill setting, capable of killing a biological organism. (TNG: "Aquiel")
Level sixteen: Capable of vaporizing rock to widen an opening in a lava tube partially blocked by rubble, or blowing large holes in walls. (TNG: "Chain of Command, Part I", "Frame of Mind")
In order to get high end of phaser firepower, I will use two examples - from TOS, which seems to be clean vaporization, with no chain reaction, and therefore low end of phaser firepower, especially given that we talk about 24th and not 23rd century phasers. Basis is same, thought. Another is TNG vaporization, where hand phaser is capable of vaporizing stone.
Stone example firepower
Phasers are able to heat stones enough to glow (again - no chain reaction or other technobablle, just good ol' energy transfer - example "Silicon Avatar"). According to this, temperature should be 580 to 730 ° C.
Specific heat capacity of granite is 1.534 J(cm^3 x K). That means, to raise temperature of 1 cubic cm of granite by 1 kelvin (kelvin is essentialy same as °C) you need to bring 1.534 joules. Now, to heat granite from starting temperature of 25 ° C to 580 ° C we need to raise its temperature by 555 K. So we have equation E= 1.534 J (6 000 000 cm^3 x 555 K). (6 cubic meters is most we ever saw being cleanly vaporized). That gives us 5 x 10e9 joules or 5 gigajoules.
If we go with "Silicon Avatar" example, we have two hand phasers heating up approx. 2-5 cubic meters of rock within 5 seconds. That gives us 116 to 290 MW or 58 to 145 MW per phaser.
Power capacity
"The Galileo Seven"[TOS1] features the use of phasers drained into a shuttlecraft's engines to enable it to take off and make orbit. (I know it might be wierd beacouse I m using TOS event to calculate power capacity of TNG phaser, but I don't have anything better. I'm still going to use TNG shuttlecraft and not TOS one).
TOS shuttle is 7.44 meters long.
http://www.st-v-sw.net/STSWvolumetrics.html
According to that, Type 6 shuttle weights 29-113 tons. For TOS shuttle, I will assume mass of 48, 188 and 200 tons.
With this calculator we can calculate energy requirements to put shuttlecraft into orbit.
Low Earth orbit is 160 to 2 000 kilometers, but below 200 km objects experience orbital decay. Given that they were concerned with losing orbit after fuel was spent - and did lose orbit - I think it would be safe to assume that they were below 200 km. However, we don't know amount of energy they needed to hold orbit.
So we have this situation:
Mass - minimum energy to reach orbit
48t - 75.264 GJ
188t - 294.784 GJ
200 t - 313.6 GJ
We know five phasors were onboard. That would give us 15 to 60 GJ power capacity.
In TNG's "The Mind's Eye" we are informed that a phaser rifle power pack can easilly hold a charge of around 53.55 megajoules as a phaser rife was test fired with a stated output of 1.05 megawatts for 34 and 17 seconds (total of 51 seconds) with no sign in sight of the power pack charge being depleated. Energy efficiency is stated to be 94.1%, Data mentions that the normal phaser discharge crystal fires with 86.5% efficiency. That means that energy cell capacity is at least 53.55 megajoules. However, given that TOS hand phasers had over 280 times greater capacity than minimum capacity we can derive from this example, we can safely assume that power capacity of phaser rifle is considerably greater than minimal capacity we might calculate from "The Mind's Eye".
Conclusion
58 to 145 MW power output for phasers. "Chain reaction" seen in TNG phasers does nothing to disprove this - it is merely additional ability to conserve energy and make use of phasers realistically possible in CQC.
Also, in most cases there is no vapor produced. So "vaporization" is actually "disintegration. We already have a canon statement from ST:ENT's "In a Mirror, Darkly, Part 2" where Mirror Archer states that TOS phasers on their highest setting are a disintegration weapon.
Power capacity is around 75 to 313 gigajoules for TOS. If it is same for TNG, that would give 517 to 5397 seconds of continuous fire (8 minutes 36 seconds to 1 hour 29 minutes 57 seconds of continuous fire).
Notes
There is "no-recoil" issue, brought up on several places - it is possible that phasers have inertia dampeners to solve that problem, just like starships.
Also, hand phasers have ability of off-axis fire, and seem to have ability of auto-aim. It is possible that hand phaser is actually aimed at target at which person holding it looks ("eye aiming").
Plus, so-called NDF effect is actually impossible to use, beacouse it would create nuclear explosion.
P.S.: Thanks to people from StarfleetJedi.net for bringing up some issues about this page (vaporization/disintegration issue, no-recoil issue, information regarding "In a Mirror, Darkly" and "In Mind's Eye", correcting me on shuttlecraft weights), and suggesting "inertia dampeners" solution for hand phasers. I hope they will keep contributing, and not only for this page.
Pictures:
TNG-era hand phaser
Hand phaser heating rocs
And he is right.
While many people tend to disregard this in order to claim lower phaser firepower, using "chain reaction" effect seen during TNG, that simply doesn't stand, beacouse we already know phasers are able to heat stones to 8 000 ° C, and NDF majic just cannot do that. Only energy transfer can.
There are sixteen power settings:
Level seven: Capable of vaporizing noranium carbide alloy. (TNG: "The Vengeance Factor")
Level ten: Kill setting, capable of killing a biological organism. (TNG: "Aquiel")
Level sixteen: Capable of vaporizing rock to widen an opening in a lava tube partially blocked by rubble, or blowing large holes in walls. (TNG: "Chain of Command, Part I", "Frame of Mind")
In order to get high end of phaser firepower, I will use two examples - from TOS, which seems to be clean vaporization, with no chain reaction, and therefore low end of phaser firepower, especially given that we talk about 24th and not 23rd century phasers. Basis is same, thought. Another is TNG vaporization, where hand phaser is capable of vaporizing stone.
Stone example firepower
Phasers are able to heat stones enough to glow (again - no chain reaction or other technobablle, just good ol' energy transfer - example "Silicon Avatar"). According to this, temperature should be 580 to 730 ° C.
Specific heat capacity of granite is 1.534 J(cm^3 x K). That means, to raise temperature of 1 cubic cm of granite by 1 kelvin (kelvin is essentialy same as °C) you need to bring 1.534 joules. Now, to heat granite from starting temperature of 25 ° C to 580 ° C we need to raise its temperature by 555 K. So we have equation E= 1.534 J (6 000 000 cm^3 x 555 K). (6 cubic meters is most we ever saw being cleanly vaporized). That gives us 5 x 10e9 joules or 5 gigajoules.
If we go with "Silicon Avatar" example, we have two hand phasers heating up approx. 2-5 cubic meters of rock within 5 seconds. That gives us 116 to 290 MW or 58 to 145 MW per phaser.
Power capacity
"The Galileo Seven"[TOS1] features the use of phasers drained into a shuttlecraft's engines to enable it to take off and make orbit. (I know it might be wierd beacouse I m using TOS event to calculate power capacity of TNG phaser, but I don't have anything better. I'm still going to use TNG shuttlecraft and not TOS one).
TOS shuttle is 7.44 meters long.
http://www.st-v-sw.net/STSWvolumetrics.html
According to that, Type 6 shuttle weights 29-113 tons. For TOS shuttle, I will assume mass of 48, 188 and 200 tons.
With this calculator we can calculate energy requirements to put shuttlecraft into orbit.
Low Earth orbit is 160 to 2 000 kilometers, but below 200 km objects experience orbital decay. Given that they were concerned with losing orbit after fuel was spent - and did lose orbit - I think it would be safe to assume that they were below 200 km. However, we don't know amount of energy they needed to hold orbit.
So we have this situation:
Mass - minimum energy to reach orbit
48t - 75.264 GJ
188t - 294.784 GJ
200 t - 313.6 GJ
We know five phasors were onboard. That would give us 15 to 60 GJ power capacity.
In TNG's "The Mind's Eye" we are informed that a phaser rifle power pack can easilly hold a charge of around 53.55 megajoules as a phaser rife was test fired with a stated output of 1.05 megawatts for 34 and 17 seconds (total of 51 seconds) with no sign in sight of the power pack charge being depleated. Energy efficiency is stated to be 94.1%, Data mentions that the normal phaser discharge crystal fires with 86.5% efficiency. That means that energy cell capacity is at least 53.55 megajoules. However, given that TOS hand phasers had over 280 times greater capacity than minimum capacity we can derive from this example, we can safely assume that power capacity of phaser rifle is considerably greater than minimal capacity we might calculate from "The Mind's Eye".
Conclusion
58 to 145 MW power output for phasers. "Chain reaction" seen in TNG phasers does nothing to disprove this - it is merely additional ability to conserve energy and make use of phasers realistically possible in CQC.
Also, in most cases there is no vapor produced. So "vaporization" is actually "disintegration. We already have a canon statement from ST:ENT's "In a Mirror, Darkly, Part 2" where Mirror Archer states that TOS phasers on their highest setting are a disintegration weapon.
Power capacity is around 75 to 313 gigajoules for TOS. If it is same for TNG, that would give 517 to 5397 seconds of continuous fire (8 minutes 36 seconds to 1 hour 29 minutes 57 seconds of continuous fire).
Notes
There is "no-recoil" issue, brought up on several places - it is possible that phasers have inertia dampeners to solve that problem, just like starships.
Also, hand phasers have ability of off-axis fire, and seem to have ability of auto-aim. It is possible that hand phaser is actually aimed at target at which person holding it looks ("eye aiming").
Plus, so-called NDF effect is actually impossible to use, beacouse it would create nuclear explosion.
P.S.: Thanks to people from StarfleetJedi.net for bringing up some issues about this page (vaporization/disintegration issue, no-recoil issue, information regarding "In a Mirror, Darkly" and "In Mind's Eye", correcting me on shuttlecraft weights), and suggesting "inertia dampeners" solution for hand phasers. I hope they will keep contributing, and not only for this page.
Pictures:
TNG-era hand phaser
Hand phaser heating rocs
Federation sublight drive
Federation impulse engines are primary means of propelling starship during sublight operations. In Federation starships, the impulse drive is essentially an augmented fusion rocket, usually consisting of one or more fusion reactors, an accelerator-generator, a driver coil assembly and a vectored thrust nozzle to direct the plasma exhaust. The fusion reaction generates a highly energized plasma. This plasma, ("electro-plasma") can be employed for propulsion, or can be diverted through the EPS to the power transfer grid, via EPS conduits, so as to supply other systems. The accelerated plasma is passed through the driver coils, thereby generating a subspace field which improves the propulsive effect.
Impulse engine can be used to maintain warp speed (TNG "Encounter at Farpoint"), but with lower efficiency than warp drive - that seems to suggest that warp drive is using EM field to generate warp field; other option is using gravitational distortion to acheve warp flight. Therefore, impulse engines and warp drive have similar model of operation, and while impulse drive is more effective in STL flight, it can be used as FTL drive; similarly, warp drive seems to supplement impulse drive in more demanding situations, and can be used for sublight propulsion.
Impulse speeds are inconsistent - a reference made in "Fair Haven" indicated that USS Voyager's impulse power would not be enough to outrun an approaching neutronic storm that was traveling at a velocity of 200,000 kilometers per second (447,387,258 miles per hour), or roughly 2/3 the speed of light. However, it is also commented in "Timeless" that at full impulse, Voyager can travel at roughly 80% light speed at impulse. It is possible that in "Fair Haven" case impulse drive was damaged; however, it is also possible that warp drive supplements impulse drive, therefore allowing starship to achieve greater speeds than possible by using impulse drive only.
Also, Enterprise D needed 23 minutes 17 seconds or 0.388 hours from Saturn to Mars (or Earth, as they were going to intercept cube). Minimum possible distance from Mars to Saturn is 1 097 900 000 km; that translates into speed of 3.5 x 10e10 kilometers per hour. Speed of light is around 1 080 000 000 kilometers per hour; this means that Enterprise-D was actually able to achieve faster-than-light velocity by using its impulse drive, as before that Riker gave command to "slow down to impulse" near Saturn.
On my site.
Impulse engine can be used to maintain warp speed (TNG "Encounter at Farpoint"), but with lower efficiency than warp drive - that seems to suggest that warp drive is using EM field to generate warp field; other option is using gravitational distortion to acheve warp flight. Therefore, impulse engines and warp drive have similar model of operation, and while impulse drive is more effective in STL flight, it can be used as FTL drive; similarly, warp drive seems to supplement impulse drive in more demanding situations, and can be used for sublight propulsion.
Impulse speeds are inconsistent - a reference made in "Fair Haven" indicated that USS Voyager's impulse power would not be enough to outrun an approaching neutronic storm that was traveling at a velocity of 200,000 kilometers per second (447,387,258 miles per hour), or roughly 2/3 the speed of light. However, it is also commented in "Timeless" that at full impulse, Voyager can travel at roughly 80% light speed at impulse. It is possible that in "Fair Haven" case impulse drive was damaged; however, it is also possible that warp drive supplements impulse drive, therefore allowing starship to achieve greater speeds than possible by using impulse drive only.
Also, Enterprise D needed 23 minutes 17 seconds or 0.388 hours from Saturn to Mars (or Earth, as they were going to intercept cube). Minimum possible distance from Mars to Saturn is 1 097 900 000 km; that translates into speed of 3.5 x 10e10 kilometers per hour. Speed of light is around 1 080 000 000 kilometers per hour; this means that Enterprise-D was actually able to achieve faster-than-light velocity by using its impulse drive, as before that Riker gave command to "slow down to impulse" near Saturn.
On my site.
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