Last Revised: 1999.07.27
First and foremost, let me state that in spite of the massive problems that I see in Graham Kennedy's website, I actually grant him much more respect than the average Trekkie fanatic. Even though I disagree with many of his claims and I have serious misgivings about his entire approach, the fact remains that he had the courage to put his viewpoints and ideas up on the world wide web, where they could be picked apart at leisure by anyone with access to a computer.
People who post exclusively in newsgroups and criticize the work of others can make some good points, but there is a lot of work involved in maintaining and creating a large website (as I well know) and there is a certain amount of risk that someone takes whenever he puts his ideas up in a forum where they are so easy to attack. Posts in newsgroups essentially melt into the background noise very quickly because of the heavy volume, thus reducing the effective accountability of the author. Posts from people who use pseudonyms or codenames instead of their real names are even worse, because there is even less accountability.
Now, time for a little bit of background: Graham Kennedy used to be one of the most prominent posters on the "vs" newsgroups. He bounded into the newsgroups with wild claims of Federation shuttlecraft effortlessly shrugging off Death Star superlasers, and attempted to lend credence to his fantasies by citing his credentials (a HND in applied physics and a BEd in physics). I chose to investigate those credentials, and you may be surprised at what I found (click here for more information). Suffice it to say that in spite of his claims, he does not have the equivalent of a university degree in science.
In any case, he chose to "retire" from the "vs" newsgroups and portray himself as the Trek version of Curtis Saxton (minus the education and objectivity), by creating his website which he called the Daystrom Technical Institute. Of course, he still cares about the "vs" arguments in spite of his newfound insistence that he is "above" such silly subjects, so he wrote a fanfic about the Empire vs the Federation which is essentially an endless string of "Fed is better than Empire" claims, strung together without the usual complications of plot or story line. And his propensity for wildly exaggerating the capabilities of Federation technology hasn't changed. It may be useful to examine some of his more extreme excesses, to see how they exemplify his refusal to obey the laws of physics. Note that all of the following examples are taken from his own website, as of April 17, 1999. I mention the date because he might remove some of these mistakes eventually. He actually did quietly remove some earlier mistakes after I sent my criticisms to him (in the areas of fuel storage density and the difference between steady-state and peak instantaneous power output), although he never acknowledged my input. I find this slightly irksome, but I should disclose that the two of us exchanged harsh words in the past, and I would have been very surprised if he ever publicly acknowledged that I ever said anything worthwhile.
Disclaimer: the excerpts from Graham Kennedy's webpage are unauthorized excerpts. This is not unusual- this site is full of unauthorized excerpts and images taken from real Star Wars or Star Trek sources, so there is no reason that Mr. Kennedy's website should be given a special exemption. As I do with the real Star Wars or Star Trek source excerpts and images, I give full credit to the original author. Furthermore, these excerpts are used for the purposes of academic discussion, and no income is derived from them. Therefore, there are no legal restrictions on the use of these excerpts, or royalties/fees which may be applicable.
For convenience, and due to the somewhat unwieldy size of this page, it is broken up into various specific examples of his arguments, and the flaws inherent in those arguments. I suppose this could be viewed as a personal attack upon Mr. Graham Kennedy, but I've probably said this before: I don't like fakers. I don't like the idea of someone masquerading to be a qualified expert when he in fact has only the equivalent of the first year of a real degree program, and I don't like someone claiming to be scientifically trained when he doesn't even demonstrate a familiarity with the basic scientific method or philosophy. Maybe I'm just a mean, judgemental person. That's undoubtedly what my detractors would say. But I don't think there's anything wrong with disliking fakers. What ever happened to the quaint little virtue known as honesty? Is it really OK for someone to be a faker so long as he does it politely? Is it wrong to criticize him for being dishonest? Maybe I'm just an old-fashioned war horse when it comes to this issue. Anyway, enjoy the rest of this page, and as usual, if you are strongly offended, feel free to direct your complaints at the nearest convenient brick wall.
Example #1: Thermodynamics? What's that?
Example #2: How not to read a chart
Example #3: Let's pretend we know about nuclear fusion
Example #4: Genesis- the fine art of wild exaggeration
Example #5: Science vs dialogue
Example #6: The warp power chart in the TM is a fundamental law, right? Isn't it?
Example #7: When starships explode
Example #8: Pegasus- putting a molten peg in a round hole
Example #9: Consistency? Do we really need that?
Example #10: Maybe the word "altitude" means something different in Britain
Example #11: Melting, boiling ... how does that work again?
Example #12: Officer, I didn't see a speed limit sign yet, so the speed limit must be infinity. Can I go now?
On July 20, 1999 he posted a response to my criticisms, which is discussed here.
In his Galaxy Class power page, he states the following:
This sixth season episode features a visit to the Enterprise-D by a young student, Amanda Rodgers. While visiting the engineering department in the presence of Lieutenant Geordi LaForge and Lieutent Commander Data, Amanda looks at the Warp Core and the following dialogue ensues:
: "It's hard to imagine how much energy is harnessed in there."
Data : "Imagination is not necessary; the scale is readily quantifiable. We are presently generating twleve point seven five billion gigawatts per-" [cut off by alarm].
At this point in the episode the Enterprise is in orbit of a planet - she is not using her warp or impulse drives, shields or weapons. The warp core would presumably be 'ticking over' to generate the ships gravity field and maintain life support and so on - rather than running at full power to produce lots of energy energy nobody is using. So we have a figure for the low end of a Galaxy class starships engine output of 12.75E6 TeraWatts.
This demonstrates that he doesn't understand the basic concepts of thermodynamics. He is convinced that the Enterprise-D consumes 1.3E19 watts simply to maintain life support and artificial gravity, without any regard for the fact that power generation must exactly equal power dissipation or the ship will be constantly heating up. Therefore, the ship must be radiating 1.3E19 watts to its environment, for a surface radiation intensity of several terawatts per square metre, which is tens of thousands of times the radiation intensity of the surface of the Sun! Either Data is incorrect about the power generation at that time, or the ship is doing something which we are not aware of. It cannot be coasting while consuming 1.3E19 watts, unless it is glowing with tens of thousands of times the surface radiance of the sun.
The density of the antimatter storage is not described, but we can get a good idea of how much there is by looking at how long the Galaxy class can go without refuelling. On page 2 the Galaxy class is described as having "independent mode exploration capability of seven standard years at nominal warp 6 velocity". Travelling at warp 6 for seven years would use a total energy of:
E = 1.56E15 x (7 x 365.25 x 24 x 60 x 60)
= 3.446E23 Joules
The first objection that anyone should have is that page 2 of the TM describes the GCS "design goals", and we don't know for a fact that they were all met. The second objection stems from a mis-reading of the TM's warp power chart, in which he erroneously estimated the figure slightly higher than it actually was (Editor's note: I had initially assumed that this mis-reading was deliberate and perhaps even an indication that he didn't know how to read a log-scale, but to be fair, this might have been due to simple chart-reading inaccuracy. A paper chart is not that accurate, especially when printed in a low-quality manner, so I have removed most of this criticism).
One of Graham Kennedy's more amusing mistakes is the following demonstration that he doesn't know a whole lot about basic nuclear physics. In fact, anyone can easily find enough information to refute his claims in a first year University physics textbook, but we must remember that he attended a polytechnical institute HND program rather than a real BSc or BASc degree program.
This indicates that the engines of the Galaxy class do not operate on the Deuterium/Tritium fusion process, but the Deuterium/Deuterium process. This is described by the equation:
2H + 2H ---< 3He >>+ 1n + 3.2 MeV
The total mass of the initial two Deuterium atoms is 4.02726 u, equivalent to 3750.25 MeV. Since the reaction releases 3.2 MeV, it is therefore at most 0.08533% efficient in its conversion of mass to energy. Hence, for each 1 kg of fuel consumed by the Impulse system 7.67E14 Joules will be released.
The performance of Impulse engines is a subject of some debate. Page 75 of the TNG TM states that the Ambassador class Starship was designed to accelerate at 10,000 m/s², but in fact this is seriously low for an Impulse drive system. In ST : TMP we see the Enterprise head out of Earth orbit at full Impulse; 1.8 hours later the ship passes Jupiter, a distance of between 628,000,000 and 928,000,000 km, depending on the orbital arrangement. Even assuming that the ship accelerated continually throughout the trip to give us the lowest possible value, the acceleration was between 29,911 m/s² and 44,200 m/s². But in fact, the true figure is likely to be considerably higher; as the ship boosts out of orbit we see the Earth shrink dramatically behind it, indicating a sizeable fraction of light speed was reached in a matter of seconds - an acceleration of over a thousand times that of the much later Ambassador class.
First and foremost, he is incorrect on the behaviour of D-D fusion. A D-D fusion reactor will always incorporate some D-T fusion reactions, and even some D-He fusion reactions. Do you know why? There are actually two types of D-D fusion reactions, which tend to occur with nearly equal probability:
²D + ²D --< ³He + n (3.27 MeV)>br<>br< >>²D + ²D --> ³T + H (4.03 MeV)
Note the D and T notation for deuterium and tritium respectively. Deuterium and tritium are invariably indicated in nuclear fusion texts by the term 2D or 3T rather than 2H or 3H as Graham uses. But again, Graham is merely a polytechnical institute diploma holder who is given to exaggerating his own level of education, so he probably has never been exposed to the standard notation. Another item to note is that roughly half of the D-D reactions form tritium and hydrogen rather than helium and a free neutron, and the reaction by-products can react as well. As a result, the D-D fusion reactions are considerably more complex than the simplistic version given by Mr. Kennedy. The complete list of D-D reactions, and their byproduct secondary (catalyzed) reactions are:
²D + ²D --> ³He + n
><²D + ²D --> ³T + H (4.03 MeV)
<²D + ³T --> 4He + n (17.6 MeV)
<²D + ³He --> 4He + H (18.3 MeV)
We can easily add up the preceding fusion reactions, cancel out terms, and discover that the fully catalyzed reaction is:
3²D --> 4He + H + n (21.6 MeV)
As a result, the average energy yield per deuteron is roughly 7.2 MeV for fully catalyzed D-D fusion reactions, not 3.2 MeV. Now, this may seem like a minor nit-pick. However, I have stated my disdain for those who pretend to have more knowledge than they really have, and this is a good example. It is actually very easy to locate this information, and if someone claims to have done enough basic research to know about the basic deuterium fusion reaction to give out quasi-education material on the subject in a public forum, then he should use the proper information. If he does not use the proper information, then he obviously is far less well informed than he claims to be, and has no business "explaining" the physics of nuclear fusion reactions to anyone.
As for the impulse engine discussion that he attached to his invalid discussion of nuclear fusion, I frankly don't recall TMP well enough to discuss this particular incident. However, I don't recall hearing that it would take exactly 1.8 hours to reach Jupiter. I would be curious how he came up with this figure. I would also be curious what numbers he derived from his analysis of the rate of Earth's "shrinkage", since he didn't bother to perform any calculations or give any numbers, other than an obvious "off the cuff" qualitative estimate.
I have described the serious scientific errors in his Genesis Device analysis before, but the full text of his "analysis" should be repeated so that you, the reader, can see the logical and scientific problems with it:
When the device detonates in the Mutara Nebula, we see the following sequence of events.
- The Enterprise goes to warp speed.
- The device detonates. A very rapid 'shock wave' races out from the centre, rapidly overtaking the Enterprise.
- Over the next few seconds all colour fades from the area immediately adjacent to the detonation.
- As the Enterprise races outward, a series of 'shells' of material begin to form, each larger than the last. Within this shell structure there is no nebula material visible, while beyond it the nebula remains intact. As the Enterprise exits the scene we see the first five shells form behind it.
- The Genesis planet and its star form. Views of the formation of the planet reveal material falling in towards it. A gaseous cloud surrounds the planet, exhibiting the same shell structure as before - albeit in a much compressed form. Both cloud and planet are glowing red hot at this point. The time between event three and four is small enough that the McCoy has only just informed Kirk that Spock has suffered fatal injuries.
Notice how he seems to ignore the fact that this entire event occured within an existing star system: the Ceti Alpha star system. The Mutara nebula was very close to Regula (the planet was still very much within visible range at its periphery), and therefore astronomically very close to Regula's star. Regula was not a "rogue planet"- didn't Graham Kennedy see the sunlight reflecting off the surface of Regula? There is no reason to assume that a new star was formed by the Genesis Device, if the entire event occured within an existing star system. In fact, the movie clearly shows that a star did not form, because if it did, there would have been two stars in that system. We only saw one.
These observations lead me to conclude the following:
- The Genesis device does not actually create matter, but 'only' modifies pre-existing matter - originally intended to rebuild a planet, in actual fact the device used the material of a nebula to make a whole new solar system.
- The mass to build the planet, and by extension the sun, collapsed into place over some ten minutes.
- The material of the nebula appears to have collapsed into the shells of matter we see almost instantly. I assume that any given shell contains all the material which had formerly occupied the volume between it and the next shell out.
- The nebula was made of Hydrogen, at a density of 100 million atoms per cubic metre - some one hundred times the density of interstellar space.
Again he demonstrates his eagerness to ignore science whenever it suits him, even when the canon films do not force him to take such extreme measures. The ST2 nebula was obviously much denser than this, simply because it was visible in spite of having no extreme energy source to maintain it in a state of excitation. Diffuse gases like this can be visible when superheated to extreme temperatures, as in the corona of a star. But in space, farther away from its star than an inhabitable planet, a cloud of hydrogen gases at this rareified density would be totally invisible. 100 million hydrogen atoms/m³ is equivalent to roughly 1.6E-19 kg/m³, which is in turn many orders of magnitude lower than the density of hydrogen in atmosphere, at 1 bar. We've seen hydrogen in atmosphere- it is invisible. Why would it glow visibly, with such a low heat energy influx, when it is millions of times more dispersed than it is in atmosphere? The simple answer is that it shouldn't. Nebulae can be very bright in nature, but that is due to an enormous outpouring of energy from something inside the nebula, usually a star.
Since the Genesis Planet was habitable, it must have been subject to a stellar radiation bombardment similar to our own, composed of a similar frequency spectrum. Knowing this, we can determine that there was not enough ambient energy to excite a super-diffuse nebula into visibility. Therefore, this nebula must have been extremely dense (for a nebula), as evidenced by the fact that cloud formations and static discharges were seen inside. It may have been held together by gravitational attraction- perhaps it was created by the catastrophic explosion of some kind of celestial body which didn't have enough energy to overcome its own gravity completely.
In any case, it is clearly not as large, isolated, or diffuse as Mr. Kennedy claims. Any rational observer can see the density, activity level, and high luminosity of the nebula to refute Mr. Kennedy's poorly supported density and size claims. Furthermore, any rational observer can see that it is ridiculous to assume that all of the matter for a planet and star came from such a diffuse nebula because there is already a planetoid and star nearby: Regula and its star. The Regula planetoid is quite small, but there are doubtless other planetoids in the system. There is no rational reason to assume that there was no solid matter for a distance of 1.5 light years in every direction, as Graham Kennedy does. But as we shall see, Graham Kennedy is deliberately exaggerating the size of the nebula as much as possible, because his analysis is designed in such a manner that a large nebula will help him generate fantastically large energy estimates.
Looking at scanned images of the first five shells reveals that the ratio of their radii is as follows:
Shell 1 = 6
Shell 2 = 20
Shell 3 = 40
Shell 4 = 82
Shell 5 = 160
We have all seen the "shells" from ST2. However, we know that a spherical shell would not look like a two-dimensional ring, so we are actually seeing some sort of graphical representation of a much more complex event. Kennedy makes no attempt to adjust for this weakness in his analysis.
Which roughly follows an exponential increase. Given that shell five has a radius of 5 light seconds, we can calculate each shells radius:
Shell 1 = 0.32 light seconds
Shell 2 = 0.63 light seconds
Shell 3 = 1.25 light seconds
Shell 4 = 2.50 light seconds
Shell 5 = 5.00 light seconds and so on, the radius doubling each time.
The mountain of assumptions and mistakes continued to build. He assumes that the fifth shell is 5 light-seconds in radius because if you ignore the third dimension, it looks like the Enterprise reaches the third ring around the 5-second mark. However, in reality we cannot conveniently ignore little details like the third dimension! The shells are clearly behind the Enterprise, not in front of it or coincident with it. We therefore cannot accurately determine how large these "shells" are. By the time the Enterprise covered 5 light-seconds, it might have been 4.9 light-seconds beyond the fifth shell. Because we never see the shell and the Enterprise in such a manner that we can determine that they are in the same place, we cannot leap to this assumption.
Furthermore, not only is this scaling amateurish and haphazard, but it is clearly wrong in the context of the film. Captain Kirk ordered Sulu to go to warp speed to escape the Genesis wave, because they would have been destroyed if they were caught by the wave. They were not destroyed or damaged by the wave, so they were obviously well ahead of it! I would have thought this would be obvious, but I was amazed that not only did Graham Kennedy himself make this assertion, but numerous Trekkies have looked at his page and not noticed the obvious contradiction.
Now, watch as he bundles all of his groundless assumptions together: the assumption that the Genesis Device creates both a planet and star, in spite of the fact that the entire event occured inside an existing star system, the assumption that perspective issues do not apply to scaling, the assumption that the shells moved outward as quickly as the Enterprise, and the assumption that the nebula was extremely diffuse in spite of the fact that it was clearly visible in spite of lacking a significant heat source, and it contained both clouds and lightning storms.
Following assumption 4, the nebula would have an average density of 1.7E-19 kg/m³. In order to collect enough matter for a star and planet, the Genesis device would need to clear a volume of some 10E49 cubic metres, a radius of equal to 1.5 light years. This is sufficient to hold 28 shells in all. By calculating the volume which must be compressed into each shell, we can work out the mass of each shell. In order for the shells to collapse to the centre within the ten minute time frame, they must move at differing velocities. The following table shows the mass and velocity of each shell:
|Shell Number||Radius (Light-seconds)||Speed of collapse (xc)||Mass of Shell (kg)|
|1||0.32||0.0005||6 x 105|
|2||0.63||0.0010||4.8 x 106|
|3||1.25||0.0021||3.85 x 107|
|4||2.50||0.0042||2.93 x 108|
|5||5.00||0.0083||2.4 x 109|
|6||10.00||0.0016||1.92 x 1010|
|7||20.00||0.033||1.54 x 1011|
|8||40.00||0.066||1.23 x 1012|
|9||80.00||0.133||9.84 x 1012|
|10||160.00||0.266||7.88 x 1013|
|11||320.00||0.533||6.3 x 1014|
|12||640.00||1.06||5.04 x 1015|
|13||1280.00||2.13||4.03 x 1016|
|14||2560.00||4.26||3.23 x 1017|
|15||5 x 10³||8.53||2.58 x 1018|
|16||10 x 10³||17||2.06 x 1019|
|17||20 x 10³||34||1.65 x 1020|
|18||41 x 10³||68||1.32 x 1021|
|19||82 x 10³||136||1.06 x 1022|
|20||164 x 10³||273||8.46 x 1022|
|21||327 x 10³||546||6.76 x 1023|
|22||655 x 10³||1092||5.41 x 1024|
|23||1.31 x 106||2184||4.33 x 1025|
|24||2.62 x 106||4369||3.46 x 1026|
|25||5.25 x 106||8738||2.77 x 1027|
|26||10.5 x 106||17476||2.22 x 1028|
|27||21 x 106||34952||1.77 x 1029|
|28||42 x 106||69905||1.42 x 1030|
This makes it clear that the majority of the mass of the system - some 87% - was in fact contained within the outermost shell. For the sake of brevity I will confine myself to this shell only for the remainder of the calculations.
I was hesitant to include the above waste of space, but it is important to see how he uses false pretexts of quantitative analysis to buttress his claims and create a facade of objectivity. His arguments could have been made without this bulky table, but he uses it to make it seem as if he's done a lot of work on this analysis, even though he obviously hasn't made the slightest bit of effort to lay down the proper foundations for an analysis beforehand (making sure that your source data is accurate, properly measured, and free of unwarranted assumptions). Now watch as he piles two more unjustified assumptions on top of this analysis:
Shell 28 would have a collapse speed of some 70,000 times the speed of light. This equates to Warp 9.999648. We don't have an equation to tell us how much power is required to move a specific mass at a specific speed, but the 5 million ton Galaxy class starship requires a total of some 4.77E18 watts to move at Warp 9.6, or 1,909c. The power curve 'approaches infinity' as it reaches warp ten, and we have no clear idea of the figures beyond warp 9.6. But projecting the graph on page 55 of the Technical Manual to make an estimate - again erring on the low side - a figure of some 1E25 Watts seems to be a reasonable value to maintain Warp 9.999+ in a Galaxy class ship.
As if it isn't enough to assume that a super-diffuse nebula can glow visibly, maintain internal cloud formations, and contain lightning storms without a significant source of heat energy (note that the nearby planet Regula doesn't have a molten surface, and the resulting Genesis Planet was habitable and therefore subject to radiation bombardment similar to Earth's bombardment), or to assume that an entire star is being made even though there is already a star nearby, or to ignore the third dimension in scaling estimates, or to assume that the Genesis Wave is moving as quickly as the Enterprise, he has to throw more groundless assumptions into the mix:
He assumes that all of this matter uses warp drive to move toward the Genesis detonation point. He therefore acts as though the warp power table in the TM is like the kinetic energy curve in Newtonian physics. In other words, he acts as though the warp drive power chart from the TM is based on some sort of fundamental law defining the energy states of superluminal matter. The evidence he has for this assumption? None. At the very least, he should be forthright enough to state just how tenuous this assumption is, rather than glossing over it.
He assumes that the outer shell has a radius of 1.5 light years, and collapses within ten minutes for a speed of 70,000c. However, we know from the film that the heavily damaged Enterprise outraced the genesis wave, even though 70,000c is well in excess of the Enterprise's maximum speed. The TOS warp speed scale was roughly based on the formula that v=WF³c where WF is the warp factor, so this would have been roughly warp 41- a little too high, wouldn't you say? If Federation ships were this fast, Voyager would have been home in roughly 1 year. Furthermore, Kirk only asked for "warp speed"- he didn't say he needed a particular warp factor, or greater velocity from his heavily damaged ship than it had ever achieved before. Clearly, he expected any warp speed (including warp 1) to outrace the genesis wave. This means that the canon film clearly refutes yet another groundless assumption on the part of Mr. Graham Kennedy.
Now that he's bundled his various mistakes, assumptions, and haphazard scaling ideas together, he can formulate a conclusion that he confidently puts up on his web page even though it completely defies the laws of thermodynamics:
Since shell 28 has a mass of some 2.82E20 times greater than a Galaxy class vessel, it would need 2.84E45 watts to maintain this high a warp factor. Over ten minutes then, the total energy required can be calculated as:
E = 2.84E45 x 600
= 1.7E48 Joules
So the total energy for all shells would (at a guess) approach 2E48 Joules.
This figure, derived from a host of mistakes, haphazard guesswork and poor assumptions, is the final nail in the coffin for this theory simply because it violates the laws of thermodynamics. There are two huge thermodynamics-related problems with this figure:
The change in energy states is negative, not positive! When a planet or even an entire star system is formed from a nebula, the energy state of the newly-formed planet (or star system, if one chooses to accept the author's mistakes) is lower than the energy state of the pre-existing nebula. In fact, given enough time, it is entirely possible that gravitational forces would have eventually drawn the nebula together into a single mass naturally! While the Death Star must take a planet in a low gravitational potential energy state and bring its entire mass to a high gravitational potential energy state, the Genesis Device did the exact opposite: it took a nebula with a high gravitational potential energy state and brought it to a low gravitational potential energy state. This means that the process of drawing a nebula together into a planet and/or star will actually tend to release energy rather than consuming it.
Where does all the excess energy go? If the Genesis Device actually releases 2E48 J of energy, it has to go somewhere! If it expends all of that energy to accelerate the matter to incredible speeds, what happens when all of that matter reaches the target? Does the kinetic energy simply disappear? It cannot simply disappear, due to the First Law of Thermodynamics. 2E48 J of energy is equivalent to the simultaneous explosion of thousands or perhaps millions of supernovae- such a massive release of energy would have obliterated the entire Regula star system and most likely eliminated all life on nearby star systems as well. There is no way to perform work on an object without raising its energy state: accelerated objects gain kinetic energy, deformed objects gain thermal energy, etc. Federation cultists ask us to believe that an input of 2E48 J actually lowered the energy state of the Mutara Nebula!
In real science, scientists incorporate assumptions into theories all the time. However, they generally qualify the results by noting the assumptions, and if the results violate the laws of thermodynamics, then they generally recognize that something must have been wrong with those assumptions, or the ensuing analyses. They do not happily ignore the First Law contradiction and publish the results! Graham Kennedy does.
Once more, let us recap the mistakes inherent in his conclusion:
He claims that a new star system is formed out of a nebula. This is clearly a mistake, since there is already a nearby star, and we see only one star after the formation of the Genesis Planet, not two.
He claims that the Mutara Nebula is extremely diffuse, being only 100 times the density of interstellar space. This is clearly a mistake, since the nebula shown in the films is dense, active, full of cloud formations and lightning activity, and luminous. The nebula he describes, so far away from the nearest star that it is close to a habitable planet, would be invisible. But by assuming a very low density, he can exaggerate the size of the nebula.
He claims that the genesis wave moved as quickly as the Enterprise so we can use the speed of the ship to generate "conservative" estimates on the size of the "shells". This is clearly a mistake, since the shells are clearly behind the Enterprise. The Enterprise was moving to outrace the Genesis wave, otherwise it would have been heavily damaged or even consumed by it.
He claims that based on his wildly exaggerated nebula size, the outer genesis wave was actually moving inward much faster than the Enterprise. This is clearly a mistake. If the genesis wave moved much faster than the Enterprise, reaching out to a distance of 1.5 light years in every direction within a few minutes at most, then the Enterprise would have been completely consumed by it. Notice how this claim contradicts his own previous claim about the Genesis wave moving at the same speed as the Enterprise, both of which contradict the film which clearly indicates that the Enterprise would have been destroyed if it were not outracing the wave.
Not only do his mistakes invalidate his conclusion, but his conclusion defies the laws of thermodynamics. With analyses like these, there is no question of whether the conclusion is valid or not: the only question is which mistake to criticize, since there are so many of them, built upon one another like a house of cards.
Graham Kennedy now demonstrates that he places dialogue higher than any other form of evidence. This is a bizarre attitude, since it places fallible humans above astronomical and scientific observations and analyses as the ultimate arbiter of "truth" in the fictional Star Trek universe. It certainly isn't the attitude of someone who is accustomed to the scientific method and mentality. Watch:
In this episode, Ensign Kim and Seven of Nine are working in one of Voyagers conduits. The scene progresses as follows:
"The optical assembly is properly aligned. I am ready to access
the main power supply."
Kim: "After you." [They climb down to a lower level. Seven opens a panel and begins to reach inside. Kim pulls her back hurriedly.]
Kim: "Wait! What are you doing, there are five million gigawatts running through there!"
Seven: "The exoskeleton on this limb can withstand it."
At this point Voyager is proceeding on impulse, and is not using any high power systems. This gives us a minimum figure for Voyagers total power output of 5³ terawatts.
Human dialogue is not like a scientific observation. The universe cannot be "wrong". People can. What if Harry Kim simply made a mistake, and gave the wrong number in the heat of the moment? What if he was describing the daily movement of energy through the conduit rather than the current power level? A confusion between watts and joules is so common in the Star Trek universe that one might almost conclude that they actually have switched meanings. How could 7 of 9 have expected her exoskeleton (even if she still had one) to survive 5E15 watts of plasma when we saw Borg exoskeletal plating being holed by 20th century "tommy gun" bullets in STFC? I think it says something about someone's scientific mentality (or lack thereof) when the occasional statement is deemed to override observed, scientifically meaningful physical occurences.
He sometimes makes assumptions without even bothering to mention them, and treats the resulting conclusions as reliable. This is a good example:
We are told in Caretaker that Voyager has a maximum sustainable cruise speed of Warp 9.975. On the Galaxy class starship total output calculations, I worked out how much power it takes to drive a GCS at various warp speeds. No solid figures are available for a velocity of warp 9.975, but at warp 9.9 a GCS consumes some 6E20 Watts. Voyager masses 700,000 tons compared to the 5 million tons of the Galaxy class; we do not know how the mass of an object affects the power required to maintain a given speed, but to make a guestiumate I will assume it is a linear relationship. The power required for Voyager to maintain Warp 9.9 would be given by:
P = (7E5/5E6) x 6E20
= 0.14 x 6E20
Or 84 million TeraWatts. Given the way power requirements increase as one nears warp ten, it is likely that warp 9.975 requires at least a tenfold increase in power over warp 9.9. Therefore, Voyagers maximum power output is likely to be in the region of 1E8 TeraWatts or more.
This entire dissertation is based on the assumption that the warp power chart is some sort of fundamental energy curve, like the kinetic energy function. In other words, it assumes that there is a fundamental energy "state" associated with the velocity of superluminal objects, and that it is a function of mass. There is no reason to believe this assumption- it is more likely a statement on efficiency (in fact, the TM explicitly describes efficiency problems as the limiting factor at high warp factors), and Voyager would therefore be faster because it uses a more efficient warp drive rather than having a far more powerful warp core.
How many times can Graham Kennedy repeat his assumption that if a starship is destroyed, its entire mass must be directly vaporized by the impacting weapon? Surely it has occurred to him that with the powder-keg nature of warp cores, the destruction of a starship would often be assisted by the explosion of its own reactor system. But it is apparently easier to ignore such concerns and simply pretend that a starship is basically an inert block of metal:
In "Unification, Part II", a Warbird decloaked and fired disruptor beams at the three stolen Vulcan ships - appearing to vaporize each with a one-half second discharge.
Where size is concerned, we can scale the ships next to a Romulan Warbird. Warbirds, at slightly over 1,200 metres, have a forward section approximately one-quarter of overall length, i.e. 300m. Scaled to this forward section, the cargo vessels are of equal length and, as a rough guess, perhaps one-quarter the height of said section. The Enterprise-A is said to weigh some 1,000,000 metric tons; that being the case, the Vulcan ships of comparable length and greater volume are certainly no less than that figure. 1E6 tons is 1,002,000,000 kg. To be conservative, let us assume it is primarily composed of a metal with similar properties to Aluminum (900 J/kg K specific heat and boiling point of 2740 K).
Assuming a relatively high 305 K initial temp, we have the following:
E = Mass x specific heat x Temperature increase
= 1.002 x 109 x 900 x 2435
= 2,195,883,000,000,000 joules
One other interesting thing is his habit of keeping so many significant digits. Doesn't he know that the inherent measurement accuracy limits of his source data limit the potential accuracy of his results? Significant figures and scientific precision are standard subject material in high school science. How can he teach that which he apparently does not understand?
In this example, he demonstrates that he doesn't understand the basic nature of fluids in zero gravity conditions:
In this episode a Romulan Warbird melts a significant portion of a large asteroid in order to seal the Enterprise-D inside a large chamber in the interior. The asteroid is described by the Encyclopedia (2nd edition, page 24) as 'moon sized'. No clear indication of the overall size is possible from the episode itself, but the when the Enterprise is on its way out of the asteroid Lieutenant Worf reports "We have passed through two kilometres of the asteroid. Now within one kilometre of the surface.", indicating that the fissure is three kilometres deep. The fissure must have a diameter of at least six hundred metres in order to accomodate the Enterprise-D. The Warbird melts sufficient rock to fill the entire fissure.
The Pegasus incident is another popular Star Trek fan subject. I could potentially go into a very long discussion over this subject, but this page is bulky enough without another lengthy discussion of one topic (the Genesis Device discussion should be enough for anyone), so I will limit myself to the following comments:
Fluids in zero-gravity (or very weak gravity) tend to free-float in random directions. No free-floating blobs of liquid were seen floating away from the "melted" area in the Pegasus asteroid.
Hand phasers tend to shatter rock rather than melting it. In fact, we've never seen any significant melting of rock from hand phasers or hand disruptors. So why would the Pegasus warbird attack be any different? It probably shattered a lot of rock, and caused the tunnel to collapse. Some rock might have melted, to fill the cracks and weld the boulders in position. But it would not be pure melting.
Captain Picard said that the entrance was "destroyed". No one ever mentioned melting on screen.
Geometric problem #1: The entire event took place in less than one minute (perhaps much less than one minute). If the chasm is indeed 600 metres wide and 3 kilometres deep, then the warbird, melting rock from outside of the asteroid, would have to somehow melt 850 million cubic metres of rock, and this rock would have to accelerate down the tunnel at a rate of roughly 1.7 m/s², or roughly 1/6 of Earth's gravitational acceleration rate. This is ridiculous- the asteroid in "Pegasus" was at most tens of kilometres wide, not thousands of kilometres wide. It is a craggy, irregularly shaped asteroidal object, yet the gravity required for this rate of acceleration would be in excess of the gravity on the Earth's moon. An object that large would not be so irregularly shaped. Mr. Kennedy's use of the "moon sized" adjective from the Encyclopedia is typically meaningless- some real-life moons are quite small. For example, the Mars moon known as Phobos is an asteroid which is only 20km wide.
Geometric problem #2: One popular explanation for the above problem is that the warbird might have used tractor beams to push the molten material through the tunnel. The problem is that if the warbird used tractor beams, those tractor beams would have had to affect the far side of the molten mass, not the near side. No tractor beam has ever been observed to be capable of manipulating matter through several kilometres of intervening solid or liquid matter.
Geometric problem #3: Another popular explanation is that the warbird did not melt from the "outside in", and instead melted from the inside out. It would have had to melt material around the bottom of the hole to fill it, and then work its way slowly up to the surface of the asteroid, filling as it goes. There are two major problems with this idea:
The tunnel was irregularly shaped. The warbird would have had a lot of trouble shooting at the rock around the bottom of the tunnel.
There is no reason that the liquid would move in such a manner that it fills the tunnel. Hasn't Mr. Kennedy ever spoken to a welder? It's a foregone conclusion that he has never operated a welding torch himself. Just try filling a through-hole (with a low 5:1 length to diameter ratio) with a welding torch, even in a thick plate. You will fail, because the liquid will not move to fill the hole. It will simply flow along the sides of the hole, and you will get unacceptable amounts of weld flowing out of both ends of the hole. That's why real life welders will always plug the hole with a solid piece, and then weld the plug in place. And since we saw no sign of molten material flowing away from the hole (never mind the free-floating blobs that we would see in extreme low-gravity conditions), this means that the Pegasus tunnel was obviously blocked with a solid "plug" which was then welded in place, rather than being completely filled with liquid that magically acted like a solid plug.
Data claimed that there were strong "gravimetric and magnetic fluctuations" around the asteroid which were strong enough to be dangerous to a shuttlecraft, hence the justification for moving the entire Enterprise inside. He even detected a magnetic fluctuation as the Enterprise was moving inside. Gravity fields will not fluctuate unless the mass of the asteroid was moving around. Magnetic fields will not fluctuate unless there is a lot of charged matter moving around (the movement of molten material inside our planet generates the Earth's magnetic field). Therefore, either Data was demonstrating his scientific incompetence again, or the "Pegasus" asteroid was mostly molten already. If this were the case, and it had recently solidified in most of the visible areas, then it would be even easier to knock boulders loose and weld them in place, because a lot of molten material would flow without the need to melt it. I can't really conceive of a reason why a mostly molten asteroid would have been floating around, but there are only two alternatives:
Data is scientifically incompetent and the Enterprise instruments are worthless
The insignificant gravitational and magnetic fields of a 20-40km wide inert solid asteroid (<0.005g's and unmeasurably weak, respectively) are actually dangerous to a shuttlecraft!
The most obvious explanation for this event is that the warbird knocked a lot of boulders loose and welded them in place. Any other explanation is fraught with obvious geometric difficulties. As usual, those difficulties are ignored because they get in the way of what would otherwise be a conveniently exaggerated estimate of Trek capabilities. Honestly, I don't even know why this sort of long-winded explanation should be necessary. Haven't any of the trekkies in the "vs" debate ever seen the way liquids behave in gravity, or in the absence of gravity? Either way, they don't behave in a manner consistent with "Pegasus."
In his discussion of sublight drive performance, he admits that the physics of kinetic energy cannot be applied to Federation propulsion systems, when he says the following:
The total work done on the ship by its engines is equal to:
W = F x s
= 4.96E13 x 2.8125E11
= 1.395E25 Joules
To supply this energy we would need to fuse some 181,877,444 metric tons of Deuterium. Unfortunately, the Primary Deuterium Tank only holds 10,250 metric tons!
Fortunately, we have a get-out. The TM describes the use of "space-time driver coils", which are described on page 75 as being "...similar to those in standard warp engine nacelles, that would perform a low level continuum distortion without crossing the warp threshold". The driver coil apparently reduces the effective mass of the ship - or multiplies the force, whichever way around you want to put it. So that the work required is reduced by some driver ratio.
I actually agree with this technobabble-based logic even though subspace driver coils are scientifically nonsensical, because it is a necessary rationalization. It is also the standard logic employed by Federation cultists to explain the impossibility of the highly relativistic speeds attained by Federation starships, and it is explicitly described in the official TM. However, in his discussion of photon torpedoes, he states the following:
Starships are normally limited to 0.25 c in Impulse flight; a torpedo launched at this speed would achieve a maximum cruise speed of 0.4375 c, or 131,250,000 m/s. Under strictly Newtonian physics, the kinetic energy is given by:
K.E. = 0.5 x mass x v²
= 0.5 x 247.5 x 131,250,000²
= 2.13E18 Joules
Using the same conversion figure as before, this would add no less than 533 Megatons to the yield - a staggering near-eightfold increase!
In other words, he feels that starships circumvent the impossibility of achieving highly relativistic speeds by reducing their mass (and therefore, their kinetic energy in spite of the high speeds), but as soon as the subject of photon torpedoes arises, he conveniently forgets all about this precedent, and claims that the torpedoes follow Newtonian physics!
His analysis of "Relics" indicates a staggering ignorance of the most simplistic geometric mathematics. Watch and enjoy:
Ensign : "We're in orbit Captain. Our altitude is 150,000 km."
Riker : "I'll see about getting main power back on line."
And later, when Data reports a large flare directly ahead of the ship:
Picard : "Shields."
Worf : "Shields are up. But only at 23%."
Data : "The star has entered a period of increased activity. Sensors indicate that the solar flares will continue to grow. In 3 hrs our shields will no longer be sufficient to protect us sir."
The Dyson sphere was initially stated to have a dimaeter of 200 million kilometres - approximately 67% that of Earth orbit around our own sun. Assuming for the moment that the sphere was sized so that the interior surface recieved approximately the same amount of energy as our own planet does from Sol, about 1,300 Wm-2, this would give us a total output for the star of 1.6E26 Watts.
The precise meaning of the altitude reference is crucial - would the 150,000 km figure be measured from the centre, or from the surface of the sun?
Obviously, it is measured from the surface of the star. If it is measured from the centre of the star, then the star must be well under 150,000km in radius. If it is that small (1/100 the volume of our Sun), then its power output would be completely insufficient to maintain the liquid bodies of water and green vegetation that we saw on the inside surface of the Dyson sphere. Since the star had a similar colour spectrum to our own Sun, and had roughly 44% of the power output of our own Sun, it must be far larger than 1/100 the volume of our own Sun. Since it is obviously much larger than 150,000km in radius, this figure must have been based on the Enterprise's distance to the surface of the star.
Furthermore, the term "altitude" is a terrestrial term that describes the distance between your current location and the ground, not the distance between your current location and the centre of the Earth! When an aircraft pilot says that the plane is cruising at an altitude of 30,000 feet, you do not assume that you must therefore be deep inside the core of the planet! The only conceivable reason for anyone to assume that "altitude" refers to their distance to the centre of the star is an overwhelming desire to exaggerate the ambient energy level. So, if we read on, we will find that Graham Kennedy does not have any surprises in store for us. Guess which interpretation of the word "altitude" he picks:
Assuming the former, we can calculate the power intensity incident on the Enterprise-D as:
Ei = 1.6E26 / (4 x pi x (1.5E8)²)
= 1.6E26 / 2.83E17
= 5.66E8 W/m²
In other words, the Enterprise is supposedly absorbing 566 MW/m², which is more than 9 times higher than the power intensity at the surface of our Sun! So Graham Kennedy feels that the "Relics" star was less than 1/100 the volume of our own sun, yet it had 67% of the power output of our sun, and nine times the surface luminosity of our sun. Does this seem self-contradictory to anyone? It certainly seems self-contradictory to me.
Alternately, if the altitude is measured from the centre of the sun then this would add anything up to another 400,000 km or so to the true figure. This would bring the capacity of the low power shields down to 66,940 TeraJoules.
Eventually, he grudgingly acknowledges the possibility that the word "altitude" might mean the same thing in Star Trek that it does in real life. However, he makes this concession only to deflect criticism. It is the former, unrealistic estimate that he references throughout the rest of his website, and which he obviously considers the better estimate in spite of the fact that it requires a ridiculously small star which has nine times the surface radiance of our own Sun.
What can be said about this? It's a mess.
Unfortunately, in the case of tritanium we do not know the mass of a 2 cubic metre block, the specific heat, or the boiling point! For comparison, let's look at a 3 cubic metre blockof aluminium (8,100 kg) raised from room temperature (293 K) to boiling point (2467 K):
E = 900 x 8100kg x (2467-293)
= 15,848 MJ
Which is some 450 times lower than the energy required for tritanium!
He is attempting to compare the statements in the TM with the vapourization energy of aluminum to make claims about the thermal characteristics of tritanium. The most obvious question is: why choose aluminum to compare with tritanium? Aluminum is junk! It is soft, flammable, and weak. But that is only the first criticism. A more important criticism is that he doesn't seem to understand the simple thermodynamics of boiling a piece of solid matter. There are several mistakes he makes:
Specific heat is not constant with temperature. At rising temperatures, specific heats also rise.
Specific heat is not constant with phase. Liquids generally have different specific heats than solids. A piece of solid matter would have to pass through the liquid phase before it vapourizes.
The achievement of a given temperature is not enough to vapourize a material. You also need the latent heat of fusion (to melt it) and the latent heat of evapouration (to evapourate it). This is basic phase-change physics, which a high school teacher should know.
Again, we have a pattern of mistakes which are either genuine indications of incompetence or proof that he is deliberately manipulating the data to exaggerate Star Trek materials science capabilities.
So, either must therefore have a much higher density, boiling point, or specific heat than aluminium - or all three. Since I can't find figures for these anywhere, we can't know which it is. Assuming only one factor differed there are three possible answers:
- Assuming the density and SH are equal to aluminium, tritanium would have a melting point of 987,976 K.
- Assuming the melting point and SH are equal to aluminium, tritanium would have a density of 1,226,653 kg/m³. Over a hundred times the density of lead.
- Assuming the melting point and density are equal to aluminium, tritanium would have a SH of 408,884 J/K/Kg
Tritanium is one of the major materials used in Federation starship and shuttlecraft hulls; given that the Type 6 personnel shuttle, with a length of 6 metres, only has a mass of 3.38 metric tons, it seems unlikely that the density of tritanium can be all that high - indeed, if it was you'd have to wonder why the Federation would use the stuff!
Boiling point is a potential candidate to be responsible for the higher energy, but the episode "The Arsenal of Freedom" indicates that the hull of the Enterprise-D can only withstand a few thousand degrees before sustaining serious damage. While I guess it's possible for a substance to melt at, say, 5,000 K and not boil until near 1,000,000 K, it doesn't seem very likely.
It is also impossible. Temperature is a measure of atomic kinetic energy. While some substances have higher melting and boiling points than others, there are limits on how high the boiling or melting point of a substance can be, because of the definition of temperature. At 1 million K, the atoms will be shooting around so quickly that the substance must be a gas.
Furthermore, boiling point is merely a result of the competition between vapour pressure and ambient gas pressure. In vacuum, water will boil almost immediately after it melts. It does not need to achieve 100 degrees Celsius. Again, a high school teacher should know this- boiling point is not a constant property of a given material because it varies with ambient conditions.
Specific heat is probably the best candidate; giving a material a very high SH would not disqualify it from use in any way I can think of, and at the same time would fit in with the melting point being reasonably low.
Of course. He concludes that the specific heat of tritanium is hundreds of times larger than any normal material, in spite of the fact that there is no empirical or theoretical basis for such a material. If he were being as reasonable as he claims, he would note that a much simpler, and more realistic explanation is that tritanium is actually some sort of layered, highly ablative reactive composite rather than a simple solid material. Such a material would be far more difficult to vapourize without requiring such bizarre, unrealistic physical properties.
Example #12: Officer, I didn't see a speed limit sign yet, so the speed limit must be infinity. Can I go now?
The shining, absolute proof of Graham Kennedy's refusal to acknowledge rationality or science is his adherence to the ridiculous "no laser" myth.
The navigations shields also posses another intriguing property; they are immune to attack from laser weaponry. This is due to the trans-static flux effect which occurs as a by-product of the deflection process.
Let us disregard the gratuitous technobabble for a moment and look at this claim. It is based on the infamous quote from "The Outrageous Okona" in which Picard snorted with derision at the laser weapons of a tiny, primitive spacecraft and muttered that "lasers won't even penetrate our navigational deflectors".
As a result, some trekkies have concluded that navigational deflectors are magically invulnerable to lasers, regardless of power. Note that Picard never said "no laser, regardless of its power level, can penetrate our navigational deflector." Kennedy assumes that Picard's statement contained the implicit words "of any power" while other, more reasonable observers conclude that the statement contained the implicit words "of that size". What do you think is more reasonable? Kennedy has actually claimed in public that a Federation shuttlecraft would shrug off a direct hit from the Death Star's superlaser! And this is someone who brandishes his little HND as proof that he knows something about science. <sigh> He may be more knowledgeable than a high school kid, but not much more.
Everything has limits. Science is largely based on finding those limits. But if we don't know what those limits are, how reasonable is it to conclude that they must not exist at all? It is unscientific, unreasonable, and has absolutely no basis in logic whatsoever. There is one obvious reason that Kennedy subscribes to this ridiculous myth about navigational deflectors being godlike in their immunity to lasers: he wants them to be, because he thinks that Star Wars weapons are lasers. No one with a remotely rational mind would assume that since Picard didn't elaborate on his statement, he must have meant that it was a universal law. No one with any grasp of logic or science would assume that in the absence of a known upper limit, there must not be any upper limit at all.
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