Sunday, 7 December 2014

Bantokfomoki in space, part 2

In the first entry of this rebuttal, we went over two of the four videos released by bantokfomoki which attempt to refute the concept of relativistic space travel. Homing in on what he calls the apex reaction engine, an anti-matter drive used in the avatar film, bantokfomki (otherwise known as EBTX) sets forth a premise: ''If it cannot be made to work in principle, then no reaction rocket of any sort is suitable for interstellar space travel.'' Variations of this theme are restated numerous times throughout his video series. EBTXs argument is that in order to accelerate to fractions of light speed, the engines will emit so much heat that they would inadvertently vaporise themselves and whatever ship they are attached to. It is the same observation made by arthur c clarke in his book, the exploration of space, and it holds a grain of truth.
While EBTX had indeed managed to prove that the ISV venture star would be inoperable under the circumstances given in the movie, that does not imply it couldn't work under a different set of circumstances (even though he frequently insists this is the case). For instance, when the ships velocity and acceleration are significantly decreased, the problems with venting waste heat are easier to manage, and mass ratios become more practical. And as for why anyone should care so much about this subject? The starship depicted in avatar is a viable merger between two of the best propulsion concepts known to science: Charles pellegrinos valkyrie, and robert forwards photon sail. If they turn out to work in some shape or form, then humanity will have a real shot at becoming a space-farring species.
Video #3
[1] If you lower anything at all that resembles an interstellar engine into the sun with a magic rope, and you pull it up 6 months later, all you will have is a loop in your magic rope with a knot... This goes for any materials anywhere in the universe. There are no chemical bonds that can indefinitely withstand solar temperatures without breaking.
This is true, but also somewhat irrelevant. EBTX seems to be confusing temperature with heat, which is a common mistake. The two are not the same. For example, while the corona of the sun can reach a temperature of 1 million celsius, the gas has a density of just 0.0000000001 times that of the earths atmosphere at sea level. The thermal energy of a cubic meter of corona gas is less than 0.002 joules.
[2] With that in mind, we can make some calculations about the venture stars anti-matter propulsion system. And because anti-matter is the most efficient fuel possible, we can be sure that no other type of engine would do any better.
Thats tough to say for certain, since nobody knows what the ships exhaust velocity is. There are many different kinds of AMAT engines on the books, and its never stated which type is used in the movie.
[3] To proceed, we need to know what the diameter of the rocket nozzle is on the venture. From the picture, we measure about 13.5 meters. The area of the hole is Pi r squared, or 143 square meters. Theres two engines, so that gives us about 300 square meters total.
The nozzle actually appears to be less than 13.5 meters across, going by this picture. Not that it really matters, given how collimated the matter stream is.
[4] The accumulated energy of the 125,000 metric ton venture star at 70% of light velocity is 2.75 x 10 24 joules. Dividing that by 15,768,000 seconds (thats six months) gives us an engine power output of 174 petawatts, which is the solar output to the earth.
EBTX is rounding up the mass of the venture star, so that the energy requirements for its propulsion are equal to the solar energy received by earth. This is a useful fiction which apparently makes the calculations easier to do, although it contradicts the mass of 100,000 tons he gave in earlier videos.
[5] Now we want to know how much of the suns surface area is devoted to lighting up the earth with its bountiful energy. The surface area of a sphere with a radius equal to the distance of the earth to the sun is 2.8 x 10 23 square meters. The area of the earth that blocks sunlight is Pi r square, where r is the earths radius, at 6,371,000 meters. So the earth subtends 1.275 x 10 14 square meters. Dividing this by the other shows that the earth takes up... 2.73 x 10 9 square meters.
Thats a long chain of numbers, but they are correct. The incident area of the sun comes out at 2,730,000,000 square meters exactly. Another interesting note: The sun radiates 63 megawatts per square meter at its surface, and by the time this energy reaches earth, it has dissipated to just 1360 watts due to the inverse square law.
[6] So, for an interstellar ship like that envisioned in avatar, if it had a mass of 125,000 metric tons and accelerated to .7 C in 6 months, with exhaust holes from whence comes the products of anti-matter annihilation that are about 300 square meters total, this means that the energy output from those holes are approximately 9,100,000 times hotter than the surface of the sun.
Thats a very pessimistic stance to take. First, the engines are being supported by heat radiators which have a surface area at least 500 times greater than them. Dividing the 2,730,000,000 square meters of the suns incident area by the 150,000 square meters of the ships radiators reveals a difference of 18,200 fold, and not 9,100,000 fold as EBTX claimed. Second, because the engines could have an efficiency rating of up to 99%, the actual waste heat that needs to be vented into space is decreased by 2 orders of magnitude. Unfortunately, that still leaves the ship running 182 times hotter than the suns surface, equal to a blistering 1,051,596 kelvin.
No matter how you twist the numbers here, one cannot help but conclude that the circumstances given in the movie are impossible to work with. 174 petawatts is way too much power for the venture star to safely cope with, since it would need to be radiating many, many times more energy per unit area than the sun does! Luckily, there is a solution in sight. We can turn back to the parameters used in the first entry of this article, which specify accelerating for 60 months up to 7% of light velocity. By accepting a significantly longer travel time (67.5 years, to be exact), we can decrease the ships power draw by 3 orders of magnitude, and get it down to just 174 terawatts. With this change to the mission parameters, the crafts temperature will have been decreased to just .182 times hotter than the surface of the sun, or 1051 kelvin. YMMV, of course.
[7] Of course, if the venture star were much lighter, the energy output of its engines will be proportionately less. So that a ship 1/10th the mass will have an orifice energy output of only 910,000 times more than an area of the sun the same size as that orifice. And a ship lighter by 1/100th, or about 1250 metric tons, will have an orifice energy output of only 91,000 times greater than that of 300 square meters on the surface of the sun.
Our host is no doubt aware that decreasing the velocity by a factor of 10 will decrease the kinetic energy (and hence the energy needed to propel the ship) by a factor of 100. And that since the ship is going to be in transit for a longer period of time, its acceleration could also be decreased by a factor of 10 without any penaltys. This neatly circumvents the need to play around with the ships mass, which wouldn't work anyway, because even if you try to make a miniature venture star, the surface area will decrease in addition to the volume. Not by a proportionate amount, but more than enough to make such a strategy futile.
[8] If you understand that an engine cannot in principle sit submerged under the surface of the sun for 6 months without being destroyed, you can also understand that an engine cannot last 6 months in an environment thats millions of times hotter still. The case is closed for anti-matter engines that propel a ship to .7 C in a mere six months.
While that may be strictly true, it doesn't imply that humanity will not achieve interstellar travel using different speed regimes. As demonstrated in this article, a velocity of .07 C reached after 60 months keeps mass ratios and heating problems to a minimum. It is a TALL order to get to nearby stars with currently known technologys, but it can be done. Not this century, and maybe not even the next, but someday...
Video #4
[9] So the engines must put out energy equivalent to all the energy coming out of the surface of the sun from an area of 2730 square kilometers, and it must do so for 6 months to get to 70% of light velocity. But in fact, that was being overly generous. The engines must actually output over twice that energy, or 18,200,000 times the suns output per unit area.
Twice your original estimate? What will you pull out of the magicians hat next?
[10] In the rocket venue, at the beginning of acceleration, nearly all the energy is wasted out the rear exhaust, with a small amount being invested in the kinetic energy of the payload. At the end of the acceleration, and if that acceleration is some reasonable fraction of light velocity (and the exhaust velocity approximates light velocity), much more energy is deposited in the craft and less in the exhaust, simply by the nature of the energy book keeping process.
 EBTX is referring to the oberth effect, a phenomenon whereby the ships propellant will provide more thrust than normal after exceeding a certain velocity (since it will have a kinetic energy close to its potential energy). Its a bit like driving your car down a steep hill and gaining a speed boost because of gravity. Whether or not this is a good thing depends on just how high your starships delta-v is: Slow ships don't get to take advantage of this, but fast ships like the venture star do. With this understood, the oberth effect cannot be construed as something which forces starships to output more energy in order to attain their cruising speed.
[11] Because temperature is related to energy output in the star as 4th root, we can estimate the avatar engines temperature by its output at 18 million times the solar output. The 4th root of 18,200,000 is 65, while the surface temperature of the sun is 5778 degrees kelvin. So the internal engine temperature of the venture engine would be 65 times 5778, which is equal to 375,570 degrees kelvin.
If you completely ignore the role played by the heat radiators and engine efficiency, then yes, that would be a reasonable conclusion. The stefan-boltzmann law acknowledges that the total energy radiated per unit time by a blackbody is proportional to the 4th power of its temperature. Whats less clear is how decreasing the surface area of a blackbody will affect its temperature. Will halving the surface area double the temperature? If so, then how much will the luminosity change? The devil is in the details!
[12] There are only a couple of things that can happen in the engine context when a proton and anti-proton annihilate. Of the two gamma rays formed, one must exit out the exhaust port, thats the wasted half. The other gamma ray can then go through the engine compartment, unimpeded, in which case it is useless as propellant.
EBTX neglects to mention that gamma rays are merely the byproducts from electron and positron collisions: When the protons and anti-protons themselves annihilate, they produce neutral and charged pions travelling at relativistic speeds which can be magnetically deflected to produce thrust. There are various efficiency losses associated with this process, since these particles have short half lives and decay into more unstable forms, but they are not major. Its worth mentioning also that a proton is 1837 times heavier than an electron, and hence has alot more relevance in terms of kinetic energy (so this commentary on gamma rays comes off as intentionally misleading).
[13] Or it can collide with the engine compartment and thereby plasmify whatever it hits, thus contributing to the propulsion of the ship at the expense of its disintegration. Or, it can collide with the engine compartment and somehow reflect back out the rear exhaust hole, thus giving up the maximum energy of the ship without destroying it.
Again, protecting the craft from ionizing radiation is not a major dilemma. We already know how to build efficient shields using a sheet of tungsten, with a v-shaped cross section to reflect neutrons and x-rays (although gamma rays are a tougher proposition). In addition, some regions of the venture star were specifically mentioned as using almost no metal, so as to reduce the possibility of gamma and x-rays ablating the hull and producing secondary radiation.
[14] A fair approximation for the venture is a cylinder around each radiator. The radiators appear to be about 300 meters long, and maybe 80 meters wide, so the effective radiative surface is about Pi times 80 times 300 times 2 radiators, equals about 150,000 square meters. The maximum temperature they can glow at is the temperature of the surface of the sun, that is they glow white hot when running for six months. Don't ask how they glow without melting, we'll just give them that.
Thats a rather conservative estimate on the area of the radiators, but even so, the ship would never reach such high temperatures (assuming that the measures adopted here are viable). EBTX trys to create the illusion of impossibility by focusing on the individual problems faced by each system, and ignoring how these systems synergistically work together. If you study things in isolation, then of course the individual parts will seem absurd and inadequate. In a combustion engine, pistons are impractical without a radiator grill to collect the heat, and pointless if you don't have spark plugs to ignite the fuel.
[15] So the engine energy output is equivalent to 2730 square kilometers on the surface of the sun, or 2,730,000,000 square meters, while the radiators give off the suns energy at 150,000 square meters. This means that the efficiency of the engine is minimally, just about theoretically perfect. Or for every erg wasted as excess heat in the engine, 18,199 ergs go directly into the kinetic energy of the ship. Wow.
If anyone designed the venture star in such a foolish way, then a perpetual motion machine of the 2nd kind would be in order.

This rebuttal should wrap up most of the loose ends raised by EBTX and get the ball of critical thought rolling again. All in all he made some valid observations, and mapped out alot of unexplored territory, to the benefit of his audience. With that said, its interesting to note what problems didn't warrant a mention from him: Most obvious is the unimaginable cost of electricity required just to power the ship out of the solar system. Even if we meter the energy usage at the same rate as BC hydro, which is 11.27 cents per kilowatt-hour, the venture star still has a power draw of 1.4 x 10 17 watts. This means that the cost of powering it for the 1st hour alone comes out at a staggering $1577 trillion! Thats more than the entire world GDP. If you were to adopt a more modest speed regime of .07 C, that still leaves the electricity bill at $1.577 trillion. The economy would need to grow many orders of magnitude larger before such an undertaking could even begin to be considered.
Heres another problem that EBTX didn't foresee. A natural consequence of the ships tensile truss is that it puts the crew habitat behind the engines, which means the exhaust flare passes within 100 meters of it on both sides. For some idea on the dangers of this engine plume, consider that a welder emits light at an intensity of around 50,000 lux (enough to damage the retina if observed for more than a few seconds), whereas the exhaust flare was described as being 'an incandescent plasma a million times brighter than a welding arc, and over thirty kilometers long.' The further an object juts out from the centerline of the truss, the more radiant heat it will be exposed to. There was no excuse not to provide the crew habitat with a cone shaped canopy for protection. Another problem is that the whipple shield stack can only offer coverage to the venture star during the departure to alpha centauri: When the ship returns to sol, the shield is forced to drag behind it, thus leaving everyone exposed to micrometeorites.
Six months is a helluva long time to remain unprotected while your ship is getting up to 70% of light velocity! There is a throwaway mention about the shield stack getting detached and moved by thrusters on a vector ahead of the venture star, but this method is only used after cruise speed has been reached. Theoretically, you could just bolt it onto the front of the ship, but there doesn't seem to be a convenient spot where it could be mounted. There is another reason why the shield stack cannot be left at the back: It is so large that even with the engines canted several degrees outward, the exhaust plume cannot help but wash against it! The dangers presented by this should be obvious. As one source put it: 'Melt isn't the proper word for what happens to a solid substance bombarded by a relativistic particle stream. Spallation is more like it. Chemical bonds simply aren't strong enough to prevent relativistic particles from stripping away affected atoms.'