Kassander

I will now publish all further parts of my work on prime numbers on my Academia account linked below: url deleted

The forces acting on this structure are not as great as many seem to think. It only serves to form the Air Pockets. The previous heat protection tiles are also very sensitive and are usually not destroyed when they are re-entered. It was already clear during the test joints that the Starshipt's fins had been unprotected for a long time and although they were particularly exposed to heat and pressure, they did not break off. This means that the Air Pockets walls would hardly break off even if they were heated to well over 1000°. In addition, the aplation dissipates heat, i.e. the structure is cooled. There is another effect that should provide cooling that I haven't mentioned yet. The Air Pockets will slowly but consistently release relatively cool air. This has 2 reasons. Firstly, the walls of the running Pockets are slowly worn away. This means that less air can bind there and thus the Air Pockets themselves are removed along with the walls of the air cushions. This results in a constant flow of relatively cold air around the Starship's hull. A positive side effect is that the walls of the Air Pockets are removed so evenly. If the erosion were stronger in one place, most of the cool air would flow out of the air cushion there. This would mean that very little would be removed there until the level equalizes again. Conversely, a lot is removed where previously little was removed because this area protrudes and is particularly exposed. The removal is therefore self-regulating and occurs evenly. The second reason why relatively cool air is constantly released from the Air Pockets is that this air also warms up slowly. This increases their volume, which leads to the Air Pockets “overflowing”. It's like slowly heating a glass of water that's filled to the brim and it then overflows. This overflow also leads to a thin but constant flow of cold air around the Starship, which should also keep the temperature down.

This is extremely helpful. Thank you! I'll definitely go through this carefully. However, the Starship appears to have a maximum temperature of 2600 degrees Fahrenheit or 1430 degrees Celsius during re-entry. At least that's what it says in the following link: https://www.ndtv.com/world-news/watch-spacex-starship-stunning-return-to-earth-moments-before-it-was-lost-5242748

True, but steel could work. The melting point of steel is around 1500°. It is heavier but also more stable. So less material would be needed. In the end one have to calculate it. The heat should remain below 1500° when re-entering. Since heat is dissipated through melting it could be enough, but without the ability to calculate this it remains an estimate. Here is a somewhat more realistic picture of what such a structure can look like. It probably shouldn't be a honeycomb structure due to the aerodynamics at take-off. This shape is also better suited to forming air pockets upon re-entry. The grey lines on the bottom are intended to symbolize the printed metal lines. Of course, the size of the lines and air pockets is not realistic and would have to be calculated precisely. This graphic is only intended to give a better idea.

Thanks, I remembered that completely wrong. I thought the melting point was over 2000°. But you are right it is at 660.3°. However, since it dissipates heat again through ablation, it could still be suitable. It is supposed to partially evaporate to dissipate heat. The additional layer of insulation is an important point. I forgot to mention this in the description of my concept, but of course it would be necessary to apply an insulating layer in between.

The material is still an open question. Aluminium would be a possibility. It is light, relatively durable and heat-resistant. It is also suitable for 3D printing. But there might be better materials. Therefore, the question of a more suitable material is one of the 4 questions that I formulated at the end.

It would take less work to replace this system if it could be done with 3D printing. Alternatively, it could probably be manufactured and anchored in individual parts. This should still be more efficient than the heat protection tiles. Spacex itself is currently looking for an ablative system for heat protection. As mentioned at the beginning, the Space Shuttle failed because of these tiles. Each individual tile has an individual shape adapted to the hull. Furthermore, they are very sensitive and expensive.

Addressing the Limitations of Thermal Protection Systems in Reusable Spacecraft: A Concept for an Ablative Shield with Integrated Air Pockets and Automated Repair The thermal protection system (TPS) has long been a critical factor in the design and operation of reusable spacecraft. The Space Shuttle, despite its pioneering role in reusable spaceflight, suffered significant challenges due to the complexity and maintenance demands of its heat shield tiles. These tiles, which protected the Shuttle from the intense heat of atmospheric reentry, were individually fragile, required precise positioning, and were highly susceptible to damage. Over time, the cost and labor-intensive process of inspecting and replacing these tiles after each flight became a major contributor to the Shuttle's unsustainable operational expenses. This limitation, among other factors, contributed to the Shuttle’s eventual retirement. SpaceX’s Starship, which is intended to be fully reusable, faces a similar challenge. Currently, it employs a heat shield based on ceramic tiles, but this system shares some of the same vulnerabilities as the Shuttle. While the technology has advanced, the core issue remains: to ensure reliable thermal protection while reducing the need for costly and time-consuming manual maintenance. In light of these challenges, I propose an alternative: an ablative heat shield system featuring air pockets formed within a hexagonal honeycomb structure and an automated maintenance process utilizing robotic arms equipped with 3D printing technology. The following graphic was created by ChatGPT and is probably more suitable for entertainment than a serious graphic representation 😁. But it should be enough to get an idea of what the whole thing should look like: The Concept Use of Air Pockets for Material and Weight Efficiency: The key innovation in this design is the incorporation of a raised hexagonal honeycomb structure on the surface of the spacecraft, where the hexagonal walls stand perpendicular to the surface, forming air pockets inside each cell. These air pockets act as thermal insulation during reentry, reducing the amount of heat that reaches the underlying spacecraft structure. By leveraging the insulating properties of trapped air, it may be possible to reduce the amount of ablative material needed, thereby saving weight while maintaining effective thermal protection. The hexagonal walls themselves would slowly ablate during reentry, gradually wearing away while protecting the spacecraft, and would be replaced as needed after each mission. Automated Maintenance with Robotic Arms and 3D Printing: Another crucial aspect of this concept is the potential use of robotic arms equipped with 3D printing capabilities to automate the repair process. In this system, robotic arms would scan the surface of the spacecraft post-mission, detecting areas where the honeycomb structure has worn down or where air pockets have been compromised. The idea is that these robotic systems could then use 3D printing to deposit new layers of aluminum or other materials to restore the honeycomb structure. However, it is important to note that while robotic arms with 3D printing capabilities are becoming increasingly sophisticated, the feasibility of this concept in the context of high-precision repairs for spacecraft TPS systems is still speculative. Currently, 3D printing with metals in terrestrial environments is possible, but adapting this technology to meet the specific demands of spacecraft reusability, precision, and thermal stress would require further development. Therefore, this concept is more of a proposal for further investigation rather than a proven solution. Seeking Feedback from the Scientific Community While this concept offers clear potential advantages, particularly in terms of weight reduction and automated maintenance, it remains speculative at this stage. I am presenting this idea to initiate a discussion and to invite the expertise of this community. I would greatly appreciate feedback on the following aspects: Thermal effectiveness: How effective would air pockets within the honeycomb structure be in insulating the spacecraft compared to traditional materials? Could this provide sufficient protection in the extreme conditions of atmospheric reentry? Structural integrity: The honeycomb walls must withstand both aerodynamic forces and extreme heat. Would a system like this remain structurally sound under such conditions, or are there potential failure points? Ablative material selection: Is aluminum a viable material for this purpose, or would another material be better suited for a system that needs to balance ablation with heat insulation? Robotic repair feasibility: Is it technically feasible to develop robotic arms with the precision needed to detect and repair damaged sections of the heat shield on Earth using 3D printing? What challenges could arise in implementing such a system in terms of material deposition, accuracy, or durability? Thank you for your time and input!

Since ChatGPT has made huge progress here is an new version of the formal approach to prove the infinite existence of twin primes!

I'm not sure if moving parts like the robot's fingers can be made water-resistant enough to ensure no water gets into the electronics, especially since the fingers move during washing. The easiest solution would be to have it wear gloves, which would also provide additional protection for the robot's plastic parts. This would prevent scratches on the palm. While this might be negligible when cooking, heavier work could cause larger scratches, and gloves would provide protection in this case as well. You're right, but if Optimus can't cook, there isn't much else left for him to do around the house. Vacuum cleaners and mopping robots already exist, and for everything else, there are household appliances. At most, he could unload and load the dishwasher and washing machine, and perhaps clean shelves. I completely agree with you here. I've also considered if there could be a better design, but the disadvantages always outweigh the advantages. As you said, everything around us is tailored to humans.

At least there are many pictures showing that the Tesla-Bot can handle an egg. So I assume they are trying to program it to help in the kitchen, at least to some extent.

That's a good point, but for example, while cooking, you also need to wash your hands frequently to avoid touching clean dishes or other items with dirty hands. Also, for hygiene reasons, if you have handled raw poultry and then want to handle fresh food, you need clean hands. I believe it would take too long in practice if the robot had to clean each individual part of its fingers separately. Many things need to be done quickly while cooking. If the robot is truly to be a help in the kitchen, it needs to be able to continue working quickly.

But how should you clean Optimus's hand after or between kitchen work? As you can see from the picture, it is very complexly designed. I don't think you can just wash your hands. It would certainly be necessary to wear gloves for such activities.

We humans wear clothing for various reasons (to avoid being naked, for temperature protection, protection from dirt and moisture, to express our individuality, etc.). Some of these reasons may not be important for robots, but others are even more critical. Protection from moisture, dirt, and dust is more important for robots than for humans. These factors can destroy robots, or at least it is very time-consuming to clean a robot constructed similarly to Optimus from dust and dirt. Even when performing simple kitchen tasks involving fats or oils for cooking, the grease will get everywhere. If he works with flour, cleaning Optimus afterwards will be more tedious than cooking yourself. He can't wash his hands like we do; he would need to at least wear gloves to do so. One might assume that a simple solution would be to cover a humanoid robot with a permanent full-body rubber or latex layer. However, if such a rubber or latex layer is part of the robot itself, it has two significant disadvantages. First, this layer will quickly wear out at joints, especially at the hands and finger joints. If it is part of the robot itself, it requires cost- and time-intensive repairs. Damage to this layer while working would have the same consequence. Second, just as we take off our shoes when we go from outside to inside, a robot that also does gardening needs this capability too. Otherwise, it would bring dirt from outside to inside. It is not enough that he can theoretically clean himself; just as we don't wash our feet when we go from the garden into our house but only take off our shoes, a humanoid robot must have this capability too. After all, there is usually no washing facility at the entrance. He must be able to take off his dirty shoes to enter the house after gardening. If the solution was simply a full-body rubber or latex coating, he would have to walk to the nearest washing facility with dirty feet, or the owner would have to wash the robot's feet at the entrance All in all, I would say a humanoid robot that is supposed to perform household tasks needs at least the following four items of clothing: A full-body suit made of rubber or latex that covers everything up to the neck. A face mask made of the same material that overlaps with the suit at the neck. Gloves that he puts on over the suit to protect it. Shoes if he is also supposed to work outdoors. I will now go into more detail about how the mentioned clothing items should be designed and why it is important to consider this clothing during the development phase of the robot. Full-Body Suit: This should look similar to a diver's wetsuit and cover everything from the neck down, including hands and feet, completely and waterproof. This would protect most of the robot's body from water and dirt. If the suit is made of latex or rubber, it would be difficult to put on. An inner layer of silk or a similarly robust and slippery material would probably be suitable to make it easier to put on the suit. Vents for ventilation fans must also be planned. Face Mask: The face mask should be made of the same materials as the full-body suit, both inside and outside. At the neck, it should overlap with the full-body suit to provide protection for the entire body. Transparent plastic should be used at the camera locations. Gloves: There should be two types of gloves, ones for indoor tasks (mainly cooking) that are thinner and allow for fine work, and more robust ones for outdoor tasks that can handle heavy work like carrying bricks without being damaged. You wouldn’t want to use the same gloves for cooking that were previously used for gardening. Shoes: To ensure easy putting on and taking off and maximum protection, they should look more like boots. Reasons why clothing must be included in the robot's development phase: The robot must be programmed to put on such clothing items. Therefore, it is essential to consider this during the planning phase of the robot. The robot must be programmed to function with the clothing. Walking with and without shoes and with and without a suit must probably be trained separately. Tasks with hands require different sensitivity and effort when the robot is wearing a suit and gloves. Therefore, the robot must be programmed to manage with these clothing items. The ventilation system and the clothing must be coordinated. The ventilation outlets should be chosen so that the clothing does not impair ventilation. The robot must be programmed to check if its clothing is properly worn and thus provides protection. Whether the clothing is dirty or damaged, which would impair protection or cause contamination, must also be checked. Another advantage would be to give your robot individuality. Many consumers value individual design. Just think of the many different smartphone cases. If a robot manufacturer offers clothing in various designs, this could be an additional source of income. Companies that purchase Optimus could have their company logo printed on the suit for advertising purposes. Overall, this could generate more money, which should be an incentive for a manufacturer like Tesla. Therefore, the question arises as to why nothing has been heard about robot clothing so far. After all, for the reasons described, clothing should already be considered during the development phase.

Based on this theory, I can even create a function that calculates all prime numbers in a certain number space exactly. By reconstructing the sieve of Eratosthenes as a function, I can calculate all prime numbers that can also be calculated with the sieve of Eratosthenes. To repeat, for example, if I crossed out all the prime numbers and their multiples up to the prime number seven, then I already know all the prime numbers in the number range between 7 and 7². This applies to all prime numbers in the sieve of Eratosthenes, if all prime numbers and their multiples up to a prime number P have been crossed out, then all prime numbers between P and P² are known with certainty. The reason for this is that every composite number in this number space can be obtained by multiplying it by a prime number smaller or equal P. I have shown before that it is possible to represent a prime number and its multiples as a sine curve. This method is already known in mathematics. To repeat, with the function y = Sin((180°/P)*x) all prime numbers and their multiples can be represented as zeros of the function if the corresponding prime number is used for P. And as already mentioned, by multiplying this function term with another function term in which a different prime number is used, a combined function can arise in which the zeros of both functions are combined. Here is the example again: In this example, the prime numbers 2, 3, and 5 are represented as zeros, as are their multiples. The Function is: Y=Sin((180°/2)*x)*Sin((180°/3)*x)*Sin((180°/5)*x) It is obvious that any number of such function terms can be multiplied. The zeros are always preserved because every multiplication by zero must always result in zero. With that alone, the promise of reconstructing the sieve of Eratosthenes as a function is already fulfilled, since in this example all prim numbers between 5 and 5² can be reliably identified. They are all natural numbers that are not Y=0. But there is a Way to improve this. Strictly speaking, prime numbers do not have to be inserted into the function at “P”. Composite numbers can also be used. If these composite numbers are not larger than P² of the largest prime number contained, then the multiples of this composite number are anyway only in the multiples of the prime numbers that make up the composite number. In other words, at position "P" of the function, all natural numbers from 2 can be substituted to any number "n". All natural numbers from 2 to n only have to be used. Then all prime numbers from n to n² can be recognized; they are the natural numbers in this number space that are not y=0. Here is an example: Y=Sin((180°/2)*x)*Sin((180°/3)*x)* Sin((180°/4)*x)*Sin((180°/5)*x)* Sin((180°/6)*x)* Sin((180°/7)*x) As you can see, the composite numbers 4 and 6 have no influence on the zeros of the sine wave in this example. And that explains how all prime numbers in a number space can be calculated with a simple function.