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Physics 'n stuff
Veld posted a topic in Builder ForumHaven't seen a lot of physics talk going on so I thought I'd start a thread. Might be too early in development for this but I'm going to do it anyway. I'm going to break this up into separate posts because there's a lot to account for here. There's some discussion going on between the posts so just skip through and find my numbered and titles posts to see the full info in one place. 1: Investigating gravity and other values In the video on atmospheric flight we can see certain values, given to us or expressed as variables, specific to the vessel and the environment: Misc. values Altitude Presumably in m above sea level given the altitude in the above pic Mass In metric tons judging by the change in mass, in kg, shown above. Thus 1 ton = 1000 kg Forces Looking at forces in the vertical plane we see: Lift = 7.3mg Force up = 8.3mg Weight = mg In the real world aerodynamic lift is a force due to the airflow under the wings of an aircraft. In this game this is not the case as the guy in the video said the vessel would have no lifting capability if there was no vertical booster. However, aerodynamic lifting parts are to be added in future: click here. Let’s look at the free body force diagram (not to scale): Here we see Force up - Weight = Lift. This means lift is in fact the resultant force on the vessel going up. There is clearly no aerodynamic lift as if there were: Force up - Weight = Lift + Aerodynamic lift. Also this diagram shows us that g is the same for the values of acceleration given for the vessel and for the gravitational field of the planet (it would have to be a pretty hard coincidence if the difference in the values of g was making up for the apparent absence of some sort of aerodynamic lift). Another thing it shows is that the acceleration value next to the force (i.e. 200 kN/ 8.3 g) is the acceleration due to that force itself and not the resultant force on the vessel. Finding g So we can find the true value of g by rearranging F = ma = mng to g = F/mn (where F = force, m=mass and n = the coefficient of g for acceleration) Using the forwards and upwards forces as input, their respective accelerations and the mass as 2 ton the two values of g we get are (to 4sf): 12.04 and 12.20 ms^-2 Averaging at: 12.12 ms^-2 It still feels a little weird having the value of g as around 12 when the whole purpose of expressing the acceleration of the vessel in g instead of ms^-2 is to make it more relateable. The thing is the uncertainty in the value of mass is 25%. Because it is rounded to 1sf it can be anywhere between 1.5 and 2.5 ton: Doing the calculations in finding g again, using the upper limit of the mass (2.5 ton), we get the values: 9.639 and 9.756 ms^2 Averaging at: 9.698 ms^2 That's pretty close. Gravity according to DU Pretty wishy washy considering the certain info: In this video (06/042017) we can see a vessel reaching what the guy describes as "escape velocity” and then proceeding to perform some sort of orbit around the planet. Whether this is some form of pseudo-orbit or a proper orbit is debatable. The guy in the atmospheric flight video also states that if we have enough initial velocity on burnout we can escape the gravity 'reel' and orbit. Otherwise we fall back down. The thing is in real physics the term ‘escape velocity’ describes the initial velocity needed for an object to escape the pull of a gravitational field altogether. It’s unclear what his terminology is describing. He also implies that the engines on a craft need to be turned off for it to start orbiting. But we can clearly see his vessel in its ‘orbit state’ has acceleration of 0.5g and is moving at increasing speed. This means he is in an eccentric orbit and the field strength diminishes with distance, meaning one can alter their orbital trajectory and orbital mechanics is a thing (at least in the context of a ship around a planet- needs stronger affirmation). In the context of the video he is moving from the apoapsis to the periapsis as he is speeding up. From a tweet on anti-gravity generators (discussed later) we find a simplified equation for the diminishing effect of gravity with distance: The real equation for the acceleration is: (in the context of NQs equation r would be x) (G=gravitational constant, M=mass of planet, r=radius from core) But at NQ they don't have time to be thinking about the average density of a planet for its mass or the gravitational constant. What they do is simplify the right hand side of the expression (GM/r^2) to other values to make it have the same dimension. Instead of GM the constant of proportionality is gr0^2. Which gives the same dimension of ms^-2. Evidence of pseudo-gravity can be found in this video (05/07/2017) but will be discussed in later topics In this video (18/07/2016), looking at the space station, we can see why there would be no spin on the planet and it isn’t orbiting the sun (that is assuming they haven't put the station in a geostationary orbit which I doubt they have). This is because the station is stationary and uses static cores (it is quoted to be 5km long so too big for dynamic core ships) as opposed to the dynamic ones for ships. NQ says (24/09/2016) they will add planet spin in the future though. But currently they use a rotating skybox. Also see this DU wiki quote: “Currently, planets do not rotate on their axis, but this feature may be added at a later date. However, planets will never orbit around their stars, for technology and gameplay reasons.” If spin is added, space stations cannot simply be static. However, if not added they can work fine. A docking ship can simply use its VTOL thrusters in braking its orbital velocity to prevent itself falling to the planet. Here we see a discussion on the fb page. This suggests static constructs in orbit will be an exception or a dynamic construct can be linked to a static construct to help it move. The latter makes sense as you would need a starting voxel to build off in space. Another speculation is anti-gravity fields could hold constructs stationary instead of orbiting. See anti-gravity section for more details. However, the tweet where JC was working on antigravity is dated to 2018 whereas the static orbit video is dated to 2016. So it is unlikely antigravity was developed by this point. Antigravity according to DU We don’t know exactly how antigravity will work but we know how it might work. Here we can see some of JC’s tweets on the matter. He has made some curves in desmos representing the effects of antigravity. One thing you can tell right off the bat is the green line represents a conventional curve of gravitational force against distance. So f(x) is probably force and x is probably distance. The first half of the equation previously discussed relates to the green line. He has also explained the orange curve. It describes a field with a point in it that will repel objects entering the zone. Anything caught in the 'distortion well' that has no forces acting on it other that of gravitational pull will oscillate around x=34 without stopping unless placed perfectly on x=34. The second part of the equation is mostly maths and does not have much to do with physics. By adding a gaussian function to the standard gravity field you are able to create a given area where g is negative (anti-gravity). The thing is you want it to be on a specific location. As if the anti-gravity function were simply a negative gravity function you would start with infinite acceleration at 0 displacement and that's why you use a gaussian function. The function as a whole effectively simulates a planet. r0 is probably the radius of the planet which creates this field and h the altitude from the sea level of this planet. So r0 +h is the distance from the core of the planet and from the graphic, in this case, it values something around 32 (kilometres I guess). In the exponential term, s is a term that indicates how far across the well is and a indicates how deep the well is (the magnitude of negative acceleration produced by it). So by choosing r0+h you can set where you want your gravity well to be, choose s to set how large it is and a to set how deep it is. If you want to have anti-gravity (so that the function is negative somewhere), you have to choose a wisely. If you choose a=0, then you have the standard field of gravity (the green curve). The well does not have much effect for small values of s. The function also could represent the field around planets in game for space stations to achieve ‘static orbit’. The point is to make the gravity field being zero at some points. Then in these points you will no longer accelerate toward the planet and if your velocity is zero then you will stay on these points and so you are able to have an ‘floating’ station without needing it to have angular velocity (as it's supposed to be built using static cores in the game). But by doing this you have to place your object very accurately otherwise it will oscillate indefinitely around the point (depending how far you placed the object from the equilibrium point supposing that the gravity field is the only force). So it is likely they will introduce some friction (or anything that dissipates energy) to stabilize the position. Conclusion g is probably 9.81. It makes sense from a design POV, being the same for the planet and for the expression of the acceleration. In the future we could see differing values of g for different celestial bodies causing different lifts. Further, more controlled testing can affirm the value of g but through mere speculation (Trusting NQ is consistent in their game design) we can assume it to be 9.81. Instead of going by the mass given in the engineer report, for more accuracy in your calculations use: m = F/g(1 + L) where F = force up and L = the coefficient of acceleration due to lift I'm pretty 50/50 on whether NQ will add realistic orbital mechanics to the game as the evidence points to no clear conclusion. Will have to await more updates and to get myself into alpha 2 to do some tests. Keeping Newtonian mechanics to the basic level until further confirmation. It is unclear as to how NQ plans to manage space station orbits as of yet. But they will orbit normally for sure. Antigravity presented in the context of JC’s ‘orange line’ seems like it is supposed to hold objects in ‘stasis’ around a point. However, if this point moves the object in stasis will jiggle about accordingly. So it may be for ‘static orbits’ but needs polishing first if so. The g against r equation from the tweet is highly suggestive of diminishing fields and itself being the equation to be used