sponsored by brilliant for the last nine years I've been building control systems for Rockets it started out simple a 3D printed gimbal with some Estus Rocket Motors I spent the first year sending rockets in every direction but up then by trial error and a little bit of luck it took over a year to get a straight flight and over the next few I started to dial it in I had a problem though these flights this Rock Solid stability isn't based on any simulation math or careful calculation I just took lucky guesses at the sensitivities for the control system and by flying enough Rockets eventually I got those numbers right I'd spend days building a new rocket get friends to drive out and help me and when the motor lit it was kind of a coin toss sometimes it would fly straight sometimes it would oscillate and sometimes [Music] the fix for these problems is a simulation not like in blender or anything is this the same shirt from the last video I think I'm an outfit repeater Lizzie MaGuire you are an outfit repeater we need a simulation not like in blender or anything we're not talking about animation we're talking about a set of equations representing the physics of the rocket developing this is outside the scope of this video and if you want more details on implementing PID control with thrust vectoring lucky for you I have a 50-minute presentation on it from a few years back linked right here they never show up linked right here there we go okay anyway this video is focused on One Singular aspect of the simulations side Force when you tilt the rocket motor to the side there's a little trigonometry you can use to figure out how powerful that resulting side force will be it's this this little line side Force created by the gimbal angle knowing this value is the keys to the kingdom and I can't stress enough how important this number is it lets you simulate your flights accurately which means you slam fewer Rockets into the ground so how do you get this number it's actually pretty easy I know that with a Thrust of 15 Newtons and a vector angle of 1° physics tells us our side force is 0.26 Newtons but here's a question What If instead of thrust vector control you want it to steer the rocket using movable fins you want to know the side Force for a fin tilted over at 1° how do you find it easy you build a little test jig add some servos to rotate your fins a load cell to measure the resulting side force and you mount it on the front of your car the measurements won't be perfect because of what the car does to the air around it but it'll be close enough then you take a drive down some empty roads in the middle of nowhere while always obeying the speed limits while always obeying the speed limits okay let's just make sure that's all good anyway this is a great approach used by Legends like Bert Rutan and scaled composits back in the day you don't need a wind tunnel the world is your wind tunnel if you've seen any of my recent videos you know that I'm on a long journey toward building a space shot a rocket that goes over 100 km on the way up I'd like to steer the rocket just a little bit which means that I need to simulate that flight a lot which means that I need to know the side force that comes when I steer a fin I don't know how much you know about going to space it's the you just it's you you have to go really fast so the main issue with the car thing is that although I always drive the speed limit even if I didn't my speedometer tops out at 160 mph the space shot will be going 3,800 m per hour so it's safe to say we're missing a good portion of that flight envelope what about a wind tunnel if we stick the model of the rocket into a wind tunnel we can evaluate lots of different points along the flight regime we can evaluate the side Force for any given deflection different speeds and maybe let's say 20 different speeds between zero and Mach 5 most supersonic wind tunnels are not designed for continuous operation that means that when we set up for a run in the Wind Tunnel we can't just sweep between Mach 1 and Mach 5 we have to run at discrete points within that flight envelope and then wait for the system to reset so let's say very generously it takes 30 minutes to set up for each run with 20 runs that is 10 hours of time that we'll need in a supersonic wind tunnel wind tunnel rental rates are kind of all over the place but I'm seeing between $200 and $2,000 per hour so let's cross our fingers really really hard and say that it's 200 per hour at 10 hours that is 2 Grand for the day and honestly that's a drop in the bucket for the space shot by the time it's done this whole program will be tens of thousands of dollars in investment and it's possible we break a 100 if you count Logistics and multiple attempts hey I just wanted to clarify some of the stuff about that number the first first is that you can do a cheaper space shot we're not opting to just get above 100 km we're trying to Loft a very heavy payload over the kmen line and ideally up to like 135 km that's the first thing the second is that cost get spread over the course of like 5 to 7even years so year over-year it's not that much and that gets supported by things like patreon sponsorships merch YouTube ad Revenue it's actually a fairly reasonable cost dayto day it's just a massive cost when you consider the whole program like buying mixers flamable cabinets certifications launch equipment Hardware avionics cameras megatronics like the the it just balloons out when you think about the whole program which is why I don't think about the whole program that much okay back to the video anyway in the grand scheme of things $2,000 is not that bad cost-wise though I guess that's not all we need we also need to know the side Force generated at different deflection angles not just one Dee but three and five and 7 7 Etc let's say we want to evaluate five different deflection angles at each speed we're doing 20 different speeds so that is 100 total runs in the Wind Tunnel provided the test work as desired and take only 30 minutes to reset between runs we're looking at 50 hours of wind tunnel time at a very hopeful rate of $200 per hour which will come out to 10 grand this is like not quite a drop in the bucket for the total space shot cost but it's maybe like a tiny cup of water in the bucket if you know anything about air pressure and the atmosphere around us you know that we can't just run these evaluations for Fin deflections and speeds in an isolated environment we also need to know how these forces are going to change as we go up to 5 km 10 km 50 km as the atmosphere gets thinner that is going to add a third dimension to our data table here so I want to run 20 different speeds with five different deflection angles each and let's say I'm really trying to keep the cost down so we're only going to run at five different air pressures you ready that is $50,000 I don't know what your bank account looks like but that is not a drop in the bucket for me that's like another bucket in the bucket hi it's me again listen wind tunnels are very nuanced and there's a lot of generalization that goes into that $50,000 number in fact it's almost certainly wrong I don't know that I could give you a correct number for how much it would cost that's because sometimes if if you know someone who knows someone you can get wind tunnel access for free and sometimes they cost a million dollars an hour sometimes the wind tunnel area is this much for testing sometimes it's the size of a room this stuff is impossible to generalize so $50,000 is entirely notional based on almost nothing that's real and in the real world and in just a second I'm going to tell you why it's still kind of doesn't matter and it's still kind of too expensive anyway back to the video 50,000 assume extremely optimistic rental rates a test setup that works every time a refresh rate of only 30 minutes and we haven't even talked about the worst part I could start getting data from these wind tunnel tests and realize halfway through that my design is flawed we might need a total redesign at some point I could go through how bad the cost could get but I think by now you get the point going through a wind tunnel characterization campaign is expensive if only there were a computer program that could give you perfect data for any flight regime you want at the cost of a slightly higher electricity bill if only there were a tool where you could hand it a cad file and it would tell you how the error around it would flow there isn't that's not a that's not a real thing that program doesn't exist it's not real what we do have is something called cfd or computational fluid [Music] dynamics we're going to talk about what cfd does from a pretty high level here and I don't mean high as in smart I mean high as in I am so completely not an expert in this area so if I do get some of this wrong just know I'm trying my best to that end I've tossed some resources in the description below about cfd if you want to learn more from people who know what they're talking about all right if I told you this was a circle would you believe me I hope not what about this probably still no I can keep adding boxes and it's still not going to be a circle in fact if you call this a circle I think I I I think you maybe should talk to your doctor about that eventually though with enough boxes involved we hit a point where it kind of is a circle let's say I ask you to find the area of that Circle how would you do it if you're someone who watches these types of videos you probably already know it's Pi * the radius squar pretend for a moment you don't know that equation but you do know how to find the area for each box by filling the circle with as many shrinking boxes as we can and adding up their Collective area we'll get an answer that's pretty close to the truth this is cfd no it's not no it's not but it's a nice demo to introduce the topic of computational fluid dynamics in Aerospace electrical engineering energy biomed Etc cfd is used to help Engineers create models of real world systems and understand how they interact with the world around them we use cfd for lots of things one of which is predicting and simulating fluid behavior and by fluid I mean literally any gas or liquid when flow is incompressible fluids move according to a set of partial differential equations called The navier Stokes equations navier Stokes navier Stokes I I actually I don't really know pdes partial differential equations like this are difficult to solve because they end up being incredibly interdependent what happens to one fluid particle depends on what's Happening to all the particles next to it and when you've got millions of particles next to each other that math becomes functionally impossible to solve so we simplify it the first step in simplifying the problem is establishing how much you want to simulate literally the physical size of the area we want to understand this is called the simulation domain for my part with these recent GNC tests I've purely been simulating the fin of the rocket not the fin along with the rest of the rocket body this is a compromise I'll elaborate on it in a little bit but let's get more background first the domain we're simulating gets broken up into little chunks we call each chunk of the domain a cell and the whole group of cells is called a mesh basically instead of simulating every single particle that will flow around the fin we know that most of the action is happening at a more macro scale so we can simplify things that way at this point you might think that's it we run the navier Stokes equations in each cell and out pops our data that is not really true though see the trick that makes cfd actually work is that we're not actually solving a ton of partial differential equations with these cells the Navia Stokes equations are highly nonlinear so we need to simplify those pdes into their linear algebraic form and come on give it up for linear algebra woo I if you if you I really mean this if you get comfy with linear algebra and trigonometry you can basically do all of the cool math needed to build Rockets if you work in the real industry on this stuff by the way like tell me I'm wrong it's all linear algebra and trig this is used in more than cfd too if you've heard of FEA or finite element analysis that is a very close cousin of cfd to convert the partial differential equations into a solvable form we use either the finite element method the finite volume method or the finite difference method none of which we're going to talk about here because we got to cut it off somewhere anyway creating a mesh for the object you want to simulate is like the actual problem with cfd this is what makes it difficult okay all right this is like one of 30 things that makes it difficult selecting the resolution of the cells at various points is critically important what you're trying to do is trade off how long your simulation will take to run versus how accurate your test results will be for instance here's a screenshot of mesh resolution around a rocket fin in the areas far from the fin the cells are large that area isn't really important so we don't need high resolution in the area by the fin and especially in the area around the trim tab the cells get very small the exact geometry here is important to capture so so it's worth spending lots of time to have high resolution in this area running a simulation without optimizing the mesh means you could spend hours even days letting the computer run a single test and it might not even converge oh we didn't talk about converging it gets more complicated so the other fun part with cfd is you can run the program for as long as you want and sometimes you'll still get no results depending on your mesh settings your boundary conditions and your solving method it's not uncommon for cfd to just fail think about it if you're a computer solving this stuff you're not just solving one equation at a time you're trying to force all of the equations to solve at once they're all interdependent that might be a 100,000 cells that might be a million it might be tens or hundreds of Millions for reference with most of the Sims that I ran on single fins in the last few months the cell count was somewhere between 500,000 and a million think about what this looks like for something the size of Starship or SLS I found this paper on ground system load simulation for SLS and the cell count for their ground system alone is 86 million we're also not going to dive too deep into cell count because again got to cut it off somewhere let's get out of the weeds everything I've talked about in the last few minutes with cfd is stuff I've learned the hard way at this point I've never done that much cfd before and I am not using the best program for it for instance the way that meshing works here is that everything conforms to a cartisian layout that sort of means that all these cells have to be rectangles in fancier programs the mesh can actually conform to the body you're simulating I would like to use fancier programs it's just that you know they do not cost Z this is also a good segue here on accuracy I spent a lot of time running cfd simulations for these fins but how do I know that the results are accurate at all cfd is garbage in garbage out if you don't know how to set up your simulation just right you'll get a ton of misleading data as an example for the first month of simulations that I ran using cfd it's pretty much all garbage out because my garbage was in my domain in these simulations wasn't large enough and it turns out you can actually induce errors via Bern's principle where a non-symmetrical mesh forces air to flow faster in the smaller area as a reminder fuli's principle says that when a fluid flows faster the pressure gets lower the sides of the domain are boundary conditions which means that in these simulations air can't expand past them they can't move outside so the air has to flow faster on this side which means the pressure here is lower which creates an induced force in this direction so in this screenshot a tab deflection to the right actually resulted in a simulation force in the wrong direction for those first few weeks I was feeding garbage into the simulation it was gobbling it up and spitting garbage out for low speeds in the past I've used that car driving open air wind tunnel method to validate cfd results I found that in general while my results in cfd were consistently higher they were certainly in the ballpark enough to be used in a robust control system for speeds faster than I can legally or physically Drive I actually worked with a few friends who had access to higher-end cfd packages to figure out how good my results were we ran a few test cases with multiple programs multiple users meshes and solvers and my results aren't that far off we're looking at estimated side force on the left versus various simulation velocities my results are in blue and while they're consistently higher than the fancier programs like they were at the low speed they're in the ballpark they're in the they're in the Outfield the their backs are like up against the wall but they're on the field these results are good enough for a well-designed control system and we should have the margin to tolerate some error here I mean they literally also were good enough if you didn't see the last video I posted you should check it out but that control system was as the youths say locked in using cfd I generated a lot of data and I really mean a lot thank goodness for the option to batch run simulations because I was entire L uninterested in Babysitting the laptop for hours on end I populated a spreadsheet full of data representing side Force at various fin deflection angles speeds air pressures Etc to get a good idea of the flight envelope with these little trim tabs using on shape I also built a mockup of the rest of the vehicle so we could evaluate how close the solo fin simulations were to the rest of the vehicle model the shape is just a rough approximation here but I did want to point out something interesting which is the dual camera bumps on the side this is because while I'm running roll control tests any asymmetries will steadily pitch the vehicle over harder and harder as long as the vehicle isn't rolling which is not an issue on rockets that spin a bunch by adding a false camera bump opposite the real camera bump we reduced the likelihood of that not only did I mock up the Single Fin option I also quadrupled the fin tabs to see if we can get some pitch and yaw control on the next flight then I ran all of that through some extremely long cfd simulations to compare the full body versus pure fin simulations the results were pretty good generally I found that things were within about 30% with consistently higher variation close to the transonic region so that all makes sense we are going to do a video on the transonic region by the way take a deep breath with me we're done with cfd you made it through congratulations I want to really quick remind you of what we're doing here remember in the beginning of the video we were looking for the side force from the TVC Mount right we use the thrust multiplied by the sign of the gimbal angle and that's our side Force every point in Flight that's the side Force it's one step all all of that cftd all those hours crunching numbers the cross program validation the cell density stuff the boundary layers that is what you need in order to figure out the side force from these fin tabs so now the question is how do you implement all of that stuff into a control system okay I am going to pause the video here I want to talk about the elephant in the room the name of the elephant is itar actually there are a few elephant itar the usml mtcr and like kind of a little bit the FAA but it's mostly those first three we're going to lump them all together and say that these government regulations are about trying to prevent the export of dangerous technology from the United States the regulations cover quite a lot but they're usually concerned with the shipping of missiles Rockets explosives and basically all manner of weapons out of the country they don't just cover physical objects though they also cover technology if you are not a US citizen and I email you a cad model and build instructions for a ballistic missile I get an all expenses paid free vacation for the next 10 to 20 years in federal prison and also it's not free it costs me multiple millions of dollars in fines so here's a question I'm steering a rocket I want to steer it while it's supersonic where is the line is it itar specifically I'm not talking about whether I steer the rocket or not that is a different question I'm saying that if I show up on YouTube and I tell you every single step you need to take to build a guided missile I'm going to be in trouble and not to get too political about it there are downsides for sure but like on the whole I think that's a good regulation to have even if I wanted to make a supersonic rocket steering tutorial I think it's probably for the best that I'm discouraged from doing that for years now I have tried to strike the balance by never publishing any of the data that I consider to be sensitive or that I haven't already found online or in textbooks and by the way where where is that book hold on all right here we go tactical and strategic missile guidance this is not some willy-nilly book there's a bunch of stuff in here that is crazy to me you have flowcharts you have control system design look here's a Monte Carlo engagement simulation to test optimal guidance that's a bunch of Fortran code that's runnable you can do stuff with that digital fading memory noise filters in the Homing Loop there's a whole bunch of stuff on here in the Homing Loop and if you're like whoa Joe how did you get your hands on a book that talks about booster simulation and homing loops and filtering and all that stuff this is AI you can buy this right now you can probably find it for free too look I am not saying that everything that gets published like this is above board I'm not saying that if this ever went to court I'm going to put this down I'm not saying that if that stuff ever went to court it wouldn't cause some problems and that is actually kind of the point that's how itar works it's not so much that there are very specific spefic limits that you hit and then you get in trouble there's no line in the usml that says Joe Barnard can't publish a YouTube video about sub and supersonic steering algorithms for rockets that would be weird for a couple of reasons it's that intentional gray area that's there to convince you to stay away from it and again I kind of I kind of think it's a good thing like this Channel I want it to be a resource I want someone who's trying to do rocketry to watch these videos and learn things that help them and I do kind of of want to tell you all the details of the steering algorithms and how to build a guidance system around them you know what I also want to do I want to like grow up and have kids and watch them grow up I want to like spend time with my parents and have a normal life I think that sharing most of the stuff I do would probably not actually cause a problem here what I'm talking about is that I'm unwilling to accept a 5% chance that it would in fact I've already been doing this for a while it's just not super explicit when when I say I am making these videos as a resource they are not a tutorial this is not a tutorial these videos are not a tutorial this is not a tutorial and by watching this you do not know all the things you need to know part of why I say that is there's stuff especially in the solid propellant videos that gets no mention I intentionally leave a decent amount out the things you find in those videos those things are online above board in other places actually in a lot of research papers too there is crazy stuff that just shows up in research papers my goodness look the long and short of it is this I don't have any secrets from Boeing or Ron or locki Martin but I'm not willing to chance it with some of the stuff that I've been able to figure out on my own I hope you'll forgive me for not sharing that part of the process but I also want to make it clear I'm a real person and I'm uncomfortable with having that level of risk to having a happy life even if it's 5% or 1% I don't think itar would be a problem and I don't want to find out anyway got a little deep on that one let's end it on a fun note want to see some cool footage y+ y minus z+ Z minus this is the third flight of eie debris with an updated roll program and an attempt at a pitch and yaw program and for the first time I got the GoPros to work in Flight whoops that's the first flight sorry I just I I really want to show you the difference that we're comparing to with quality on these new cameras [Music] [Music] this is some of the prettiest onboard footage that I've seen from a rocket launch not just from the GoPros but the rooll control as well I also want to give a huge thanks to the folks from the Colorado School of Minds rocket club they were the ones who actually found this rocket on the ground I had some issues with Telemetry on the way down that made recovery tough and if it weren't for these folks that that footage might still be in the desert anyway thanks so much to them and now let's talk about the roll program we had a hard time at the beginning of the flight controlling roll and I'm starting to get the sense that I should be modeling the disturbance from spiral channeling that can sometimes occur in the rocket nozzle I actually ran into this problem before too with some of the old Echo Landing tests during the burn exhaust coming through the nozzle at a slight angle can cause mild roll torqus the pitch and yaw control on this flight did not work not even a little bit you literally cannot tell that all four fins are trying to pitch the rocket over honestly it's fine I put in basically no effort on the pitch and ya modeling side I kind of figured that because the trim tabs were this small it would result in no real control and indeed it resulted in no real control we're going to talk more about this flight but for now I have a question for you what do you want to see next Simplex V2 recently fired and I've got a couple of videos to make about it or we could talk more about rocket cameras or something else let me know but for now I want to thank the sponsor for today's video which is brilliant I've worked with brilliant a bunch of times before as a sponsor and I'm probably going to keep doing it because I really love what they do if you're new here brilliant is an interactive platform built around the idea of learning by doing and I say this every time but learning by doing is basically every video you watch here that's my bread and butter sometimes I get questions from folks about motivation or pushing through difficult projects and a huge part of that for me is because I'm like doing the work I'm putting the things I learn immediately into practice rather than working through some textbook example problems for me it makes the process a whole lot more fun and I think it's more effective too with brilliant you can learn math science computer science data science and a whole lot of other types of science also all of the lessons are interactive as you work through problems you're playing around with the fundamentals in real time which means your understanding becomes more intuitive not only are there thousands of different exercises and lessons to broaden your horizons many of them can be chunked up into 15-minute segments which like I'll be honest makes it hard to say I can't do it I don't have the time come on like everyone's got 15 minutes here there you should give brilliant a shot and you can do that for free for the first 30 days by going to brilliant.org BPS space or clicking the link in the description and the first 200 people to do that will additionally get 20% off an annual premium subscription to brilliant thank you so much to brilliant for sponsoring this video thanks to you for watching and my name is Joe Barnard may your skies be blue BL and your winds below
