me. This meeting is being recorded. So I am going to waste no more time. We will kick things off with Laurie and Erica. Thank you. Hello, everyone. Go ahead, Erica.  Hi, I'm Laurie Jones. I am a teacher in the K-12 system currently, but I have worked in online open educational resources as sort of a consultant for tech things and also to provide my own for my students. And I am coming to you from the traditional territories of the Synaics, the Sylaics, and the Tanaha, which is in the Cooties in British Columbia. And oh, I guess I'll introduce myself. I'm Erica. I believe I'm on Musqueam territory here, but there's in Vancouver, there's a few different First Nations in the area. But I believe it's, I believe my, I believe Richmond is Musqueam, although it was a transient place. So with, on my background is kind of as a storyteller and an educator. And I've sort of done everything from preschoolers to elder hostels in these days that sort of at the college level. And this, because she's been quite noisy in the background is Ms. Ella. So anyhow, I'll pass things over to Laurie. All right. So our talk today is, are you listening to accessibility of open educational resources? So my question to all of you would be, what does accessibility mean to you? Just think about that for a second. If you want to quickly type something in the chat, we'll start to look at that. But what does it mean to you? What does accessibility mean to you in all areas of things, but specifically in open educational resources? Accessibility is a civil right to full participation. Everyone can access it. No barriers not being let out. Anyone can access it. Okay. Having something is all people choice. Okay. Those are some good starting places, resources that are usable. A variety of formats and equal experience, intentional design. Okay. Availability of variety of formats discoverable and meaningful. Okay. We're on the right track. Okay, I kind of covered Erica. Sorry, Erica. An online education. So is it different for you in online education? I like giving everyone an opportunity to participate, including those with like parenting responsibilities. Format doesn't change the definition. All right. Oh, I just made the chat very large. That's not helpful for me. Go ahead, Erica. Okay. Oh, I thought you were doing all the questions. Oh, yeah, I can do them all. Sure. When you answered the last question, where were you coming from? What perspective did you have when you answer that question? Are you a parent? Are you someone who accesses online education as a student? Or are you coming in from it as an instructor or an institutional organization or a designer? Like what perspective did you come from when you answered that question about what it looks like? I'm going to hit you with a lot of questions here at the beginning. So instructional designers, creators, student parent techie. I like the techie tag. And designer faculty advisor course. Okay. Perfect. All right. So for those of you that are instructional designers, we're going to hit you with what we've got. So if you want to go the next one, Erica. So where does your knowledge of what makes something accessible come from? So where did you get your information about accessibility? Have you been, has it come in form of PD? Was it part of maybe your training? Where did it come from? So where are you getting your information about accessibility? Disability Services Office. So from your institution. Okay. Professional organizations. So professional development. All right. Experience, that's a valid one. WebAIM, a lot of Googling. Fair. Those are all fair places to get information. So following the sub following the experts on the subject. Okay. So a lot of accessibility offices and campuses. Awesome. Do you want to keep going, Erica? Um, so I actually can't see the, oh, never mind, I'll just read it off my page. So who, who basically who, sorry, my screen, there's a big thing in the middle of it because of the recording. Do you mind just reading that, Laurie? Which thing? The question on the screen. Oh, sure. Who decides what makes something accessible. So who gets to who gets to give you the parameters of what is what is accessibility. I've seen a lot of campus accessibility offices, but why did they get to decide? So I've got the students, some of the people who you are using the resource, those using the service. It seems we're in agreement anyway, you're all mostly in agreement about who gets to decide. And are they the right person to decide? So you're you all most of the most of the answers were like the people using the service. Oh, I've also got the government. So what gives them the right to make something just to decide if something is accessible. So he's saying who has expertise on accessibility. The end user should decide. So in my experience, most of these things that you're talking about a special consortium, we're talking about a large body of people that have given sort of parameters around accessibility. A lot of you talked about your accessibility departments within your institutions. And they're usually the ones making decisions about how accessible something is. Now, does that relate to the end user? Does that give us the end user's perspective? So if I am a student, can I say, Hey, this doesn't work for me. I need for it to come in whatever format, or I need more time or I need all of those things within an open educational context. Are we allowed to do that? Or are we being dictated to by the people that are supposed to know the experts in the institution? So just to streamline this a little bit because we're running out of time. I eat all these questions are questions that that Laurie and I asked this summer when we were taking an course on ableism, equity and technology. And we're both students that have disabilities, as well as both being instructors. And so I know, for myself, I had, I was going into my master's with a concussion, or I didn't have a concussion at the start, I was going in right after a car accident and had just been diagnosed with ME and fibromyalgia and a bunch of damage to my spine.  And I took about six months off. And I thought I was totally fine. And then I went back into courses, and I discovered that I was having post concussion that I had post concussion syndrome now. And that made it difficult sort of going through my academic readings, especially online. And had I not taken charge of my accessibility, I probably would have failed out of the program, even though I know that I'm getting some of the highest marks in the program. But that took me sort of advocating for myself. And it's not necessarily the same for every student who has accessibility issues. There's another gentleman in our program who's dealing with the same sorts of diagnoses as I've got. Yet what works for him does not work for me. And some of the things do. So like, for example, one of the things that we've been building a lot of resources around is mindfulness and relaxation. And we're putting I'm putting those into my students, my classes now at BC it. We've I had, and I'll just quickly hop out of my slides. I had a wonderful chat yesterday with this woman. And her name is actually I'm not going to go into her words right now. So I'm looking at the time and I don't think we have the time for it. So I'll share it afterwards. It'll take me a little bit of editing to do. But this woman by the name of Jane Bernard is like this wonderful author. And she has one minute remaining. And she actually left her master's program because she didn't have any say over how to make her program accessible. So Laurie, do you want to take the last little bit? Sure. So what we've done, what we're attempting to do is create a resource for instructors and designers and students alike to include the voice of the student with a descent with disability. So we have an open educational resource that is available on so far it's on story to go, which we are hoping to continue to add the voice of those who have disability into what actually works. So are you listening to the accessibility of open learning? We actually made a faux pas in the beginning of this. And if anyone can find out how we were ableist in the title of our talk, kudos to you because we


My question is, the day to day, when you struggle, reminding yourself that it's for a less upon time, because I'm the one who struggles with hijab, because the inner, you know, doll wants to just always be there. So how do you keep that momentum, when in the morning you wake up and you just don't want to put it on, and you're just like, my hair looks good, I really don't want to put it on. So you just remind yourself that it's for a lot, and not resent the whole day. You're just like, the sun is shining, the sun is there, and I can't feel it.  Yeah, Tezakla Okran for sharing that. You know, you said it right. Faith comes in and out in so many different levels. Eman comes in and out. We're not expected to have this, this equilibrium of Eman, Eman. Nobody, if that was it, we're gonna be in Jannah, man. You know, that's not, that's not this world. It happens, and there are going to be days that you have that. Those are the days that you push through just a little bit harder. It's not just about reminding yourself, okay, this is for the sake of Allah. Sit with yourself. Sit with yourself that, yes, today this is hard for me. Yes, today I don't feel like wearing it Allah. It's so hard for me to wear it today. I really don't want to wear it. It's okay to feel that way. It's okay to tell yourself that. Acknowledge that, because what you're doing is you're fighting your soul.  Don't come. It's okay. Let it come. Sit with that emotion. And remind yourself that, okay, today was harder. What was easier for me the other day? What made it easier? Okay, maybe the sun wasn't out. That made it easier, right? Yeah, it's cold. Yeah, I know. There's snow on the mountains. But it's okay. Continue to, there are going to be daily things that you have to do to replenish your soul, right?  If we don't do things to recharge our battery, it's going to be so much more harder to continue to do that just like a bank ATM, right? You need to put in money to take out money. If you keep putting, if you keep taking out from that bank of yours, without replenishing that bank of yours of soul and recharging yourself and giving you that self care that you need, it's going to be, it's going to be harder to do. So for, so for that, start to, you know, some things that I've done that have helped me is that I read the salat, the salam on the prophet Salaam every single day. I read the astaghfar every single day. This helps, this helps me in going through, because one salam on the prophet Salaam gives you 10 mercies from Allah. And perhaps one of those mercies is going to be that strength to plow through. So may Allah make it easy on you. I have one more question to add. So I feel like there's a little bit of disconnect between our generation, like 30s and younger is like, we understand what it was like post 9-11 and everything, but we don't understand what the sahabi'at really struggled with, because all we ever hear is they tore their clothes and they put it on their hijab and they were like that bad, you know, they were like so hardcore. And then we're over here like, so like, what examples do we have of them struggling or them going through their lives and what hijab was like for them back then, so that we can be like, Oh, they've been there, they've done that, you know, on top of replenishing our iman bank, you know, keeping that flow. But how do we also connect that our sisters in Islam went through this? They did it, it's written, you know, how do we connect that? Yeah, so I don't have any particular stories at the top of my head, but what I can share is when the command, how Allah swt brings down a command, it wasn't just he brought it down just like this. There were years in between, and one example would be there was, when the command came down to pray into the right, the Muckin period, there was a lot of struggle that happened in the Muckin period. And on one particular one, I remember hearing a sheikh talk about this, that about alcohol specifically, that alcohol wasn't said to, okay, that's it, can't do it. First was, okay, don't be intoxicated while coming near prayer. Then it was another step. Then it was another step. When the when the migrated to the Medinan period, it was 10 years of that. Then came the commandment down to now no more alcohol. It was baby steps.  No, start slowly, start slowly and work on that. Just like the progression piece is that you put your hijab on, may not wear your clothes properly today, that's okay. Like maybe that act of yours is going to give you the strength later to conform and change to that. Maybe Allah loves an act of yours that He will give you that strength and guide you to that. Right? We try to see, okay, they did it, they did it, but they struggled. They struggled a lot before they were able to do it. And this is our struggle. This is, and it, you shouldn't look at it as, oh, this is just a very little struggle compared to what they did. Oh, this is your struggle. Own your struggle. It's okay to have this struggle. So, you know, it, it's essentially, you know, kind of working towards it.


on NPI. Okay, we're not stopping. We're gonna we're gonna keep checking this out because every week there's new stuff. There's new stuff and this is a partnership at Digikey. New stuff every week. New products. Your NPI. New product. Introduction. Introduction. Okay, I'm gonna grab my notes. What is this thing? Okay, so this one is actually interesting because last couple weeks we've picked chips or components or sensors or something and this week actually wanted to feature some of the educational resources that you could also get with new products. New products are just about products. I know you're like but products in the name. It's also about resources for engineers and this is actually something I would have found really handy when I was designing the wave bubble.  You can't just eat a plot part on where you want and connect traces, you know, the fitness trace you can get, send it out to Oshapark and hope that you get the best performance. For a lot of these parts, especially as you're getting into, you know, 100 megahertz, gigahertz plus range, the type of PCB, the way you lay out, the components you use is really important. So this week's IMPI is gonna look at a nifty collection of RF reference designs and deval boards that are published by NXP. So it's NXP slash free scale.  They use in science, military, medical, you know, all kinds of technology, cellular, telecommunications.   So this one is the AFIC 901. It's a two-stage high gain amplifier. You can see there's an input SMA, output SMA. It's like a beautiful ceramic PCB.  These are really nice little plug and pay pieces. And then when you go to NXP's website, you can see they have, you know, data sheets and DXFs of all the layout information. And I like how they're really clear about exactly where you want to put every part, you know, what's the component values, how far it has to be away. It's not, you know, the one I downloaded, it wasn't like an Altium file. It was a DXF, but it still had enough information that you could duplicate it into your design. So you can use this as a little building block, a proven RF design, so you don't have to worry about like, oh, what if I didn't do a perfect job because RF is so tricky to get right. Little things, you know, the twist of an inductor, the thickness of a trace can make a huge difference. To see, these are some of the other eval boards available. They also like look really cool. These are like beautiful designs. I think I saw, you know, there's this eval board for this two gate amplifier. There's about 400 designs for download from NXP. So, you know, you have to register, but it's free. Some you have to request, maybe because there's some export compliance or because of the technical requirements. But I saw like 50 of them were downloadable and I just started picking through them. I was learning a lot about different layouts. Now, if you want to get it, you can type in this code into Digi-Key site. You can search for it in the ways that they did. But this is the Digi-Key part number and they also have a section. This is the website. So this is what I was interested in. I was like, oh, this is a kind of handy. It's like, you know, all these little gain stages and amplifiers and maybe splitters, PLLs, all that stuff. So check out NXP. They make a lot of good RF chips. And that is IONMPI.


Day three of the Hilltopper holiday classic in Duluth brought about a familiar matchup. After 6-2 and 4-1 victories yesterday respectively, Brunner and Bemidji found themselves in a battle for the consolation title earlier this morning. Early in the first, Lumberjack skating down ice and a big collision here between Zach Justice and Matt Fischer. Both players would be okay though. Scoreless until the second period, Mitch Andre lights the lamp. Warriors go up one. Later, Jack's trying to even the score, but look at this save from Jimmy Engin. One of 21 for him on the day. This one would go to overtime, tied at one, but Brunner would pull it out two to one. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.


Hi everyone, Joe for jazby's casebreaks.com coming at you with 2022 tops chrome baseball jumbo pack number two and nine At the end of the break will re-randomize everyone's names top six gets into that luminaries random team break big things to gg Todd and chat There's the teams right there. Let's roll it and randomize it three into three six the hard way Now we'll do the break first different dice roll for the giveaway part One two three four five and six one two three four Five six All right, there's the first half of the list right here second half the list right there And let's print and rip. All right, and here's the print out hot off the presses Is that an autograph maybe Rafael Devers and it is an autograph. It's mason jar Thompson Rookie auto for the Nats Chad with the Nationals That's a rookie auto blue parallel 84 out of 150 Brandon Woodruff refractor as well. Alright, there you go. Now. Let's flip back over here. Now. We know Chad's gonna get spots Just because of the odds But will gg or Todd a sneak in let's find out. Let's roll it randomize it four to one five times one Two three Four and a one fifth and final time Well, no, unfortunately. No for zing And it's the top six right Todd. I think you got it. I don't see your name here It's Chad Chad Chad Todd Chad and Chad. All right. Well Chad. Thank you Appreciate you grabbing all those spots and Todd look at you a lucky duck you've snuck in to that luminaries break We'll see you for that a little bit later tonight. Jasper's case breaks.com. Bye. Bye


for a Thursday afternoon after the big success of the initial co-op home build event last year it's returning to the initial gateway hotel this Saturday a new and improved show for 24 so if you're building or extending or improving or maybe just decorating well be a chance to go along and see what's on display there chat to suppliers and experts and to find out some of the the latest trends gareth whitmore CEO of initial co-op and joins me now in the studio gareth thanks for coming in you've you've teamed up with initial development partnership this time round that's right we're collaborating with initial partnership as part of the home build event on saturday in the initial gateway their initial development partnership are doing a talk and discussion on the defective defective concrete block scheme the facilitator michelle coil will do a presentation from 11 to 12 just answering questions and taking a step-by-step approach to the to the scheme for those that are interested in affected so it would be a very worthwhile event to attend for those affected and when when you're doing something about building at the moment especially in any show and then it just cannot be ignored and i suppose it's only right and proper that you partner up with them because there'll be a lot of people there that will be looking for information and they'll be on maybe different stages different pathways yeah that's right there's a lot of people affected unfortunately and a lot of people who's concerned out there to not knowing what to do or how to access it so hopefully this will will bring the answers to those people if they come along and attend the show on saturday right um a lot of stands what i see we're 50 exhibitors in total 50 exhibitors in total yeah this this comes from the success of last year's event as you said we have everything there that you need to build a home from the architect right up to the to the roof so we have suppliers of roofing materials insulation alternative energies and renewable energies so you know we have household names like Cedral for roofing you have iso for insulation Manox local companies as well like Brandon Donahue plastering and retrofits Eileen Callahan for interior design Mark McLaughlin's greeting we also have household names attending like Waterford Stanley local other local companies like efficient renewables and new form as well as timber frame and modern modern timber frame housing so we'll cover the full specs from a couple of architects as well um Shane Daherty and Damian McKay who will also be giving a talk from one to two on their experiences their knowledge again it's an opportunity for people to come along get some information get some inspiration maybe right and talk to the suppliers and it's important to have the likes of architects and and others there that it's it's not sort of a bricks and mortar but important for those that are building or rebuilding absolutely and it's a chance like I said if they're doing retrofits or you know a small project a build project like we have all the the paint suppliers there can idea flooring there the dual looks dog will be there from 12 to four photo opportunities for children and it's an opportunity to come along and talk to the suppliers and uh as well a chance if energy efficient is energy efficiency I should say is is important to you a chance to get more information and why would it not be in the current climate absolutely it's a very very um I suppose talked about topic at the minute with the changing regulatory regulations and the cost of oil and heating home heating and one thing another especially in the the current crisis okay um so it's uh it did last year did the how successful last year was it come as a bit of a surprise because you know it was into you know it was a jump leap into the the great unknown but it proved to be a big success there was a lot of positive feedback from it last year yeah there was a lot of attendees there and I don't have the exact figure but it was it was in the hundreds um there's a lot of people you know came got a lot of information appreciated the day and left happy and that's that's what we want the great thing about it is it's uh I know it's a much used cliche a one-stop shop but it is great if you're you know building renovating thinking about building it's on the horizon whatever it's the one place you can come along and check the people pick up brochures get information get some ideas it is and like like you say they get the ideas and you can get the ideas firsthand from the suppliers and manufacturers themselves not secondhand so you know ask the tough questions take the opportunity get some inspiration get some ideas and get the information and for those that um are concerned about the defective blocks and want to find out more about the scheme as you said there at the start it's it's important that uh in a show and co-op are there and be able and we'll be able to talk to them about all aspects yes and uh Michelle Coyle will be there all day in a show and development partnership will have a stand there and they'll be able to answer the questions Shane and Damien will be there with stands and they're doing the talk as well so you know there'll be more information from them as well yeah yeah sorry I had to show development partnership I meant to say but your own team is going to be there as well our own team will be there yeah from from 11 to 5 our own guys will be there and appreciate them taking the time out to be there uh the staff have worked very hard to shout out to Lizzie Kelly for organizing it all um also Sean O'Neill and Chris Daherty for for setting it up tomorrow I don't know if they were told before but now they know yeah um so fair play to them all right so it gets underway at 11 continues to until five five all right and that is this Saturday in the initial gateway hotel yes all right thanks guys thank you very much appreciate it


Like a homogeneous system, a non-homogeneous system of linear equations with multiple solutions can have its solutions expressed in parametric form, where we're going to see that the solution set is a line, a plane, or some other flat, which can be expressed as a vector equation or with parametric equations. So consider the matrix A that's 3 by 3 given right here, 3 5 3 4 5 4 6 1 6, and consider the linear equation AX equals B, where B equals 0 6 3, and this is actually the exact same coefficient matrix we used in a previous example, and recall that we actually are working mod 7 in this example here. So without going through all the details, if you augment the matrix A with the vector B right here, so we have this matrix A augment B right here, when you reduce this, I would actually invite you to compare this example to the previous one we did. When you reduce this matrix A augment B, you're going to do the exact same row operations to put this matrix into its row reduced echelon form right here. The fact that the system is non-homogeneous compared to homogeneous makes no difference. The row operations you do will be the exact same, although the consequence on this final column will change as you switch from one B to another B. But the row operations necessary to reduce this matrix depends entirely on the coefficient matrix A. And so because of that, I'm going to skip over the details, and we're going to see that the RREF of this system will look like 1 0 1 6 0 1 0 2 and 0 0 0 0, and I invite the viewer to double check these calculations on their own to verify them. Well, when you take this RREF right here and switch it back to a linear system, you would get that x1 plus x3 equals 6, x2 equals 2, and then 0 equals 0, which that last equation is non-consequential whatsoever in this conversation. So because of this, we still identify that x3 is going to be a free variable, and x1 and x2 are dependent variables. x1 is going to look like x1, well it's going to look like 6 minus x3, but as we're working mod 7, we're really going to write this as 6 plus 6x3, and again, x2 is just going to be given as a specific number, in this case it's a 2. So using those substitutions, x1 is 6 plus 6x3, x2 is just 2, and then as x3 is free, we haven't really made any assignment there. Now what we're going to do is we're going to separate this vector into two separate vectors. One of the vectors is only going to depend on the multiples of x3, so we get a 6x3, a 0x3, and a 1x3. When you factor out the x3, like we did here, that leaves the vector 6, 0, 1, like so, and then if you then focus on the constant terms, right, there's this constant 6, there's this constant 2, and then in the last one there's a constant 0. If you take away the free variable portion, what's left as a constant, you get this 6 to 0 right here. Now if you did go and watch the previous video when we worked with this, the same matrix as a homogeneous system here, you'll notice this 6, 0, 1 might look a little bit familiar. 6, 0, 1 was the exact same spany vector we had before. We noticed that the null space of this matrix, that is its solution set to the homogeneous system, is just going to be the span of this vector V given as 6, 0, 1. So this wasn't a coincidence. This spany vector is based solely on the matrix A. It has nothing to do with B whatsoever. On the other hand, this vector 6, 0, 2, we're going to call it X null right here because this vector 6, 0, 2 is a solution to the equation AX equals B. If you take the matrix A and you multiply it by the vector 6, 2, 0, you'll see that that actually is equal to our vector B which was 0, 6, 3. I invite you to double check that calculation yourself. Pause the video if you need to. And so what we've now discovered is that the solutions to this, so because X here is just the general solution, the solutions to this linear system can be expressed in the following form. You have a particular solution, X naught, plus any scalar multiple of this directional vector 6, 1, 6, 0, 1 which actually spans the null space of this matrix. And so when you write this equation again, you see the following. X is equal to X naught plus Tv, right? And this right here looks like the vector equation of a line. You have a specific vector that's on the flat, and you have this spanning vector which tells you the direction, the slope, you could say, of the associated line. And in particular, this Tv is just a generic vector from the null space. Tv is the general solution to the homogeneous system right here. And so what then, when you compare these things, you see that you get the general solution for the homogeneous system, right? And then this right here is what we call a particular solution. So it's a vector that does solve this non-homogeneous system. And if you combine a particular solution with the general solution of the homogeneous system, that actually gives you the general solution to the non-homogeneous system. And as we can see that this is a line, X equals X naught plus Tv, using the specific points on this line, we could describe this solution set as an affine span, in which case you have X naught right here, G2 0, 620, excuse me. And then this other one, like if you take the T value right here to be 1, X naught plus V, you would get 521. That gives you two points on this line, two points to terminate a line. And so we would actually see that there are seven points on this line. And it's exactly these seven points that belong to the affine set spanned by 620 and 521. And this example demonstrates a much more general property. If we have any system of linear equations, AX equals B, where we can, I mean B could be the zero vector, or we could also think of it as any vectory, right? So it could be a non-homogeneous system here. So suppose the equation AX equals B is consistent for some given B. So B belongs to the column space of the matrix A here. And we're going to let X naught be a particular solution. That is, we're not talking about the general solution. We're saying this is a specific vector that solves this system of equations. Then the solution set of AX equals B is going to be the set of all vectors of the form X equals X0 plus Xn, where X0 is the particular solution before. And Xn is any solution to the homogeneous system of equations. And this vector equation gives us the solution to this linear equation. So in general, what I'm saying is the solution to a non-homogeneous system of equations is you take a particular solution, which we will actually find this as we roll over to the matrix, plus the solution to the homogeneous system. Now this is a pattern that shows up all over in linear algebra and has its consequences outside of linear algebra. For example, when one tries to solve differential equations, which one can recognize that differential equations have something to do with linear algebra, but I won't go into the details of that right here. But once one tries to solve a non-homogeneous differential equation, we relate this to a homogeneous differential equation. We solve it, we find the general solution. But then we go back to our non-homogeneous differential equation, we find a particular solution to the differential equation, and we squish the things together. We take a particular solution, plus the general solution of the homogeneous system, and those together form this general solution for this non-homogeneous system. And so every solution set to a linear system can be broken up in this way, a particular solution, plus the general solution to the homogeneous system. And therefore, as the solution to the homogeneous system is always a subspace, we are taking the translation of a subspace, which is in general going to be this affine span. It's this affine set, these flats, we have all these different names that describe all the same things, that affine sets and solutions to linear systems are one and the same thing. And so that brings us to the end of section 2.6 about solution sets, and kind of summarizes this three-part lecture, you could say, as we've talked about affine sets, subspaces, and solution sets, how the things are all very related to each other. And this is a geometric interpretation of these algebraic problems of solving linear systems that we're trying to do here. So as usual, if you feel like you've learned something in these videos, feel free to give it a thumbs up, a like, click, that'd be great. If you want to learn some more stuff about linear algebra in the future, please subscribe, or if you want to see other math videos as well, click the subscribe button. And as always, if you have any comments, questions, or concerns as you're watching these videos, feel free to post them in the comments below, and I will gladly reply to you when I can. Have a great day, everyone. I'll see you next time. Bye.


Hi everyone, Joe for jazby's casewrakes.com coming at you with 2021 Leaf Pro Set Sports. Five box, half case, random letter break number six. So second half of the case that we just popped open. Pretty easy. First letter, first name. C for Chloe, Kim, Ichiro goes to I, Pele goes to P, so on and so forth. There's all the letters plus some combos right here. Two autographs per box. It's nice surprises in this break too. Big thanks to everybody here for giving this a go. There's all the letters here and let's roll it, let's randomize it. Two and a six, eight times for names and letters. One, two, three, four, five, six, seven and eighth and final time. Christopher down to Daniel. Two and a six, eight times for the letters. One, two, three, four, five, six, seven and eighth and final time. We got the combo letters up there and some combo letters down there. All right, Christopher with Z, V, W, Z, V was Daniel with F, Bennett with J, Daniel with NO, the NO combo, Bennett with G, Brad with L, Barry with A, Nick with T, Barry with D, Daniel with E, Bennett with P, Monty with K, Ed with B, Daniel with R, David with S, Nick with C, Christopher with M and Daniel with H, I. Let's order these alphabetically and remember I marked the previous boxes with a six right there so you know that they're from the same case. We're going to pause the video. When we come back, we're going to pause the video, see if there's any trades, maybe alleviate some letter anxiety. Sometimes people get anxious about like, wait, what does my letter have? I don't think I have anybody, but then the chat will help them out and then we'll be like, right, those are the guys. All right, we're going to pause the video and when we come back, we'll have the break. Stick around. All right, welcome back. No deals were done and everyone seemed okay with their letters. The next break is already available in the store on jaskiescasebreaks.com and so it'll be a half case from a fresh case. Not any interesting stuff. Good luck. All right, there's Spudweb to 75. S, that's going to be for David with the letter S. We've got Aaron Rodgers, nice. Letter A, Barry with Aaron, Jeremy, yes, we will. We get, Jeremy, we get pretty much 99% of all major new releases, if not 100% of all major new releases of the four big sports. We certainly will not be, we certainly would absolutely be doing something like luminaries. I love that stuff. Oh, we got a coach, coach Rudy, Rudy T, Tom Jonovich, Rudy T, letter R, Daniel, and a dual auto. Wow. Matt Curry and Tim Hardaway, three out of eight, letter S, David, letter T, Nick Stober, one person happy, one person sad. Yes, well, I don't know. I'm not the one that posts the breaks, so I'm not sure when Nick Jaspy will be loading up those breaks, so I would check jaskiescasebreaks.com multiple times, frequently, to see when those pre-orders get loaded up. Here's Vinny Castilla, V, Christopher with the letter V, last Bon Mojo, not numbered. Next one is Joe Montana, J, Bennett with the letter J. No worries, Jeremy. Yeah, Matt, what's up, man? Yeah, it's a pretty solid product. Sometimes you get something quirky, like you get like a, we've seen disc golfers in here and everything, but, but yeah, so it's, it's a lot of different sports too, some golf, tennis, I think we've seen tennis in here too. All right, next up is Lexi Thompson, speaking of golf, four out of nine. She's one of the top golfers, right? Her and the cortis sisters, maybe? L, it's for Brad in the letter L. Next up is an MMA fighter, George Sampierre. G, that'll be for Bennett, not numbered. And the final one is Errol Spence Jr. Boxer, letter E, Daniel. And the last one here, we got some baseball, we got Cal Ripken Jr. Letters C, Nick Stober, I don't see a number on, yeah, not numbered. Got pro set portraits on this one, I don't think I've seen a portrait yet. And that's that, all right, now let's make one person happy and the other person sad, Steph Curry, Tim Hardaway. So let's grab some new dice. There's some new dice right there. There's the list, S for Steph, T for Tim. Let's roll it and randomize it. Letter on top after three times gets it, one, two, and three. Goes to T after three, and that's Nick Stober with the letter T. You can thank Tim Hardaway there for getting you this dual autograph, Steph Curry, Tim Hardaway. There you go, ladies and gentlemen. Next half case break will be from a fresh case. So if you want to do another one, jaspyscasebreaks.com. Thanks for watching, I'll see you next time for the next break.


I might just drop a smoke right here Which I where'd you get that right come buddy? I? E-dated a riot dev Men said I eat it alright dev


Far as and of the gate brought through you from out the pages of Edgar Rice Burroughs romantic novel Everybody down in the bottom of the boat. You like me swab You poor young don't antagonize But it's too cold in the boat already yonked that daddy left and I can't swim with that crew shoving at me in the water Or me neither, but if these Has moved up Now if you kill me When you do snikes, we'll navigate the ship I mean I you will you I you can't even keep her on a straight course You can't read a chart you couldn't take a bearing to save your life You navigate a ship why you That changes the situation name I find sailors Much of land lovers warp rats come so easy or easy easy ain't the way to handle rats Quick till I get aboard Lay down those guns quick now.  I don't know I haven't for years Not since Colleen you have I how about you blender?  Yes, take that rifle Keep your head below the gumball if you see a suspicious move shoot and for kill. Oh, but I can't I I could Are you new master if you don't kill them first?  All right They've seen us. Will I will I shoot not yet that fellow by the way he is Did you get him? I I don't know Uh, uh, that one came through the boat Rained my knee again James that one on the after wheelhouse This again, yes, but if they don't get it then They'll get out by hide the lock On the next wave you were sure All together No Meanwhile On the beach we come on Tarzan the apes Tracy The last wrench pulls tracy clear the quicksand Pulls the apes back Tarzan leaps to his feet springs to tracy side His torn bleeding fingers worked feverishly to free the captain from the tangled bind The apes their attention drawn from the game of pulling tracy free Center is on tracy himself tell They start forward Tarzan glances up yells to them to go back to the jungle. They stop but only for a moment Their long arms swing forward closer closer closer yet they come Tracy stunned right with pain only partly conscious struggles the apes see the movement start forward Again Tarzan calls to them to go back a jerk freeze the bind from tracy Tarzoops lifts into his shoulders A glance shows him that retreat to the jungle is cut off. He starts to run heads for the sea the apes follow quickly They're gaining Tarzan's double burden forces his feet into the soft sand But he struggles on the distance between them lessons the apes are dangerously close Tracy stirs opens his eyes sees the apes knows Tarzan can never make it. What's wrong? What's wrong? Tracy shouts Tarzan understands the meaning if not the words puts Tracy on his feet points to the sea Then wheels around arms outstretched face to face with the nearest of the apes. They stop He's different again that shout to go back Come stay where they are not so turquoise Biggest of the tribe and Tarzan's enemy He comes steadily stealthily cunningly forward The ape growls reaches forward Leaps curling fangs bared the bristling hair on the boonex stands out muscles Tarzan again commands the ape leaps Tarzan jumps to one side turns springs lands on the brooks neck Turtles growls Hose himself backwards back on the sand Tarzan leaps clear the ape is up on his feet lunges Tarzan reaches for his knife the ape watches as it waits Tarzan leaps every muscle tense The right knee drawn up fists doubled head down show his hunched all his weight his tremendous strength behind the bended knee Pull me in stomach the ape pulls Doubled up all the wind knocked out of him Tarzan yells his triumph bounds away Up the shore he goes he springs into the lower branches of a silvery Hand over hand he climbs up into the higher jungle terrace A glance through the foliage shows him Tracy well on his way swimming to the steamer He fills his lungs with a sigh of satisfaction Good to be back in the treetops again A lot of screeching of unseen pirates and the tangled branches overhead his music to him He lives in some thrill of brilliant emerald wood snake dozing in a patch of golden sunlight Drops through the trail again and swings into the well-worn past through the matted labyrinth of jungle green With the shot the jungle noises stop Tarzan hangs from a branch still tense ears strained listening Tarzan's heart beats fasts the sounds the sounds come from the hut his hut Anger seizes him are these hairless ones from the thing that floats upon the water coming to his hut He moves forward quickly silently gathers speed flashes through the branches with the speed of a bird Tarzan reaches the familiar clearing below is the hut here's hut He glances toward the beach sees Jane for father Clayton and Philander headed in the direction of the hut Then why don't you come on all of you he drops silently swiftly cautiously through the branches lifts the latch on the door opens it and entered Standing in the center gloom Lightened only by the darting rays of sunlight as they filter through the lacy leaves thoughts feelings Inexpressible longing search up in him He glances at the bare wall the rude cupboard rough-hewn table Emotion to mulch The primitive sense of possession stirs in his breast The door with its latch has always been a barrier against the beasts of the jungle but against M-e-m He runs his hand across the rough uneven planking of the table Days weeks Months he is sat there laboring over that primer with its childish pictures of a M-a-m and then A-p-e Here with stubby pencil and yellowed paper He had laboriously struggled with those bugs as he thought of the alphabet putting into words The things he couldn't say He had taught himself that he was a m-a-n not an a-p-e In this hut he had found that intangible That instinctive something that made him different from the age That indefinable quality reading And now Again, he glanced about was he to lose it all Far as and here's the voices he goes to the window Like a blow the realization that his hut his home is to be invaded tries him to sudden action Taking a pencil and paper from the shelf. He prints a message and then Remembering the little shiny thing on the silver chain He takes the locket containing lord and lady gray stokes pictures Hangs the chain about his neck And lifting the paper with its message Opens the door quietly Fixes the message to it with a pointed stick And leaves the hut


You know that parasites are fatal to pets such as dogs or cats and a lot of people would take vaccines or medication for their pets to prevent worms and parasites and things like that. So why not supplement that with frequency? And with frequency you can actually make your body resonate and your cells resonate and all your organs resonate at such a level that it's nearly impossible for it to be unwell. Basically make your body very uncomfortable or not desirable for a parasite to live in. A parasite lives off the host, right? But if we can send the frequency to target a parasite it can make them not want to live in that host because it's just not hospitable.


Guys check out Idahoans shreds They're delicious. I just had one. I'm actually gonna probably go grab another one. Yeah, I'm gonna grab another one actually They're delicious. I have the in Valley original ranch version. Yeah, they got all kinds of stuff They got hash brown mashed potato. They got everything so they're big potato guys over over the The old Idahoan


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Good morning. So, in the last class we have been discussing the nozzle flow. We looked at various aspects of nozzle flow and we compared the performance of a converging diverging nozzle with the performance of a just a converging nozzle. And we have shown that the advantage of the diverging portion is essentially restricted up to the optimum design. So, we have drawn this diagram yesterday, which was the area ratio, which is the exit area by the throat area. And the thrust ratio corresponding to the actual thrust for a converging diverging nozzle, non dimensionalized by the thrust produced by a converging nozzle alone. And we have seen that for a converging nozzle of course, the thrust if the nozzle is converging that is the exit area is equal to the throat area, then this ratio is going to be 1. So, that is the base line. After that we have discussed that for a limiting case when the pressure atmospheric pressure tends to 0, we get the ultimate thrust and that is going to behave like this. Then for other values of atmospheric pressure the thrust increases reaches a maximum and then starts to decrease. This is for increasing P a by P c naught. And there is a point corresponding to each one of this P a, which gives us the optimum thrust. This will be the thrust produced when the area ratio is such that P e is equal to P a. That is the exit pressure at the nozzle exit is equal to the atmospheric pressure we get the maximum thrust, because in that case the expansion is ideal. And we have shown that for ideal expansion the thrust is going to be maximum. We have also discussed that all these curves by the way, we see that beyond a certain area ratio the thrust decreases below the thrust produced by a converging nozzle. Therefore, the diverging portion is not giving any advantage beyond this point. Second point we have seen from this is that there is a shock line at which for all this pressure ratios we stop the nozzle operation, because there is a shock that either sees as the exit or it goes into the nozzle. Therefore, the flow is no longer isentropic the flow becomes subsonic as it goes across the shock wave normal shock wave. So, therefore, anyway it is going to match with the exit pressure, but the performance is going to be very poor, because a lot of losses. So, we ended our discussion yesterday on this point shock line. So, we had said that this condition which will give us the shock wave can be estimated. So, let us now look at this condition. Let us consider that we have a rocket with a converging diverging nozzle like this. And let us assume that a normal shock wave given here sits at the exit of this rocket nozzle. So, the condition just ahead of this shock are mark number is m e the pressure is p e. And after this shock wave, so this is the flow direction after this shock wave the pressure is equal to p a. If that is the case only then the shock will sit at the exit of this nozzle. So, across this shock wave there is going to be a deceleration of the flow and the pressure will reach the ambient pressure. And this pressure is going to increase between p a and p a, because the static pressure increases across a shock wave. So, this is the condition we want to derive now. Let us consider first the normal shock relationship. We know that from normal shock relationships which you can find in any textbook on gas dynamics or fluid dynamics the normal shock tables are also given, because these are very important properties of the flow. So, from normal shock relationship we can get the pressure change across a normal shock. For this case this is 2, this is 1. So, this is equal to p 2 by p 1 which is equal to p a by p e for our case is a function of the Mach number at 1. So, at 1 our Mach number m 1 is m e, because that is the Mach number coming up to the exit of the nozzle.  We can write the normal shock relationship like this. At the same time the flow before the shock wave from the nozzle inlet to the nozzle exit is isentropic. So, therefore, for this part of the flow we can write isentropic relationship. So, from isentropic relationship we can write p c naught, because the stagnation pressure here is p c naught. So, p c naught by p e this is the static pressure at the exit is equal to 1 plus gamma minus 1 by 2 m e square to the power gamma upon gamma minus 1. Now, if we combine these two relationship we can get this pressure ratio p a by p c naught which corresponds to this points of this curves.  So, from this we get the pressure ratio here which will give us a shock wave standing at the exit. So, that is one point. Second point we want to find out is let us say for this case what is the corresponding area ratio, because when we are designing the rocket nozzle it is the area ratio which is more important because we are designing for the area. So, therefore, we want to estimate what will be the corresponding area ratio which will give us this normal shock standing at the exit. For that what we do is we use the area relationship which we had already derived before. So, in this case the area ratio we will be defining we will be deriving based on this Mach number, because this area ratio will give us this exit Mach number m e.  So, this expression gives us the area ratio corresponding to which the exit Mach number is going to be equal to m e. Now, if you look at these two equations P a by P c naught and A e by A star what we see is that both of them are function of the exit Mach number and gamma. Understand one thing this exit Mach number by the way is not the exit velocity because there is a shock wave here. So, the Mach number is going to be m e just before it when the flow goes across the shock wave the velocity is going to decrease. So, the thrust producing velocity is going to be less that is why we get such a huge drop in thrust because there is a shock wave sitting here which will reduce the velocity. So, this m e would have been the exit velocity if P a is equal to P e otherwise it is not going to be. So, coming back to this description now. So, according to these two equations that we have just derived we see that for a given value of gamma now where on what parameter gamma will depend it will depend on the composition of the propellants after combustion or after the energy production. So, for a given value of gamma there is only one pressure ratio P a by P c naught for which there is a normal shock standing at the exit because once gamma is fixed m e is of course, fixed by this right. So, therefore, there is only one value of pressure ratio for which the normal shock will stand at the exit for other values of pressure ratio or other values of ambient pressure the normal shock will either in enter or it will be not a normal shock, but an oblique shock at the exit. So, therefore, there is a for a given exit area ratio a by a star there is only a unique value of exit pressure or ambient pressure for which there will be a normal shock at the exit. So, that corresponds to this points in this curves. So, for this value of P a there is a particular area ratio for which we get the normal shock at the exit. So, that is how we obtain this shock line. So, one of the parameters that is repeatedly appearing in all our description of chemical rockets is the pressure at the chamber P c naught is the chamber pressure this is a very important parameter. So, let us now take a look at the chamber pressure. Now by the way chamber pressure is not something that evolves because of combustion whereas, we see that in order to increase the thrust we have discussed it again and again we have to increase the chamber pressure, but chamber pressure is something that you supply you supply to the chamber and then the design is such that because of this presence of this throat this throat does cannot go out. So, the pressure is maintained because of the without the throat it will just become the ambient pressure everywhere the throat actually chokes the nozzle. So, therefore, the pressure is maintained at a high value and now let us see that how we choose this value of P c naught. So, that is the next topic that we are going to discuss that how this P c naught is chosen because this is a very important performance parameter as far as chemical rockets are concerned. First of all what is desired? The desired P c naught is a high value of P c naught because if P c naught is high P a by P c naught is going to be low and we have shown that it will produce more thrust. So, and we want to produce more thrust. So, therefore, for high thrust we will like to have as high a value of P c naught as possible. Now if we go to higher thrust or rather higher thrust or higher thrust P c naught what will be the advantage is not only the thrust is increasing. If you go to high P c naught we remember that the throat area m dot mass flow rate is also a function of P c naught and is inversely proportional. So, as P c naught increases m dot decreases therefore, essentially the throat size decreases. So, as we increase P c naught the throat size decreases as the throat size decreases in order to maintain the same area ratio let us say the overall size of the nozzle is going to decrease. So, the rocket becomes smaller. So, this higher P c naught reduces a star implies a smaller rocket. So, both of them are advantages we are producing higher thrust at the same time we are reducing the size of the nozzle or the rocket. So, the weight is going to decrease and we have seen that that weight is part of the structural mass. So, if you reduce the structural weight either you can carry more payload or can carry more propellant and go further. So, essentially both of these are advantages as far as the performance is concerned. However, the question is if that is the case we can continuously keep on increasing P c naught and we can get better better performance but is it possible the question is are there any disadvantages if we keep on increasing the P c naught. So, we see here that P c naught is advantages but is there a limit to which we can increase it. So, let us look at the disadvantages when we increase P c naught. First of all when we have high P c naught we get higher chamber stress. We get higher chamber stress because this high pressure gas has to be contained within the combustion chamber. So, increasing the P c naught means the more pressure is acting on the wall. So, therefore, the chamber stresses are going to increase. So, the material or the structure has to withstand the increased pressure. So, there is a limit to it that how much it can withstand. Second point is so first of all it gives higher structural stresses. Second point is as P c naught increases the rate of heat transfer to the wall also increases. So, increased rate of heat transfer to the wall. So, now out of the heat produced by the combustion more is going to the wall. So, therefore, available energy for thrust production is reducing at the same time the structure is experiencing higher thermal stresses also. So, you have to have more efficient or more cooling. So, the energy spent in cooling is increasing. So, overall energy content of your complete system is constant. Now, you are spending more in cooling it. At the same time you are losing some of the energy because the energy is going there waste. So, because of this the higher P c naught puts a limit to how much thrust can be produced. Now, these are the two disadvantages which are essentially universal for any type of rocket motor either solid propellant or liquid propellant. Any chemical rocket that if you go to higher pressure there is going to be higher stresses at the same time increase rate of heat transfer. Now, let us come into specific for specific type of rockets. For example, for liquid rockets first of all how do we create this high P c naught that is a question it comes from the supply. We send the propellant at high pressure and then that pressure is maintained because of the choke. So, if we are talking about liquid rockets the propellants have to be send at high pressure. So, if you have to pressurize it more the liquid propellant have to pressurize more the pumping requirement is going to increase. You have to push it at a higher pressure. So, the pump has to push it at higher pressure. So, therefore, the pump power increases at the same. So, essentially you have to pump in more at higher pressure. So, the power requirement for the pump is increasing. Now, once again this power is not coming from anywhere it is contained in the rocket. So, you are losing some energy there. So, that pump power is increasing. Secondly pump size will also increase because now since it said to withstand higher pressure and I have to put it at higher put it at higher pressure the piping also has to be stronger the pump has to be bigger the power requirement is more. So, all of this essentially adds weight and these are all structural weights. So, as we keep on increasing P c naught the at one point of time the power requirement for pump or the size of the pump and the other fuel feed system becomes. So, bulky that we do not get much of advantage because structural weight has increased too much. So, therefore, all of this puts a limit because we do not want the structural weight to go beyond a certain value because this structural weight will eat up either our payload carrying capability or our fuel carrying capability. So, therefore, this is something that puts a limit to how much P c naught we can get. Now, last but not the least again this is applicable to all type of chemical rockets combustion behavior is altered when we go to higher pressure what happens is that your chemical reaction changes because as we go to higher pressure the rate of reaction increases. Typically the reaction rate is a function of pressure. So, as we go to if you look at a chemical reaction how how does it happen is intermolecular collision right not only intermolecular collision this collision has to be energetic enough only then the chemical reaction can take place. So, there is a finite probability of having some energetic collisions within a certain volume. Now, if you increase the pressure essentially what we are doing we are packing more and more molecules within the same volume. So, therefore, the chances of energetic collision occurring is increasing that is energetic collisions which will lead to chemical reaction is increasing. So, as we go on increasing the pressure the chemical reaction becomes faster. So, there is a direct influence of increasing pressure on the chemical characteristic time. Now, that chemical characteristic time or the time of reaction plays an important role in combustion dynamics how the combustion is taking place and it may lead to combustion instability because if the heat release which is because of the chemical reaction and the pressure because there are going to be certain perturbation in the pressure also there are acoustic phenomena also occurring occurring because this chamber essentially is like a acoustic resonator right. So, there is a pressure oscillation because of acoustic and there is a heat release which is also now the time is changing. If there are small perturbations then the heat release starts to change with time pressure is also changing with time if these two are in phase then there can be a feedback to pressure by the heat release leading to an increasing pressure oscillations. This phenomena is called combustion instability which can be very dangerous because now what we have is that we are seeing that high pressure we have high chamber stresses. Now, this stresses are periodic. Now, if high stress is applied in a periodic manner that are more dangerous from the structure than a steady high stress. So, therefore, the periodic phenomena which is combustion instability can set in if you go to high pressure combustion. So, at the same time even sustaining the flame may become difficult because now the flame is burning at a very fast rate we may not be able to supply the fuel at the same rate in that case the flame will go off. In a previous flame it is called flashback, but does not happen in diffusion flame, but the flame may not be sustained. At the same time since the burning is so fast the stresses acting on the strain acting on the flame is more. So, flame may not sustain itself. So, flame may blow off. Thirdly when these oscillations occur, this oscillation essentially lead to a change in the chamber pressure periodic change in the chamber pressure. So, if I look at this chamber pressure chamber pressure is the oscillating like this. Now, the fuel and oxidizer are coming at a fixed rate because we may maintain a higher pressure here and this pressure is lower than this pressure. So, because of this pressure differential the flow of oxidizer as well as the fuel comes into the combustor. And now if this starts to oscillate we keep this fixed then this differential starts to oscillate. As the differential starts to oscillate the flow rate also starts to oscillate. So, m dot of fuel and m dot of oxidizer both of them become function of time. So, now there is a oscillation of fuel flow rate oscillation of oxidizer flow rate. The net result is the oscillation of composition fuel here fuel oxidizer ratio is changing. So, the equivalence ratio is changing now. As the equivalence ratio keeps on changing the composition keeps on changing. So, no longer we have constant gamma or constant C p. So, everything locally keeps on changing and that is something that leads to catastrophic failure either we may have a flame out flame may go off or the structural stresses can be so high that it will rupture the combustor. So, these are few things that needs to be avoided and that is why we do not want to go to exceedingly high pressures. We want to operate at high pressure, but not exceedingly high pressure and as we go to higher and higher pressure we have to ensure that we take care of this combustion instability problem because if the instability creeps in we have major problem in our hand. So, what we see here is that these are some constraints of choosing a high pressure and this needs to be addressed if the design state itself that how much pressure we can allow the system to go to. Now, however if I look at this effects the structural stresses that increase heat transfer rate, the pumping power, the combustion instability none of them are linear none of them are straightforward and all these essentially are also coupled to in certain extent. So, therefore, the analysis is not very simple is a highly coupled because here we are talking about structures, here we are talking about heat transfer, here we are talking about power requirement for the liquid fuel let us say. So, the pumping requirement of a liquid phase, here we are talking about combustion instability all of them put a limit to p c naught, but all of them also occurring together cannot be analyzed easily. So, the analysis is very complex and difficult it there is no simple way to analyze how to handle all these problems together. So, therefore, because of the complex nature of this disadvantages as well as there is interlink nature because as I said that if you combustion instability occurs the structural stresses will be periodic. So, they are interlinked. So, there is no simple treatment possible to pinpoint that if you do this the if you change the pressure so much this is going to be the effect it is not a simple treatment essentially it will be obtained by trial and error. We choose a particular value of pressure and see whether it is safe or not and there are some limited analysis also available for combustion instability for pumping requirement for structural stresses, but again coupled analysis is at the present state of the art is very very difficult to do. Now, if I look at p c naught first of all what are the parameters that dictate the value of p c naught p c naught is governed by your first of all mass flow requirement m dot what is the requirement of the mass flow rate and the throat area a star. So, if you have a specific requirement of m dot and we choose a particular a star and then after combustion there is a particular value of p c naught then p c naught is fixed. Now, m dot is related to the thrust. So, the total thrust will depend on how much m dot we have a star and a e we have seen that the exit pressure is dictated by that p c naught is the chamber combustion temperature. So, therefore, that dictates on the reaction that is occurring all of this together will fix the value of p c naught. So, p c naught is not a parameter that will appear independent of other parameters. So, this parameter then we choose that if you have to give this much of mass flow rate at this temperature through this area this is the required p c naught and then we maintain that p c naught in the chamber. So, p c naught then this depends on the rocket chamber fluid mechanics combustion these are the two things on which the chamber pressure will depend. So, then how do we estimate this we require advanced combustion theories nozzle flow dynamics remember that as we are seeing here these are the nozzle parameters m dot and s star are nozzle parameters. So, we cannot decide on p c naught independent of the nozzle we have to specify the nozzle performance also only then we can decide on p c naught. So, it is not that we can design the chamber separately and the nozzle separately we have to first do a coupled analysis. So, we have to have the nozzle flow we have to have the combustion all of them together when then we will tell us how much p c naught is going to be there. Now, here is the catch after doing this we decide p c naught, but in order to do that we need to know p c naught as well as another parameter that will be coming again and again is gamma right gamma and r that is the propellant properties based on this we choose a value of p c naught, but the question arises how are these known because these are also dependent on p c naught because our reaction rate is going to depend on p c naught. Therefore, the gamma and r that is the final composition of product is going to depend on pressure and if that is dependent on pressure the temperature is also dependent on pressure. So, these parameters all of them are dependent on pressure. So, this again initially we can choose a value of this and analyze this, but are they correct choice that is the question because here of course, if you are employing advanced combustion theories the chemistry has been considered otherwise we have to do an iterative process. We choose a value of p c naught derive this estimate this quantities check whether this meets the requirement or not and iteratively we get all these parameters. So, once again the pressure as we can see is coupled or not only pressure all the properties are coupled with each other. So, therefore, that makes it a very complex problem. So, just to summarize what we discussed now is that we know that the chamber pressure is an important parameter because if you go to higher pressure we can get higher thrust. At the same time if you go to higher pressure we can we operate with a smaller throat area therefore, the nozzle size decreases. So, we get an advantage of reduced weight also. However, we cannot keep on increasing p c naught as we want to because there are some disadvantages associated with it. First of all as we go to higher pressure the chamber stresses increase there is increased rate of heat transfer. In order to accommodate this chamber stress stresses the structure has to be stronger. So, structural weight will increase. Secondly if you are talking about liquid rocket the pumping requirement is going to increase we need more power for the pump as well as the pump size and the piping everything has to be increased and that is all add to the weight. And thirdly we have the combustion dynamics is a function of pressure. So, that may go may be altered. So, that may lead to in onset of combustion instability which can be this devastating for the rocket performance. So, because of this we cannot increase p c naught as much as we want to then coming to on what parameters p c naught depend they depend on rocket chamber fluid mechanics and the combustion. Therefore, the analysis also should take into account both of this that is we should have the rocket chamber combustion the combustion has to be modeled properly as well as the nozzle flow dynamics needs to be modeled properly. So, now we are discussing primarily the nozzle flow in the this lecture and as well as next couple of lectures we will primarily focus on nozzle flow dynamics. But keep this in mind as I have just discussed that p c naught and this parameters will also dictate how the nozzle is going to behave. So, therefore, this needs to be estimated as well which will be done through this combustion analysis.  In the combustion analysis what we are we will be focusing on is estimation of this that is the composition of the propellant after combustion which will give us what is the value of gamma and r and what is the temperature p c naught. And we will see the dependence of this parameters on p c naught as well because remember as I have just discussed that the combustion depends on pressure. So, we will see the dependence of this parameter on p c naught when we go to combustion analysis at present we continue our discussion with the nozzles. So, we have established the importance of p c naught let us now continue our discussion with the nozzles. So far we have not talked about the shape of the nozzle we said just is a converging diverging nozzle or something like that. Now, let us come to the shape of the nozzle. So far our analysis is essentially just estimation of the area area ratio and all. Now, this area ratio we can take any shape and get that area ratio right, but what is the optimum shape. So, now we come to the shape of the nozzles. So, the next topics we will be discussing is the nozzle we have shown that the area how to we estimate the area. Now, we will be seeing what is the optimum shape having the desired area that will give us the best performance. So, next we will look at nozzles, but now we look at the detail geometry of the nozzle. So far what if I recall what we have been interested in in the nozzle is only this area a star and this area a e, but as we can see here at every location there is a different area right. So, how do we estimate this area that is what we will come to now. So, for that let us look at the nozzle first of all when we estimated this area relationship what was the first assumption that we made that it is quasi 1 day, but nozzle flows as we can as we have said at that time also they are not a not one dimensional flow they are usually 3 D flows. So, in reality real nozzles are not 1 D flows. Now, if it is not a one dimensional flow then the shape of this wall plays a very important role in the amount of losses that will incur as well as the flow acceleration and since we are talking about supersonic flow the shock wave whether we get a shock wave or not will be dictated by the shape. So, therefore, the shape of the nozzle, nozzle wall is very important. Now, when we this then talk about the nozzle as part of the design of the rocket when we talk about design of the nozzle then nozzle design should actually give us the entire shape at every location the geometric variation of all the walls that is what the nozzle design is. So, the design of actual nozzle requires first of all specification of entire nozzle, nozzle shape should take into account variations in velocity and pressure that is how the velocity is changing across the nozzle length, how the pressure is changing across the nozzle length all of this should be taken into account when we talk about the nozzle design. At the same time the influence of friction heat transfer composition change or shock waves must also be considered. We assume that the flow is frictionless, but in reality we cannot have frictionless flow. So, the effect of friction should also be incorporated in the nozzle design heat transfer as we have just said that as the pressure increases heat transfer rates are going to increase. So, heat transfer is something that also needs to be considered when we are designing the nozzle. At the same time the composition may not be frozen because as the flow is expanding through the nozzle the temperature drops and the reactions if the reactions are still continuing then the composition keeps on changing. At the same time we have talked about the formation of shock waves that the shock waves are present then how they are going to alter the flow field and do we need to have a change variation in design to first of all ensure that there are no shock waves. So, all these things must be incorporated in the nozzle design. So, nozzle design is not just estimating the exit area and the throat area it is the variation everywhere because of the fact that if this curvature is not proper if the acceleration is sudden then we can suddenly get into shock waves or the frictional losses can be higher or if the throat is not designed properly if you have a sharp throat then we can have very high heat transfer and it will melt the throat. So, all these things must be incorporated when we are talking about the nozzle design. So, these are the issues that we are going to address now that what is the proper shape of the nozzle and for a given shape how do we estimate the performance of the nozzle. This is what we will be focusing on for the next couple of lectures. We will first start with the determination of the suitable shape of the nozzle is not what we are going to talk about. We will initially will not have the extra complications like the effect of friction, heat transfer etcetera. Actually we will not go into details of this in this course just give some passing remarks on this. We will primarily focus on the required shape of the nozzle. So, that is what we are going to discuss in the next couple of lectures. So, let us stop here now and in the next lecture we will first start with a basic shape look at the performance of the nozzle with that shape. We will start with a conical shape then we will go to how to determine the exact curve shape that is employed in practical rockets. We will discuss that later. So, I will stop here now. Thank you.


What's going on everyone? Sam here with late in sports cards. We've been one box of 22 Panini Daunras Optic football hobby for Mohamed A. So let's do it Mohamed. Good luck buddy. See you downtown. Let's see a downtown. There's blue Devon Singletary to 170 iron. JMO Draftkings, Silver Circle, Sam Howell. Nice. The 125. Grats on that Mohamed. It's a pretty solid card right there. Very nice. Josh Pascal. Auto. Tyler Algier, 69 of 125. Nice one there on the Falcons. Auto. Trayvon Walker-Rookin. Orange, Vilas Jones Jr. to 199. Yep, for the Bears, Ty Chan. Silver Donuts. Yeah, Titanium Donuts is another one. Smack, Keonte Ingram, Rated Rookie Hala. Jaquan Briskir. There he goes with Conway. Orange, Devon White to 199 for the Bucks. Skymore. 299, Jordan Davis Aqua for the Eagles and Kyle Phillips. There's White Hot Rookies, Brian Robinson Jr. and Aidan Hutchinson Rookin. Minka Fitzpatrick Aqua to 299 and Kyle Hamilton. Blue, Mike Gasicki. That is going to be 2-1 at 79. Go Dolphins. It's Patriot now. That basically means go Patriots. See what that card says? Red Hot Rookies, Kenneth Walker III for the Seahawks.  If you understand English, it's Brian Robinson Jr. Clearly. Okay. I don't know. Trayvon Birks, Rated Rookie. Gridiron Kings, Garrett Wilson. Sam Williams. Smack, Steve. Yeah, Smack. Who are you a fan of? Matt Judon to 125 for the Patriots. Yeah, for football. Smack is definitely like a Texans fan. Daniel Jones and Evan Neal. Chris Olava, Rated Rookie. Q Vaughn coming in. What's wrong with being a Jaguars fan? My ice cream. There's Jermaine Johnson Jr. That'll do it for your break there, Mohammed. Thank you as always, buddy. Do appreciate it. We'll get it right out to you, man.


Mustang showing a little blitz. Now Peatrick back in his spot Gardner back to pass four-man rush over the middle It's high deflected up in the air. So let's see what the call is here on the field It looks like the referees have picked up the flag and they have and Billy Lewis Flow the sophomore cornerback for the Mustangs two receivers to the left Gardner takes a snap back to pass over the middle It's picked off by Corey Peatrick Peatrick to the 20. He's got blocking at the 10. Peatrick inside the five He's down as his does it again Stevenson is on the board first with five thirty six to go in the first quarter Poles in the sophomore tight end that of Frederick His first career touchdown here Sternfeld on for the extra point Billy Lewis does the holding snap is good The hold is up the kick is up and it is good Williams eight of nine in the first quarter 29 yards and a touchdown low snap Williams handles it goes back to pass looking over the middle deep for Addo up in the air Mustang sports network powered by Sfm sports net Here we go third and ten at the 46 Gardner back to pass quick drop it is intercepted by Austin, Tennessee 50 45 Tennessee could go 25 21 at the six yard line Austin Tennessee does it again for the Mustangs Third interception are the first half for Stevenson back Williams Williams back to pass close to the left for Addo Jump ball Addo comes down with it Touchdown Mustangs Preston Addo second of the game Orchard football program in Gaithersburg with his second touchdown of the game Equaling his total from a year ago And who's over to seven at the Stevenson 44 Gardner play action pass rolling to his left under pressure Bros, and it's stuck on an intercepted by Corey Petrick, and he's down at his own 35 yard line As this opportunistic defense had 40 takeaways a year ago, and they've already got four here tonight covers here And it looks like a week one game in that regard first and ten play action looking deep for Adams It's up in the air. It's intercepted by Billy Lewis inside the 15 yard line So the Mustangs take it away for the fifth time as Nathan Gardner put that one up for grabs and Lewis with his second pick of the game 16th in his career Usually the referee had it at the one hand off the Lambert Crawley Lambert Crawley off the left side pushing the pile He's in for the touchdown Mustangs take the lead on the first career Stevenson touchdown for sophomore J. Nard Lambert Gardner takes a snap Fakes the handoff gets out of the way of lash. He throws deep over the middle. It is picked up by Billy Lewis He's got three Billy at the 30 25 20 10 5 touchdown Mustangs Take the lead on the pick six by Billy Lewis Give some credit to Mike Datto for creating the pressure a 37 yard interception Return for a touchdown by Billy Lewis nobody laid a hand on him he too at midfield handoff to Lambert And he breaks away at the 40 35 30 down the sideline. He's got the first down and more It's a touchdown running situation and the bishops fell asleep and J. Nard as he just broke it to the outside And who just stayed in bounds for wide receivers to bunched wide to each side Williams back to pass on third and 15 Williams looking deep Williams going for it all over the middle It is caught for a touchdown by Preston at oh 12 the hard way first and goal at the eight handoff to Crawley Lambert bus outside right racing to the corner. He's got a step Crawley Lambert dives is he in touchdown? Mustangs J. Nard Crawley Lambert his fifth touchdown run of the season Quarter right in front of us Peroni here Peroni rolls right it's deflected diving interception by Jimmy Lauer and there it is 36 straight games with a turnover for the Mustang defense to the left ball spot on the left hash Williams back to pass Looking left floating end zone open and caught for a touchdown Kenneth Scott Kilo and the Mustangs Up 20 to nothing converting that turnover into points Lewis the holder it's a good snap Sternfeld's kick is up plenty of leg And it is good on the goal line next to green green back to pass throwing deep down the right sideline intended for motion by Billy Lewis He looked like the wide receiver on that play and Billy Lewis made it an amazing One-handed interception we get a chance to look at the replay Lewis One hand snag with the right hand in the small of the blocking tight end in motion Williams back to pass on second I'm sure going for it all at oh back in the end zone makes the catch Did he hang on? He did touchdown Mustangs. You think the Mustangs will be licking their chops It's third in three for the Devils at the Stevenson 17 green rolls right throws. It's intercepted Again by the Mustangs this time It's Jimmy Lauer that pass intended for the tight end Pellegrini went over his shoulder Shouldn't at the nine yard line. We had the perfect vantage point for it Glenn We could see right away that it was Over and out as high and outside of Pellegrini and at the 37 yard line in Devils territory Williams quick pass out The Salisbury makes the catch of the 35 makes one man miss has a block 20 15 10 5 touchdown Devon Salisbury a 37 yard catch and run Art in a minute 49 Is capped off a 37 yard touchdown pass from Dan Williams to Devon Salisbury Salisbury With his first touchdown catch of the season he had five a year ago Harris kicks off right to left Frans alone to left Williams back to pass under pressure Williams completes it to add over the 10 5 touchdown Preston at old and seconds left third and seven one more play here Williams back to pass Williams going for the end zone has a man Open at Salisbury touchdown Mustangs with three seconds left They knew what they were doing the whole time 29-yard touchdown pass from Williams to Salisbury Salisbury just wide open the outside for the field goal The kick is up. It's got plenty of leg And it is good a 26-yard field goal Four wide receivers green back to pass green has time green loads up deep for Mobley up in the air Intercepted by who else Billy Lewis second pick of the game for Lewis Williams on second and four play action Williams loading up going deep add-oh open add-oh makes a catch of the five touchdown Mustangs Preston at oh his third exceptions third and goal from the six Williams back to pass Williams looking for Salisbury. There he is Devon Salisbury third touchdown He couldn't let Preston at oh with the Score in situation green back to pass under pressure zone on the left side picked up by Austin Tennessee Tennessee's got blocking down the sideline Tennessee untouched 30 25 10 5 touchdown Austin Tennessee the end of the game This oh, no, I'm sorry. It's Sternfeld still look like a 12 But it's still 19 and Sternfeld knock three wide receivers to the left another handoff on first down Came out Mustangs are but there's a huge pile up at the 14 yard line Billy Lewis says the Mustangs have it Stevenson says they have it the referees Say they have it Austin Myers the fumble recovery and Stevenson will have a golden opportunity To get the first points of this football game First in ten at the Aggies 14 play action throwing left add-oh makes a catch at the six Ado died to the other touchdown and he's in Mustang strike for 14 yard touchdown pass from Dan Williams To Preston at oh our player to watch with his eighth touchdown catch of the season That leads the middle Atlantic Conference all he ever does is catch touchdowns now make it eight of 25 catches second and 17 from the 18 For the Aggies Darden over the middle it's up in the air the interception Darden just over through the slot man and Lauer I believe it's about a 38 yard Interception return for a touchdown he had Austin Tennessee leading the way a caravan in front of him and really no Aggies in sight First half they take over first in ten at their own 24 quick screen out to the left side. It is complete to Marquis LSE fumbled at the end of the play in his loose Was he down? No, it is Stevenson football If it was one of those other leagues, let's watch Ellis Trying to stretch Datu and Leshy there Reaching reaching it was Datu on the recovery. There were six penalties in the third quarter We had six in the first half first of all for the six Williams right side. Alison touchdown mustangs up by three scores Wake up Owings Mills First in ten at their own 19-yard line Taborah design rollout left throws over the middle intercepted by Austin Tennessee Tennessee being Wrangled down at the 33-yard line. He was one of those seniors For Williams Ado alone to the right the deep threat Williams looks left wants to go right going for it all to add Oh, I don't make the catch Untouched touchdown Second eight Williams back to pass Williams going it for it all. He's got chair. Go wide open for the touchdown Mustangs up 13 to nothing Tyler chair ago One to the right to borrow back to pass looking right it's Intercepted by the Mustangs Isaiah pits and he's on his feet and diving out of bounds at the 30-yard line Isaiah pits With a big play for the Mustangs perhaps that gets the juices flowing again for the home team Trying to urge this defense on to borrow back to pass as time tucks looks fires deep for Deemer It's up in the air. It's intercepted by Austin Tennessee Tennessee is tackled at the 20 third down take a shot down field Why not just hanging now look you say the ball hung up there yet hung up there But he had no real idea where it was going. Yeah, it's a board is actually getting high fives on the sideline It's like the guy in baseball that moves the runner over no He did the right thing a thousand percent just throw the ball down field and see what happened Second five and 15 Dan looking left floating for the end zone has a man wide open So Ado made the catch in the end zone touchdown catch of the season We get to take a look at the replay Ado leaps up in the air makes the catch Low snap Williams gets it to Devonte Devonte over the right side of the 10 the 5 touchdown Devonte Williams summer salts into the end zone the Mustangs the lead 27-24 Third and 10 for the Mustangs at the kernels 48 Williams back to pass four-man rush Williams lead deep over the middle Ellison is open. He makes the catch of the 15 on his feet the five touchdown Mustangs Williams To Ellison 48 yards and the Mustangs on top by two scores Converting on third and ten certainly has Wilkes staggered. They are against the ropes. I think Wilkes was kind of expecting a 10-yard


Welcome to the Fiji Symposium 2019 in Cairo, Egypt, where I'm very pleased to be joined in the studio today by Jamie Zimmerman, who is a Senior Program Officer for Global Partnerships for Financial Services for the Poor for the Bill and Melinda Gates Foundation. Jamie, welcome to the studio. Thanks for having me. Now, this symposium is all about financial inclusion. I wanted to ask you, what do you think it will take for the world's poorest people to prefer digital financial services over cash? And do you think that digital financial services will be enough for this to happen? Thanks for having me. It's so great to be here in Cairo for the second annual Fiji Symposium. And it's a really great question. I mean, here we are in Egypt, which is a robust and growing economy. And yet, there's only 33% financial inclusion in Egypt. Only 1% of Egyptians use mobile money. It's a much of a, it's a really cash-based economy. And so when we think about the question of what does it take for people to prefer digital financial services over cash, I mean, you can look right here in Egypt and really ponder that question. And I think what it really boils down to is that the other digital financial services needs to be better than cash for that poor person. It needs to provide an additional value to them that cash cannot bring. And I think for that to happen, it needs to be cheaper than cash, more accessible, and to link them to other types of opportunities within the digital economy that cash alone cannot provide them. And so, no, I don't believe that digital financial services alone is enough to make someone prefer it over cash, just to have the phone in the pocket isn't really that helpful if you're not able to take that phone to the local store or to the place where you're buying your groceries or into be able to purchase something with it or if you're not able to use that phone to send a payment to a relative in a rural area or vice versa. So there needs to be a system in place that is cheaper, more accessible, more convenient. And only then, when that system is really in place, I think will people start to prefer not having to have that cash in the pocket, but really trust that it's there on the phone and whenever they want to use it, wherever they want to use it for any type of purpose, it'll be there for them. And so that's what the Fiji program is about, is thinking about what are the elements of that system that need to be in place to make it really robust and also really resilient. So it's something that will always be there and be something that's trustworthy as knowing that cash is in your pocket. And so I think that that's critical. I was going to say, is it the technology or is it people's attitudes towards this particular way of transacting? Yeah, so that's a really great question and I think that the answer is that it's both the technology and it's the trust. And so the technology needs to be secure and it needs to be robust enough, as I was saying, for someone to know that when they want to use it, they can. And so there is great technology out there. We are able to build and do so many amazing things. But if the service is down when you go to use it, the best attitude in the world is going to change if it's inconvenient for them. And so it's really, it's a bit of both. I mean, it's a little bit of a balance there, chicken and egg, as we say, where you need to have one in order to have the other. And so when the system is in place and it's working, and that technology is something that you know that is always going to work for you and you can trust it, then you'll start to use it more. And the opposite is true if it doesn't. And so part of the intent of the Fiji program is to say, what is the infrastructure that's needed to have secure, trustworthy, ubiquitous financial services that you can, that you can access through your mobile phone? Now, Bill and Melinda Gates Foundation here are obviously a partner of this event. I wanted to ask you, what are the main expectations for this edition of the Fiji Symposium? So the Bill and Melinda Gates Foundation is really excited to be partnering with the ITU, the World Bank, and the Committee for Payments and Market Infrastructure at the Bank for International Settlements. This is the triad that makes up the Financial Inclusion Global Initiative partners. It's a really powerful group of global bodies that are able to bring together experts, technologists, regulators from different sectors and from all over the world. And so these symposiums that we're doing, and this is our second symposium of this program here, and to be doing it here in Cairo is really exciting for us because it's a midway point in the Fiji program. And Fiji has this triad of partners, as I was saying, but it's also a very robust program that not only doing these symposia where we bring together these global experts, but also hosts three working groups, one that's looking at cybersecurity and infrastructure, trust in digital financial services, one that's looking at electronic payments and acceptance, and then a third on digital ID, all considered really core components for having those inclusive digital financial services that people want to use and will trust. And then beyond that, there's also implementations that are happening in three very critical markets, one here in Egypt. We have really strong partnerships with the Central Bank of Egypt, with the NTA, and we're really grateful, especially to the NTA for co-hosting this event with us, but also Mexico and China. So these symposia bring together the country implementations as well as all of the great work that's happening within the working groups to raise awareness of these best practices, lessons and insights that are coming out of the country implementations and what the technical experts are doing, and exposing to the world all of the interesting things that are happening that can be replicated in their markets. And what we hope at the foundation that happens by doing this is that other countries will start to replicate and that we will speed up the process of financial inclusion through these types of replications and through this global awareness. And so here we are in the midway point, and we're really excited to hear how things are going and start to look forward to all of the amazing progress that we hope is going to come from here. And you also encourage, of course, the germination with a hackathon here today. Yeah, so really excited to have a hackathon as part of the Fiji Symposium. More than 50 different technology start-ups and fintechs. I think we're down to the 14 finalists. We have eight technology providers from Orange, the GSMA, Payfort. There are many of them, and it's really exciting to be able to feature that as part of the symposium to have the actual start-ups and technologists who are working to build that infrastructure on the ground to come in and work with the APIs, work with the technology and come up with new solutions and new ideas that would work for their markets. And so it's a great feature to have, not just having the global institutions and experts, but also having those on the ground who are the experts in their home turf telling us how does this work here and how can we make it work better. And so really excited about the hackathon. And I believe that they're going to be announcing the winners of that during the symposium as well. And so really excited to see who comes out on top and what they've created. Finally, what do you hope the hundreds of people, the hundreds of delegates that are gathering here will take away with them from being at this year's symposium? I hope that the delegates who are either from here in Cairo and Egypt or have come from all over the world, what I hope that they take away is that there is a proliferation of activity in digital financial services that is really building momentum, that we are learning so many things now about how to make the systems work, not just make them robust but make them resilient and make them responsible. And that they will learn not only about what those different methodologies are, different insights from the countries, but they'll also connect with others from around the world who are asking the same questions in their markets and maybe be looking for the same types of answers or maybe be learning different types of lessons, but they can share that together and take that back home and that'll help to keep that momentum going in their markets as well. And finally, the global landscape, how do you see it now in the next five years or so? So the global landscape for digital financial services is evolving rapidly. Just in the last few years we've included more than a billion people into the financial system through digital financial services. Our hope at the foundation is that within the next three to five years we've included them all. And so this type of initiative, like the Financial Inclusion Global Initiative, is just one of our big partnerships that we've supported to make that a reality. But I think that when you look at all of the really exciting work that's happening that we're putting a spotlight on here at this symposium, that you are able to see all of that momentum moving forward and that we really are in a trajectory where we're accelerating towards that goal of universal financial access. Jamie Zimmer, thank you very much indeed. Yeah, thank you.