Course Page Improvements in Moodle 4.2 An admin setting controls indentation in courses. Teachers can duplicate course sections. There's a perma link for easy linking to sections and they can add activities anywhere. Activity names are displayed only in edit mode and text and media areas display in the course index. From site administration, plugins, course formats, topic format, our administrator is going to allow indentation for the topics format. She has a similar screen for the weekly format. If after careful consideration and consultation she decides to reset all previous indentation, she can do this by clicking the link and then the reset indentation button. In his critical thinking course, teacher Mr. Wilson wants to indent his about this course book so he enables edit mode, clicks the three dots and clicks move right. This change is also reflected in the course index as we see here. He then wants to duplicate his first section, module one, in order to prepare module two. He simply clicks the three dots to the side to duplicate it and then can easily rename the section and any activities. Note too that he has a useful perma link if he wants to reference the section anywhere. Adding activities is much more efficient now as he can click into the place he wants to add them. When he's in edit mode, he can see the type of activity or resource he has added but learners don't see the names at all. Finally, if he adds a text and media area this will also show in the course index. To summarise, admins can allow indentation in topics and weekly course formats and can reset previous indentation. Sections can be duplicated and have perma links. Activity names only show in edit mode and text and media areas are now displayed in the course index.


A youth organization of the R Progressives Congress, APC Progressive League of Youth Voters for Tinibu and Shatima has employed President Bola Meir Tinibu to introduce policies targeted at reducing unemployment in the country. In addressing lack of jobs, the APC Youths act as the president to tackle the growing unemployment by appointing young Nigerians into his cabinet. Lamenting the rising cost of living among Nigerians, the youth organization hives a bet the recent withdrawal of youth subsidies saying it was a bold step in the right direction. Speaking during a press conference in Abuja during the investiture of the National Patron Engineer Ayola Oyajidei National Coordinator of the APC Youth Group, Ambassador Abdul Usman Shuaibu described three policies and appointments made so far by President Tinibu and Vice President Kashim Shatima as square pegs and square holes. At least half of Nigerians are on the ground. A figure that drives youths to do thoughts for young people who make up the majority of the population. The president is expected to tackle this problem and reduce it to be at its minimum. Two, national security. The previous state of national security in Nigeria is Warsaw. The recent Oklahoma-Iraa insurgency in the North East is being substituted by mandatory altruism in the North West. The North Central is facing deadly farmer-hidden crises. The South East is immersed in securities, violence and associated criminal obtuse. There is an upstream, upstream engulfed in ritual activities in the South West, while the South South is inflicted with militancy, piracy and oil theft. The President should get a grip on this serious security threat. Thank you.


Hey there lads and ladies, it is Petrifying Pumpkins here and today I want to make a video about the future. The next generation Playstation Virtual Ryazi heads us. Now the PS viewer that we have right now is actually 5 years old today, today is the 5th anniversary and we've all had a good 5 years I would say. We've had some ups, we've had some downs but overall it's been a good bit of gear. Now that we're approaching the end of its life cycle, we're looking towards the horizon, we're looking at 4K screen, we're looking at boosted performance, proper hardware pushing this thing, we're looking at proper controllers that actually are top of the line instead of the glow sticks that we have now that are trash, we're looking towards hybrid games, we're looking towards all these things and some of those things have been confirmed, some of those things have been leaked by Without Parole and some of them have been speculated on but you know we're pretty sure we're getting a lot of us, if not all of us and that sounds fantastic. What we don't know however is when Sony are actually going to reveal this thing, we don't know what it looks like, we don't know how much it's going to be, we don't know when it's released and we don't even have a name for it yet, we're all kind of calling it the PS viewer 2 or the PS5 viewer or the next generation PS viewer, you know a lot of these names going around but all those questions will presumably be answered whenever Sony do have some kind of an event but what about the games that they're going to show us at this event, whenever this event happens, these games are going to have to get us really excited for the future of PlayStation Virtual Reality and that's what I want to do in this video is I want to look at these things, I want to speculate, I want to predict the games that we might see at this event, this reveal event whenever it comes around. Some of these predictions are going to be you know, educated guesses based on rumors that are flying around and things like that, some of them are going to be wishful thinking and some of them will just be like logical I think. So my first guess, my first prediction is a game that I think is actually going to be a safe enough, best although there are people out there who would you know be pretty vehement, that's not common I would say half life addicts, I think that's what we're going to see at the reveal event, half life is a huge IP from a huge developer and well I will admit it's not as relevant these days as it was 10 or 15 years ago and maybe you know younger audiences might not care about it as much as we would but half life is a big name, it's a big IP and it is beloved. So all Sony have to do is come to some kind of arrangement with Valve and I should know that Valve have openly came out and said, well I'll read the quotes, it's from a push square interview, I'll have it up on the screen now, designer Greg Coomer reconfirms that the initial release of Half Life Alyx will be available for Steam VR only, it definitely sounds like Valve is aware of the desire to see the game come to PSVR however, we believe Sony's VR platform has been a huge success for the medium and we assume that lots of Sony customers would love to experience this new chapter of half life, that's a Valve developer saying that, I mean you would not say that unless you're very very open to the idea of these Sony customers getting to experience half life, you know, as far as I'm concerned it's a done deal, the only potential issue I can see here is the fact that Sony have like a very close relationship with Epic games recently and Epic and Valve have become rivals in a way ever since the Epic game store came along to compete with Steam, so maybe there's a bit of you know sour milk going on there but I don't think so, I think it's, I don't think Valve will be that spiteful towards Sony and in fact I think that if the PSVR that we have now if that was powerful enough and if it had the controllers that were good enough I think we'd already be playing Half Life Alyx on PSVR, unfortunately we didn't have that hardware but that's gonna change and in fact I think that's gonna be true of a loss of PC VR exclusives, that's why my next prediction isn't gonna be just one game but a bunch because you know I'm predicting we're gonna see these PC VR games that maybe wanted to come to PSVR, maybe the developers actually tried to make it happen but they just couldn't fit enough clowns into the clown care to make it actually work, so those games I think they will come and I'm talking about games like Boneworks and if I remember correctly the developer for that game is actually tweezing about you know his interest in bringing us to PSVR too or whatever it's gonna be called I'd also put Fallout 4 in the mix there I know that IP is now owned by Microsoft so maybe that makes it a little bit less likely however keep in mind there's another version of Skyrim coming to PS5 this year you know Fallout 76 just came to PlayStation now this month so you know Microsoft are definitely not holding Bethesda back on at least certain releases so the fact that Fallout 4 is already made all they'd have to do is ported over the PlayStation I think you know there's a high chance that could happen then there's the kind of smaller scale PC VR stuff your games like Phasmophobia your blades and your sorceries those kind of games now I know those games are still early access they're still being developed but I would not be surprised if we see like a little teaser little trailer saying coming soon even or something like that because I can't imagine Sony is like not approaching these developers these small indie developers and saying hey doesn't have to be launch day or whatever but sign up with us and we get your game into more people's houses you get more cash you know so my next prediction is that we are going to see PlayStation 5 games that will have already been released or some games that are even already out now that will be getting updates or patches to turn them into hybrid games so immediately what springs to mind Gran Turismo 7 Resident Evil Ace I mean the sky is the limit here in terms of speculation it's all going to come down to you know how many checks Sony are willing to rise to these third-party developers to make these updates happen Gran Turismo 7 seems pretty much guaranteed based on the history of Gran Turismo sport the fact that Sony actually own it so they can you know they can force it if they really wanted to then you've got Resident Evil Ace again Resident Evil 7 was such a success I find it hard to believe that Sony wouldn't make the exact same deal with Capcom again to make you know Resident Evil 8 happen on VR now a lot of us are probably already expecting Gran Turismo 7 and Resident Evil Ace but I think we're gonna be hit with some kind of megaton announcements from third parties that are maybe going to get us really hyped or really surprise us or wow us and I'm talking about games like GTA 5 Red Dead Redemption 2 maybe even Sony have great relationships with Activision Epic so why not some Battle Royale games like Warzone, Fortnite these things could happen and even if it's not Battle Royale or whatever or Warzone you've got such a good relationship with Activision and Call of Juicy that's you know could be a standalone Call of Juicy title maybe Vanguard gets a VR optional hybrid mode or whatever and of course we know thanks to job listings that Rock Stair are working on a AAA open-world virtual reality game so while it is possible that is a new IP I think it's probably more likely that it is a port of either GTA 5 or Red Dead or something like that so either of those being there is gonna be very exciting we could really get lost in the weeds you know going over every single third-party game or big game because this is what it's gonna be about like Sony are gonna want to have these big names these recognizable brands that's gonna hook people in this is how you make a mainstream so yeah four nights even if you don't like your four nights or your colleges these are your GTA's they're still important and I think we should all want them plenty of other games is there as well you know that could be in contention your Rainbow Six's Rocket League Destiny 2 all these big games big names well-known things that would help the medium grow so next up then I want to take a look at Sony's own in-house first-party stuff and I'll start with Horizon virtual reality so this is a game that we've been talking about on the channel for maybe it feels like years now it was first leaked as a game that Sony London were working on and then everything went quiet and then it reappeared again as another leak that fire sprites were working on Horizon VR and then things went quiet again and then Sony acquired fire sprites so that kind of reinforced my belief that yes something's going on there so I think that's all adding up to me I think Sony gathered the fire sprites maybe they saw what fire sprite were doing they were really impressed with what's going on there and that's why they decided to acquire them because that acquisition kind of felt like it came out of nowhere fire sprite did have experience making the persistence but that was kind of really ace when it comes to collaboration with exclusives with PlayStation so that kind of came out of nowhere so Sony must have seen something that they're very excited by or something that they like the look of at fire sprites hence acquiring them and in fact I think if I had to guess of what game is going to end the show because when it comes to these shows these conferences or whatever they always have like a big bomb at the very end you know one more thing I think Horizon VR will be that big showstop or whatever it's a big IP it's you know broadly recognizable and it's probably gonna look pretty impressive in terms of other first-party studios we know Sony London have a very strong history with PSVR we know they're hiring we know they're working on something and I think they'll probably have something ready to show in time seasons it's been quite a while since we've heard anything from them from blood and truth they did a bit of DLC they've gone silent they've been hiring I think they might have at least a teaser something to show Insomniac and team is so they then are two other first-party studios with some heritage of virtual reality now Insomniac have so much under place that's I think if we do see Insomniac there it will be to confirm that's either Spider-Man 2 and or Wolverine will be hybrid games I can't see them coming out and announcing another brand new game which is like the or only however as I say this you know Insomniac have been surprising everyone with you know how much they're able to output so I'm not sure how many teams I don't think anyone knows how many teams they have over there they seem to have a bunch so it's possible they do have a dedicated VR team and they might have something to show I will not rule that out but on the other hand then team is so be their history is with Astro boss they recently released the PS5 launch game Astro's playroom I don't think they'll have something ready in time they're not a big studio like Insomniac they recently even formed like team is so be used to be you know they're made up of what was PlayStation Japan PlayStation Japan dissolved so they all got restructured around I'm not sure they'll be ready to have something to show I'd like to be wrong of course another Astro boss would be fantastic my next prediction then is a bit of a wild-cared prediction PlayStation home virtual reality not really a game but kind of you know an app something like that it's a social space it existed on the PS3 it wasn't a massive success although it does have a loyal following it was kind of weird but if PC viewer has taught us anything and if you know viewer chas has taught us anything it's that social spaces and virtual reality are like a match made in heaven so it seems like an easy fit this seems like the best way if PlayStation home is ever going to come back surely virtual reality is the way to do is it just makes the most sense to me and there's definitely loads of potential there so my final prediction then I've saved the best for last first contact entertainment tease firewall to first of all let me say quickly that I am a community moderator for first contact entertainment and I have got a good relationship with that studio and you know there's obviously some bias there I'm kind of a fanboy of that channel but not without good reason you know most of the people watching this now who know me know me because of firewall zero hour you know that I really got into that game and kind of got obsessed with it for a while and I can build channel around that or built it up at least so obviously an X-Gen firewall is something I really really want to see and it's something we've already been speculating about on this channel here based on some recent job listings from first contact entertainment the reason why this might be more wishful thinking and kind of unrealistic is because they did just release Solaris this year on psvr and they're not like a massive studio that I'm not sure how many teams they have but I think it's just the one team they're not like insomniac you have like you know 300 employees and God knows how many teams but on the other hand you know Solaris was a port of a 2020 game and if we look at what has happened since then in terms of post launch support Solaris hasn't really had like a huge amount of content added to the game in terms of like maps and characters and weapons and stuff like that it's kind of just been a few smaller things and fixes and updates and stuff like that you know Solaris in general just felt smaller scale compared to something like firewall and then if we look at firewall itself you know they're still supporting firewall with seasons boss those seasons have been you know downscaled in scope compared to the seasons that we were used to so we're not seeing maps anymore we're not seeing weapons or contractors or skills or isms really all we're seeing is new missions to keep us you know give us something to do and some cosmetics and even the cosmetics then they're not new assets they're more pallets so like different colors different smoke colors and different you know versions of camouflages that were already created so you have to ask yourself what are the people at first contact doing who make these assets and of course they're hiring for this other mysterious next-gen game so obviously they're working on something else now will it be ready in time to show as this event whenever this event might be who knows that's why it's kind of like a wild card guess but even if they just showed like a five-second CGI glimpse of like you know okoro or something like that and then the logo appears on screen firewall too that'll be enough for me you know lose my mind if you're looking for any more like evidence that they might be doing another firewall you would have to look at this graph I have here which shows the top 10 grossing virtual reality only games globally as of September 2020 so as you can see at the bottom here is firewall zero hour which is really impressive for a game that just released only on psv or it is 10th globally and we're talking about it's up there with the heavy hitters beat saber you know job same here so those games that like never come off the charts so firewall is very successful at least in terms of grossing you'd have to imagine if Sony have any sense at all the second they've decided to green-lice psv or two or the next gen viewer headsets one of their like top priorities must be at least reaching out to first contact and seeing if they can get a sequel you know if I was in Sony's position I'd be trying to buy first contact entertainment but I'm not unfortunately I just hope Facebook don't do this before we get a chance to see anything from them so anyway those are my predictions for a next-gen PlayStation virtual reality event if we get 10% of what I just said I'll be happy I think predicting when this actual event will take place is a whole other kettle of fish or whatever the saying is let me know your predictions what you think we might see is there anything obvious I missed in the comments below as well as you know maybe what you thought about the predictions I did make and with that I will end this video but before I do let me thank the patreon supporters his names are on the screen as we speak thanks to their generosity they're helping keep this channel going in particular the top tier patreon supporters Daniel the pumpkin patch kid tradition Pete Hawkins and crumb thank you very much for that generosity it is very much appreciated if you'd like to help out on the patreon the link will be in the description below if not still like share comment subscribe all that usual YouTube and shies will help us immensely also finally before I go let me thank Decepticon for letting me use his music in all of my videos you can check him out Decepticon calm link in the description for him also with that I'll say goodbye take care stay moist stay safe you know streets are dangerous


Okay. We've never worked with agencies, for PR, for marketing nothing. Our press is all organic. We just, yeah, we get reached out to a lot, we gift a lot, we really did. We did. And we organically vogue, GQ, Forbes, everything that we have was super unpaid, which we pride ourselves on. And you know why we did that? We wanted to track our growth, like genuinely we wanted to track our growth. You wanted to understand it. Yeah, we wanted to see what the hype was about, what editors really wanted our product, like. What could we do? They wanted to say about it, yeah. So we wanted the feedback. So if someone's listening and they're like, how did you get in a vogue without an agency? Well, like how'd you do it? Honestly, create amazing content, create an amazing product, put it everywhere.


Good afternoon, Miss Kristin a Can you hear me okay, and we can maybe test your sound I can really Good evening Andy. Let's let me go ahead and resend that prompt to make you a panelist So it'll be right there. Hopefully We can get your sound check Thank you. Can you hear me? Can you see you with your lovely Santa Rosa background there nice turn off my audio and video until a few minutes before Okay, again. Thanks. All right. I think we have a member of our applicant team here Marcus Griffin If you want to try a sound check, let me go ahead and send a prompt there for you All right. Can you hear me okay? Are you great sounds good? I'm glad I came early Yeah, it's nice to be able to do the sound check. It's a The root awakening when you discover yourself. I know in between my monitor and my Headphones and you know everything trying to Mess with you.  We go go ahead and send a prompt. I'm gonna give that give that a try. Can you hear me? Yes, we can I'm gonna say okay. I'm gonna say check here I was gonna say go up by the microphone and see how you're I figured it out Okay, good so if you want to go ahead and keep yourself muted until it's the appropriate time then We won't have to go through prompting. I'll mute myself right now Good afternoon. We'll be Commencing the zoning administrator meeting here in about two minutes give everybody time to join us at 5 p.m Official start time it's 5 p.m. September 7th, and I wish to call to order the zoning administrator meeting This is a special meeting and we have one item on the agenda Before we start with that matter like to just review a little bit about the meeting protocol This is a zoom meeting because of the Covid pandemic The governor issued an executive order Which allows us to suspend certain requirements of the Brown Act that enable us to fold this Meeting in a virtual or zoom format All participating members will be able to Waste their comments or add information as if this were an ordinary face-to-face meeting which we hope called soon To participate just as in a regular face-to-face meeting. I will call upon you whether your project planner Project applicant or an interested party And as I said, we do have one meeting item on this meeting agenda And we'll basically follow that order. We'll hear from the project planner first and then the project team and anybody else who might want to comment from the public Today's meeting the outcome a decision made today is Appealable 10 working days full working days After the meeting and I always have to look at my Calendar the 10th day will fall on it's today being Tuesday The 7th it will fall on The 21st or the 20th of September make sure I get that right seven. Yeah, so we'll be on the end of business day Monday the 20th of September All right, so with that introduction and Announcing the appeal date. Let's let's start in on our Schedule on our agenda the first and only item is a public hearing for one eight eight five and one nine Zero fives of basketball road multi-family project with affordable housing and the project is christenate humans Thank You mr. Gustafson. This is christenate me and senior planner and the project we're discussing this evening is acne family apartment It's a request for minor design review and The project site is about 2.43 gross acres and their request is for a predominantly four-story affordable housing multi-family housing project for 77 units There is a one-story community building that will face a basketball road and there will be 130 parking spaces This is the project location. I believe it was an auto dismantling dismantling yard at its previous life and as you can see to the To the east there is a housing development right next door and this area long sabastral sabastral road is Changing quite dramatically from what it was in the past and it's becoming more Residential and commercial in nature the general plan and zoning for the site is CG and r318 so it's got dual zoning and dual general plan designations however, the multi-family use is Allowed by right in both zoning districts The zoning code section 20-16 0 6 0 modifies the review authority for certain entitlements in this case What would normally be a major design review will becomes minor design review because this project is in the Roseland plan development area um it's allowed to You reduce to minor design review as long as the Project goes before the designer view board as a concept designer view which this project did on February 4th of this year This is the site plan for the project as you can see the clubhouse faces sabastral road down at the bottom there It's the one-story releasing an amenity building directly behind it would be a shared amenity that you you can see better in this landscape plan that I'll show in a minute and the Apartment buildings are behind it with parking tuck under tandem parking and surface parking Your elevations for for the project You can see the tuck under parking the original Project when it went to the designer you board featured garage doors and the designer view board thought the garage doors would be a very prominent look and The applicant went ahead and instead of garage doors, they would be open car ports That would encourage parking covered parking to be used as covered parking and We wouldn't have prominent garage doors as you're driving along sabastral road This is the elevation for the community building This is what Drivers and pedestrians would see Along sabastral road Here's the first and second floor plans for the units You can see the parking on level one third floor And I believe I misspoke. I said four stories. These are actually three stories. My my apologies. It's not four stories Here is a 3d rendering of the project site. So you can see the tuck under parking You can see the view there of the surface lots and The tuck under parking Here's a little bit closer view of the community building on the left the apartment buildings behind it And you can kind of see the amenity area behind the community building there just a little glimpse You can see some of the balconies that the apartments would have Here's some more ground level view looking down the project site from the community building and Here's a across-the-street view of the community building. So this is what The pedestrian output what would be what people would see at a pedestrian level or at a car level Here is the landscape plan. This is that the landscape plan for the entire site You can see the that half circle sport court that's proposed behind the clubhouse on the left in the area it will be landscaped with various trees and shrubs Here's a close-up view of the sport court clubhouse and Landscaping along the subasphal road if I go back you can see the Trash enclosures Are well-screened and not readily visible from the street Another thing to mention is in order to get to the 77 units the applicant Requested a 35% density bonus and they qualified for that and that allowed them to achieve the 77 units that they're requesting And with that planning and economic development department recommends that the zoning administrator approve the minor design review permit for Acme family Apartments project and the applicants and his designer are available to go through any design details Questions you might have about the design and staff is also available Thank you very much Chris today quick question about the density bonus It's great. This project is taking advantage of that Is has the type of affordability been defined for this project very low low income I Can look that up. I believe it's in one of the attachments, but I can look that up for you Yeah Yeah, you'll have a moment Let's see and then to clarify you mentioned the trash enclosures being Well concealed those were the ones indicated Under the trellises along the West property line. Is that correct? Did I read that plan correctly? I believe it was the East property line. Oh, I meant these. Yes. Okay. Yes. That's right. That's right. Okay, okay I was making sure the North was pointed in the right direction My mistake And let's see Oh, is there a You mentioned concept design review and and you noted that the Previously proposed garage doors were removed and and made those parking spaces made open as carports Were there any other substantive design? changes in response to the Committee's comments from that meeting. There were a lot of considers not shells. They like to Separate their comments that way. They didn't have any shells for the applicant the original design they felt was a little too Residential and they wanted that wanted the designer to explore a little bit more modern aesthetic The color palette changed to more cool tone And I believe the cladding on the community correct me if I'm wrong design Andy But for Marcus the the cladding on the community building changed as well Or maybe it's just the colors that change, but it made a dramatic difference Okay, cool. No, I just I think it's important to memorialize the design review boards Comments and how that project Changed or not in response to that. So thank you for that Okay Thank you for clarifying those points If any member of the project team or applicant wishes to comment, please raise your hand and you'll be recognized Looks like everyone is On zoom and we have Marcus Hi, Andy. Thanks for having us tonight at the meeting I just wanted to respond to the one question about the affordability This project won an award for the special disaster Tax credits that were Competed for last year So it's a typical what you know, we call 9% project that the overall average affordability is 50% So it's very low income 100% of the project is affordable There's a small component that's at the low income level. So the ranges go from 30% Am I up to 60% Oh, yeah, so moderate. Yeah. Well, yeah, I guess 60% they call low income. Yeah in Sonoma County, they're pretty reasonably high income. So it's it does hit a broader spectrum of households and This project's a large family project. It has a lot of two bedrooms and three bedroom units to try to You know houses many families as possible So that's the the basics there really appreciate your time and we're here for any questions Yeah, thank you. Yeah, I said moderate but 60% would be the low income very low, right? Thank you Any other member the team wish to comment as its point if not Let's give opportunity for any other member of the audience and attendance that wishes to comment Please raise your hand and you'll be recognized seeing none, I'll close the public hearing on this item and and Get to deliberate with myself So it's really great to see a project of this quality Coming forward and building a powerful need that we have for affordable housing and Utilizing the density bonus. I really like seeing that You know that the obviously a lot of thought went into the design I Appreciate and respect the team for responding to the design review committee's comments Making adjustments. I Have one major question if I could see the site plan showing the Activity area I Got a wonder if there could be something I might contribute to the project. Maybe you can respond Okay, I'm just thinking about basketball right now Would it be better to flip that court 180 degrees? So Amateurs like myself who might miss the backboard aren't putting the ball into the wall of the building but rather maybe to the neighbor I don't know if there's some consideration of the property line This is a profound comment and question. I know but maybe practical and I Don't know am I still able to speak or am I I don't know? Yeah, so we could we've crossed that path before and and It's funny that the building there's a building right up against the property line very tall You know the commercial building, but we were also going to put some kind of netting there with that exact concern But we just felt that it worked better in this orientation, but we definitely have to Actually now I hear what you're saying in my mind, it's the opposite like I don't know if you keep on the line But I was thinking that the hoop would be against the building side And we'd be able to put up something that kind of keeps any ball from going in between the fence and the the building Well, in my power as zoning administrator, I grant you authority to flip it around On consideration No, but otherwise in all seriousness, I think What what I appreciate is not just the availability of the units I think more than myself the tenants will appreciate the space provided outdoors And it looks like you've paid attention to that Breaking the buildings up into three parts kind of creates Nice individual clusters. It's not a monolithic footprint It really breaks it down in a very human way so and the clubhouse at the front of the property is The great transition in massing but also puts that public face towards the street. I think that's a really good idea That's a great project. So I Hope it's able to break ground Expeditiously and I know there will be people waiting to Come in and live there So I read the resolution it does Memorialize the steps that it got to get it to this point Including the density bonus, which I think it's important to acknowledge and it makes all the necessary findings for design review here and And they're appropriate the conditions are appropriate And I just would echo or restate my basketball option for you guys and and I have the pleasure of approving the minor design review as proposed and Go forward build it. Thank you And that concludes we appreciate it we're gonna get under construction in December Good one way or the other Well, I wish you all good luck and look forward to seeing it come out of the ground Thank You Kristen a and everyone and with that I'll adjourn this meeting at 518


We continue with our examples of superposition of different plane potential flows. So the next example that we will consider is a vortex. So when we consider a vortex, remember that we are talking about an irrotational flow and a vortex. So it is an irrotational vortex or a free vortex. So what should be its velocity components? We already know v theta equal to c by r and v r equal to 0, right. So now this c may be related to the strength of the vortex. Strength of the vortex is the circulation. So what is the circulation? You recall this one, right. So this is c by r into 2 pi r. If you take a circle of radius r and find out circulation around that, so c is equal to gamma by 2 pi where gamma is the strength of the vortex or the circulation. Now your df dz that should be v r-iv theta into e to the power of –i theta, okay. So –i c by r e to the power i theta. So –ic by z. So –i gamma by 2 pi z. So what is the form of f? f is –i gamma by 2 pi ln z, right. You have to keep in mind that this gamma we have considered as positive if c is positive and that is anticlockwise. So here this – sign is for anticlockwise circulation and plus sign for clockwise circulation. That we have to keep in mind that so if gamma is just a number, just a positive number then this – sign will imply that it is anticlockwise and plus sign will mean clockwise. So if where we are considering gamma as itself a positive number. Now let us say that we want to simulate flow past a circular cylinder with circulation. So flow past a circular cylinder without circulation was uniform flow plus doublet. If you want to introduce a circulation then you have to use this vortex. So it is uniform flow plus doublet plus vortex. That means how do you write f? First for uniform flow u infinity z plus doublet. For the circular cylinder, flow past a circular cylinder we have seen doublet strength is special u infinity into r square where r is the radius of the cylinder. So u infinity r square by z plus the vortex – i gamma by 2 pi. Now let us see that using this can we really simulate the flow past a circular cylinder because you have to remember that the radial location of the cylinder should represent psi equal to 0, the streamline. Let us see whether that is satisfied by this or not. Intuitively that will not be satisfied because up to this part if we consider that satisfied psi equal to 0 on the radius. Now we have added one extra part. So how do you ensure that? Let us look into that issue.  So 1 i with this i i square becomes – 1 and that is how this has become plus. So if you want to write it in terms of the real and imaginary components u infinity r cos theta.  This is the real part. Imaginary part is more important for us because that gives a stream function form. So plus u infinity r sin theta – u infinity r square by r sin theta – gamma by 2 pi ln r. Clearly if you see this form does not satisfy the requirement of 1 i has to be put here. This form does not satisfy the requirement of psi equal to 0 at small r equal to capital R. Because when small r equal to capital R these 2 terms will cancel out but the third term will remain. But small r equal to capital R should correspond to psi equal to 0 for flow past a circular cylinder of radius capital R. So what is the way out? The key here is that this definition of f may always be remain unaltered if you just add say a constant p plus iq. Because it is just the choice of the reference. So just add p plus iq. So here you will have 1 p and here you will have 1 q. The q should be such that it should be gamma by 2 pi ln of capital R. Then you may, so if q is equal to gamma by 2 pi ln of capital R then psi equal to 0 at small r equal to capital R. So in this way if you want to generate a body of a particular shape you have to be very very careful about the choice of the f. It is a superposition but you also may need to add certain constants to make sure that you represent the correct shape of the body. When you have a body of a particular shape what are the important things of interest? One important thing of interest is the stagnation point. So where is the stagnation point? For example when you have flow past a circular cylinder say without circulation. So when you have without circulation this gamma term is not there. So when you have flow past a circular cylinder without circulation then you have when the first term is u infinity. So if you find out df dz, so df dz if you calculate for flow past a circular cylinder you got 1 vr which is 0 for all r and theta on the cylinder and 1 v theta which is proportional to sin theta. So when theta equal to 0 then or may be r equal to capital R and what r equal to capital R is okay but you see the expression of v theta-2 u infinity sin theta. So when theta equal to 0 you have v theta also equal to 0. What about theta equal to 180 degree? Same. So those points on the cylinder are special points where you have both vr and v theta equal to 0. So those are locations of stagnation points on the cylinder. Stagnation points need not necessarily be located only on the surface of the body. They may also be located at outside. So the only important condition that you need to find out is where the resultant velocity is 0. That means vr, v theta individually 0 okay. So if you consider the flow past a circular cylinder you will see that if you just want to consider streamlines without the rotational effect or without the vortex effect. So you have a point here which is the location of a stagnation point. Then the streamlines follow like this and this point is also like a sort of stagnation point. So here you see that the theta in the way it is measured classically by polar coordinate positive sign convention this should be the angle theta but even here 180 degree-theta is also fine. So you may also consider by convention this as the angle theta. The reason is that the answer where it comes in the form of sin theta. So it does not really matter and of course in terms of pressure distribution the sin also is not important. It is just the value because you have sin square theta coming there. It is like even more inconsequential what is the sign of that trigonometric expression. So by convention we take this as theta. So this is like theta 0 theta 180 degree like that and you have such shapes of streamlines. Such beautiful shapes of streamlines are not there in the real case because in the real case when you have adverse pressure gradient at some point close to this one you have boundary layer separation. Beyond that you do not have such streamlines, such symmetric shapes. So we will look into that issue more carefully. Now regarding the effect of circulation let us try to see that what is the effect of net effect of circulation. To understand that what we will do is we will try to calculate the total lift and drag force on a body. So our next objective is calculation of lift and drag force, drag and lift force. In one of our previous lectures we discussed that if you have a plane flow whatever is the resultant force acting on a body that if it is resolved into 2 components one in the direction of the flow stream another perpendicular to the direction of the flow stream. The force in the direction of the flow stream is known as the drag force perpendicular is known as the lift force. So let us say that we have an arbitrary body. Let us also consider this as a cylinder but not a circular cylinder. So a very general case of a cylinder we are not committing ourselves that whether it is circular or whatever shape. Now let us say that this is the free stream direction and let us try to identify that what are the forces acting on a small element. Let us say this is a small element of length dl. Remember we are talking about only potential flow not the viscous flow. So on this element what will be the origin of the force? Only pressure distribution. If it is a viscous flow then the shear effect will also come. So you have the pressure distribution. So this is strictly only for potential flow you have to keep in mind. So this is not a drag and lift force for any general case for potential flow. So now this dl you may say that it is as good as traversing dx along x and dy along y where x and y are these directions. So you may just break it up into 2 parts. One is like dx along x another is dy along y. Let us say that the angle made by P with the horizontal is theta. Therefore we may say that angle made by dy and dl that is also theta. Dl is like tangent to the contour and P is normal to the contour. Now let us find out that what is the resultant lift and drag force due to P. So you have a P force like P here you may dissolve it into 2 components. So one is the vertical component another is the horizontal component and this angle you have to keep in mind is theta. So this is the P direction. We have just separately drawn the sketch for clarity nothing more than that. So you have a vertical component you have a horizontal component. So what is the vertical component? P into dl into what cos theta or sin theta. What is dl sin theta dx? Just look into this triangle of dx, dy and dl. So P into dx and what is the horizontal component of the force? P into dl into cos theta – that is – Pdy. So let us call this as so this is after all on an element. So let us call this as so this vertical force is nothing but the lift force because the free stream flow is horizontal. So anything perpendicular to that relative to the flow is the lift force and this is the drag force. Elemental force so we have represented by differential quantities. Let us now try to find out this complex quantity again to use the complex calculus dfd-idfl. So that is equal to –Pdy-ipdx. So –ipdx-iddy. dx-iddy you can just write in a short hand notation of the complex conjugate of dz. Now what is the total force? You have to integrate it over the contour of the body. So why we are evaluating it? See because if we evaluate if we integrate this in the form of a complex number its components will give us the real and imaginary components will give the lift and the drag force together. So if we want to find out the contour integral of that is nothing but fd-ifl that is equal to the –i contour integral of Ppx-iddy.  This v square is like what?   What will be the integral contribution of this term? This term is like a constant right. It would come out of the integral. So it will be contour integral of something into dx plus something into dy. So what is the total dx as you have traversed along the contour 0? What is the total dy that you have traversed along the contour 0? So basically what you are doing by evaluating the contour integral is evaluating this integral as you are traversing the contour along a path particular direction. So this integral of this term will become 0. Let us try to look into say the form u plus i v into dx-i dy because that is one part of the integrant that you have to evaluate u plus i v into dx-i dy. So you can write it as u dx plus –i 2 dy. Now what can you say about this term? The contour of the body itself is a streamline. So you have dx by u equal to dy by v. So this term will be 0 on the contour of the body. So this is 0 because contour of the body is a streamline. Similarly you can show that this will become nothing but u-i v into dx plus i dy just the conjugate terms because there in place of this –i you will have a just a plus i and since this term is 0 it does not matter. So what you are left with? You are left with the equation.  So fd-ifl is equal to –i the contour integral of half rho u-i v. In place of u plus i v into dz star we can write this will not be there. It will go to the other side. So this will become plus. So u-i v into dz.  This is dz. What is the advantage of this? You see what is u-i v? This is df dg. So we can write this as i. So what is the advantage of this? If you know what is the complex potential capital F for the superposition of flow you may just use this simple integration. Equate its real and imaginary components to get the lift force and the drag force. This is known as Blasius force theorem. So it is as good as evaluation of an integral of the form. So half i, half i rho into some function of z dz where the function of z is df dz square. This is the mathematical form. Now let us look into this mathematical form for flow past a circular cylinder with a circulation. Before that we will try to understand one important thing that how to evaluate these integrals. There is a very simple way in complex integration known as residue theorem by which you may very simply evaluate such complex integrations. How it is possible? Let us say that you have a function fz which has a singularity at z equal to a. So this you may expand in the form of a series like you will have some negative powers and some positive powers. So let us say you have, so it is just like an extended form of a Taylor series where you also have the possibilities of incorporating the negative indices. This is known as Lorentz series. So what is known is that integral of fz dz is nothing but 2 pi i into the sum of residues, points of singularity in the domain. To understand that carefully let us assume that or just as an example let us assume that a equal to 0 as an example, a equal to 0 means 0 is a point of singularity like if you have a form of 1 by z or 1 by z square. So that has a point of singularity. Now the question is that when you have that as a point of singularity how do you handle that? So let us say that you want to evaluate an integral of, see when you have a equal to 0 that means you are having to deal with integrals of the form 1 by z, 1 by z square like that. Let us just look into one such form. Let us say you are interested to evaluate the integral of dz by z square because integral of the function evaluation is as good as like integral of the evaluation of the integrals of the corresponding terms term by term. So if you do that, so let us say z is equal to r e to the power i theta. So we may convert it from z to r theta system. So what is dz? i r e to the power i theta d theta. So this will become, so contour integral of this, i r e to the power i theta d theta by e to the power 2 i theta by r square. So what will be this? So now the basis of this is changed from theta equal to 0 to theta equal to 2 pi. So if you see now forget about the 1, forget about the i r, r square those contributions you will get a basic form e to the power – i theta d theta. So cos theta and sin theta both integrated from 0 to 2 pi. So what will that give? That will give 0. So this will be 0. Similarly the higher powers of z will do the same but if you just consider integral of dz by z, i r by, now in place of z r e to the power i theta, so i r by r integral d theta 0 to 2 pi. So that is 2 pi i. That means the key is this term. All other terms of that type 1 by z square or whatever, those terms do not contribute to the integration and the residue is nothing but it is coefficient. So c-1. So it is as good as, so if you have just one point of singularity, this residue is c with substitute-1. If you have many such points of singularity, just it will be some of such coefficients. So it is very straight forward actually. I mean it is not a very complicated theorem but a very convenient and powerful theorem. So now for our special case of flow past a circular cylinder with rotation or with circulation, we have to just evaluate what is df dz and what is the coefficient of 1 by z in that. That should be good enough for us to evaluate this integral. So let us do that.  Let us consider that we are assuming a clockwise circulation. So if we assume a clockwise circulation, we just put a plus sign here with an understanding that we are assuming a clockwise circulation. So the circulation is clockwise plus you have that p plus i cube whatever. What is important for us is df dz that is u infinity plus, sorry minus u infinity r square by z square plus i gamma by 2 pi 1 by z. What is our matter of evaluation that in the square of this one, what is the coefficient of 1 by z? That is the integration that we have to do for the Blasius force theorem. So what will be the coefficient? So it is just like a plus b plus c whole square. So the corresponding coefficient will come only when you have these 2 ac that term. So what will be that? u infinity i gamma by 2 pi. So this will become i rho by 2 into just 2 u infinity i gamma by 2 pi into there is a 2 pi, 2 pi i by the residue theorem it is 2 pi i into the residue. So what are the terms that get cancelled out? One is this 2 pi get cancelled out, these 2 gets cancelled out. So you have this as minus rho u infinity gamma i because i square is minus 1. So 1 i remains. So this is fd minus ifl. So what is the drag force? 0. What is the lift force? Rho u infinity gamma. So the drag force equal to 0 was thought of as a paradox for a long time because if you have a say circular cylinder or cylinder of any shape immersed in a flow when the fluid is flowing on the top of it there is some drag force that is experimentally calculated. But when this was evaluated theoretically then it gave rise to a 0 and this was a paradox for apparent paradox for a long time and it was called as a D'Alembert's paradox. The whole idea of this paradox is this is not at all a paradox. It was a paradox only at that time and the reason is that this neglected the effect of boundary layer. So it just considered a drag force with pure potential flow based calculation where viscous effects were neglected all together. But although the Reynolds number may be large but there is always a very thin layer called the boundary layer within which the viscous effect is very very important. So we cannot disregard that and calculate the drag force. So that was the whole origin of this apparent paradox. But this lift force was something which was found to be quite accurate even later on and one of the important consequences or conclusions of this is you see that in the lift force expression of course these are forces per unit length perpendicular to the plane of the figure that you have to keep in mind. This force is apparently not having anything in the expression which is a function of the shape of the body. So this type of lift force expression is not just valid for a circular cylinder although we establish this case through an example of a circular cylinder. But even for bodies of other shapes and one of the interesting shapes for which the flow induced lift force is very very important is the aerofoil shape and even for an aerofoil shape this similar expression for the lift force is valid. And this is therefore known as a very important theorem or very important expression in aerodynamics known as Kutta-Zukowski theorem. So it just gives basically an expression for the lift force. See this expression for lift force is something which may be quite interesting because what is happening here you have a circular cylinder you have a uniform flow like this you make the cylinder rotate like this okay. Once you make the cylinder rotate like this there is a force which is exerted on the cylinder towards the top just in place of a cylinder if you replace a sphere qualitatively it does not change much. So think of a case you have a ball which you are rotating with this type of axis and it just goes upwards that is the top spin of a ball. So this effect is known as Magnus effect in fluid dynamics. So with this background of potential flows we have come to a stage when we may appreciate that what is the consequence of the pressure distribution around the body at least and till the boundary layer gets separated the consequence of the pressure distribution is something which is consequential for flows of past bodies of all shapes except flat plate where the pressure gradient is not important. Now let us look into some bodies of other shapes we will not calculate similar expression because we have just seen a strategy of doing this and in fact there are many interesting transformations by which you may convert from one shape to the other. So for example you have a transformation which may transform a geometric transformation which may transform a very thin flat plate or a very thin foil like this into the shape of a circle. So there are similar so this transformation I mean there are certain special transformations which do that and in general these types of transformations are known as conformal mapping or conformal transformations. What they do basically if you have set of lines in the original configuration and a set of lines in the transform configuration it retains the angle between that to preserved in the original and in the transform coordinate system. But we will not go into that transformation we have in our one of our homework problems we will be giving you a problem to solve related to this transformation but I mean that you may do by considering all the basic theoretical backgrounds that we have already developed. Now what we will try to see next is that keeping in mind that shapes of different I mean bodies of different shapes may be generated by suitable transformation from a simple shape to may be a complex shape and so on. Generically we are in a position that if we know how to generate potential flows past simple shape bodies we may generate such flows even for bodies of complicated shapes. But what are the important consequences to do that we will study the flow past 2 important shapes of bodies one is like a aerofoil section and another is flow past a circular cylinder in somewhat more details than what we have done till now. So when we consider the real flow you have to keep in mind it is not the potential flow you have the boundary layer effect plus the effect due to the pressure distribution that we are seeing. So the pressure distribution is there which is imposed from the free stream into the boundary layer. So that you can calculate from the potential flow more or less it will not be very very inaccurate till there is boundary layer separation. But in reality there is boundary layer separation therefore in reality whatever the pressure distribution is predicted by the potential flow does not work. It works approximately well till the point of separation or very close to the point of separation but not far away from that. So first of all we will consider the case of say flow past aerofoil sections. We will just learn some important terminologies. So flow past aerofoil sections so let us first make a sketch of the section that we are considering. Just consider it like a section of like a aircraft wing okay. So now there are certain important dimensions which are given to it. One is the dimension of this transverse one and another is this one which is called the cord of the aerofoil. This is called the cord. If you calculate the lift and the drag force and the corresponding coefficient say you calculate the lift coefficient. So what is that? That is the lift force divided by half rho u infinity square into the reference area. We have seen that for flow past bodies layer of like shapes of cylinder or sphere like that the reference area is what? The reference area is like the projected area. In this case where the bodies are of much slender shape and slim shape so to say the reference area is called as a planform area. Reference area is different by engineering convention for different things like if you have a ship in water then it is the submerged area that is considered as a reference area. So it depends on what is the object that you are looking about. So reference area the planform area that is the area that you view from the top that is b into c. So that is the reference area and the second thing is that what is important is to know that what is the, so if you just draw the sketch of a section, so this is the cord of the aerofoil. Now what is the angle made by the incoming flow with this one? So let us say the incoming u infinity is like this. So the angle made by the u infinity with this cord let us say alpha this is known as angle of attack. This angle of attack is very very important because if the angle of attack is very small then the original flow is almost aligned with the direction of the cord. And then the flow boundary layer separation takes place almost at the trailing edge almost the entire flow is unseparated. But as you increase the angle more and more you will see that beyond a critical value of the angle there will be a very quick boundary layer separation. And because of that very quick boundary layer separation the lift force will go down. So if you just draw the coefficient of lift versus the angle alpha, so it will increase then it will come it will attain a maximum layer roughly at about say alpha equal to roughly 10 to 12 degree let us say 12 degree as an example. And then it falls down because then there is a large separated region because of the great mismatch between the direction of the flow and the direction of the cord the flow separation takes place quite quickly very early and this kind of situation that is at this angle it is called as that the aircraft or that aerofoil is stalled. So this is known as a stall. So one of the important objectives is to generate a lift force. So you may increase the value of alpha to generate a greater lift force if you want to go to a greater elevation. So you can see that if the aircraft has to have a different elevation say higher elevation it should have its aerofoil wing section oriented in a particular fashion with the relative velocity of the wing that is there outside or the relative velocity between the outer ambient and the aircraft. So that angle has to be adjusted properly to get the proper lift but once it is in a particular height or a particular level then you do not expect a net thrust or a net lift that means the weight is balanced by the lift force and it is just in sort of equilibrium. Similarly the drag force is balanced by the thrust. So if it is in a sort of an equilibrium and moving. So these are some of the important things. Let us look into some animated descriptions of how fluid flow takes place past an aerofoil. So first let us so we will see quickly that what are the impacts of different angles of attack. So if you calculate the lift force obviously that will come from the proper evaluation of the expression. So if you evaluate the proper lift force for flow past an aerofoil you will see that it will depend or it will increase with the alpha so long as you do not have a large separated region that is quite clear. So just think very physically if there was no separation and a flow is like from the bottom it would lift it very significantly. If it is horizontal and inclined with it how can it lift it? So as we increase the inclination you have a chance of lifting it more and more but if you have boundary layer separation altogether then that effect is lost. So let us look into the different cases of aerofoil flow. This is like sort of a potential flow type of situation. So this is a simulated condition of course. This is a flow visualization example. So see carefully some dies injected around the section and how the die takes its turn. So these are like examples of streak lines in a steady flow these are like stream lines. Let us look into the next example. So now we will see the effect of different angles of attack. So this is aerofoil section where you have 0 angle of attack. Now let us say 15 degree angle of attack. So with the increase of the angle of attack you see what is happening. You see a flow separation that is taking place quite quickly. So whatever is that circulating region that is the region of low pressure beyond the separation. Look for the angles of higher and higher orientations. You see that the effect of the separation becomes more and more severe. So these are just this is a 60 degree angle of attack. So you can see that as you increase the angle of attack the severity of the consequence of separation becomes more and more prominent. So that is one of the important things that we learn from this. Now if we go on to study the flow past different shape bodies till now in the boundary layer theory we have considered cases with high Reynolds number. The reason is quite obvious that if you have high Reynolds number then only the boundary layer theory you may apply. But there may be interesting cases when the flow is very very slow or the relative motion between the fluid and the solid is very very slow that is also flow past the body. Therefore let us quickly see what is the consequence of very low Reynolds number flows. So when we say very low Reynolds number flows it of course depends on the length scale what we are talking about to describe the Reynolds number. But let us say much much less than 1 that type of Reynolds number we are talking about. So such flows are called as creeping flows as if there is an object which is creeping or moving at a very slow pace relative to the fluid. So when you have such a situation think of the Navier-Stokes equation. In the Navier-Stokes equation the left hand side is a representative of the inertia forces. Right hand side the viscous term is a representative of the viscous force and then you have a pressure gradient force due to pressure gradient. So if the Reynolds number is very very small then obviously the inertia effects you may neglect. Now there will definitely be some error because there will always be some inertia effect may be present but if the flow is of very very low Reynolds number that effect is not predominant. So then the Navier-Stokes equation will take of the form 0 is equal to – gradient of p plus mu. Now what we will do is we will proceed further with the curl of both sides. So to do that we will keep in mind that if you want to evaluate for example this curl of this one that is del cross del cross v. So this identity we have used earlier also for developing some other theory. So now if you have a situation where this it is an incompressible flow as an example. So this will be 0 if it is incompressible flow and the curl of the velocity is what? It is the vorticity vector. So you can write this equation as 0 is equal to – gradient of p – mu into curl of the vorticity vector. We are replacing this del square v by this one. Now let us take a curl of both sides. So 0 is equal to clearly what is this curl of gradient of a scalar is 0. So vector identity this is 0 and this again we may write in the form of this identity. So we will write now what is this one? The vorticity is curl of the velocity. Divergence of a curl of this is 0. So this is 0 and therefore you come up with the final very simplified form. The Laplacian of the vorticity is 0 starting from this form. So one can start with a velocity or a stream function. Evaluate the vorticity as a function of that. So get a governing differential equation which does not have pressure. So this in a way what it has achieved? It has eliminated the pressure. So from this it is possible to get the velocity field. So once you get the velocity field it is possible to evaluate the drag forces and for a very low Reynolds number flow it is you will have the shear effect very very important. So you have the shear force. You have also the force due to pressure and then you may use that to calculate the net drag force and see for very low Reynolds number flow you do not have boundary layer theory valid because if you call something as boundary layer that is extended till infinity that is the viscous effects propagate far and far away from the body. So there is nothing called such a of course technically we may say that still it is a boundary layer with an infinite thickness but fundamentally the boundary layer theory is not valid because it is valid only if delta by L is very very small. So for such cases you do not have the boundary layer theory valid. So if you take an example of flow past a sphere if you go through this calculation you will find out that the drag force is 6 pi mu into u infinity into r where r is the radius of the sphere provided that the Reynolds number is much much less than 1 this is known as Stokes law. So in one of the assignments that we have given you we have asked you to prove this by solving the Navier-Stokes equation and its corresponding through this vorticity form that is given in one of our assignments if you evaluate it. So it will give you a practice of using the spherical polar coordinate system for solving the Navier-Stokes equation. Now if you want to calculate the drag coefficient the cd cd is the drag force divided by half rho u infinity square into the reference area is the projected area. So what is the projected area of a sphere? Pi r square. So what will be the expression for cd? 6 pi mu u infinity into r divided by half rho u infinity square into pi r square. So this will become 24 by rho u infinity into 2r by mu. Why we have used 2r? Because the diameter or the 2r is usually considered as the reference length scale for the Reynolds number. So this is 24 by Reynolds number based on the length scale of the diameter of the sphere. So low Reynolds number flows are the other extremes of the high Reynolds number flows where you have certain very interesting effects and in reality the combination of low and high Reynolds number flows are important that is we may cover a wide range starting from very low Reynolds number and we go further and further to very high Reynolds number. In our next lecture we will see a lot of video demonstrations on how the flow passed up body say of circular cylinder shape will change as you change the Reynolds number from a low value to a gradually very very high value and whatever we get inference from that we will look into the second set of the demonstrations where we will see the dynamics of sports balls that is how you may control the movement of the sports balls by utilizing the basic aerodynamics that we have learnt. So that we will do in the next lecture. Thank you.


At Arbor Day we've had a tradition of working with the city of Columbia with planting trees, lessons that teach students about the importance, how that cycle works with oxygen, carbon dioxide, all those things, so that our students learn the importance of trees and environment at a young age and that carries with them throughout their life. It is something we see every day, sometimes we may take our trees for granted, but part of the lesson and part of the activities that this event and others bring is showing students how trees impact our environment, impact our economy here in the state, so it's an opportunity to see that impact in action and so that they can be better citizens of our community if you will with regard to our environment and also how that works in our everyday life.


Personal Finance PowerPoint Presentation. Adjustable Rate Mortgage or ARM. Get ready to get financially fit by practicing personal finance. Most of this information can be found at Investopedia Adjustable Rate Mortgage. What happens when your interest rate goes up, which you can find online. Take a look at the references, resources, continue your research from there. This is by Donna Foscaldi, updated February 8th, 2022. Adjustable Rate Mortgage, what happens when your rate goes up? So clearly if we're in a home purchasing process, typically we can't put just simply the cash down upfront, but need to take some kind of loan. We need some kind of financing. The typical loan we think of is the 30 year fixed loan, which I would think of as the baseline type of loan, one which we will make comparisons to. One type of comparative loan you could think about is of course the adjustable rate loan, where we have the risk going from the lender more on over to the borrower as changes in the market going forward could have an impact on the rates. We gotta take that into consideration. So adjustable rate mortgages or ARMS can say borrowers a lot of money in interest rates over the short to immediate term. So obviously when you're thinking about this situation, typically the reason you would get an adjustable rate mortgage is because you would have a lower interest rate upfront. Just consider why this would happen. Remember we're in a business negotiation. This is a business setting. There's two people involved. We're not really talking about the seller here. We're talking about the buyer and the bank. And then the buyer takes the money and then we could talk about the seller and the buyer. But we got A and B here in the negotiation. We're thinking about the bank or the lender or the financial institution and the buyer. And clearly the bank wants to make the loan because they wanna make interest on the loan. However, they gotta mitigate the risk involved with the loan as well. Therefore, if they're gonna fix the rate, meaning if the rate's not going to change, that's gonna put more risk on the bank because if there's a rate change going forward into the future, if rates go up in other words, then the bank has now has a loan out there at a rate that's below the market rate possibly. So if they're able to lower the rate, then they can give you a lower upfront rate because they'd be taking on less risk. So it's all about the balance between the risk and the benefit. So if you take on more of the risk by saying, I'm gonna allow you to adjust the rate in some way, dependent upon some future circumstance, perhaps for example, changes in the market rates, then the bank has less risk and you'll be able to get lower rates typically upfront, but you have then the capacity or the possibility that rates will go up in the future that you need to take into consideration. It gets much more complex to do longer term plan and calculations that you wanna make sure that you're aware of. So but if you're holding one, when it's time for the interest rates to reset, you may face a much longer monthly mortgage bill, a much higher mortgage bill. So clearly if the rates then adjust and you're subject to the adjusting rates and the adjustments happen in an increase, an increase, then of course, you'll have higher bills at that point. That's fine if you can afford it, but if you are like the vast majority of Americans an increase in the amount you pay each month is likely to be hard to swallow. So clearly most people are trying to get as much house as they can. And if they're doing it with an adjustable rate mortgage, they're probably paying close to the top that they can pay at that point, any increase in the mortgage, especially a substantial one, could be detrimental to the budget. So what is an adjustable rate mortgage? Consider this, the resetting of adjustable rate mortgages during the financial crisis explains why in part, so many people were forced into foreclosure as had to sell their homes in short sales. So clearly if a lot of people are in adjustable rate mortgages and there is a decrease, I mean, if there's a decline in the economy, which or an increase in the interest rates, then that could force large amounts of people that weren't like prepared for that to happen into foreclosure. So that's of course why the banks, you would think would be in a situation where they would want to mitigate the risk and they might be more adverse or skeptical of adjustable rate mortgages or might have other conditions in play. But remember, anytime you have the third parties into the market, which includes government intervention, for example, selling things on a secondary market to quasi-government entities like Fannie Mae and Freddie Mac, that distorts the whole picture. So just because you can get a particular loan, in other words, doesn't mean of course that you should get the loan. And even if the benefits are there in order for you to allow you to qualify for a loan, that you want to make sure that you're taken into consider the factors that could happen in the future, which is more difficult when you're looking at an adjustable rate mortgage. While the arm has gotten a bum wrap, it's not a bad mortgage product provided borrowers know what they are getting into and what happens when an adjustable rate mortgage resets. So there's nothing really wrong with an arm, although it takes on more risk. Now at this point in time, it seems fairly clear that interest rates are on an uptick.  We don't really know. So you can kind of get a general idea in terms of whether the rates are going up or not and whether an arm would be a good risk to take or not. But whenever you're taking about a negotiating situation between A and B, in this case, the bank and the borrower, as long as both people are making decisions with all the information necessary to make an appropriate decision, that would be good. But in many situations, and again, when the government gets involved, oftentimes if the bank can offload some of the risk on their end to secondary markets or something like that, then the bank has an incentive to do more of those kind of riskier types of loans and the borrower might not have all the information that's gonna be this longer term information to make the best decisions. So there's nothing wrong with an arm, but the borrower has to be, you gotta be an informed borrower to determine whether or not it's worthwhile to take an adjustable rate loan. And again, we can't really depend on the financial institution, even if we feel like they're being enforced by the government in some way to provide these types of loans. That doesn't mean it's good. That means you have the opportunity or the possibility to take out that loan and then you wanna do your own research on it to see if it would be a beneficial thing to do or not. Interest rate changes with an arm in order to get a grasp on what is in store for you with an adjustable rate mortgage, you first have to understand how the product works. With an arm, borrowers lock in an interest rate, usually a low one for a set period of time. So you're gonna say, okay, if we go from a 30 year fixed to this arm, we're able to give you a lower rate than we would give you for the 30 year fixed and I used a 30 year fixed as the standard, right? That's like, if you had all the boxes checked off, I got good credit. I've got enough revenue that the bank is okay with that. And I have debt to income ratio is good, 30 year loan. Then that would be my baseline starting point. And then when we deviate from that, that can give you some kind of judgment to compare it to kind of where the market is at that baseline. So obviously if you're at the 30 year fixed and then you're saying, I'm gonna go to an arm, an adjustable rate, you would expect everything else equal that you would have a lower rate than the 30 year fixed. Now, some of the reason you might be going into an arm is because you might not have everything, all the boxes checked off. But again, that's kind of like the baseline. When that timeframe ends, the mortgage interest rate resets to whatever a prevailing interest rate is. So after whatever that timeframe is, then you gotta take a look at the market and the rates gonna reset and you don't have any control over it at that point. So you better be ready. So the initial period in which the rate doesn't change ranges anywhere from six months to 10 years, according to the Federal Home Loan Mortgage Corporation or Freddie Mac. Some arm products, the interest rate and borrower pays and the amount of the monthly payment can increase substantially later on in the loan. So clearly there could be a substantial increase depending on market conditions at that point. And obviously the bank could give a, the sweet loan amount at the beginning if they think that they're gonna be able to get the benefit back in the long run after that timeframe has passed. Because of the initial low interest rate, it can be attractive to borrowers, particularly those who don't plan to stay in their homes for too long or who are knowledgeable enough to refinance it if interest rates go up. So if you're savvy on the purchasing side of things and you're saying, hey, look, I'm just buying this home for a couple of years and then I'm gonna do something after that couple of years noting that worst case scenario, you could actually have the housing market go down and then you kind of be locked in at that point in time. So you're still taking on a substantial amount of risk if that were the case, but that would be more attractive to get an arm in that case. Also, when you see the change happening to the rates, then you could refinance at that point, possibly locking the rate at that point in time. That would be an option if you had the capacity to do that, if you had the capacity to act fast, but again, you're kind of judging the market in order to do that. If you're in a situation where you expect the rates are not gonna go up, the rates are gonna stay the same or possibly go down, then you're betting on the idea that the rates are gonna go down. Probably not what most people are betting on now at this point in time. Now most people are betting on the rates going up at least in the short run and possibly going up into the longer run depending on your trust on the Federal Reserve and the government and so on. So in recent years, and the market conditions, in recent years with interest rates hovering at record lows, borrowers who had an adjustable rate mortgage or adjusted didn't see too big a jump in their monthly payments. So we've had a fairly decent timeframe where the rates have been kind of held constant. Now you might argue they were artificially held constant. And again, anytime something happens which often happens in the home market, housing market, you have these longer time frames, there's still business cycles, there's ups and downs, but they tend to be longer and you have government incentives in there to try to keep the status quo for a long time. So they've been keeping the interest rates pretty low pretty much artificially for a long time. That means at some point, if something hits it, it's kind of like the immune system is down and they don't really have as much recourse because the government is already doing everything they can to do something. So at this point in time, we might have hit a point where it looks like the government doesn't have the ammo anymore to keep rates artificially low but that's just my perspective. It's possible that they do and things will, the other argument would be every 10 years or so people get the argument of, well, things have been fixed, things are good now, the government has figured it out, we're never gonna have a decrease in the market again, interest rates will never go above so much percent because economics has been figured out, but and then it's disproved every 10 years or so. So we'll see what the trend happens in the future. So in any case, but that could change depending on how much and how quickly the Federal Reserve raises its benchmark rate. So know your adjustable rate period in order to determine whether an arm is a good fit, borrowers have to understand some basics about these loans in essence. The adjustment period is the period between interest rate changes. So take for instance an adjustable rate mortgage that has an adjustment period of one year. The mortgage product would be called a one year arm and the interest rate and thus the monthly mortgage payment would be changed once every year. So then they would lock you in for basically a year and then the year had passed, they make the adjustment, whatever that adjustment is, it might not be, then they make the adjustment on a yearly basis. So if the adjustment period is three years, it's called a three year arm and the rate would change every three years. So that would mean of course you'd have three years before they then adjust the rate in that case. Notice that if you're talking about shorter timeframes like a one year adjustment, that would you would think be more taking more risk away from the bank than a three year. So once you start thinking about what kind of adjustable arms are in there, you can have different factors on the adjustable arm. If you have a three year adjustable arm, well now you've got a longer cushion of time which you're somewhat more stagnant where you can depend on and therefore, whereas the bank is taking on the risk during that three year time period if rates were fluctuating substantially within that range. Whereas if you're talking about a one year, that means that you're only getting that static timeframe for one year and the bank again is taking on less risk at that time because they get to re-up to whatever they think is reasonable based on market conditions every year in that case. So that would mean if you were comparing the one year to the three year, it's possible that the bank would give you a better rate on the one year arm than the three year arm. So now you've got different levels of risk versus reward and the interplay between risk versus reward less risk to the bank, the more favorable terms they'll be able to give. So more risk that you take on the more favorable terms the bank is gonna be able to give in general. So there are also some hybrid products like a five one year arm which gives you a fixed rate for the first five years after which interest rate adjusts once every year. So now you get that five year timeframe upfront while I'm fixing it, I'm locking it down for five years and then after that point in time you could have that substantial difference depending on what if there's substantial change in the market. So understand the basics for the rate change in addition to the knowledge of how often your arm will adjust, borrowers have to understand the basis for the change and the interest rate lenders base arm rates on various indexes with the most common being the one year instant maturity treasury securities, the cost of funds index and the prime rate. So meaning these are gonna be rates that should give you kind of a broad indication of market conditions.  In other words, you might say, well, how are they gonna know what the rate should be at something? Do they just make it up at that point? No, they're gonna go on some kind of market rate that isn't under their specific control and then base it off of that rate, right? That would be the general idea. Before taking out an arm, make sure to ask the lender which index will be used and examine how it has fluctuated in the past. So you can try to think of what the fluctuations have been. You're probably not gonna be able to guess exactly what's gonna happen in the future, of course, but you might get a general idea of what's going on in the market. Like right now, again, you would expect rates to go up, they're kind of on the increase. Again, some people will argue that it's gonna be a short-term increase and the Fed will stop it down and the economy is strong and it'll be fixed going forward and other people are less, have a little less faith in the process but we don't really know, you don't really know, right? So if you think you're gonna get it exact, you're probably not because you'd be out guessing the market which is a difficult thing to do. So you want to basically try to just mitigate your risk when you're making your decision-making process, taking it into consideration adverse conditions and trying to see what would happen and say like a worst case scenario, would you be able to deal with that? How likely is that to happen and so on? So avoid payments, shock. So one of the biggest risks arm borrowers face when their loan adjusts is payment shock when the monthly mortgage payment rises substantially because of the rate adjustment.  I had a case of payment shock. It was terrible. This can cause hardship on the borrower's part if they can't afford to make the new payments. So that clearly would be a problem. To prevent sticker shock, which is something I get all the time because I'm allergic to that glue that they put on the back of the stickers, it puts me into shock. But in any case, to prevent sticker shock from happening to you, be sure to stay on top of the interest rates as your adjustment period approaches. So you're gonna be saying, okay, when's that adjustment period happened? I'm gonna brace myself for the sticker shock, be ready budget plan. And then so you know what's happening. According to the consumer financial protection board, the CFPB mortgage services are required to send you an estimate of your new payment. So they're gonna say, hey, here's your payment. It's coming, the payment is coming, be ready. So if the arm is resetting for the first time, that estimate should be sent to you seven to eight months before the adjustment. So you get the seven to eight month time period to brace yourself. So if the loan has adjusted before, you'll be notified two to four months ahead of time. What's more, with the first notification, lenders must provide options that you can explore if you can't afford the new rate, as well as information about how to contact a HUD approved housing counselor. So knowing ahead of time what the new payment is going to be will give you the time to budget for it, shop around for a better loan or get help figuring out what your options are. So you might say, okay, this is happening at this point. Do I have, can I refinancing or something? What are my options? What do I do? I'm gonna sit here and wave with my arms wildly and scream at the wall or you can try to refinance or something like that or budget or take some action. So the bottom line, taking out an adjustable rate mortgage doesn't have to be a risky endeavor as long as you understand what happens when your mortgage interest rates reset. So unlike fixed mortgages, mortgages where you pay the same interest rate over the life of the loan with an arm, the interest rate will change after a period of time. And in some cases, it may rise significantly. So again, the idea would be that you're shifting the risk from the bank to the borrower, you're lowering at least the first payments in order to do so. It got a bad rap. These arms did because they were part of the mortgage downturn, the housing bubble, downturn and so on. But it's not a bad thing that the loans itself, it's just that obviously both sides of the table need to understand the benefits and the risks involved with it in order to make an appropriate type of decision. And again, if there's outside incentives, governments for example, putting in incentives programs that clearly incentivize banks to not be as transparent or to kind of push those more risky loans then the buyers might not have as much information to be going into the negotiation properly. But if you do have that information, if you're going in with your eyes open and you're saying, hey look, this is what I plan to be doing. I'm taking on more risk. I know I'm taking on more risk and I have a plan for it. That's why I'm doing it. Then it could be a good option. So knowing ahead of time how much more you'll owe or may owe each month can prevent sticker shocks. So don't do that sticker shock and don't do those sticker, that glue on the back of the stickers. Just keep it away, that glue, because it's so more important, it can help ensure that you are able to make your mortgage payments each month.