We're just going to wait one more minute as people are continuing to join. If you could help me out and let me know in the go-to webinar questions panel, let me know if you can hear me. That would be awesome. You can enter in the color shirt you're wearing today. We will wait one more minute and then get started with. Hi, everyone. We're just waiting maybe 30 more seconds. People are still joining. If you could let me know that you can hear me by just typing in your name or whatever you want in the go-to webinar questions module, that would be very helpful. Thank you so much, everyone. We are going to go ahead and get started. I wanted to welcome everyone today to the Give Education Training webinar. My name is Dawn, and I'm going to be leading you through today's presentation. I have a few housekeeping items to note before jumping in. First, I want everyone to know that the webinar will be recorded and posted in the toolkit on the Give Education site under the Resources tab. And then you can use the go-to webinar questions slash chat module to send across any questions that you have during the presentation, and we'll get to as many as we can after the webinar. So again, my name is Dawn. I'm with Mighty Cause, the platform for Give Education Day. I also have Carrie on from Alumni Nations. She and Josh, who's also here from Central High School Foundation, have both been working really hard to really help make this giving day great for everyone. So I wanted to welcome both of them. And Carrie, if you have anything you'd like to say, then now is a great opportunity. Thank you, Dawn, so much. Again, this is Carrie Dayton with Alumni Nations. And I just wanted to say thank you all for attending this call. Today is really all about strategy and trying to help you understand or give you the tools rather that you need to set yourself up for success. And I specifically had asked Josh with Central High Foundation to come on the call today, the reason being they have had a tremendous amount of success with online giving days for their foundation. And Josh, I'm going to say that you are the expert oracle of how to raise funds with online giving and really engaging your guests and their platform. And so I wanted to just welcome you to listen to Josh, learn what he's going to do. And if you do have any questions or have any technical challenges or any questions or anything that I can do to help you make this a successful event, please don't hesitate to email me at the give givee-educationatalumniations.com. We will answer your questions. And if I don't know the answer, I will find someone who will help you. And I am here as a resource for you. Dawn, thank you so much. Yeah, and hello, everybody. Like Carrie said, my name is Josh Busy. And I'm the creative director and database administrator for the Omaha Central High School Foundation. And I believe this is our seventh consecutive giving day participation of some kind. And so a day like this is something that we've had a lot of success with in the past. And we've kind of worked it so we have a kind of a strategy every year for our campaign. So as Carrie mentioned, as you're going along, if you have any questions about maybe a campaign that we run in the past or any tips or suggestions, we would be happy or I would be happy to help you out. We do our best to kind of create a campaign for social media that ties in with quotes from some of our students or teachers and people that we impact at the school. And it's just an incentive for people that want to give and participate. And Dawn has a lot of great stuff for us to discuss today, including like a matching gift possibility. And that's something that we've taken advantage of quite a bit. My boss, my executive director, Michelle Roberts, tries to reach out to donors who she knows that will participate ahead of time and secure a matching gift. So it incentivize people to want to participate in our day of giving. And yeah, so if you have any questions, feel free to reach out. But there's a lot of great stuff that Dawn's going to talk about today. And there will be a chance for questions at the end, I know. So I guess, Dawn, I can turn it back over to you. Actually, Josh, can I ask you a quick question? This is Carrie. Oh, sure. Josh, with regard to your participation and giving days in the past, would you say that you guys put a ton of time into it? Or is it an average amount of time with a great reward? What's your opinion on how it works for your organization? No, I definitely think it's something very manageable. I'd say, obviously, the first year is probably the hardest just because you're trying to get used to everything. But in all honesty, I think it's one of those things where you put in some work ahead of time. And then when the day of giving arrives, you kind of just have to sit back and see what happens. So ideally, you're scheduling social media posts ahead of time to kind of get the word out there. Maybe you send a postcard out a couple weeks out to let people know about the date and how to participate. But for the most part, most of your work should be happening ahead of time so that by the time the actual day arrives, you're in pretty good shape. But I would say for sure, obviously, the first year's the hardest. But I mean, it's a very manageable process. It should be super overwhelming or daunting. It's a great way for people to get involved and participate. So the platform is super easy to use and set up. So I don't think it should be a time-consuming process. Great, thank you so much, Josh, Don, thank you. Yep, yeah, thanks to you both. Like Josh mentioned, I am gonna be going through just a little more in-depth look at email marketing, social media marketing, later on in the presentation. And again, if you have any questions at all, please feel free to put them in that questions module and we'll get to them at the end. We are just really excited to partner with both of you for this inaugural event. And we're looking forward to providing the technical support as everyone gears up for the big day.  We've been around since 2006 and we're actually one of the first platforms to host giving days. So we've been doing this kind of event for a long time and we're just really excited to host to help host Give Education this year. So here's a look at today's agenda. We're gonna be going over some of the basics for the Give Education Giving Day. Then we're gonna go through the prizes available during the Giving Day and then move into strategies that you can use to really make this campaign successful for you. And then again, we'll do a Q&A session at the end. So if you do have a question, feel free to type it in that questions box and we will see it and be able to answer it at the end. So Give Education basic. Give Education is hosted by alumni nations and is going to take place on March 24th. It's a 24 hour giving day that runs from midnight to midnight central time. Early giving started on March 1st, but the main giving push is definitely going to be on March 24th. So there's still obviously plenty of time to register, get set up and start soliciting donations. Registration is required for this Giving Day and really any 501-MT3 organization or school any schools with NCEES codes are welcome to participate and there's no cost to register. So first things first, if you haven't already done so you're going to need to register your organization for Give Education to register, just go to give-education.com and click register. On the registration page, you can search for your organization and create an account if you've never used money cause before. And once you take that step, a short registration form will appear and you can fill that out and click submit and that'll complete your registration. Then within 24 hours you'll receive an email with next steps to help your organization get onto the site, customize and really plan for success.  And of course, if you have any questions at all please don't hesitate to email the Mighty Cost support at supportatmightycost.com. So once you've filled out and submitted your registration form you'll want to click on the user icon in the upper right on the give-education.com site to access your organization account. Your organization account is gonna be the hub of your activity for the Give Education Giving Day. So I recommend taking some time to get to know your account dashboard that'll appear on the left hand side of your organization account. So when you log in, you'll automatically land in your overview section. So this is where you'll find a really handy to-do list that outlines some great next steps that you can take to customize your profile on the site as well as metrics that will come in handy once you start actually raising funds. And then under the fund raising section on your dashboard you can customize your organization page by toggling on the edit mode. You can include page metrics like adding a goal for the Giving Day that will enable a progress bar on your page which is really handy when you wanna send people there they can see very easily how close you are to your, to the goal that you've entered in. Then within the fund raising section you'll also find a checkout flow which we're gonna talk about later on as well as a matching grants tool which we're also going to touch on later. And then below that fund raising section on your dashboard is a reports section. This is where you'll be able to preview and export different types of donation reports, disbursements reports, et cetera. And then you can manage your organization settings like URL customization and admin control from your settings section within the dashboard. So jumping into the overall profile for your Give Education account your profile is the face of your organization for the Giving Day. So you're gonna wanna make sure it looks good and represents your organization well. And just so you know, your profile link is the link that you'll wanna share with your supporters to ask them to donate to your Give Education page. So to share your page just copy and paste that URL into an email or a social post or wherever you're advertising the campaign. And then as you're going through your to-do list you'll wanna customize your profile to match your organization's brand. You can change your theme color to match your logo. You can upload media to your gallery to add some visual interest on your page. And your story or description is really the centerpiece of your organization profile. So in your story you can put your mission statement, you can add photos and a video. You can embed something like if you have an existing video that's on YouTube or Vimeo you can embed that into your story. So then when people come to your profile as you're promoting Give Education Day they'll be able to watch that video right on your profile. So this story section is just really where you can go in depth about your work. You can make a strong appeal to donors just tell them why your organization needs their support and you can show the impact of your work here as well. So after you get registered I really recommend spending some time customizing this profile because really the more work you put into it your donors are going to notice that and the more information that they know about your organization and really what you're focusing on that'll help them to know oh I definitely want to donate to this organization. They know what you need then they'll be sure to complete that. So the next item that I really recommend customizing is your organization's checkout flow. So the checkout flow is located within your fundraiser section on the dashboard. The checkout flow is what your donors experience when they make a donation towards your organization. The first part to customize is your checkout steps. This is probably one of the more important features to focus on when you're setting up your organization's profile page. The checkout flow section just gives you a lot of control over the donation process for your organization. It allows you to opt into collecting certain information you want from donors like addresses and phone numbers. You can also set up custom suggested donation amounts and add descriptions to help tie those amounts to items or services that your organization provides which just strengthens your appeal to donate. So the checkout steps within your checkout flow also allow you to preview the whole checkout process without having to make a test donation. So you can see what your final process looks like and then use that to edit yourself if needed. So moving on from the dashboard in your Mighty Cause Give Education account I just want to make sure I mentioned the really great tools that you can use as you get ready for Give Education. And that's going to be the organization toolkit. The toolkit is located on the home page for Give Education Giving Day which is give-education.com. The toolkit has a lot of tips and tricks. It's got FAQs, it's got walkthroughs. It has templates you can use for your email and social media to help you get inspired and really figure out how to promote your campaign. And then the toolkit is also where you'll be able to find today's training recording as well. And we do have the previous training recording already on demand within the toolkit. So if you missed that one, feel free to go back and watch at any time. Definitely check out the toolkit if you haven't already and refer back to it as you're planning your campaign. Prizes. So this year, $6,000 in prizes will be given away to participating organizations. These prizes are provided by the Comer Family Foundation. Basically every hour, during Give Education Giving Day, there's gonna be $250 given away to a randomly selected organization that has raised funds during that hour. So the first winner will be pulled at 1 a.m. Central on March 24th and we'll continue pulling those winners with a new winner being drawn every hour until the Giving Day ends. So for more details on the prizes, definitely check out the Prizes tab on give-education.com. Okay, so jumping into campaign strategy. So the prizes provided during Give Education Giving Day, definitely allow for additional incentive for your organization to get donations every hour of the day. So keep tabs on which organizations have won so far. If you've won yet, there will be a list of all the winners that will show on the site on March 24th. So you'll be able to check that out and keep track of it. And if you haven't won yet during the day, then that's definitely a great messaging piece to keep your donors and supporters updated on if you've won one of those random hourly prizes yet or if you're close to your own goal that you've set for Give Education as well. Basically, emphasize how much is at stake during the Giving Day. How much money, could the money that you raise due for your organization, what would that money help you achieve? Tie everything back into your overall messaging about what you do, why you do it, to just really get people excited about helping you win that money. And then if you do win one of the prizes during the day, then that is an awesome messaging piece to just really pump your donors up and get them excited. Just everyone likes to win things. Whenever, if you are one of the winners during the day, then make sure that you communicate that to your donors and just get them pumped up about it as well. So mapping out your campaign with mini goals. Give Education is a 24 hour event. So the trick to making the most of it is to sustain your fundraising momentum. One really great way to do that and to make sure that your campaign's on track too is just that mini goals for your organization to help generate buzz and build excitement. So set mini goals for certain hours in the day so you can keep people excited about your goals and continue working towards your overall fundraising goal that you've set for the day. Mini goals just really help sustain your fundraising momentum and they get people excited about helping you reach your goal. So to set mini goals, you'll wanna think about your overall fundraising goal for the day and what you'll need to raise or if your goal is like number of donors, how many donors that you'll need to get each hour or section of the day to reach your goal. So be sure to keep in mind too when your donors are most active to kind of adjust your hourly or section goals accordingly. And when I would say section, I mean like our goal this morning until 10 is to get this many donors and then our goal during the lunchtime portion of the day is to get this many and then our goal in the evening is to get this many. So just keep track of everything, adjust those goals depending on when your donors are most active.  And we'll talk more about matching grants in just a little bit. Something else that you can do to get your campaign rolling is to ask for seed donations. So seed donations are donations from people in your organization's inner circle that essentially break the ice with donors. No one really likes to be the first donor. There are exceptions. Some people are like really love to be the first donor but for a lot of organizations, what works best is if they have a little bit of momentum built up before they really make some big pushes. So to help get that ball rolling that people ask for a seed donation from their board, staff, especially those who are director or C-suite level leaders at your organization, volunteers are great. People to ask for those initial first donations before you go out to your wide net.  Seed donations do not have to be huge donations but getting a little bit in the bank by tapping people in your inner circle really does help you move your campaign forward and get those donations coming in. So securing a matching grant. A great strategy for driving donations on a giving day is securing a matching grant. So a matching grant is essentially a large donation that your organization leverages to bring in other smaller donations by offering that large donation up as a match. So for instance, if you had someone willing to give you $1,000 instead of just putting that money in the bank and calling it a day you could use it as a matching grant. So basically you take that $1,000 and say to your supporters, hey between this hour and this hour our donations are gonna be matched up to $1,000 which basically allows those donors those smaller donors to double their donation. So you can do a lot within our matching grants tool within your account.  Our matching grants tool we talked about it in the last training recording. So it's just really cool. It's a complex little tool that just allows you to do a ton with your matching grant. And on our platform specifically we have seen that matching grants especially on a giving day can be a really powerful way to drive donations. So since a matching grant is ultimately just a large donation you'll wanna follow the same process as you would to create one when you secure matching gifts.  So people you should consider as prospects for a matching grant are board members. Sometimes an individual board member will be happy to provide a match but one thing you can also consider is asking your board to work together as a group to provide a match. So if your board still has to pay dues for instance you could utilize their dues by turning that into a matching grant. A major gift donors who have given large donations to your organization in the past are also really good prospects and providing a matching grant can be a really fun way to liven up their donation. So instead of just writing a check they're helping your organization grow and drive other donations as well. So you can also give a donor who provides a matching grant some extra recognition when you're promoting the match. So major gift donors who like a little shout out are even better for those matching grant prospects because of that. Corporate sponsors are also really good prospects. It's a fun proactive way for corporate sponsors to get involved in a public way and draw attention to their philanthropy. So at this stage in the game you can start making phone calls, sending out emails and just start cultivating those prospects by letting them know what you're doing. We're participating in Give Education Day. We would really like to utilize a match to make our giving day exciting. This is especially helpful if in the middle of the day when you know your donors are not super active then maybe having a match to kind of make that portion of the day more profitable for you then a match might be a great opportunity at that time too. In the coming weeks then as you're kind of searching out these prospects you can make the ask and then shore up the details of the match as well. You can also have more than one match running at the same time on Mighty Cause. So if you get a lot of great responses, that's awesome. Don't feel like you have to just pick and choose one. So at the end of the day a matching grant is really a marketing tool. So in order to make the most of your matching grant you're gonna need to promote it. So the first step is going on to the matching grant tool on your Give Education profile and adding the matching grant there. There are some marketing tools built right into the platform for your matching grant. So for example, if you set one up as soon as it goes live it's gonna put a little sticker on your donate button that notifies everyone coming to your profile that the matching grant is active. There's gonna be some changes to your checkout process to reflect the match and the match also gets listed on your organization profile. You'll also wanna add some information to your story though especially if it's a big match and you'll wanna promote it on your social media channels. You know, send out an email basically pull out all the stops to let all of your followers know about the match. Countdowns also add urgency. So counting down and sharing your progress can be a great way to get people excited and urge them to stop what they're doing and make a donation. So since Give Education Giving Day is a 24 hour event if you do have a matching grant you're welcome to set it up for the whole entire day but if you know that your donors are most active between certain hours like I said before you could set up the match to just last for a few hours so that you can really try and drum up on the urgency during those few hours. But again, it's totally up to you the tool is very flexible. If you're not quite sure how you wanna do it or what would provide you the most success then feel free to email Carrie or Josh or our support team at Mighty Cause to get some strategy insight into your specific organization. So moving on from matching grants I wanna talk a little bit about ambassadors. So ambassadors are people who are usually in your organization's inner circle who can help boost your campaign. So that includes board members, volunteers, volunteers especially ones who are highly engaged staff members, et cetera. Utilizing ambassadors can help you break out of your list of existing supporters and engage new people, new donors people that you wouldn't otherwise have access to. So an ambassador can help you in a few different ways they can simply share a link to your page within their social circle to ask their family and friends to donate. And that'll obviously help boost your campaign to give education. So like if you have a board member for instance who's very well connected this can be a really big boost or your ambassadors can help by getting involved in peer-to-peer fundraising. So peer-to-peer fundraising is a fundraising technique where you basically deputize your supporters to fundraise on your behalf. The Mighty Cause platform is set up for really easy peer-to-peer fundraising and peer-to-peer fundraising can be a great way to kind of shake up your campaign and acquire new donors. So if you wanted to try peer-to-peer basically what you do is you ask supporters to set up a fundraising page for your organization to help you raise funds for give education.  How they came to work with you why your work is important to them. And their story, their participation doesn't distract or draw attention away from your campaign. They're operating alongside your campaign. They're reaching out to people they know personally for donations, which in most cases their friends and colleagues and family they're not people that your organization would typically have access to to solicit for donations. So in the peer-to-peer process you're actually picking up new donors most of the time. So for people like your board, volunteer staff, program alumni, this can be a really great way for them to get involved without just being asked to give money. And it can make the whole experience just more meaningful for them than just making a donation or sharing a link. So you could take this peer-to-peer fundraising and make it part of your stewarding process, building sustaining relationship with that specific reporter. We've seen organizations on the platform get some really great peer-to-peer action going by just inviting people on social media or sending them an email asking for their help. And for younger people who have a big social network and are really comfortable online, maybe they don't have a lot of cash to give but asking them to be a fundraiser for you, this can be a really great way for them to help out and make a meaningful contribution for your organization. So to help make things easier for them, for your ambassadors, you can set up a fundraising page template for them within your account. In that template, you can add image, talking points, facts and logos. You can even offer to help them set up their page since hopefully you'll be pretty comfortable on the platform soon if you're not already. Organizations that utilize peer-to-peer fundraising do tend to raise more money on giving days. So it's definitely worth talking about how you can incorporate into your campaign strategy. So the timeline is great to get started on this. We've got a couple of weeks until Give Education Giving Day. So now is a great time to kind of put out the word to ask people to join, get them comfortable with it. And then there's not like a ton of time for them to back out beforehand. So now is a great time to put the word out there and then start putting things together to send to them, get them signed up, all that good stuff. So that they can start raising money as soon as they're on the site really, but big pushes on March 24th. So if you're able to generate a lot of interest in peer-to-peer, or let's say you've done that and you've participated in a Giving Day in the past and you've done that before or you wanna try something new, I would consider trying out team or event fundraising as well. So teams and events can be a great way for groups of people who wanna fundraise together like your board or companies or just volunteer groups to make that statement for your organization. Teams and events can be a great way to get people working together and united for your cause. They also are a great way to inspire some friendly competition to keep people motivated at the same time. So the difference between teams and events is basically that an event allows individuals and groups of people to participate and fundraise together while a team fundraiser is just a group of individuals working together toward a collective goal. So one of the cool things about using our teams or events products for Giving Day is that there's tools built in to make it managing really easy. So for instance, you can create a template fundraiser for a team and event as well. Then as we discussed previously, it really helps people get set up on the site quickly since it pre-bills some of those sections on their pages. You can also email team and event members through the platform to keep them motivated. So teams and events are essentially just more complex peer-to-peer campaigns. They can be a really great option if you've got a lot of people willing to fundraise for you or if you've done peer-to-peer before and just kinda wanna try your hand at a new type of campaign for a Giving Day. So your email list is going to be one of the most important tools during Give Education because emails are a direct line to your supporters. So unlike social media, you don't have to worry about an algorithm getting in your way or preventing people from seeing what you send them because unless they've unsubscribed, your message will end up right up in their inbox and probably send them a notification on their phone as well. So I wanna talk for a bit about email strategy because that's going to be important for Give Education.  Most people read their email on their phone these days. So they're not going to be interested in reading a novel. They're gonna wanna be able to skim it and get to the point. People are much more likely to read emails that pertain directly to them. So I highly recommend segmenting your email list by sorting donors into a few key groups. Donors who have given a lot or give on a regular basis, one-time donors and people who have utilized your services but have never donated. Other segmentation groups can be your board, volunteers and so on. So you don't need to craft entirely new emails to reach each of these groups, but you can tweak small things about the emails for each group to make it more personal. So for instance, in an email to volunteers, you wanna acknowledge how they already help your organization. And you wouldn't wanna send an email to a major gift donor asking for a $25 donation. So be strategic about it. Really think about what kind of messaging you wanna send to each group. Just identify those key segments and tailor your message to them. Again, when an email is tailored to who the recipient is and the relationship they have with your organization, they are much more likely to read it and take action on it. And how you segment depends on the program you're using, but most services like constant contact and MailChimp, they use tag to segment people on your email list. So one of the first things in creating your email strategy is definitely going through and identifying the different segments that you wanna target and kind of working through to figure out what message you wanna send to each. The other thing that you'll wanna pay attention to is the timing of your email. So I would recommend taking the time to schedule as much as you can beforehand. And if you have a template email ready, for things that you need to send out day of, like a blast email asking people to help you get to your campaign goal or an announcement that you won one of the hourly prizes. As I mentioned before, most people read their email on their phones these days. So make sure that you choose a mobile friendly email template and definitely test it out beforehand. Look at it on an iPhone, an Android, make sure that it looks the way that you want it to look. And then leading up to the event, I also recommend doing some AB testing, especially with subject lines, because you'll wanna make sure that not only people are receiving your emails, but people are driven to open your emails for give education as well. So try out different subject line formats, try things like, if your audience is like that, add emojis, see what works better to get people to open your email. So when you're sending out the critical emails, this way you'll have an idea of what tends to work with your email list. AB testing, if you're new to that term is basically splitting an email up 50-50 and testing a variable. So let's say you're testing a button color or a subject line, half your list gets email A with one subject line, the other half gets email B with another subject line, and then whichever email gets the most opens basically wins. For button color or placement, the email with the most clicks would win. So you just wanna be careful about testing too much, throwing too many variables in there, because then it's really hard to say why something won the test and performed better. Lastly, your call to actions within your emails should be very clear and action oriented. Call the actions like give now, donate now, help us today. More passive calls to actions like thanks for donating or please contribute aren't as effective. So you're gonna wanna be crystal clear and urgent with your call to actions within your emails. Have multiple people look at the emails that you write and create within your email program. That way you get other people's opinions. If you've already done a lot of extensive email testing and work within your organization, that's awesome. You're ahead of the game and you already have an idea of what works with your supporters. So for a high stakes day, like give education, we really recommend staying in your comfort zone when it comes to social media. Go where your audience is. What I mean by that is if you've never logged into TikTok before or if you've never logged in in your whole life, that's fine. You do not need to use TikTok for give education if that's the case. If however, you have 1,000 followers on your Facebook page but only a handful on Instagram, then you should probably spend more time and effort on promoting your campaign on Facebook than Instagram. Put your efforts into the platform where you're most likely to reach people and have an impact. So I definitely, Josh kind of touched on this at the beginning, schedule any posts in addition to emails that you can't ahead of time just to save yourself a lot of trouble during the giving day and leading up to it. Get your key content scheduled. You can do that with Facebook's publishing tools or Creator Studio. You can go into Tweet Deck and schedule your tweets. Basically save any live posting on the day of the first stuff that needs to be done that day. Like if you want to tweet or post every time somebody donates and thank them, that would be an example of something you'd save for day of. If you wanna save posts for updates on your progress, prize announcement, get templates set up early. That way, if you do win a prize, whenever someone does donate, you can just copy and paste and enter in the applicable information and really save yourself a lot of trouble on the day of. And doing this allows you to quickly respond to comments on those posts. It allows you to interact with your followers more since interacting with followers is really important on social media and the interaction can also help you in terms of the algorithm since most platforms show priority to posts with lots of engagement. So scheduling everything ahead of time, writing out templates for yourself, make sure you sit down and take some time to do that. That way on the day of, all that you're really actively doing that day besides monitoring your page is putting out announcements for real time stuff and then interacting with the posts that you have previously scheduled that people are just now commenting on. I do recommend budgeting a little money if you're able to boost some posts or promote some tweets and on social media, $20 for an ad can go a pretty long way. So you'll wanna make sure that your ad is targeted properly. And if you're not sure how to target an ad, you can always just default to targeting people who just like your page already or follow you. So in terms of what types of content will do well on social media, it depends a little bit on the platform but in general, photos and videos do really well. And you may wanna consider doing something out of the box like a Facebook live video or a watch party for a campaign video to help generate some of that additional engagement because that kind of stuff, anything visual is really algorithm friendly and will kind of push you up and bump you up on people's news feeds. And then of course too, if you're asking them to share then that just gets you additional exposure to people outside of your supporter group and is always a great ask in those posts. So finally, when you're planning your campaign, follow up is also very important to consider. So when you're planning your content, you'll also wanna plan your thank you to donors, things like making a video or a photo of your staff can be really, really great for this. Be sure to talk about the impact of the funds that you've raised and kind of close the loop on your campaign. So if you were fundraising for something specific during give education or if you had a specific goal that you were really marketing that day, then those would be great opportunities for you to kind of close the loop. Obviously you'll wanna send out emails periodically on your progress during the day, but closing the loop after the fact is also a great practice too. And then you'll also wanna make sure that you've got a good onboarding plan in place for any new donors that you've acquired during give education to basically encourage them to come back and donate again. If you collected addresses, then mailing donors or any existing donors, information or a welcome packet, that can be a great way to kind of steward them. And then you can also create an automated email journey where donors can get more information about what you do and why it's important to support your work. So really take into consideration after give education day. How are you going to steward the donors that have given new donors that you've acquired? What are you going to do to keep them engaged with your organization? So make sure that you include that in your planning strategy as well as you're getting set up for the day. So lastly, as we wrap this up, I wanna make sure that all of our support contact information is here for you to reference. This support information specifically for Mighty Cause as the technical partner for give education day, if you have any technical questions or if you wanna strategize around some of our tools that we provide within your accounts, you can reach our support team at supportatmightycause.com. They're available Monday through Friday, nine to five Eastern. You can also call them at the number there as well. And then on give education day specifically, they'll be available 24 hours. So if you have any problems at all during the course of the day on give education giving day, our support team will be here to help you as well. Okay, so let me see if there were any questions that came in. Hey, Don, I can speak for just briefly about a couple of thoughts that I had as you're going along. So for the many goals, some organizations, we haven't done this in the past, but I know some organizations have done such a thing where they set certain thresholds and if they have a donor that will give an additional amount of a certain threshold is reached. So for example, say you raised $10,000 and the donor says, I will give an additional $5,000 on talk of my matching gift. If you reach that threshold, kind of another incentive for people, if you're really close to that $10,000 for people to say, oh yeah, like I need to donate because we're so close. And for us, the busiest times of the day I would say are in the morning, that 4 a.m. to 9 a.m. time. And actually at night, we have a decent number of people who donate after work. So we kind of have like a late push in the day for some donations. For seed donations, I would definitely suggest even if it's just the people in your office making a donation, a $5 donation, it adds some legitimacy and creates some momentum for your profile if you're able to show, oh look, five people have already donated and like $50 has already been raised. It kind of creates that sense of participation, I would say, or like I said adds legitimacy almost to the cause. Our email strategy, we usually try to send an email out maybe a week or the week of. The giving day, we send an email on the morning of. The giving day and then depending on how close we are to reaching our matching gift goal, we might send a second email throughout the day. We use MailChimp, that's the platform that we've used and had a lot of success with. And then after the event, we try to send a postcard to thank our donors. I'm the graphic designer and so I have the postcard already created before the event is even beginning, but all I need to know before we go to print, of course, is how much money we raise and how many donors we have. So that's something else where, kind of what I mentioned earlier, a lot of this stuff you can kind of already have completed ahead of time. You just kind of need to have some of the pieces in place. So when the giving day comes around, everything's already kind of scheduled out and you're kind of, you've already spread the word, you've already educated people. It just has to see how things go. Yep. And one of the other things in terms of follow-up, having everything scheduled ahead of time is just really convenient when it comes to timing. Really the recommendation is to make sure that donors are thanked in some capacity within at least 24 hours after they've given. The nice thing with your account that you have with on Mighty Cos for Give Education is you can customize that initial thank you receipt that gets sent out automatically after a donation so you know your donors will be getting thanked and get their donation receipt right away. So that's been done, but then knowing that, we also have a postcard to send out and they're all ready to go by end of week that day or that the week of Give Education or the first thing the following week. So just having it scheduled in a timely manner to know that this is already done, I don't have to worry about it and people will feel they'll get nice warm fuzzy feelings from donating to us because we're thanking them and letting them know that they're helping make a difference in what we do. We do have a couple of questions that came in. One person asked, do you require that the match go through the portal? I have a donor who doesn't want the fees to be taken out of their match. Great question. We do not require matching sponsors to donate through the website. So if you have, if you've been fortunate to secure a matching grant and that specific sponsor does not want to pay online, totally fine. Our tool has a way for you to still count those, their donation into your total. And so as people donate, like let's say you set up a one-to-one match, then you could set the tool up so that whenever somebody donates $10, then their donation actually goes up by 20 on your total count. So you don't have, your sponsor does not have to pay through the site. And so sometimes that helps in terms of securing a matching grant. And then you're still able to utilize that grant on the site and get the benefits from it. Good question. And then the next question, how far out should you send your first email or social media post? Another great question. Josh, you had mentioned that you guys typically will send an email out the week of. That's obviously great practice. Since early giving, for Give Education is already open, you could really send an email or social post whenever you're ready prior to Give Education because the site's accepting the donation. So if donors go to your profile to check it out from the email or social post that you put out there, they will be able to complete an action. It's not like they're gonna be going there and not be able to do anything and then maybe forget to come back later. So if you wanted to send it out as soon as possible, you could definitely do that. But at least sending them something the week of to let them know this is happening, mark your calendars. If you wanna donate ahead of time, if you know you're gonna be out of town that day and not able to donate, please consider donating ahead of time to help us out during this giving day, then that's a great option too. Yeah, I was just gonna hop in and say we, about a month out, we say in our newsletter, kind of save the day. We don't really offer a lot of details, but we kind of just try to get it on people's radars and calendars. We really start hitting the social media posts hard about two weeks out, I would say. So we try to every day have some kind of post about impact. Maybe it's a pick for us, we use a lot of pictures and quotes from students. So we try to highlight the best that we can where some of our teacher classroom grants are going to students and teachers and field trips, stuff like that. So there's a lot of very heavy visuals on our social media in the lead up to the actual day. And then on the day of it's still some of that, but for the most part, we're just trying to inform people of how close we are to hitting some of our goals or certain thresholds for goal amounts. So again, a lot of the things we're doing, we're kind of just trying to build momentum, get the date out there, especially since people can donate now, we include the link to donate in all of our posts and encourage people to even kind of double dip. So maybe donate early and then also try to donate again on the actual day of giving since people can do that. So that's another option as well. Yes, and I mean, that's a great point too. A lot of people are willing to give more than once. So if they give during that early giving period, don't hesitate to send them information again the day of to ask them to donate an additional time, especially if during the giving day, you have something more exciting going on like a match, then don't exclude them from your communications just because they've already given. A lot of donors are willing to give more than one time when it comes to causes they care about. The other thing that I wanna mention really quickly is you do it, like let's say for your give education, giving day campaign, you do receive cash or check donations. You do have the ability to input those, record those on your account and that way they show up in your giving day total. There's no fees charged on the cash or check donations that you record, it's literally just a record. So if you do receive any sort of cash or check donations or let's say you have an older donor base who prefers to give by check, totally fine. Just collect what you can and then you can input it in on your profile. That way those donations, you can see your total raised for the day and any records that you do input on your profile will be included in your donation report. Again, there's no fees charged on the offline or cash or check donations, but that is an option as well. I think that was all the questions that we had. If anyone thinks of something later or you need some help with anything else, our support team is ready, support at mightycost.com. Carrie or Josh, do you guys have anything additional that you wanna end with before we let people go? I just had a question. I think some people might be interested. How do people get the payouts from the day of giving? Such a great question. So basically there's two options on MightyCause. We can do direct deposit. So if you sign up for direct deposit, then you can get your funds twice a month. So give education day is March 24th, which means organizations who utilize direct deposits would get their funds on the following month on the 10th. So April, around April 10th. We also allow check donations too, or check disbursements rather. So if you don't wanna sign up for direct deposit or let's say there's too much red tape with your district or whatever, check donation is possible and we will send the check to the address that you have on file with the IRS. You can find that address within your profile as well under the settings. And then if it needs to be changed at all, you can just contact us and we do ask for additional paperwork to confirm that that's the address that you want it sent to. But yeah, so check or direct deposit. And it's all automatic. So you'll get your funds through whatever method you decide. Okay. So two minutes left, but I just wanna thank everyone again for your interest in Give Education Day. We're really, really excited to be the platform for this inaugural Education Giving Day. Again, if you have any questions or think of anything, please don't hesitate to reach out. And our team is here to help you strategize, help you get set up, whatever you need, let us know and we'll be happy to help. And lastly, again, this webinar was recorded. So I will be posting the recording in the toolkit on the Give Education site, which is give-education.com. I'll be posting that by tomorrow morning at the latest. So if you wanna review anything, have any of your team members watch it, then it'll be up there in the toolkit for you to check out at any time. So thank you again for your attention and your time. And we are just so excited and I hope everyone has a great rest of their day.


The basic rules of the road say drivers of vehicles, bicyclists, and pedestrians will obey traffic control devices on AUAB unless otherwise directed by security forces or fire officials. Although these are the official rules, driving can be a unique experience to control differences, which can also lead to hazardous situations. Take stop signs for example. Some drivers treat them as yield signs. You might often see drivers roll through these stop signs without slowing down or checking their surroundings. That's why it's important for you to exercise extreme caution when driving on a base. Speaking of posted signs, you might have noticed that the speed limits here on a base are in kilometers per hour rather than miles per hour. This could make it feel like the speed limit is slow in certain areas of the base, but please remember, they are set for the safety of yourself and others using the road. We work with many different militaries all from different nations with unique driving behaviors. Bottom line, be cautious around intersections and mindful of your speed.


Hello and welcome to lecture number 16 of this lecture series on jet aircraft propulsion. We have been talking about axial compressors over the last few lectures and we are going to continue our discussion on axial axial flow compressors today. And this would be the last lecture on the theory of axial flow compressors and subsequently in the next lecture we are going to discuss about we will basically have a tutorial on axial compressors. Now, what in today's lecture we are going to cover two very important aspects of axial flow compressors. One of them is to do with a very fundamental form of design of axial flow compressor blades and that is what we will initiate our discussion on. And subsequently we are going to discuss about the characteristics, performance characteristics of single and multi stage axial flow compressors. And the performance characteristics is a very important part of axial flow compressor design and also it plays a very significant role in the performance of the engine as a whole. Because the compressor is to be matched with the turbine and matching of the compressor and turbine is in some way related to the performance characteristics. And that also reflects the performance of the engine as a whole in the sense that performance characteristics would tell us that what is the band of operation for this particular compressor wherein the operation is safe. And what happens if we exceed these bands of operation obviously the performance is going to decreed. And in some cases as we shall see today the compressor might enter might enter into certain unstable modes of operation, which can affect which can drastically affect the performance and working of an engine as a whole. So, in this context it is very important for us to understand the significance of performance characteristics. So, but before that let us discuss about a very fundamental form of or method of design of axial flow compressors in what is known as a free vortex design. And we will see what is the principle behind a free vortex design and why we need to consider such a design methodology. Subsequently we will discuss about single and multi stage compressors. And we will also towards end of the lecture discuss in brief about two instability modes of operation of an axial compressor. These are known as rotating stall and surge. So, that will take up towards the end of the lecture. So, we are going to discuss begin the lecture today with the discussion on what is known as free vortex design. And subsequently we will take up the performance characteristics. So, let us discuss about what is meant by free vortex design. But before that let me give you a background about what is meant by radial equilibrium. Basically radial equilibrium is one of the conditions that needs to be satisfied in the sense that all the flow parameters in terms of velocity pressure etcetera need in the radial direction also needs to be considered. In whatever design methodology or the velocity triangle etcetera which we have discussed over the last few lectures, we have not really considered variations of properties in the radial direction. We have assumed that in a particular cross section the blade speed is a constant, the tangential velocity is constant and many other properties remain a constant. But in an actual blade you know that the blade speed is going to vary all the way from the hub to the tip. And so how do you consider or account for this in a design methodology? So, radial variations of all these properties need to be considered and factored into when we take up a serious design of an axial compressor blade. And that is one of the principles that will be made use of in what we will be discussing about in free vortex design. So, for a realistic design what we need to do is to consider radial variations of the following. One is of course the blade speed which we know will vary anyway from hub to tip because it is a direct function of the radius. The other parameter that will need to be considered is the axial velocity then the radial variation in tangential velocity and static pressure. So, if we have to maintain a reasonably uniform flow at the compressor exit and why do we need to maintain that we need to maintain a uniform flow at the compressor exit because the next stage or that is going to follow a particular stage will depend upon what is coming into this stage from the previous one. And so if there is a uniform flow that exits one stage of an axial compressor that is also beneficial for the succeeding stages. So, one of the ways of ensuring that we can have a fairly uniform flow exiting the compressor is to ensure that there is a uniform distribution of specific work input at each of the cross sections that is starting from the hub all the way to the tip. If we can maintain or at least try to maintain relatively uniform distribution of specific work in the radial direction then it is possible that we should be able to get a fairly uniform flow at the compressor outlet which is obviously a good thing for the succeeding stages. So, now in order to ensure that we have uniform specific radial work distribution now we know that the enthalpy difference across a stage delta or even a compressor delta H naught is equal to enthalpy rise across a compressor stage that is equal to the product of the blade speed that is u multiplied by delta C w right that is something we had discussed in one of the earlier lectures that the enthalpy rise specific enthalpy rise will be equal to the product of the blade speed times the difference in the tangential velocity between the inlet and exit. So, delta C w is basically the difference in the tangential velocity. So, if we equate this now we are trying to maintain a relatively uniform specific work input. So, we should be able to get some hints from this as to how we can do that. So, we know that delta H naught which is specific enthalpy change across a stage is equal to blade speed times delta C w or C theta and which is equal to omega r which basically the blade speed is the product of the angular velocity times the radius this multiplied by delta C w is basically equal to the specific work input. So, what this means is that for a given rotational speed that is if we fix omega then r times delta C w must be a constant. So, the product of the radius and the tangential velocity must be a constant. Now, this can ensure that we can have for a given rotational speed we can ensure that the specific work is a constant. So, one configuration or one design methodology which can ensure that this is satisfied is known as the free vortex design and in a free vortex design basically we keep the product r times C w it is kept a constant at the exit for each of these blade rows and. So, given the axial velocity and the blade speed at different cross sections from the hub to tip we have the axial velocity and so on and. So, from hub to tip we know all these parameters and if we to if you were to ensure that the product r times C w is kept a constant we can actually solve the velocity triangle all the way from hub to tip. So, in free vortex design methodology that is one of the basic principles trying to keep the product r times C w a constant which will ensure that the specific work input required for this particular blade would be a constant. So, if that is the case we can ensure that r times C w is kept a constant. Now, for example let us take a look at one example wherein we can see what happens if we were to maintain the velocity triangles if you were to solve the velocity triangles keeping r times C w a constant if you were to do that. So, let me repeat what I was saying. So, basically if we have r times delta C w which we are trying to maintain a constant for different cross sections all the way from hub to the tip then from axial velocity which is known at the inlet and blade speed we can solve the velocity triangle. So, let us take one example of what would happen if you were to do this what is shown here are three cross sections at the hub the mean and the tip and their corresponding velocity triangles and if you were to use a free vortex method for designing such a blade this is how the velocity triangles are likely to look like this is just one example. Now, let us take a look at the hub section where we have the velocity triangle at the inlet and exit of the blade. So, this particular velocity triangle which is shown here C 1 is absolute velocity entering the blade at the leading edge at the hub v 1 is the corresponding relative velocity u is the blade speed and at the exit we have C 2 which is the velocity absolute velocity exiting the blade and v 2 which is the relative velocity exiting the blade and if you try to maintain r times C w a constant we can see that the blade cross section well the orientation of the blade itself changes drastically as we move from the hub towards the tip which means that and we can see the velocity triangles at the mean and also at the tip. So, what you notice is that if you were to were to stack these different cross sections from the hub all the way to the tip you can clearly see that the blade is going to be twisted it is no longer going to be a straight blade as we have been discussing so far where we can at least the velocity triangles we have discussed in the last few lectures we were seeing that the blades were relatively straight. Now, here with the free vortex design methodology we can see that the blade is no longer going to remain straight it is going to have a fairly significant twist the other significant thing that you can try and notice is that during our discussion on degree of reaction we have seen that when degree of reaction is close to 0.5 or is equal to 0.5 the velocity triangles become symmetric. So, that is something that you can probably try to see here at the mean cross section of the blade we can see that the velocity triangles are more or less symmetric and this is an indication that the degree of reaction here is likely to be close to 0.5 whereas, at the hub and the tip it is quite different. And what comes out is that in most of the design process that one would encounter the degree of reaction approaches 0 close to the hub it becomes very low and towards the tip it becomes much higher than 0.5 it might approach 1 and even though we are maintaining a degree of reaction of around 0.5 at the mean section. So, this is just an example of one case of how we can use free vortex design methodology to design a blade cross section and there are of course, the other variants of this methodology which we shall discuss now and by using certain modifications to the free vortex design methodology we can of course, arrive at other methods of designing a blade. Now, what is important in all these methods is that we need to satisfy the conditions of radial equilibrium that is the equations of motion the three dimensional equations of motion needs to be satisfied that is one fundamental requirement in all these design methodologies. So, based on this besides free vortex wherein we have r times C w is equal to constant there are other methods like forced vortex which is r times C w is equal to a r square exponential method which could be r times C w is equal to a r plus b and constant reaction which is r C w is a r square plus b where a and b are of course, constants and needs to be fixed apriary. So, these are other variants of methods wherein we can try to ensure a constant specific radial work and that is required because we would like to maintain fairly uniform set of properties the exit of particular rotor blade. So, free vortex design basically is one of the atoms or one of the methods by which we can try to ensure a constant specific radial work criteria. So, what we have discussed in brief for now is one of the ways of one of the methods or popular methods of design of an axial compressor blade and what we shall discuss next would be as I had discussed initially we shall be talking about the different performance characteristics of single and multi stage axial compressors. So, we will begin our discussion with the consideration of a single stage axial flow compressor will first discuss about performance characteristics of single stage axial compressor followed by this we will we will be talking about the multi stage characteristics. Now, a stage of an axial compressor as you probably know by now comprises of a rotor and a stator. So, let us take up a characteristic rotor and a stator and then we will discuss about how we can characterize this particular rotor and see what happens as you change different properties. Now, we have a typical axial compressor stage here which consists of a set of rotor blades followed by a set of stator blades we have already seen this velocity triangle earlier on. At the rotor inlet we have an absolute velocity entering at c 1 relative velocity at v 1 blade speed is u. And at the exit of the rotor we have absolute velocity is equal to c 2 and relative velocity is v 2 and blade speed of course, remains the same it is u. And this velocity triangle is what is basically goes into the stator it is basically the absolute velocity that enters the stator and exits at velocity of c 3 leaving at an angle alpha. So, here we can see as the as the flow enters the rotor and exits the rotor there is a deceleration in terms of the relative velocity and that is what leads to diffusion. And similarly, as the flow enters the stator the absolute velocity decelerates from c 3 from c 2 to c 3 leading to diffusion. So, the combined velocity triangle is something which we had discussed earlier as well. If you were to overlap the two velocity triangles at the inlet and exit of the rotor then we get a combined velocity triangle with all the angles indicated here as well. Let me just quickly go through this these velocity triangles we have absolute velocity at an angle alpha 1 at the inlet of the rotor and relative velocity v 1 at an angle beta 1 at the inlet. At the exit we have the absolute velocity leaving the rotor at an angle alpha 2 and relative velocity leaving the rotor at angle beta 2. And c w 1 corresponds to the tangential component of the absolute velocity c w 2 corresponds to the tangential component of the absolute velocity at the exit of the rotor.  Delta c w is the difference between c w 2 and c w 1 and c a is the axial component of the absolute velocity. So, with this in mind from the velocity triangles we can infer that c w 2 is equal to u minus c a tan beta 2. So, let us see where that comes from c w 2 is this component. This should be equal to u which is the blade speed minus this particular component which is what is given by c a tan beta 2. So, c a is this component c a times tan beta 2 is this component. So, u minus c a tan beta 2 is c w 2. Similarly, c w 1 is c a tan alpha. c w 1 is this. So, c a tan alpha 1 is this component. Now, we also know that delta H naught that is the specific enthalpy rise across a stage should be equal to u times delta c w. And delta c w is c w 2 minus c w 1. So, if we were to substitute for c w 2 and c w 1 here we get delta H naught is equal to u multiplied by u minus c a times tan alpha 1 plus tan beta 2. Or delta c w by u is equal to delta H naught divided by u square which is 1 minus c a divided by u into tan alpha 1 plus tan beta 2. So, what we have here is the specific work ratio or the stage loading which is expressed in terms of two important parameters. One is the axial velocity and the blade speed and of course, the angles the blade the inlet angle alpha 1 and the blade outlet angle. So, the specific work ratio or the blade loading has been expressed in terms of two distinct parameters. So, what this means is that if we were to change the design mass flow rate mass flow rate is directly proportional to the axial velocity c a. And so, if we change design mass flow rate or the blade speed either of them is going to affect the loading characteristics because delta c w by u is equal to 1 minus c a by u into tan alpha 1 plus tan beta 2. So, the stage loading is directly a function of either the mass flow or the blade speed besides of course, the angle. So, if you are to assume that the inlet angle angles are fixed this means that the performance of the stage will directly depend upon the mass flow which is in turn equal to the axial velocity or the blade speed u that is this ratio c a by u plays a significant role in the stage performance characteristics. So, the blade performance or the stage performance is a direct function of the ratio c a by u. And so, we have already defined c a by u if you are called earlier on we have defined c a by u as the blade loading in terms of c a by u as we had defined the last lecture. So, let us look at what happens as you change c a by u that is basically the flow coefficient as defined last slide. So, what we have plotted here are two parameters one is the stage loading in terms of what we have just now derived delta h naught by u square which is delta c w by u and the stage efficiency. So, delta c w by u is equal to delta h naught by u square that is 1 minus c a by u into tan alpha 1 plus tan beta 2. So, if you want to plot this for different values of the flow coefficient c a by u as we keep changing the flow coefficient what happens to this loading characteristic. So, what we will see is the one indicated by this thick blue line refers to the measured loading characteristics as c a by u is changed which could be either by changing the mass flow or by the speed. So, we observe characteristic as shown here which means that as we reduce the mass flow the pressure rise or the stage loading increases up to a certain point and then subsequently if we continue to reduce the mass flow it will decrease and this has certain implications which we will discuss during the multi stage performance characteristic as well. And so, we see that at this point that is indicated by c a by u which is corresponding to the design condition we have this particular characteristic and if we were to look at the corresponding stage efficiency we get the maximum efficiency around that point that is corresponding to c a by u design which is of course, less than 100 percent of there is a certain efficiency associated with the stage. And if we were to draw a tangent at this point where c a by u is given by this point if you draw a tangent at that point the slope of that is basically given by tan alpha 1 plus tan beta 2 corresponding to the design condition. So, this the slope of this line basically is what is given here by tan alpha 1 plus tan beta 2 corresponding to design condition. So, what is shown here is basically how a particular stage of an axial compressor is going to behave as we change the mass flow or the speed. So, in terms of either of them we have represented them by the flow coefficient that is c a by u. So, as c a by u changes how is it that the stage performance changes in terms of the loading of the stage as well as the efficiency of the stage. So, what we see here is that basically the measured performance and how it performs in terms of the efficiency corresponding to c a by u design. So, what this means is that as one deviates from c a by u design the stage is not going to perform as it is supposed to be for the design conditions. So, what we will see next is for off design conditions where in c a by u is either greater than c a by u design or c a by u is less than c a by u design how the performance of the stage would get affected. So, let us take a look at what happens in terms of the velocity triangles as well as what happens on the blade as we change the flow coefficient from its design value. So, as c a by u let us take a look at three different cases here the first case is when c a by u is actually equal to the design condition then we have the stage performing normally that is normal operation under design condition of this particular stage. So, the velocity triangle with the relative velocity at entering the stage at an angle beta 1 and absolute velocity at c 1 c 1 entering at alpha 1. Now let us consider the first off design condition that is if c a by u is less than c a by u design and if you assume that this is only by reducing the axial velocity or changing the mass flow alone keeping the blade speed same that means if we fix u and just change the mass flow it means that for a lower mass flow how the stage is going to perform. So, as c a is less than c a by c a design this means that this axial velocity is now less than the design axial velocity as we reduce axial velocity what happens is we can see the velocity triangle getting altered. So, this was the original velocity triangle and as we reduce axial velocity the velocity triangle has gotten altered because c a is now less than c a design which means that the relative velocity will now enter the rotor at an angle which is greater than what it was at the design condition. So, here beta 1 is actually greater than the beta 1 at design. So, and so therefore, it means that if the flow approaches the stage at a very high angle of incidence which is basically positive incidence here there is a chance that the flow would separate from the suction surface of this rotor. So, there is flow separation occurring here on the suction surface of this blade therefore, this is basically a positive incidence flow separation. The other extreme of this is if c a by u is greater than c a by u design which means c a is greater than c a design if u were to be fixed if blade speed is fixed then there is a possibility that the incidence is now negative and there could be flow separation from the pressure surface and that basically means a negative incidence flow separation flow might separate from the pressure surface of the blade. So, these are two extreme cases of operation of the stage even the flow coefficient is different from the design flow coefficient it is either less than design flow coefficient or greater than if it is less than if the blade speed is fixed then c a is less than the design axial velocity and the flow separates from the suction might separate from the suction surface leading to positive incidence separation. And if c a is greater than c a design then it could lead to negative incidence separation. So, having understood some aspects of a single stage performance characteristic of an axial compressor let us now move on to a multi stage axial compressor that is if there are multiple number of these stages one after another how does the performance how can we evaluate the performance of such an axial compressor. Now, to do that we need to understand what are the different parameters or variance or variables based on which we can evaluate this performance. So, at the outlet of the compressor we are interested in two things one is the pressure ratio stagnation pressure ratio across the compressor and the other parameter is the efficiency of this compressor. So, these are two parameters which we will be interested in and. So, we will need to see what are the other variables on which these two parameters depend that is efficiency and pressure ratio of the compressor expressed in terms of other variables. So, that we can then go ahead and look at the performance characteristics. So, for a multi stage compressor now we are going to denote the inlet of the multi stage compressor by station 1 and exit by of the compressor by 2 that means the overall pressure ratio of the compressor is P 0 2 by P 0 So, the compressor outlet pressure and efficiency, acentropic efficiency is a function of several properties or several variables. So, it could be mass flow rate the inlet stagnation pressure inlet stagnation temperature the rotational speed the ratio of specific heats gas constant for the working fluid viscosity of the working fluid the design of the blades themselves and the diameter D. So, these are different parameters on which the outlet pressure outlet stagnation pressure and efficiency depend upon. So, if we were to express this in terms of non-dimensional parameters. So, if we carry out dimension analysis of these terms that we have listed here then non-dimensional parameters come out to be on the left hand side we have the stagnation pressure ratio of the compressor P 0 2 by P 0 1 and the efficiency. This is a function of mass flow rate multiplied by square root of gamma R T 0 1 divided by P 0 1 D square. The other parameter is omega D by square root of gamma R T 0 1 then we have omega D square by viscosity nu then the ratio of specific heats and the design. Now, for a particular design suppose we have frozen a particular design and we can assume that gamma which is for this particular fluid and the viscosity do not really affect the performance significantly or do not change much. And for a given diameter of the engine because the design has been frozen the diameter is also frozen and the gas constant fixed. So, this particular set of non-dimensional parameters will now reduce to P 0 2 by P 0 1 and efficiency as a function of m dot root T 0 1 by P 0 1 and n times T 0 square root of T 0 1 where n is the rotational speed. So, the pressure ratio and efficiency of the compressor depends upon basically two parameters here one corresponding to mass flow rate and the other corresponding to the rotational speed. And so, let us further reduce it in terms of standard conditions which we will see that is known as corrected mass flow and corrected speed. So, pressure ratio and efficiency as a function of mass flow rate times square root of inlet stagnation temperature divided by P 0 1 and the speed that is n times square root of T 0 1. So, we will further express them in terms of standard conditions that is standard ambient pressure and temperature. So, that this performance characteristics can be used in any other ambient conditions. So, that once it is standardized and corrected it can be used under other conditions as well. So, if we process this further in terms of standard day pressure and temperature then we have P 0 2 by P 0 1 and efficiency are functions of m dot square root of T theta divided by delta and n divided by square root of theta. Where theta is equal to T 0 1 divided by T 0 1 standard day and delta is equal to P 0 1 divided by P 0 1 standard day where T 0 1 standard day is 288.15 Kelvin and P 0 1 standard day is 101.325 kilo Pascal. So, if we were to express these performance parameters in terms of the characteristics of a compressor multi stage compressor. So, what I have shown here is one typical performance characteristic of a particular axial compressor. We have on the y axis the pressure ratio P 0 2 by P 0 1 and expressed in terms of the x axis that is mass flow rate m dot square root of theta divided by delta. We also have the efficiency as a function of the mass flow rate m dot square root of theta by delta. So, let us look at the pressure ratio characteristics first. So, a typical compressor multi stage axial compressor characteristic would comprise of pressure ratio versus mass flow at different speeds. So, these lines that are shown here are for different speed ratios that is n by square root of theta that is for different speeds of rotation how the characteristics change. Let us take up one particular speed let us say 0.7. So, what this line means is that as we change the mass flow rate as the mass flow reduces the pressure ratio increases and it reaches a particular peak beyond which the pressure ratio which is not shown here it will droop or it will fall drastically. The reason why I am not shown points on to the left hand side of this line which is indicated here as surge line is because after this point if the compressor operation is unstable because of what is known as surge which I will discuss shortly what is meant by surge. So, there is an instability in the compressor performance which prohibits compressor operation on the left hand side of this line. So, compressor operation is possible stable compressor operation is possible only on towards the right hand side of this particular line. So, the surge line dictates one of the limits of the compressor operation and. So, what performance characteristic here shows how the performance in terms of pressure ratio varies as we change the mass flow. We also have the efficiency characteristics shown here how the efficiency changes as we change the mass flow. So, we have peak efficiency corresponding to the mass flow which is shown here. So, for a particular mass flow at 0.85 speed we have the peak efficiency occurring at a mass flow somewhere around here and that is true for other mass flows as well. So, mass flow versus efficiency mass flow versus total pressure ratio both of these put together define the performance of a multi stage axial flow compressor. Now, let me take a closer look at the pressure ratio versus mass flow characteristic. So, you might have noticed here that the peak efficiency is occurring at a point which is slightly away from the surge line and at the same time I mentioned that operation on the left hand side of the surge line is not possible because of the presence of instabilities. So, we would like the compressor to be operating at a point at a safe operating line which is away from the surge line and. So, what is shown here in terms of this dotted line corresponds to the actual operating line of an engine which means we are not really operating very close we would not want to operate very close to the surge line because there is always a risk that the compressor might go into surge if there is a certain fluctuation in the mass flow rate. So, the engine is the compressor is usually operated or designed for operation along an operating line which is away from the surge line and the difference between these two points is basically referred to as the surge margin. So, there is always a certain margin provided between the engine operation and the surge line which indicates or denotes that there is a certain margin provided for safe operation of the compressor. So, surge line is one of the extremes of operation of the compressor where the engine actually operates slightly away from the surge line which is known as the engine operating line. So, the multi stage performance characteristic as defined here is in terms of the efficiency as well as the pressure ratio. So, in some books and literature you might also find that the efficiency plots are shown in the same pressure ratio plot as well. So, you will also find contours of constant efficiency plot around the same graph. Now, I mentioned that the axial compressor performance is limited by surge on one of the sides and that there is one of the instability modes of operation of the compressor. And so, before I discuss surge let me talk about yet another mode of instability which is known as the rotating stall. So, axial compressor performance is hindered by two instability modes based there are of course, other modes as well, but primarily two modes of instability one is known as rotating stall and the other is known as surge. Now, rotating stall is a non axisymmetric mode of instability and on the other hand surge is an axisymmetric mode of instability and it is periodic whereas, rotating stall is not necessarily periodic it is a periodic in nature, but both of these modes of operation eventually can hamper the performance of a compressor drastically. So, rotating stall basically involves progression around the blade annulus of a stall pattern that is the stall pattern progressively moves around the annulus of an axial compressor wherein either one or more adjacent blade passages are instantaneously stalled. And then the stall cell continuously moves or progresses around the annulus of the compressor. So, this means that rotating stall can lead to alternate loading and unloading of the blade which means that there is a possibility of fatigue failure eventually if rotating stall mode was to be present continuously. So, let us see what actually happens during rotating stall. Now, during rotating stall let us say there is a certain pocket of non uniformity in the incoming flow and this pocket of non uniformity may cause a certain one either one blade or a set of adjacent blades to operate under stall condition. So, here we have a non uniform flow that means there is a flow entering the compressor at very high incidence than the design condition. So, high non uniformity entering into this particular a set of blades causes this blade let us say to get to be to be stalling which means that as this blade stalls it also causes the flow entering the second the adjacent blade to enter at a higher incidence because the blades are actually rotating. So, there is also a relative motion here the blades rotate and because of this the non uniformity now progresses and moves towards the adjacent blade causing the adjacent blade also to now stall. Now, as this blade stalls it un stalls this particular blade which was earlier under stall because the flow is now deflected in this fashion here and also because of the rotation of the blades themselves. So, this stall blade which was undergoing a stall and this stall cell as you see here moves towards the adjacent blade and the new stall is now on this particular blade and eventually it unloads the previous blade which was undergoing stall. So, this continuously happens and this stall cell progressively moves from one end to the other around the annulus and what you can immediately see here is that the direction of rotation of the stall cell is opposite to that of the rotation of the blades themselves. So, rotating stall cells of rotate in a direction which is opposite to that of the rotor rotation and you can see the rotor rotation obviously for this compressor is in this direction from right to left whereas, the stall cells move from left to right. So, similarly on an annulus you can imagine that the rotating stall cells will actually move in a direction opposite to that of the rotor rotation. So, rotating stall is an instability which often precedes surge and we will see that little later and the stall patterns will obviously move in a direction which is opposite to that of rotor revolution and the frequency of rotation of stall cell of course, is not fixed it can keep changing, but it can be as high as about 50 percent of the rotor frequency and rotating stall may usually be initiated by the presence of a non-uniform flow impinging the rotor blades. So, what I have shown here are three different modes of operation of rotating stall one is that the rotating stall may be affecting only part of the span this is the annulus of the compressor this is the hub and this is the casing. So, rotating stall may affect a part of the span or it may be a full span stall that it affects all the way from hub to the tip and eventually it may lead to surge wherein the entire annulus undergoes a stall. So, this means that rotating stall is one of the precursors is likely to be one of the precursors of surge that is if rotating stall were to continue and progress leading to full annulus stall it may eventually lead to surge. So, which brings us to what is meant by what is actually meant by surge we have already seen a surge line in the compressor characteristic which was on the left hand side on one of the limits of compressor operation and I mentioned that you cannot really operate the compressor beyond the surge line because of the occurrence of surge itself. So, let us understand what we mean by surge now surge is surge line is obtained as by joining all those points on the speed lines of the compressor where surge is likely to occur. So, surge line is the locus of all the points of surge of a multi stage axial compressor. Surge basically involves fluctuation of fluid back and forth along the annulus axial fluctuation of the fluid of the working fluid and the entire annulus of the compressor is affected by surge which is why I mentioned that surge is axis symmetric that is the entire annulus of the compressor is affected by a separating flow and it is violent oscillation of the fluid back and forth. So, the onset of surge can lead to very drastic effects on the compressor and as the engine as a whole because compressor is feeding into the combustion chamber and then the turbine and so on which means that if there is something drastic happening to the compressor it will immediately affect the combustion chamber and therefore, the turbine which means the whole engine gets affected as a result of surge. So, surge is characterized by violent and periodic oscillations in the flow it might lead to flame blowout in the combustion chamber because if there is a back and forth movement of fluid in the combustion in the compressor it can lead to a flame out a blowout in the in the combustion chamber and obviously, it can lead to substantial damage of compressors which is why surge is something that always needs to be avoided designers always try to keep a safe margin between the surge line and the operating line which is basically known as the surge margin. I mentioned that there is a certain margin provided between the surge line and the engine operating line and this is basically referring to the surge margin and so designers would always like to keep a certain margin there. So, now let us now try to understand what we actually mean by surge and let me take up the performance characteristics once again we have the mass flow in terms of the flow coefficient I have taken only one stage of an axial compressor here we have flow coefficient and the pressure rise coefficient what happens to the stage performance as we keep changing the mass flow. Now, let us say we have the stage characteristics which have been plotted here and in solid line and the throttle characteristics in terms of these dashed lines which means that as we throttle the compressor as we reduce the mass flow the throttle characteristics you can see keeps changing and so this particular stage which was let us say operating at point A as we throttle the compressor will continuously move towards the left and it keeps moving along these throttle lines from A to B to C D and so on. But beyond a certain point what we see what are indicated by these points here with dash that is D dash C dash and B dash are those points which correspond to the unstable operation of the compressor and why is it exactly unstable because what happens here is that as we reduce mass flow in on the right hand side of this particular line let us say after on the right hand side of E as we reduce mass flow it is accompanied by an increase in the pressure ratio. Whereas, on the left hand side we have as we reduce the mass flow rate it also results in reduction in pressure ratio which means as the pressure ratio reduces the pressure downstream is lower than the pressure upstream and so there can lead to sudden fluctuation in mass flow rate and that is why operation on the left hand side of what is given here as the throttle characteristic can lead to an unstable operation of the compressor. So, what happens really here is that beyond this point which is given here as the tangent to the stage characteristic any point on the left hand side of this where the stage characteristic will have a positive slope which will mean that reduction in mass flow will be accompanied by a reverse flow which can fluctuate back and forth because momentarily you would have a lower pressure upstream than the downstream which means that there would be a reverse flow and as the flow moves from the downstream stages to the upstream stages there is a decrease in pressure downstream as compared to upstream and then this continues in a cycle leading to rapid fluctuations in the flow back and forth. So, this is what leads to what is meant by surge wherein there is a violent oscillation of mass flow back and forth and something that can be explained using the stage characteristic and the throttle characteristic. So, as we change the throttle characteristics from extreme left hand side right hand side as shown here as we keep throttling which means it indicates increasing flow resistance we obtain different performance characteristics as denoted here by these points, but all these points as you can see have a negative slope whereas as the stage characteristic reaches a point wherein the slope is positive that indicates that these are the points where basically the operation of the compressor is unstable and this is what is reflected in the multi stage characteristic as well. So, what I had shown was one particular line here and beyond this as you can see the slope will have will be basically positive whereas on this side we have a negative slope. So, operation of the compressor is safe on all these lines and all these points where the slope is positive and all the locus of all these points together constitute what is known as the surge line. So, operation of the compressor is unstable on the left hand side of the surge line whereas it is safe to operate the compressor on the right hand side of this surge line. So, surge is basically the one of the modes of instabilities of an axial compressor which is something that the designer would always want to eliminate and avoid and rotating stall is one of the possible one of possibly one of the precursors of surge and that is something that would eventually lead to the occurrence of surge. So, let me wind up today's lecture wherein we were discussing about two important aspects one was the stage characteristics the single stage characteristics as well as the multi stage performance characteristics of an axial compressor and the other aspect that we were discussing was the free vortex theory we started the lecture today with some preliminary discussion about the free vortex theory and how it can be used for in preliminary design of axial compressors. Subsequently we started discussing about single stage characteristics and how we can how we can basically evaluate the performance of a single stage by relating the flow coefficient to the pressure rise or the stage loading. And subsequently we discussed about multi stage performance characteristics in brief and then we also discussed about two modes of instabilities one is known as the rotating stall wherein a stall cell progressively moves along the annulus. We then saw that rotating stall can eventually or if allowed to progressively continue may lead to occurrence of surge as well wherein the entire annulus of the compressor undergoes flow separation or flow reversal and there could be rapid oscillations of fluctuations in the flow which could also lead to extensive damage to the engine as a whole. So, single stage multi stage performance characteristics the significance of that and also the free vortex theory these were some of the topics we had discussed in today's lecture. And what we will take up for tomorrow's well for the next lecture would be basically a tutorial on axial compressors and we will wind up our discussion on axial compressor with the next lecture which will basically be a tutorial. We will try to solve some problems pertaining to axial compressors and also we will have a few exercise problems which you can solve based on the discussion in the next lecture. So, let us take up these topics for discussion in the next lecture.