 So let's talk a little bit today about orthographic projection, basically a way that we can take three-dimensional objects and visualize them on a two-dimensional piece of paper. So for our example, since this is an aerospace class, let's take a look at a paper airplane. So if you follow along with me, what I would like you to do is I want you to go ahead and construct a paper airplane of your own. Take a few minutes, pause the video, and create for yourself a simple paper airplane. Now that you've completed it, let's talk a little bit about this three-dimensional paper airplane that you have. Notice it's a three-dimensional object. But in our three dimensions, there's many ways that we can look at this object. Right now, we're looking down at the top of the airplane. OK. But if we rotate it, we can take it, we can look at it from different perspectives. There are an infinite number of perspectives that we can look at to describe the airplane. The question sort of becomes, do we have to show all these pictures? Yes, a picture is worth 1,000 words. Do we have to show all these various pictures of this to get a sense for what the airplane really is? Well, it's definitely helpful, but that contains lots and lots of information. Can we get most of the information down simply by looking at it from a few perspectives? And because this is a three-dimensional object, we can actually convey almost all the information using just three sort of views. So we're going to start by considering, we're holding the plane here. Let's start by looking down on the plane. If you focus directly down on the plane, this is what we call the plan view. All right? So there's one way that we can look at the plane. Now I'm going to rotate the plane 90 degrees. I have two choices of how to rotate it 90 degrees. But instead of looking at it from the top to the bottom, let's rotate the plane 90 degrees. And we're going to look at it from the left side through to the right side. So this, depending on how you sort of orient or think about this, can either be called the front elevation or the side elevation. Now this is the side of our plane. So maybe we can call it the side elevation. But the idea, again, is that it's elevated. It's going across the bottom here. But then we're also going up and down. So that's the idea of an elevation. So now we've looked at it from the top, what we call the plan. From the side, what we call the side elevation. And then let's go ahead and rotate it one more time. 90 degrees from the side elevation. This is also an elevation, but this would be what we would call the front elevation, or perhaps the back elevation, depending on how you rotate it. But generally the terms we use are plan, side elevation, front elevation. Notice if I rotate it again, another 90 degrees. There's a different way of looking at the plan. With it rotated, but we'll have to rotate it this way to sort of see it the way that we saw it originally. So we take a number of different rotations to sort of look at this. And notice if I take that picture, that picture, and that picture, I should be able to get a pretty good idea of what the entire plane looks like. So that's what we're going to try to go ahead and do here, is to map out those three things. Let's start by drawing, as best we can, the plan. So to begin, to create our plan view, we're going to want to go ahead and sketch this. And we're going to want to get a sense for how big it is. So I'm going to start here by measuring my plane from the front of the plane to the back of the plane. And we're going to say that's about 7 inches. And notice if the plane is sitting normally, we'll measure it across the width of the plane. And it changes a little bit as I stretch the plane, but we'll say that's approximately 6 inches across the plane. So we're going to call this dimension here our x dimension, the sort of side to side dimension. And this dimension here, from the front, which is close to me, I'm in this direction down. I'm in this direction to the back. We're going to call y. Let's go ahead and create an axis so we can sketch this. I draw here. So there's our first axis, our x and our y. And we can go ahead and sort of sketch what the plane looks like on our x and y axis. I notice that this started. We're going to sort of put a medium, a middle point there that the plane runs right down the middle. And that was about 7 inches. Let's see if we run down the sort of middle of the plane there that's a little closer to. So it's about 6 inches to that middle point of the plane and then it extends out to 7 inches. And again, I'm doing a rough sketch. One, two, three, four, five, six. So my plane comes out, the middle sort of center line of my plane runs there. And then I measure it out to the points of the wings that were about 3 inches away on either of those sides. There's a little bit of a nose here on the tip here that's about an inch across. And I'm going to go ahead and see if I can roughly recreate, let's see, that's supposed to be 3 inches down from there, what my view of my plane looks like from the top. So there's a rough view of my airplane from the plan view. Now, if I want to express this information on the same page, I can recognize that everything here in this dimension along this x dimension, as I turn and look at the plane for what we call the side elevation here. As I turn to look at, now I need to decide what I'm rotating it about. I'm going to go ahead and rotate it around this flat point so that the plane looks actually around the bottom of the plane, so that the plane looks something like this and the wings slant up a little bit. I'm going to recognize that it still has these side-to-side measurements. I still have an x-axis. However, now I have dimensions that are also vertical. In fact, this rises up to be about, let's see here, it looks to be about 3 inches or so. So if I'm going to actually sketch my airplane here, what I can recognize is things like the nose of the plane. Here's the front of the plane, and I can recognize that the nose of the plane has a position on the x-axis. So I'm going to try to locate that same nose of the plane in the same position on the x-axis. And the back of the plane also has positions on the x-axis, so I can locate the tips of the wings in that same place on the x-axis, but now they have a different z-location. So I'm going to put them up about 3 inches off. Let's see here, 1, 2, 3, about 3 inches up off the top. So you can sort of see that this location here shares an x-position, but on this lower picture, I'm drawing this with an x-axis, but I'm also drawing it on the z-axis. So for my plan view, I have two coordinates that I'm concerned about, x versus y, but for my side elevation here, I have two different coordinates, the z-x and the z. Let's see if I can sort of continue sketching what that looks like for the rest of the plane. Notice we see something that looks a little bit like this. We'll go ahead and connect the top of the plane to the top of the plane. And the bottom of the plane to a location that's a little bit inside there, then that rises up some amount and connects to the wing. But there are some other sort of pieces in here. For example, there's a little bit of a piece that's right here. And if we see if our wing extends up just a little bit, if we look at our wing, we can sort of see that a little bit. Maybe that extends out just a little bit, that we line up that tip with where it's located there and what we can see from this perspective here. So the idea is we're lining up points along the x-axis because that's the axis that they share, but we have different values on the z. And there's sort of a sketch of what the airplane looks like from the side. If I want to, I can also include those other sort of pieces here, those internal pieces of the wing that sort of drop down here. All right, so that gives us two perspectives of the plane. Now let's go ahead and rotate the plane one more time and look at it from the back slash front elevation. Notice in this case we sort of see this strange v shape with the wings that are extended. And we want to sort of keep things aligned with the other two parts of the picture. Well, now this is where we have to be sort of, we have to consider where we draw this. Notice when we drew the side elevation, we drew it directly below the plan. Well, for this other elevation, the front elevation, we're going to draw it immediately to the right of the side elevation. And we're going to try to line up the pieces that, well, have the same z-axis. So I'm going to create another area over here, another axis. It's the same z-axis. But now I'm also going to need to create a different axis because what we're seeing here across this dimension now, across this dimension here now, this is side to side. This is the same as what was up and down on our plan view. So this is going to be our y-axis. And we're going to make sure these y-axes line up by creating something, by creating a diagonal line. Here's a diagonal line here. This line has a name. It's called the miter line. Sometimes you see it spelled with an R-E. Sometimes you see it spelled with an E-R. But it's a miter line. And the idea here is that anything that has a y-dimension on my plan view will line up with the similar y-dimension on my front elevation. So for example, the wing tip on the side of the plane here, I'm going to go move out until I hit the miter line. And then I'm going to bounce it off that miter line and move down to some point. That's going to be the far left side of my wing. And similarly, the far right side of my wing is going to come out. It looks like I might need a little more space. Do I have it? I'm not quite going to have enough space there. But the far right side of my wing is basically going to extend right there up against the side of my paper. So there's the extent of my wing. The middle of the plane is going to be located. I go across from the plan and then drop straight down when I hit the miter line. And now we have a y-coordinate for the middle of my plane. So let's go ahead and take a look here. We see that there's this, for example, this point that's right here on the wing. Actually, let's do this point right here. You see this point that's right here, where the v shape comes up? I'm going to keep my finger on that point and then turn and rotate so we see the plan view. So notice we know where that point is right there. Let's go ahead and locate that point. But see where it is located on this front view? Let's see if we can locate that and sketch it. So here's where the point is located. I'll mark it here in red. There's where that point is located. We know what its y-coordinate is. I'm going to follow that y-coordinate over and drop it down. But we don't know its z-coordinate. Unless we go over here, let's take a look in the side elevation. Where is it on the side elevation? Well, basically, it's right up here at this peak point, maybe a little bit beneath our wing. There's the point right there. So now we can go across from that point, which is right here. And now we've located where the point here is the point here. And here is the point on our picture. So now I know that that sort of extends from here down to the front of the airplane. Let me go ahead and draw that in. And now I've established, whoops, that's a little too far. We notice the bottom of the airplane. We know that the bottom of the airplane is located at this z-coordinate. So let me go ahead and sketch. There's the line that creates that v at the back of the plane. And I'll create a symmetric one on the other side. So now I've created that v perspective. I can also figure out where the tips of the wings are. There's the tips of the wings that come out. Here I've located, let me circle those in yellow. There's the tip of the wing there. There's the tip of the wing there. Let's see if we can figure out where the tip of the wing is on the front elevation by lining it up. The z-coordinate we get from the side elevation. The y-coordinate we get from the plan bounced off of the miter line. And there is where we see the tip of the wing. So now we can connect that wing tip. Again, from our perspective here, I'm running out of space here, we can go ahead and connect to that wing tip by drawing the line out to that point. And I will replicate that on the other side. So each piece of this is actually connected the same way. For example, if we look down this line here, you'll see that there's the nose of the airplane. We can just barely see the nose of the airplane touching right there. If this was perfectly flat, we would just see just a little bit of the nose in that you see some sort of these planes where the wings are attached there. Well, let's see if we can find where that nose of the plane does have a z-coordinate. It does have a direction in the vertical. So let me come across from there. We notice that that's located directly in the middle here. So that little bit that's extended there gives us another place that we can make a connection. I made this a little bit dark and thick when I made those lines. So let's see if we can erase those and make them a little less thick so we can see the distinction between them. One line drops down from the wings to the back of the plane. And then there are other lines that drop down from the wings to the front of the plane. So you can see just a little bit of the dimension of the back of the plane from there. And then we also notice when our wings, we can sort of see the basis of our wings, the bottom of our wingtips. Our wingtips come out to a point. I think our wingtips extend down a little bit. Once we actually get out here, they extend back down a little bit, back down. And then we notice from that point, those extend out toward the front part of the plane. And now I believe we've sketched at least the basics of our plane. The key element here is to notice that our side to side, if we're moving side to side, that is our x-axis there. If we're moving and that x-axis appears in two places, both in the plan view and on this elevation written below what we're calling the side elevation right now, if we're back to front, that appears in two places, both in the plan view but actually in this rotated view over here that we call the front elevation. And then up to down is repeated in both of these. Now I will say that we call this the side elevation because it was the side of the airplane. And this is the front elevation because it was the front or the back of the airplane. But typically, these terms are actually interchangeable, that the side elevation is the one that's drawn on the side, that this is the side elevation, and that this is the front elevation. Not interchangeable, they're interchanged. Usually we call this one the front and this one the side. I just didn't want to confuse the terminology of it being the side of the airplane with a different elevation. But this is the way you draw an orthographic view. You have a view from the top, the plan view. You have a view that's drawn directly below the plan view, typically called the front view, and then one that's off to one side called the side view. So I'm going to ask you to do now, just do your best to sketch your own airplane. Can you create a similar orthographic view from a three-dimensional object?