hi I'm Mike Thompson in this video I'm going to talk more about the math behind Rockets ability if you've seen the other video you know how to do it simply here we're going to talk a little bit about the math so I've got here a two-to-one scale drawing of a model rocket you can see here I've got all the dimensions all the linear dimensions are in blue all of the areas are in red and distances are in orange so what you do is you first look at your rocket from the side from pick aside and then you project it onto a surface that projection has an area if you calculate the centroid of this area you can figure out where the center of pressure of your rocket is going to be so this is what we're doing right here you've got a triangle here that's 2x1 so obviously 1/2 base times height so the area of this triangle is 1 you've got this segment here the body which is just a rectangle it's 11 inches long by 1 so it's area is 11 we come down here in the area of this little trapezoid tail cone here is the average of the bases times the height and that ends up being 7/16 of a square inch really really small almost negligible in our case and then you've got the fins here which are 2 inches tall they've got a 1 inch tip and they are an inch and a half in span so you have two and a quarter inches they're square inches I mean times two so you get all your areas what you're going to do make sure make it easy for yourself is to break it up into areas that you know which is pretty much triangles and rectangles if those are really easy to do so we take this fin here and we're going to break it up between a triangle and a rectangle and calculate their area separately now we've got all our areas we have to find where the center the geometric center of all those areas lies so that we can calculate the centroid of the whole thing well there's tables online wikipedia has a bunch a list of centroids if you just look that up for any triangle the centroid is one third of the way up from its base well it's too high so one third of two is two thirds but we're measuring from the nose coming you pick a distance and you measure all your distances from there so that you have consistency and then if the math works out right so in our case we need to subtract 2/3 from here so our centroid distance for our triangle is one point three one in a third now we come down here and we have to take care of this rectangular section the centroid of any rectangle is just in the middle of a rectangle this piece here is 11 ordinarily that would be half of that which is 5.5 however we have to account for the two inches that we've already offset our rectangle from the measuring datum up there so the center of this is at 7.5 we do the same thing let's go ahead and do our little trapezoid here at the end it's almost negligible we're going to go ahead and include it the centroid is this it's kind of a fairly screwy formula here it is a B and H H over 3 times the whole thing of 2 a plus B over a plus B well that works out to be a little under a quarter so we take this Plus this now one thing to note here this and this are flipped so we have to measure from the big side in our case which is what we're doing so we go ahead and measure down because on the big side on our trapezoid here is on top so we end up with 13.2 as a distance for here I went ahead and round it down to one decimal place the fins here you got a rectangle that's easy enough to do we know that we're coming down it's 13 inches to right here to the base of the fins that's 13 inches well we've got to come back up half the distance of our rectangle which the distance is 1 so we come up 1/2 13 months 1/2 is 12.5 we do the same thing here the base of this is now at 12 we have to come up one-third the height of this triangle which is 1 we come up a third so we have 11.7 because we have to lose point three so we have all of our areas and all of our centroid distances which is what we need to calculate this instead of forces we're using areas so but it all makes sense so some of the moments over the some of the areas in our case moments we're just taking instead of a force we're just taking an area so 1.3 times 17.5 times 1111 seven three-quarters you get all this now one thing to note here is you have to multiply your each pin by two which is what I did here you've got the triangle portion and the rectangular portion times two because we have two of them so we do all that we add all those up and then we divide that by the total area of our figure here which ends up being 16 and 15 16 square inches that gets you eight point five four so measuring down from here we come down eight point five four so the centre of pressure of our rocket is six seven eight and a half centre of pressure of this rocket is right here I don't know where the centre of gravity is at this rocket because that depends on lots of other things but that's exactly where the center of pressure is going to be now there's one little thing that could catch it this rocket I drew has four fins this rocket over here only has three which is a very common number of fins to have when you project this area onto a flat plane you don't get the full length of your fin here that's projected down here you only get fin length times the cosine of 60 so you only get actually 3/4 here if you calculate it with the full length of your fin you'll get a false sense of stability so make sure to calculate this area here if you have three fins or if you use five you'll have a different number and everything but three and four the most common so that's the example I used because you might want to make sure that you definitely go conservative on your stability here anyway I hope that kind of helps explain things a little bit it's really not that hard we're just breaking things down into simple shapes finding the centroids take the sum of all of the forces in our case all the areas times the distance over the area's we get our number that's right here and hopefully this is behind the center of gravity if it is we're going to be stable thanks for watching I really appreciate it