1 00:00:00,640 --> 00:00:01,510 ‫Welcome back. 2 00:00:02,440 --> 00:00:05,050 ‫So let's go back to our airfoil here. 3 00:00:06,340 --> 00:00:15,550 ‫Your task was to find the D.H as a function of diesel and in the way you do it is like this. 4 00:00:16,940 --> 00:00:20,640 ‫To get the horizontal component of this vector. 5 00:00:20,960 --> 00:00:33,680 ‫In other words, to get this component here, you simply have to multiply your Deedes times cosine phi 6 00:00:34,580 --> 00:00:35,180 ‫like this. 7 00:00:36,270 --> 00:00:45,660 ‫And to get the horizontal component of the DL vector, well, for that you have to take your DL and 8 00:00:45,660 --> 00:00:56,790 ‫you have to multiply by Sine and Phi and that's when you will get this component here and then you will 9 00:00:56,790 --> 00:01:03,480 ‫add them together and that will be your D.H force vector. 10 00:01:04,620 --> 00:01:07,650 ‫So, again, this is the top few of your blade. 11 00:01:08,710 --> 00:01:12,730 ‫This blade is rotating at an omega radians per second. 12 00:01:13,920 --> 00:01:23,700 ‫This is your differential airfoil element, this is your D.H force factor, which is this one here, 13 00:01:25,080 --> 00:01:31,450 ‫and then the distance from the center of rotation till this D.H vector. 14 00:01:32,010 --> 00:01:34,980 ‫That's what we're going to call an R. 15 00:01:36,180 --> 00:01:43,920 ‫Since we had a small fire angle approximation here, we could say that our sign five would be simply 16 00:01:43,920 --> 00:01:47,790 ‫a fire and then our cosine PHI would be one. 17 00:01:48,880 --> 00:02:02,590 ‫That means that this D.H vector will be DL Times PHY and plus the D, and by the way, the width of 18 00:02:02,590 --> 00:02:14,410 ‫the airfoil is the R and in order to get our differential air resistance moment dequeue, we would have 19 00:02:14,410 --> 00:02:25,060 ‫this formula d.h, which is this one times the distance from the center of rotation to the airfoil. 20 00:02:25,480 --> 00:02:26,590 ‫So times are. 21 00:02:27,650 --> 00:02:37,630 ‫Or you can simply rewrite this equation like this, where this part here, that's this part here. 22 00:02:38,480 --> 00:02:45,080 ‫So that's your differential moment due to air resistance because your blade is rotating at Omega radians 23 00:02:45,080 --> 00:02:45,800 ‫per second. 24 00:02:46,590 --> 00:02:54,110 ‫And now from the previous videos, you know what our differential lift and differential drag was? 25 00:02:55,110 --> 00:03:02,670 ‫Just to be clear, D.H is in Newtons and dequeue is in Newton meters. 26 00:03:03,670 --> 00:03:11,410 ‫And so now we are going to rewrite this dequeue in this way so you can write it out like this. 27 00:03:12,190 --> 00:03:13,820 ‫This portion here. 28 00:03:14,410 --> 00:03:15,490 ‫That would be. 29 00:03:16,670 --> 00:03:26,900 ‫DL Times, Sefi, and this portion here would be your DEEDI and that are here, that's, of course your 30 00:03:26,900 --> 00:03:27,770 ‫aunt here. 31 00:03:28,250 --> 00:03:29,690 ‫That's the distance. 32 00:03:31,190 --> 00:03:34,490 ‫You can do some factoring and you'll end up in this form here. 33 00:03:34,820 --> 00:03:39,230 ‫And note that now I've put this R into the brackets. 34 00:03:39,230 --> 00:03:49,400 ‫So that's why now instead of R squared, you have R cubed here and now in order to get our total q our 35 00:03:49,400 --> 00:03:58,520 ‫total air resistance moment, we have to consider each infinitesimal airfoil on this blade. 36 00:03:59,360 --> 00:04:09,860 ‫So we have to integrate this thing from zero up until Capital R, so this side will be from zero to 37 00:04:09,860 --> 00:04:16,440 ‫Q and this one from zero to R meters. 38 00:04:17,630 --> 00:04:28,910 ‫So as your R goes from zero meters to capital R meters, you take each differential airfoil element 39 00:04:29,270 --> 00:04:30,410 ‫on this blade. 40 00:04:31,370 --> 00:04:38,960 ‫You compute the differential moment for the specific blade and then you move onto the next differential 41 00:04:38,960 --> 00:04:46,430 ‫blade and then as you scan through the blade, you will add them all up continuously or accumulatively, 42 00:04:46,820 --> 00:04:49,150 ‫which is essentially what an integral is. 43 00:04:50,120 --> 00:05:00,410 ‫In other words, if you're D-R was here instead, then you would be computing the area under the curve 44 00:05:00,860 --> 00:05:02,870 ‫of this function here. 45 00:05:03,770 --> 00:05:05,270 ‫And that's integration. 46 00:05:06,270 --> 00:05:14,970 ‫Now, in addition, since Armorer has two blades, then we're going to put two here in order to get 47 00:05:15,750 --> 00:05:22,580 ‫the total air resistance moment for the entire model, taking into account both blades. 48 00:05:23,040 --> 00:05:25,530 ‫So I'm just going to put here and one. 49 00:05:26,670 --> 00:05:29,580 ‫If we do that, we can cancel out these TOS here. 50 00:05:30,780 --> 00:05:39,900 ‫And so the left side will be queues up and one equals and then I'm going to take some stuff out of the 51 00:05:39,900 --> 00:05:42,330 ‫integral, like we talked about before. 52 00:05:43,110 --> 00:05:50,400 ‫So I'm going to take an Omega squared and the air density out of the integral and inside the integral. 53 00:05:50,400 --> 00:05:51,940 ‫You will have everything else. 54 00:05:52,890 --> 00:06:01,580 ‫And so this Kyuss up and one that's your total air resistance moment per motor with two blades. 55 00:06:02,550 --> 00:06:11,290 ‫So simply a cube would be for one blade, but Kyuss up and one would be for one more with two blades. 56 00:06:12,210 --> 00:06:20,010 ‫And now the moment that the drone applies to the motor is then like this. 57 00:06:21,140 --> 00:06:21,680 ‫Ms. 58 00:06:22,160 --> 00:06:35,930 ‫D m equals minus Q, sub M and remember this M sub D.M. and put one because it's four more one. 59 00:06:37,190 --> 00:06:40,430 ‫That's your talk for M one. 60 00:06:41,430 --> 00:06:52,230 ‫So your MS up D.M. one equals and I'm going to put here Omega squared and then I'm going to put here 61 00:06:52,470 --> 00:06:55,950 ‫minus one, the air density. 62 00:06:56,980 --> 00:07:06,880 ‫The integral C times are cubed, and then in the brackets you have the lift coefficient times PHI plus 63 00:07:06,880 --> 00:07:14,900 ‫the drag coefficient and then these are your differential width of your airfoil. 64 00:07:15,610 --> 00:07:18,170 ‫And why did I put this minus one here? 65 00:07:18,940 --> 00:07:22,170 ‫Well, that's just to account for this thing, right? 66 00:07:23,350 --> 00:07:34,300 ‫And now I'm just going to say that this entire thing here, it's C, sub Q and there you go, you now 67 00:07:34,300 --> 00:07:40,750 ‫have an expression for the moment that is applied from the drone to the more. 68 00:07:41,960 --> 00:07:45,050 ‫And you can also write it out like this, Ms. 69 00:07:45,500 --> 00:07:58,520 ‫D.M. One equals CQ Times Omega squared, and since we're dealing with more one than this would be Omega 70 00:07:58,520 --> 00:07:59,450 ‫one squared. 71 00:07:59,930 --> 00:08:03,070 ‫And I should put here on one squared as well. 72 00:08:03,590 --> 00:08:06,920 ‫And also here and even here. 73 00:08:07,640 --> 00:08:12,080 ‫But here we just worked in general variables. 74 00:08:12,080 --> 00:08:21,140 ‫So I'm just going to leave Omega's like this and again you can find this constant C subcu either by 75 00:08:21,140 --> 00:08:26,690 ‫integrating these equations or people also determined it experimentally. 76 00:08:27,410 --> 00:08:36,020 ‫This C subcu can be called a torque factor and this torque factor has a different value from the thrust 77 00:08:36,020 --> 00:08:39,160 ‫factor that we had before C sub T.. 78 00:08:39,680 --> 00:08:49,670 ‫So these are two different things, but both total thrust promotor and told moment that is applied to 79 00:08:49,670 --> 00:08:51,140 ‫the more by the drone. 80 00:08:52,280 --> 00:08:56,150 ‫Both of them have Omega squared in it. 81 00:08:57,300 --> 00:09:08,880 ‫So the thrust force was the thrust factor times omegle, one squared, and now the torque applied to 82 00:09:08,880 --> 00:09:14,070 ‫the motor equals C subcu times omegle one squared. 83 00:09:15,170 --> 00:09:20,980 ‫And now we can find our EUFOR and we're going to do that in the next video. 84 00:09:21,350 --> 00:09:22,790 ‫So thank you very much.