1
00:00:00,430 --> 00:00:07,990
‫And so if I run the simulation, considering the drag forces, well, then you see that nothing has

2
00:00:07,990 --> 00:00:09,040
‫really changed.

3
00:00:09,940 --> 00:00:14,120
‫So perhaps the values that I have here are too small.

4
00:00:14,320 --> 00:00:17,250
‫Maybe I should put bigger values.

5
00:00:17,860 --> 00:00:21,250
‫Let's put one hundred point five and see what's going to happen.

6
00:00:22,000 --> 00:00:29,350
‫OK, so now with those bigger values, you can see that the red beam tilts down.

7
00:00:30,160 --> 00:00:31,350
‫But it's super small.

8
00:00:31,360 --> 00:00:32,840
‫It's almost nothing.

9
00:00:33,280 --> 00:00:33,810
‫Why?

10
00:00:34,270 --> 00:00:36,400
‫Well, let's print our.

11
00:00:36,400 --> 00:00:42,120
‫You've lost this, so I'm going to print my you lost this right here.

12
00:00:42,670 --> 00:00:45,190
‫I'm going to uncommanded and print it.

13
00:00:45,980 --> 00:00:50,820
‫I'm going to run the code now and let's see what's going to happen.

14
00:00:51,400 --> 00:00:55,500
‫You can see that these are the you velocities here.

15
00:00:55,510 --> 00:01:02,130
‫So they are about zero point three one meters per second, about zero point three meters per second.

16
00:01:02,620 --> 00:01:03,730
‫That's very small.

17
00:01:04,480 --> 00:01:10,100
‫And so if you look at this formula now, then you have your you velocity squared.

18
00:01:10,360 --> 00:01:17,230
‫So if you're using velocities zero point three meters per second, then the zero point three times zero

19
00:01:17,230 --> 00:01:22,200
‫point three would give you zero point zero nine.

20
00:01:23,050 --> 00:01:30,040
‫So that gives you even a smaller number, because if you square a number that is less than one, then

21
00:01:30,040 --> 00:01:31,500
‫you get a smaller number.

22
00:01:31,510 --> 00:01:32,460
‫If you square it.

23
00:01:33,280 --> 00:01:37,390
‫So you're a drag force will be extremely small, almost nothing.

24
00:01:37,720 --> 00:01:44,680
‫We really need higher velocity to see the effect of the drag force and we can see that in trajectory

25
00:01:44,680 --> 00:01:45,130
‫six.

26
00:01:45,970 --> 00:01:55,570
‫I will now make this drag coefficient one point five again and now I'm going to choose trajectory six

27
00:01:55,750 --> 00:01:56,470
‫right here.

28
00:01:57,250 --> 00:02:00,490
‫Here you have a tornado shaped trajectory.

29
00:02:01,060 --> 00:02:05,470
‫Not that the simulation length is always one hundred seconds.

30
00:02:06,550 --> 00:02:12,850
‫So no matter how long the trajectory is, the other needs to cover it in 100 seconds.

31
00:02:13,450 --> 00:02:20,950
‫So if you have more distance to cover, then your propeller's need to produce more thrust to make the

32
00:02:20,980 --> 00:02:22,210
‫other go faster.

33
00:02:22,930 --> 00:02:31,870
‫If you compare trajectory one and six, then in both cases you make two point five rotations in one

34
00:02:31,870 --> 00:02:41,230
‫hundred seconds on the X Y plane, and in both cases you go from five to twenty five meters in altitude.

35
00:02:42,040 --> 00:02:49,690
‫However, in trajectory six, your spiral radius increases as a function of time.

36
00:02:50,320 --> 00:02:54,340
‫In trajectory one, your radius was two meters always.

37
00:02:54,730 --> 00:03:03,760
‫However, in trajectory six, you go from two meters at the beginning to forty two meters in the end.

38
00:03:04,120 --> 00:03:11,470
‫So you see if you look at the scale then you go from two meters at the beginning to forty two meters

39
00:03:11,590 --> 00:03:12,340
‫in the end.

40
00:03:13,150 --> 00:03:20,890
‫So in the X and Y dimension you clearly see that you have to cover more distance in one hundred seconds

41
00:03:21,160 --> 00:03:22,210
‫a lot more.

42
00:03:22,840 --> 00:03:28,780
‫So that means that the other you will have greater you velocities, especially in the end.

43
00:03:28,780 --> 00:03:32,890
‫The bigger the radius then the larger your you velocity.

44
00:03:33,700 --> 00:03:37,530
‫And so let's print the velocity again.

45
00:03:37,540 --> 00:03:40,540
‫But now for trajectory six.

46
00:03:41,620 --> 00:03:45,820
‫If I do that, then you can see that the velocities go up.

47
00:03:46,750 --> 00:03:53,350
‫So you see this is already quite at the end of the trajectory and you can see that when you're very

48
00:03:53,350 --> 00:04:01,770
‫much at the end of it, then you velocity becomes six point six meters per second.

49
00:04:02,560 --> 00:04:10,990
‫So in the first trajectory, you went from zero to zero point three meters per second and now you went

50
00:04:10,990 --> 00:04:15,750
‫from zero to six point six meters per second.

51
00:04:16,240 --> 00:04:17,740
‫That's quite a difference.

52
00:04:18,490 --> 00:04:21,700
‫And if you square it, then you will have even bigger numbers.

53
00:04:21,730 --> 00:04:28,630
‫So if I put here U times you then you will see that you will have pretty big numbers.

54
00:04:29,470 --> 00:04:31,720
‫So this is now U squared.

55
00:04:31,840 --> 00:04:37,900
‫And you see that at the end of trajectory, six euro squared will be forty four.

56
00:04:38,860 --> 00:04:44,040
‫And so you'll drag force in the body frame X direction becomes much more relevant.

57
00:04:44,050 --> 00:04:49,360
‫Now you see that your drone tilts forward a lot more.

58
00:04:49,360 --> 00:04:59,260
‫Now you see higher velocities produce higher drag and the other needs more forward force to overcome

59
00:04:59,260 --> 00:04:59,650
‫that.

60
00:05:00,000 --> 00:05:04,080
‫We drag that grows with the growth of the radius.

61
00:05:05,100 --> 00:05:13,620
‫And it gets more forward, forced by tilting its nose down more and more, and the more you tilt down,

62
00:05:13,920 --> 00:05:17,040
‫the larger the horizontal component of the thrust force.

63
00:05:17,760 --> 00:05:20,550
‫You see, in the end, it's quite tilted already.

64
00:05:21,600 --> 00:05:27,870
‫So you see, if your drone is tilted like this, then you're horizontal component will be very small.

65
00:05:29,010 --> 00:05:37,230
‫But if you're tilting more, then your horizontal component becomes much bigger and that will help the

66
00:05:37,230 --> 00:05:39,600
‫drone overcome the growing drag.

67
00:05:40,440 --> 00:05:49,710
‫And so if I now turn this drag off and make this drag switch zero, then you have only a little bit

68
00:05:49,710 --> 00:05:54,660
‫of tilting in order to increase the velocity of the drone.

69
00:05:55,470 --> 00:06:02,790
‫Remember that since the radius of this trajectory is growing, but you still have to cover the entire

70
00:06:03,000 --> 00:06:09,930
‫distance within one hundred seconds, then that means that as this radius is growing, your forward

71
00:06:09,930 --> 00:06:11,300
‫velocity needs to grow.

72
00:06:11,310 --> 00:06:17,940
‫You have to become faster and faster and so on, like in the first trajectory where your radius was

73
00:06:17,940 --> 00:06:25,200
‫constant and therefore your body from X velocity was also constant, then you didn't need any extra

74
00:06:25,200 --> 00:06:27,910
‫force to increase your velocity then.

75
00:06:28,080 --> 00:06:34,350
‫Now, in this case, you do need more velocity, so you need some forward acceleration even without

76
00:06:34,350 --> 00:06:35,340
‫air resistance.

77
00:06:36,060 --> 00:06:45,110
‫And so the drone still tilts down in order to at least increase the UVs forward velocity.

78
00:06:45,900 --> 00:06:53,730
‫But this thing is a lot smaller because as far as the US is concerned, it is traveling in vacuum.

79
00:06:54,240 --> 00:06:57,810
‫So there is nothing impeding the forward motion.

80
00:06:58,560 --> 00:07:05,550
‫And so, again, if you travel along the spiral with a constant radius, then you use velocity stays

81
00:07:05,550 --> 00:07:06,660
‫pretty much the same.

82
00:07:07,350 --> 00:07:16,860
‫So once you align yourself with the spiral, then without air, all you need is one push in the forward

83
00:07:16,860 --> 00:07:25,540
‫direction and you will not need any additional force in the forward direction to move in that direction.

84
00:07:26,460 --> 00:07:33,380
‫You only need constant force in the body frame y direction to keep the drone flying in circles.

85
00:07:33,960 --> 00:07:42,060
‫You need that centripetal force that you get by tilting your positive body frame y side down.

86
00:07:42,980 --> 00:07:50,750
‫But in the forward direction, you don't need extra velocity in the forward direction, your velocity

87
00:07:50,750 --> 00:07:52,430
‫stays pretty much constant.

88
00:07:53,090 --> 00:08:00,410
‫And that's because in one hundred seconds, you have this distance to cover and your radius is constant.

89
00:08:00,530 --> 00:08:08,990
‫So since in this trajectory, you have two point five rotations, so you start from here and then you

90
00:08:08,990 --> 00:08:15,650
‫have your one rotation, another rotation, and then half of the circle more.

91
00:08:16,310 --> 00:08:23,120
‫You can see that each rotation has an equal amount of distance, so therefore your velocity stays the

92
00:08:23,120 --> 00:08:23,540
‫same.

93
00:08:24,350 --> 00:08:30,260
‫But in trajectory six, your first rotation will be this one.

94
00:08:31,080 --> 00:08:38,780
‫Then the second rotation will cover more distance on the X Y plane and then the final half rotation.

95
00:08:39,050 --> 00:08:47,240
‫You can see that you really need to cover a lot of distance because now your radius is not constant

96
00:08:47,240 --> 00:08:48,330
‫and two meters.

97
00:08:48,530 --> 00:08:52,940
‫Now it goes from two meters to 42 meters.

98
00:08:54,150 --> 00:09:03,300
‫So even without air resistance, your drone needs to go faster, and if you want to change your velocity,

99
00:09:03,300 --> 00:09:07,500
‫you need more force for that because you need a bit of acceleration in that direction.

100
00:09:08,460 --> 00:09:16,040
‫And that's why even without air resistance, your positive body frame, Exide keeps tilting down.

101
00:09:16,740 --> 00:09:24,880
‫But of course, the other thing is that right now, since the drag switch is turned off, the you of

102
00:09:24,900 --> 00:09:27,850
‫things, that it is traveling in a vacuum.

103
00:09:28,740 --> 00:09:31,320
‫However, of course, all that is a simplification.

104
00:09:31,530 --> 00:09:34,760
‫In reality, you have drag, you must have air.

105
00:09:34,950 --> 00:09:39,060
‫How else would your propellers produce thrust then?