‫And so if I run the simulation, considering the drag forces, well, then you see that nothing has
‫really changed.
‫So perhaps the values that I have here are too small.
‫Maybe I should put bigger values.
‫Let's put one hundred point five and see what's going to happen.
‫OK, so now with those bigger values, you can see that the red beam tilts down.
‫But it's super small.
‫It's almost nothing.
‫Why?
‫Well, let's print our.
‫You've lost this, so I'm going to print my you lost this right here.
‫I'm going to uncommanded and print it.
‫I'm going to run the code now and let's see what's going to happen.
‫You can see that these are the you velocities here.
‫So they are about zero point three one meters per second, about zero point three meters per second.
‫That's very small.
‫And so if you look at this formula now, then you have your you velocity squared.
‫So if you're using velocities zero point three meters per second, then the zero point three times zero
‫point three would give you zero point zero nine.
‫So that gives you even a smaller number, because if you square a number that is less than one, then
‫you get a smaller number.
‫If you square it.
‫So you're a drag force will be extremely small, almost nothing.
‫We really need higher velocity to see the effect of the drag force and we can see that in trajectory
‫six.
‫I will now make this drag coefficient one point five again and now I'm going to choose trajectory six
‫right here.
‫Here you have a tornado shaped trajectory.
‫Not that the simulation length is always one hundred seconds.
‫So no matter how long the trajectory is, the other needs to cover it in 100 seconds.
‫So if you have more distance to cover, then your propeller's need to produce more thrust to make the
‫other go faster.
‫If you compare trajectory one and six, then in both cases you make two point five rotations in one
‫hundred seconds on the X Y plane, and in both cases you go from five to twenty five meters in altitude.
‫However, in trajectory six, your spiral radius increases as a function of time.
‫In trajectory one, your radius was two meters always.
‫However, in trajectory six, you go from two meters at the beginning to forty two meters in the end.
‫So you see if you look at the scale then you go from two meters at the beginning to forty two meters
‫in the end.
‫So in the X and Y dimension you clearly see that you have to cover more distance in one hundred seconds
‫a lot more.
‫So that means that the other you will have greater you velocities, especially in the end.
‫The bigger the radius then the larger your you velocity.
‫And so let's print the velocity again.
‫But now for trajectory six.
‫If I do that, then you can see that the velocities go up.
‫So you see this is already quite at the end of the trajectory and you can see that when you're very
‫much at the end of it, then you velocity becomes six point six meters per second.
‫So in the first trajectory, you went from zero to zero point three meters per second and now you went
‫from zero to six point six meters per second.
‫That's quite a difference.
‫And if you square it, then you will have even bigger numbers.
‫So if I put here U times you then you will see that you will have pretty big numbers.
‫So this is now U squared.
‫And you see that at the end of trajectory, six euro squared will be forty four.
‫And so you'll drag force in the body frame X direction becomes much more relevant.
‫Now you see that your drone tilts forward a lot more.
‫Now you see higher velocities produce higher drag and the other needs more forward force to overcome
‫that.
‫We drag that grows with the growth of the radius.
‫And it gets more forward, forced by tilting its nose down more and more, and the more you tilt down,
‫the larger the horizontal component of the thrust force.
‫You see, in the end, it's quite tilted already.
‫So you see, if your drone is tilted like this, then you're horizontal component will be very small.
‫But if you're tilting more, then your horizontal component becomes much bigger and that will help the
‫drone overcome the growing drag.
‫And so if I now turn this drag off and make this drag switch zero, then you have only a little bit
‫of tilting in order to increase the velocity of the drone.
‫Remember that since the radius of this trajectory is growing, but you still have to cover the entire
‫distance within one hundred seconds, then that means that as this radius is growing, your forward
‫velocity needs to grow.
‫You have to become faster and faster and so on, like in the first trajectory where your radius was
‫constant and therefore your body from X velocity was also constant, then you didn't need any extra
‫force to increase your velocity then.
‫Now, in this case, you do need more velocity, so you need some forward acceleration even without
‫air resistance.
‫And so the drone still tilts down in order to at least increase the UVs forward velocity.
‫But this thing is a lot smaller because as far as the US is concerned, it is traveling in vacuum.
‫So there is nothing impeding the forward motion.
‫And so, again, if you travel along the spiral with a constant radius, then you use velocity stays
‫pretty much the same.
‫So once you align yourself with the spiral, then without air, all you need is one push in the forward
‫direction and you will not need any additional force in the forward direction to move in that direction.
‫You only need constant force in the body frame y direction to keep the drone flying in circles.
‫You need that centripetal force that you get by tilting your positive body frame y side down.
‫But in the forward direction, you don't need extra velocity in the forward direction, your velocity
‫stays pretty much constant.
‫And that's because in one hundred seconds, you have this distance to cover and your radius is constant.
‫So since in this trajectory, you have two point five rotations, so you start from here and then you
‫have your one rotation, another rotation, and then half of the circle more.
‫You can see that each rotation has an equal amount of distance, so therefore your velocity stays the
‫same.
‫But in trajectory six, your first rotation will be this one.
‫Then the second rotation will cover more distance on the X Y plane and then the final half rotation.
‫You can see that you really need to cover a lot of distance because now your radius is not constant
‫and two meters.
‫Now it goes from two meters to 42 meters.
‫So even without air resistance, your drone needs to go faster, and if you want to change your velocity,
‫you need more force for that because you need a bit of acceleration in that direction.
‫And that's why even without air resistance, your positive body frame, Exide keeps tilting down.
‫But of course, the other thing is that right now, since the drag switch is turned off, the you of
‫things, that it is traveling in a vacuum.
‫However, of course, all that is a simplification.
‫In reality, you have drag, you must have air.
‫How else would your propellers produce thrust then?