‫Welcome back.
‫And now it's time to find our EUFOR, so you have your equation that gives you the moment that the drone
‫applies to the motus.
‫So for more one, it was this MSBA and one equals and then.
‫The torque factor times Omega One squared.
‫That's the moment that the drone applies to the rotors.
‫So if this is your drone, then this moment here will make this rotor rotate like this.
‫And this, of course, is more one.
‫And so in total, you have four murders, so the total net moment is the following.
‫Let's call it simply Ms.
‫D.M. equals Amsterdam one plus Amsterdam two plus Amsterdam three plus M, some D and four.
‫And so they're are all four more, one more, two more, three and more four, respectively.
‫So this moment made this model rotate like this, then this moment will make this rotor rotate, but
‫now clockwise, the third movement will make more three rotate counterclockwise and moment for more
‫for makes more for rotate clockwise like this.
‫So this is M2 M three and M four.
‫You can rewrite this entire business like this.
‫C.
‫S Q times omega one squared minus.
‫S. Subcu Times, Megadose squared plus.
‫S. subcu times, omega, three squared and minus.
‫S. Subcu times, omega four squared.
‫And of course, you have a negative sign here and here, because the moments for more two and more four
‫are negative, they are clockwise moments.
‫So if you rotate them like with your right hands, if you curl your right hand fingers in this rotation
‫direction, then your thumb would point into the screen.
‫Note that here, it doesn't matter that the omega's for more two and more four are negative because
‫yes, they are negative.
‫For example, actually it's minus Omega two, right.
‫However, if you square it then you will have omega two squared.
‫However, here you are not thinking in terms of Omega's, you're thinking in terms of moments, what
‫kind of rotation direction do the moments have?
‫Are the moments positive or negative?
‫And according to the right hand rule for more two and more for the moments are actually negative and
‫therefore Amsterdam two equals minus C sub Q Omega two squared and.
‫Ms.
‫D.M. four equals minus C subcu times Omega four squared.
‫And now, of course, you can simplify this entire thing, you can factor out the sea cues, and if
‫you do that, then this is what you will get.
‫So this is the net moment that the drone applies to the motors.
‫You have four motors.
‫And so if you add them up, then you will have a net moment and let's just assume right now that the
‫moments for more three and more one are bigger than four, more two and more four, meaning that your
‫net moment will end up being counterclockwise because M one and three, they have bigger moments and
‫they are counterclockwise.
‫So this term and this term will end up being bigger than this term and this term, and so in the end
‫you're going to end up with a positive net moment, which is like this.
‫So that's your positive net moment that is generated from all the four moments that you had here.
‫And so what happens when the drone applies moments to the voters and then the net moment of the roaders
‫is this one what will happen then?
‫Well, if the drone applies, for example, a moment to more one, then that means that more one applies
‫the same moment to the drone, but in the opposite direction.
‫And so if you sum up all the four moments that you have that came from the drone and apply to the mortars,
‫if you end up with a positive counter-clockwise moment, then that means that the drone will experience
‫the same moment, but in the opposite direction.
‫So this in blue, this is what the four motors collectively applied to the drone and this blue moment
‫that's our you for.
‫So EUFOR is the moment that the models apply to the drone and it is mathematically written like this,
‫EUFOR equals minus M sub D.M..
‫And so that means that you're going to put a minus sign here and so you equals C. Subcu and then this
‫plus Omegle one squared will be minus Omegle, one squared, then plus or minus two squared, minus
‫Omega three squared and plus Omega four squared.
‫So what I have done, I have simply distributed this minus sign to all the terms inside the parentheses.
‫And this is your you for your your control moment.
‫And of course it's units are also in Newton meters like this.
‫And there you go.
‫You have your equations for you one, you two, you three and you form.
‫It's a system of equations.
‫And if you think about it, then EUFOR is in fact the same, like the air resistance movement.
‫Q For all the motors combined, because if you remember then the Q one, which was the air resistance
‫moment for model one that was caused by the air resistance and that was minus M sub D.M. one.
‫And so the total queue, let's put it cuttable QST, it would be the negative summation of all these
‫moments that the drone applies to its mortars.
‫So this QST would be the total air resistance moment that the air applies to the voters.
‫But if you look at this expression, then EUFOR equaled minus this total moment that the drone applied
‫to its mortars as well.
‫So that means that this expression also equals EUFOR, because I can also rewrite this expression like
‫this, I can put here parentheses and I can make all these signs positive here and I can just have this
‫negative sign here.
‫It would be the same thing.
‫And this portion here would be m sup D.M., which is this one here.
‫And so you can see from here that your you for your your control moment in fact equals the air resistance
‫moment, that the air applies to all the models.
‫But we could only make that assumption because our omega dot equals zero radians per second squared.
‫Without this assumption here, this expression here would not have been true.
‫And so having these equations, I want to give you a short exercise.
‫What would be the units of your thrust factor and your torque factor?
‫What would be the units?
‫And try it yourself and you will see the solution in the next video.
‫Thank you very much.