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‫Welcome back.

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‫And now it's time to find our EUFOR, so you have your equation that gives you the moment that the drone

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‫applies to the motus.

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‫So for more one, it was this MSBA and one equals and then.

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‫The torque factor times Omega One squared.

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‫That's the moment that the drone applies to the rotors.

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‫So if this is your drone, then this moment here will make this rotor rotate like this.

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‫And this, of course, is more one.

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‫And so in total, you have four murders, so the total net moment is the following.

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‫Let's call it simply Ms.

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‫D.M. equals Amsterdam one plus Amsterdam two plus Amsterdam three plus M, some D and four.

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‫And so they're are all four more, one more, two more, three and more four, respectively.

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‫So this moment made this model rotate like this, then this moment will make this rotor rotate, but

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‫now clockwise, the third movement will make more three rotate counterclockwise and moment for more

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‫for makes more for rotate clockwise like this.

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‫So this is M2 M three and M four.

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‫You can rewrite this entire business like this.

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‫C.

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‫S Q times omega one squared minus.

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‫S. Subcu Times, Megadose squared plus.

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‫S. subcu times, omega, three squared and minus.

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‫S. Subcu times, omega four squared.

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‫And of course, you have a negative sign here and here, because the moments for more two and more four

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‫are negative, they are clockwise moments.

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‫So if you rotate them like with your right hands, if you curl your right hand fingers in this rotation

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‫direction, then your thumb would point into the screen.

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‫Note that here, it doesn't matter that the omega's for more two and more four are negative because

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‫yes, they are negative.

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‫For example, actually it's minus Omega two, right.

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‫However, if you square it then you will have omega two squared.

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‫However, here you are not thinking in terms of Omega's, you're thinking in terms of moments, what

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‫kind of rotation direction do the moments have?

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‫Are the moments positive or negative?

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‫And according to the right hand rule for more two and more for the moments are actually negative and

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‫therefore Amsterdam two equals minus C sub Q Omega two squared and.

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‫Ms.

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‫D.M. four equals minus C subcu times Omega four squared.

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‫And now, of course, you can simplify this entire thing, you can factor out the sea cues, and if

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‫you do that, then this is what you will get.

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‫So this is the net moment that the drone applies to the motors.

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‫You have four motors.

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‫And so if you add them up, then you will have a net moment and let's just assume right now that the

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‫moments for more three and more one are bigger than four, more two and more four, meaning that your

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‫net moment will end up being counterclockwise because M one and three, they have bigger moments and

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‫they are counterclockwise.

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‫So this term and this term will end up being bigger than this term and this term, and so in the end

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‫you're going to end up with a positive net moment, which is like this.

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‫So that's your positive net moment that is generated from all the four moments that you had here.

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‫And so what happens when the drone applies moments to the voters and then the net moment of the roaders

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‫is this one what will happen then?

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‫Well, if the drone applies, for example, a moment to more one, then that means that more one applies

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‫the same moment to the drone, but in the opposite direction.

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‫And so if you sum up all the four moments that you have that came from the drone and apply to the mortars,

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‫if you end up with a positive counter-clockwise moment, then that means that the drone will experience

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‫the same moment, but in the opposite direction.

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‫So this in blue, this is what the four motors collectively applied to the drone and this blue moment

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‫that's our you for.

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‫So EUFOR is the moment that the models apply to the drone and it is mathematically written like this,

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‫EUFOR equals minus M sub D.M..

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‫And so that means that you're going to put a minus sign here and so you equals C. Subcu and then this

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‫plus Omegle one squared will be minus Omegle, one squared, then plus or minus two squared, minus

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‫Omega three squared and plus Omega four squared.

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‫So what I have done, I have simply distributed this minus sign to all the terms inside the parentheses.

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‫And this is your you for your your control moment.

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‫And of course it's units are also in Newton meters like this.

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‫And there you go.

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‫You have your equations for you one, you two, you three and you form.

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‫It's a system of equations.

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‫And if you think about it, then EUFOR is in fact the same, like the air resistance movement.

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‫Q For all the motors combined, because if you remember then the Q one, which was the air resistance

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‫moment for model one that was caused by the air resistance and that was minus M sub D.M. one.

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‫And so the total queue, let's put it cuttable QST, it would be the negative summation of all these

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‫moments that the drone applies to its mortars.

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‫So this QST would be the total air resistance moment that the air applies to the voters.

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‫But if you look at this expression, then EUFOR equaled minus this total moment that the drone applied

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‫to its mortars as well.

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‫So that means that this expression also equals EUFOR, because I can also rewrite this expression like

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‫this, I can put here parentheses and I can make all these signs positive here and I can just have this

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‫negative sign here.

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‫It would be the same thing.

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‫And this portion here would be m sup D.M., which is this one here.

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‫And so you can see from here that your you for your your control moment in fact equals the air resistance

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‫moment, that the air applies to all the models.

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‫But we could only make that assumption because our omega dot equals zero radians per second squared.

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‫Without this assumption here, this expression here would not have been true.

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‫And so having these equations, I want to give you a short exercise.

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‫What would be the units of your thrust factor and your torque factor?

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‫What would be the units?

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‫And try it yourself and you will see the solution in the next video.

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‫Thank you very much.