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‫Welcome back.

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‫So when you have a propeller that rotates like this.

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‫Then, since there is air everywhere, that air gives air resistance to this rotating propeller.

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‫If we now, again, only consider one blade, let's take this right one here.

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‫And think in terms of differential with airfoils.

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‫Then each airfoil experiences this air resistance differential force parallel to the rotation disc,

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‫meaning that this is your.

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‫Rotation disk, and then each differential element here would experience some kind of.

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‫Air resistance differential force that goes.

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‫Parallel to the rotation disk surface, so this vector is laying on the surface of the rotation disk

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‫and we call this air resistance force on the rotation disk surface D h.

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‫In other words, if you look at this picture here, then this would be this d.h here, this component

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‫that we had ignored previously.

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‫So let's call this one D.H one, let's call this one D.H two, and let's call this differential force

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‫vector D.H three.

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‫And of course, the units here are Newton's like this.

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‫And then if we multiply each force here by its distance from the rotation center that said this would

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‫be R one, this would be R two and this would be our three, then we get the differential moment that

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‫the air exerts on that specific airfoil due to the rotation of the blade.

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‫So let's call it dequeue, and then it's units would be Knewton meters.

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‫So dequeue, one would be D.H one, which is this force here times are one, which is this distance

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‫here.

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‫Then your dick, you two would be.

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‫The two times are two, so this time this.

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‫And dequeue, three equals the three times are three.

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‫So this force times this distance, and so these are your differential moments that the air exerts on

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‫that specific airfoil because of the fact that the rotor is rotating.

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‫So dequeue one is for this airfoil dequeue, two is for this airfoil and three is for this red one.

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‫And so if you add up all these differential moments from zero meters to the capital or meters to the

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‫end of this blade, if you do that, then you will get the total moment that the air exerts on this

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‫blade.

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‫In other words, you would integrate over the entire blade length.

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‫But now you would integrate all the products of this, the force vector and its distance from the center

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‫of rotation.

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‫And now, if the angular velocity of the rotor is constant, meaning that or make a dot or the change

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‫of Omeonga with respect to time, if it's the zero radians per second squared, then the moment that

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‫the air exerts on the rotating blade in one direction is equal to the moment that the drone exerts on

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‫the blade in another direction like this.

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‫So, again, if you have a bleed here and then that bleed is rotating at omega radians per second and

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‫we assume that the Omega Dot or the change of Omega with respect to time is zero, meaning that our

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‫Omega is constant, meaning that the rotation of the rotor is not increasing or decreasing.

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‫Then the moment that is applied to the blade by the air has the same magnitude, like the moment that

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‫the drone applies to the blade, but in the opposite direction, so absorbed, that's the moment that

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‫the drone applies to the rotor so that the rotor would rotate.

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‫And then this cue moment is the moment that the blade experiences due to air resistance.

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‫So if you integrate over the entire blade length, then you will have here this cue moment.

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‫And if your omega dot is zero, then that means that these two moments are equal in magnitude, but

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‫opposite in direction, meaning that one is clockwise and the other one is counterclockwise.

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‫And it makes sense, right?

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‫They have to be equal because if not, then you would have some kind of net moment here, meaning that

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‫the moments would not be balanced.

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‫And in that case, your Omega would either accelerate or decelerate.

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‫And that would mean that your omega dot would not equal to zero radians per second squared.

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‫But our omega dot is zero and therefore Omega is constant, and therefore these two moments are equal

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‫in magnitude and opposite in direction, and therefore they are balancing each other out.

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‫So because of that, our rotor is rotating at the constant rate.

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‫And this situation is really good and I mean really, really good, because that means that we have

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‫to find the moment that the air applies to this blade.

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‫So we have to find this cue.

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‫And then the opposite of that moment is the moment that the drone applies to the blade, which is what

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‫we are looking for actually.

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‫Now, just to be clear, this condition that our omega dot equals zero, which allowed us to make this

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‫assumption, it's an approximation, a more precise analysis you would have to consider Omega Dot.

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‫That is not zero, however, for approximate Rhorer talk calculations.

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‫It is a reasonable assumption.

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‫And so now let's find our Q.

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‫Because once we know our cue, we know that our MS up D, which what we are really after equals.

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‫Minus Q.

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‫And now what I would ask you to do, I would ask you to write down this differential, each force,

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‫this D.H force in terms of DL and D, just like you did it with this differential thrust force the other

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‫day.

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‫However, now write down this DH and in terms of DL and.

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‫All right.

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‫So see you in the next video.