‫Welcome back.
‫So when you have a propeller that rotates like this.
‫Then, since there is air everywhere, that air gives air resistance to this rotating propeller.
‫If we now, again, only consider one blade, let's take this right one here.
‫And think in terms of differential with airfoils.
‫Then each airfoil experiences this air resistance differential force parallel to the rotation disc,
‫meaning that this is your.
‫Rotation disk, and then each differential element here would experience some kind of.
‫Air resistance differential force that goes.
‫Parallel to the rotation disk surface, so this vector is laying on the surface of the rotation disk
‫and we call this air resistance force on the rotation disk surface D h.
‫In other words, if you look at this picture here, then this would be this d.h here, this component
‫that we had ignored previously.
‫So let's call this one D.H one, let's call this one D.H two, and let's call this differential force
‫vector D.H three.
‫And of course, the units here are Newton's like this.
‫And then if we multiply each force here by its distance from the rotation center that said this would
‫be R one, this would be R two and this would be our three, then we get the differential moment that
‫the air exerts on that specific airfoil due to the rotation of the blade.
‫So let's call it dequeue, and then it's units would be Knewton meters.
‫So dequeue, one would be D.H one, which is this force here times are one, which is this distance
‫here.
‫Then your dick, you two would be.
‫The two times are two, so this time this.
‫And dequeue, three equals the three times are three.
‫So this force times this distance, and so these are your differential moments that the air exerts on
‫that specific airfoil because of the fact that the rotor is rotating.
‫So dequeue one is for this airfoil dequeue, two is for this airfoil and three is for this red one.
‫And so if you add up all these differential moments from zero meters to the capital or meters to the
‫end of this blade, if you do that, then you will get the total moment that the air exerts on this
‫blade.
‫In other words, you would integrate over the entire blade length.
‫But now you would integrate all the products of this, the force vector and its distance from the center
‫of rotation.
‫And now, if the angular velocity of the rotor is constant, meaning that or make a dot or the change
‫of Omeonga with respect to time, if it's the zero radians per second squared, then the moment that
‫the air exerts on the rotating blade in one direction is equal to the moment that the drone exerts on
‫the blade in another direction like this.
‫So, again, if you have a bleed here and then that bleed is rotating at omega radians per second and
‫we assume that the Omega Dot or the change of Omega with respect to time is zero, meaning that our
‫Omega is constant, meaning that the rotation of the rotor is not increasing or decreasing.
‫Then the moment that is applied to the blade by the air has the same magnitude, like the moment that
‫the drone applies to the blade, but in the opposite direction, so absorbed, that's the moment that
‫the drone applies to the rotor so that the rotor would rotate.
‫And then this cue moment is the moment that the blade experiences due to air resistance.
‫So if you integrate over the entire blade length, then you will have here this cue moment.
‫And if your omega dot is zero, then that means that these two moments are equal in magnitude, but
‫opposite in direction, meaning that one is clockwise and the other one is counterclockwise.
‫And it makes sense, right?
‫They have to be equal because if not, then you would have some kind of net moment here, meaning that
‫the moments would not be balanced.
‫And in that case, your Omega would either accelerate or decelerate.
‫And that would mean that your omega dot would not equal to zero radians per second squared.
‫But our omega dot is zero and therefore Omega is constant, and therefore these two moments are equal
‫in magnitude and opposite in direction, and therefore they are balancing each other out.
‫So because of that, our rotor is rotating at the constant rate.
‫And this situation is really good and I mean really, really good, because that means that we have
‫to find the moment that the air applies to this blade.
‫So we have to find this cue.
‫And then the opposite of that moment is the moment that the drone applies to the blade, which is what
‫we are looking for actually.
‫Now, just to be clear, this condition that our omega dot equals zero, which allowed us to make this
‫assumption, it's an approximation, a more precise analysis you would have to consider Omega Dot.
‫That is not zero, however, for approximate Rhorer talk calculations.
‫It is a reasonable assumption.
‫And so now let's find our Q.
‫Because once we know our cue, we know that our MS up D, which what we are really after equals.
‫Minus Q.
‫And now what I would ask you to do, I would ask you to write down this differential, each force,
‫this D.H force in terms of DL and D, just like you did it with this differential thrust force the other
‫day.
‫However, now write down this DH and in terms of DL and.
‫All right.
‫So see you in the next video.