Lecture - 10 Propeller Geometry Part - I
摘要
TLDRDans cette séance, le conférencier aborde les hélices à vis, en commençant par l'effet de la géométrie sur leur fonctionnement. Il décrit comment un moteur entraîne un arbre d'hélice, créant une rotation qui génère une poussée axiale dans l'eau, permettant au navire de surmonter les forces de résistance. Le conférencier explique en détail les termes clés tels que couple, vitesse de rotation et vitesse d'avance (VA). De plus, il examine les différents aspects de la géométrie des pales d'hélice, y compris les types de sections de pales comme les sections aérodynamiques, segmentales et lenticulaires, ainsi que des caractéristiques telles que l'inclinaison et le décalage. Les avantages d'une pale raked pour minimiser les vibrations et les forces hydrodynamiques sont également discutés.
心得
- ⚙️ Les hélices transforment le couple du moteur en poussée.
- 🔄 Le couple est mesuré en Newton-mètres.
- 🌊 La vitesse de l'hélice impacte la résistance à l'eau.
- 📏 Les sections de pales peuvent être aérodynamiques ou segmentales.
- 🔄 Rake aide à réduire les vibrations au niveau de la coque.
时间轴
- 00:00:00 - 00:05:00
La présentation débute par une introduction aux propulseurs à vis et à leur géométrie. Un navire est équipé d'un moteur relié à un arbre de propulsion, qui transfère le couple fourni par le moteur au propulseur. Ce dernier, en tournant dans un milieu hydrodynamique (l'eau), génère une force axiale appelée poussée, permettant au navire de se mouvoir en surmontant la résistance à son déplacement.
- 00:05:00 - 00:10:00
Le couple, noté Q, en newton-mètre, fait tourner la pale du propulseur à une certaine vitesse comme indiqué par 'rpm' (révolutions par minute). La poussée générée est mesurée en newtons, et la vitesse d'avance du propulseur, VA, dépend de son environnement marin. En eau libre, VA égale la vitesse de l'eau, tandis qu'à l'arrière d'un navire, elle peut être inférieure à la vitesse du navire (VS).
- 00:10:00 - 00:15:00
On présente un modèle de propulseur à trois pales, détaillant ses composants : le boss (partie centrale), les pales, le bord d'attaque (leading edge), le bord de fuite (trailing edge), et les extrémités (tip et root). Le sens de rotation du propulseur est défini (sens horaire, propulseur à main droite) et d'autres configurations, comme le propulseur à deux vis, sont discutées.
- 00:15:00 - 00:20:00
Les éléments caractéristiques d'un propulseur sont définis : visage, dos, bords, racine et pointe. On aborde les sections et la forme des pales ainsi que leur inclinaison (rake), avec l'idée que la variation d'inclinaison aide à réduire les vibrations causées par les forces pulsantes sur la coque du navire.
- 00:20:00 - 00:25:00
Le concept de la torsion (skew) est introduit, la torsion d'un propulseur correspondant à une inclinaison par rapport à l'axe. Différents types de torsion sont expliqués, de la non-torsion à la torsion prononcée, avec des implications dans la réaction du propulseur face à différents champs de vitesse.
- 00:25:00 - 00:30:00
La géométrie des propulseurs est décrite comme tridimensionnelle, formant une surface hélicoïdale. Chaque pale de propulseur agit comme une vis à l'intérieur d'un milieu fluide. La procédure de définition des positions à l'aide des coordonnées cylindriques (R, θ, z) est abordée, illustrant comment chaque point sur la surface du propulseur peut être représenté.
- 00:30:00 - 00:35:00
L'importance de définir la pression (pitch) et la distance parcourue par rotation est soulignée. Le calcul de l'angle de la vis est obtenu à partir du rapport entre la distance de la vis (P) et le périmètre (2πR), illustré mathématiquement. Cela souligne la relation entre les dimensions physiques et la performance du propulseur. Les bases du calcul des sections d'un propulseur sont données.
- 00:35:00 - 00:40:00
Trois types d'outlines de propulseur sont identifiés : expanded, developed, et projected, avec des définitions spécifiques pour chaque type de surface. Ces surfaces sont critiques pour comprendre les performances et la conception des propulseurs. Chaque zone est définie, et les ratios de surface sont calculés pour une approche d'analyse dimensionnelle.
- 00:40:00 - 00:45:00
Un aperçu des types de sections de pales est fourni, y compris les sections aérodynamiques, segmentales et lenticulaires. Chacune possède des caractéristiques géométriques spécifiques. La section aérodynamique est traditionnelle dans la plupart des hélices modernes, tandis que des variations peuvent être utilisées en fonction des besoins opérationnels des navires.
- 00:45:00 - 01:00:28
La montée de la poussée et de la traînée par l’angle d’attaque est examinée, soulignant le concept d’angle de décrochage (stall angle). Le but est de concevoir des pales qui fonctionnent efficacement entre les angles de non-portance et d’angle de décrochage, afin de maximiser l’efficacité du propulseur.
思维导图
视频问答
Comment fonctionne une hélice à vis ?
L'hélice fonctionne en transférant le couple du moteur, créant une rotation qui génère une poussée dans l'eau.
Qu'est-ce que le couple ?
Le couple est la force de rotation fournie par le moteur, mesurée en Newton-mètres.
Quelle est la différence entre la vitesse de l'hélice et la vitesse du navire ?
La vitesse d'avance, VA, est souvent inférieure à la vitesse du navire (VS) en raison des interactions dans l'eau.
Quels sont les types de sections de pales d'hélice ?
Il existe des sections aérodynamiques, segmentales et lenticulaires, chacune ayant des caractéristiques spécifiques.
Pourquoi raker une pale d'hélice ?
Le raking réduit les vibrations en augmentant l'espace entre la pale et la coque du navire.
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- 00:00:54Good morning, gentlemen. Today, we will start on screw propellers and we will start with
- 00:01:04geometry.
- 00:01:06Every ship has an engine which is connected to a propeller shaft, a sort of shafting system
- 00:01:14consisting of a number of units ultimately as aft and the shaft is known as propeller
- 00:01:23shaft to which is attached the propeller; this propeller is rotated by means of the
- 00:01:36moment or torque supplied by the engine at a particular RPM, so once this propeller rotates
- 00:01:49it moves in a hydrodynamic medium and through interaction of water and the propeller blade
- 00:02:00an axial force is generated, which is known as thrust, in the direction in which the ship
- 00:02:10is moving. A ship when it moves forward it experiences resistance to its motion in the
- 00:02:20reverse direction, this force generated by the propeller known as thrust overcomes this
- 00:02:28resistance and allows the ship to move forward- this is the principle on which the propeller
- 00:02:38works.
- 00:02:40Simply said or diagrammatically said it is like this: you have the engine here somewhere,
- 00:02:51now, you have got a shaft coming here, and then this comes out of the ships, out of the
- 00:03:06ship on which is housed the propeller; now, the engine provides the moment to the propeller
- 00:03:17at a particular RPM, this propeller works in this fluid medium- this medium is fluid,
- 00:03:23water- and produces a thrust or an axial force in this direction, which is finally transmitted
- 00:03:32to the ship along the propeller shaft, and since the propeller shaft houses a baring
- 00:03:40here, thrust baring, through the thrust baring it is transmitted to the ship structure and
- 00:03:45the force is applied to the ship and the ship moves forward overcoming this force, R, resistance,
- 00:03:55which is experienced by the ship at a particular speed V .
- 00:04:05The propeller geometry is such that when it rotates the one side of the propeller forms
- 00:04:18more or less a part of a screw- I suppose all of you have seen a screw, a nut and bolt,
- 00:04:27a bolt on which a screw is carved out and when you rotate a nut it travels in a particular
- 00:04:36fashion- a propeller blade surface, one of the surfaces is a part of this screw surface
- 00:04:45and that is why a propeller fitted behind a ship is called a screw propeller, so, this
- 00:04:55is, this is called a screw propeller. Before we go further it is necessary for us to understand
- 00:05:08the geometry of a propeller.
- 00:05:15So, what have we got so far? The torque coming out from the engine being applied on the propeller
- 00:05:24is called torque Q represented as capital Q, and its unit is Newton meter- we are all
- 00:05:36talking about SI units; rotates the propeller blade, rotates at rpm at revolutions per second
- 00:05:46denoted as small n, rps, unit be second inverse, sometimes it is more convenient to say revolutions
- 00:05:58per minute in which case you write capital N, rpm, which is equal to n into 60; and then
- 00:06:08we have thrust generated, which is called thrust and the unit is that of force, Newtons.
- 00:06:19And this operates at a speed normally called velocity of advance VA. Now, this velocity
- 00:06:28of advance varies from, varies as where the propeller is working, if the propeller is
- 00:06:39working in open water, which will be seen, the VA will be equal to the speed of water
- 00:06:46whereas, if it is working behind the ship, it will also, the VA will be the mean velocity
- 00:06:55of water on to the propeller, which may be less than the ship’s speed that is, if I
- 00:07:04write VS as ship speed, VA will be less than VS- units of all speeds will of course be
- 00:07:17meters per second, or more conventionally knots, which can be converted to meters per
- 00:07:23second by multiplying with 0.5144.
- 00:07:28I have got some propeller to show you here. I will show you this propeller, this is- can
- 00:07:40you see this?- this is a model propeller having three blades- can you see this?- this portion
- 00:07:52is called the boss of the propeller on which there are three blades. So, this is a three
- 00:08:01bladed propeller and this boss has a hole as you can see, which sits on the propeller
- 00:08:10shaft like this, so the shaft is on my right and the ship is also on my right that means,
- 00:08:22this side is the aft side, or this is, this portion is behind the ship, the ship is in
- 00:08:29front and it is moving that way. How is the propeller rotating? This is, if you are looking
- 00:08:37from behind the propeller, behind the ship let me say- still we have not said which is
- 00:08:45front and back of the propeller- suppose, I am looking at the propeller from the from
- 00:08:51behind the ship that is, from this side, then, if it rotates in the clockwise direction-
- 00:09:00is it the clockwise direction. this direction? Anticlockwise- so, how will be the clockwise,
- 00:09:10how will it be clockwise here, this way? Right. If it rotates.
- 00:09:16Looking from aft, looking from aft that is, this side, if I rotate it like this, then
- 00:09:21this is clockwise, this is called the right hand screw, right handed screw; if it rotates
- 00:09:28the other way, then it would be call the left handed screw. Normally, single screw propellers
- 00:09:34are all right handed propellers, right hand screws, but if I have a twins screw propeller
- 00:09:43that is, one on the fore side and one on the stable side to balance the uneven forces that
- 00:09:48may be generated, I would like to rotate the propellers, each propeller in the opposite
- 00:09:54direction, so, that means, one will be right handed propeller and the other will be left
- 00:09:58handed propeller. So, right now let us look at this right handed
- 00:10:02propeller, what are its characteristics? The side that is facing you when you are standing
- 00:10:11behind the ship and propeller that is, this side, is called the face of the propeller-
- 00:10:21this is the face- actually, it is behind from the aft side, and this is the back of the
- 00:10:30propeller, and the edge that meets the water first, if it is rotating like this, this is
- 00:10:40the edge that is meeting the water first, so, that is called the leading edge of the
- 00:10:46propeller, and the other one is the trailing edge, this edge trails the propeller- am I
- 00:10:58clear? The furthest point of the propeller blade is called the propeller tip and the
- 00:11:05one that joins the propeller blade to the boss is called the root. So, I have got the
- 00:11:12root, the tip, the leading edge, the trailing edge, the face and the back. This would more
- 00:11:18or less define all the main features of a propeller and number of blades of course,
- 00:11:23and along with RPM and torque it is supposed to observe; what we have not defined yet is
- 00:11:29section shapes and the outline of the propeller blade now, we will see how they can be defined.
- 00:11:35Showing it in the form of a diagram- can you see this, is it visible to you, yes, clearly
- 00:11:43visible? So, this is the shaft where this shaft is rotating in the clockwise direction
- 00:11:57looking from this side, and this is the face, this is the back, leading edge, trailing edge,
- 00:12:09this is the boss, this is the tip and this is the root where the propeller joins the
- 00:12:18boss- is that clear? Now, let us look at some other features of the propeller blade.
- 00:12:32Now, you see here- is this visible, clear, or should I draw it? So, if the propeller
- 00:12:45axis is perpendicular to the shaft center line- this is the propeller center line, propeller
- 00:12:54axis as it is called, the shaft center line on which the propeller sits is called the
- 00:13:02propeller axis- if the propeller blade as in this case, as in this case, is the propeller
- 00:13:10blade is perpendicular to it in this plane, if it is perpendicular like this, then this
- 00:13:21is called a propeller with no rake. But sometimes it may be necessary to rake the propeller
- 00:13:30or tilt the propeller blade to one side of the plane perpendicular to the propeller axis
- 00:13:41like it is shown in the next diagram, this diagram- can you see it, is it understandable,
- 00:13:51can you understand? What benefit do we give, do we get if I rake
- 00:13:57the propeller? You can see this distance between the propeller trip and the hull here is less
- 00:14:05than the distance between the propeller trip and the hull here. We know that propeller
- 00:14:13works in a velocity field, which is varying and therefore, it is possible the propeller
- 00:14:19may transmit pulsating pressure forces on to the ship hull, which may cause vibration
- 00:14:27in this overhang portion of the hull that is, the stern, which may be transmitted to
- 00:14:34accommodation and the other areas. One way to reduce the effects of this vibration is
- 00:14:40to increase the clearance between the propeller tip and the hull- this minimum distance as
- 00:14:50I have discussed earlier is given by classification societies. So, if you do not get adequate
- 00:14:57clearance here, rake propeller is one way so that we can get increased clearance between
- 00:15:04the hull and the propeller. Next, we have what is called skew of a propeller.
- 00:15:19Normally, propellers do not have forward rake normally, they do not have forward rake, but
- 00:15:26can always have a forward rake, it is not denied, but it is generally not there, because
- 00:15:35if you here forward rake the clearances reduce, the way the propeller is fitted behind the
- 00:15:42ship. Skew is, if I take the propeller axis like
- 00:15:51this and if it is perpendicular to this, it is called no skew. So, there is another way
- 00:15:56to define this.
- 00:16:03This is the propeller boss, I have got a blade here; now, at each section if I draw a radial
- 00:16:15section, radius here, and this is my section, I draw the mid line here, midpoint, if I join
- 00:16:22the mid points of all sections like this, all radial sections with this as center and
- 00:16:29I find they lie in one line, which is perpendicular to the center like this, then this is called
- 00:16:45a propeller with no skew, but if I have this blade shifted like this where the center point
- 00:17:03gets shifted to this, then this axis, the propeller’s vertical axis is tilted to one
- 00:17:16side, then it is called skew.
- 00:17:19Now, some of these diagrams, this diagram shows you various types of skew that exist;
- 00:17:28this is a propeller blade with no skew, this is a propeller blade with slight skew and
- 00:17:34this is a propeller blade which is called heavily skewed that is, the skew is very high.
- 00:17:42And you can see the center line of each blade plotted here, and the measure of the skew
- 00:17:49is generally the angle between the propeller non-skewed axis to the line joining the propeller
- 00:18:01center with the tip, that line, this is the skew line and the measure is up to the tip,
- 00:18:10the skew at the tip, that angle- is that clear? So, this is normally how propeller rake and
- 00:18:18skew are designed. Why is propeller blade skewed, there should be some reason why we
- 00:18:25do these heavily skewed propellers, particularly, one can appreciate that moderately skewed
- 00:18:32propellers can be designed to suit the geometry and other constants, but why heavily skewed
- 00:18:38propellers? It has been found that heavily skewed propellers can adopt themselves to
- 00:18:45varied weight field or varied velocity field much better than normal propellers so therefore,
- 00:18:54these propellers have been advocated and have been fitted to a number of ships who, where
- 00:19:03the velocity field is very uneven, which might have caused vibration.
- 00:19:13Sir it been right handed skew also increase the gap in both the ways
- 00:19:26Skew may increase gap, but may not because skew is actually in this plane, so when the
- 00:19:31propeller blade rotates at someplace the gap may reduce, someplace it may increase, but
- 00:19:38of course, a well designed, a well skewed propeller may actually improve the gap.
- 00:19:44Now, let us look at this. Propeller geometry is actually very interesting, it is a highly
- 00:19:58three dimensional geometry, the face and, the propeller face forms a part of what is
- 00:20:07called a helicoidal surface. Now, what is a helicoidal surface? We have already mentioned
- 00:20:16that it forms a part of the screw surface, if I have an axis here like this and I have
- 00:20:25a line here perpendicular to the axis and I rotate this line here, then the tip of this
- 00:20:33line will form a circle. But along with rotating I also give a forward speed to this line that
- 00:20:43is, I not only rotate at a constant speed, but I also move this along this axis, so,
- 00:20:48how will it form? It will go like this. Now, the line that is formed by the tip is
- 00:20:58a three dimensional curve known as a helix, the three dimensional curve is known as a
- 00:21:09helix, now, if this entire line I trace, it will form a three dimensional surface, which
- 00:21:18is called a helicoidal surface- is that ok? So, here what we have shown is this diagram,
- 00:21:37if you look at this diagram- can you see, is that clear?- this is a cylinder of a constant
- 00:21:45radius R and on top of this I have tried to move this R at a constant speed along the
- 00:21:53cylinder, it will move on the cylinder surface- is it not?- because R is constant, so this
- 00:21:58is the, line A will trace a line like this, a three dimensional line up to A1- it is shown,
- 00:22:04it is shown in a plane, but it is actually a three dimensional curve, this line actually
- 00:22:08goes like this. Now, there are two planes I have, we have,
- 00:22:17defined here: one is the perpendicular plane to the, in one, one perpendicular plane to
- 00:22:22the propeller axis, which is called the theta equal to 0 axis; and another one normal to
- 00:22:29the both this propeller axis as well as this plane, which we have called as z axis. Why
- 00:22:35I have done this?
- 00:22:36Normally, we know Cartesian co-ordinate system; in Cartesian co-ordinate system we defined
- 00:22:44the position of a point by x, y, z co-ordinates in three dimensions- is that right?- in space
- 00:22:53if I define an axis system x, y and z, then any point here will be defined by x, y, z;
- 00:23:05x is the distance this way, y is the distance this way, z is the height, from this plane,
- 00:23:11how far it is. Now, in propellers since, it is connected with a cylindrical movement it
- 00:23:22is easier for us to define the propeller, a point on the propeller blade in what is
- 00:23:26called cylindrical cylinder co-ordinates- this is Cartesian co-ordinates- that is R,
- 00:23:47theta and z- this z remains same as the Cartesian co-ordinates, but r and theta that is, if
- 00:24:01I have got this propeller, this propeller let us, let us compare this with this diagram
- 00:24:06that we have seen.
- 00:24:10This is the propeller blade, this is the propeller blade, and a point here if I move, it will
- 00:24:20form a helix, this line, this plane is the theta equal to 0 plane, this plane that means,
- 00:24:32if I take a radius r, I take a radius r here, if this plane is defining theta equal to 0,
- 00:24:42then the point passing through that circle that I have drawn would be theta equal to
- 00:24:480, but any other point here we will have to move through an angle theta- am I clear, Mr.
- 00:24:59Mukharji? So, this point can be defined by R and theta, but it has also a co-ordinate
- 00:25:06in this direction, that I am calling z, if I pass a plane here, a z equal to 0, then
- 00:25:15the point from that plane to this point will be the z point; so, this point we will have
- 00:25:20a R co-ordinate, will have a theta co-ordinate, which is how much it has moved angularly from
- 00:25:26this axis and the z co-ordinate that from standard plane how far it has gone, how far
- 00:25:32deep it is, how deep it is- is that clear? So, any point in space can be defined by three
- 00:25:42co-ordinates; in Cartesian co-ordinates we had x, y, z, where all the three co-ordinates
- 00:25:47are measured linearly from the three defined axis; in the cylindrical co-ordinate system
- 00:25:53we are defining by a point, by R theta and z. So, R and theta define a point in a plane
- 00:26:04perpendicular to the propeller axis- R is this distance and theta is the angle, and
- 00:26:10z is the distance from that plane- so, that defines the co-ordinates of a propeller.
- 00:26:20So, that is what is shown here, the axis theta equal to 0 and z equal to 0 are shown, so
- 00:26:26any point on this can be...Now, you see this is the face of the propeller blade, this is
- 00:26:31propeller blade- this is the face corresponding to the diagram we had seen earlier- this helix
- 00:26:39forms a part of that face, or rather the face forms a part of this helix that has been shown
- 00:26:45here, this part of the curve. Now, if I open this cylinder up, I have drawn this line on
- 00:27:03the cylinder now, I open it up, what do I get? You see here, this is the cylinder of
- 00:27:11radius R, so if I open it up, it will open up to 2piR and the distance here along this
- 00:27:20axis if it has moved, it has moved through a distance called pitch- I have not defined
- 00:27:29pitch earlier that is, when this, when this line moves through one revolution, the distance
- 00:27:38it has travelled longitudinally or axially is called the pitch of the helix, or helicoidal
- 00:27:50surface if the entire surface is moving the same distance.
- 00:27:54So, when I open this cylinder up, what do I get? This side will be p and this side will
- 00:28:02be 2piR, this is what is shown here P is, one side will be distance P the other side
- 00:28:10will be distance 2piR, and this helix will convert itself to a diagonal, it started from
- 00:28:18one end and ended at the other end- do you understand? So, this A, A1 that we had here
- 00:28:28is converting itself when I, when I open up the cylinder into a diagonal of the rectangle
- 00:28:35the two sides of which are P and 2piR ; now, this section that was here, this helix that
- 00:28:51was here on this face, face section that was here that will now appear here on this diagonal.
- 00:29:03Now, this section that you have seen this side is the face and this side is the back;
- 00:29:10now, I said that the face is a part of a helicoidal surface, or at a particular radius it is a
- 00:29:17part of a helix, what is shown here is the helix, but you will notice that if I expand
- 00:29:27this, this is the diagonal going and my section shown here is something like this, is not
- 00:29:36actually, the face is not actually on this line there is little bits of deviations from
- 00:29:40here, and this is the back, this is the face – is it not?
- 00:29:53So, this is what is shown here, I have just expanded this, you see here, the face is more
- 00:30:01or less falling on this helicoidal line just slightly adjusted, slightly offset at the
- 00:30:07leading edge and the trailing edge, this is the leading edge L and this is the trailing
- 00:30:11edge T, the projections of L and T on the exact line is shown here as Ldash and Tdash.
- 00:30:22So, this is the actual section shape of the blade at that radius R- am I clear? Now, if
- 00:30:43this, it is projector, in other views they will look like this, I think we can skip it
- 00:30:51for the time being and proceed further- any doubt so far regarding how wave propeller
- 00:30:58should behave? Sir this ensures it will be flat face
- 00:31:04No, it will not be a flat face. Of course, it is a curved face, this is what I have shown
- 00:31:11here, this is curved, this is curved; this is, this is face, this is supposed to be on
- 00:31:24the helicoidal surface and this you can see is not strictly on the helicoidal surface,
- 00:31:30but it is slightly offset from the helix at the ends that is, at the leading edge and
- 00:31:35the trailing edge; back is not on a helicoidal surface, we are not saying that same thing
- 00:31:42for the back, we are more concerned about the face, but it is more or less on a helicoidal
- 00:31:49surface, this is what we are trying to say. So, if the propeller actually moved as a helicoidal
- 00:31:56surface in a solid medium, please understand, if it moves in a solid medium, then there
- 00:32:03will be no slip, when you move the propeller forcible like a nut moves on a screw of a
- 00:32:10bolt, it does not have any facility to slip away unless the screw has broken. The nut
- 00:32:20will move when you move it, one revolution- sorry- one rotation, it will move a certain
- 00:32:27fixed distance, if you move it ten times, it will move ten times of that distance, that
- 00:32:35distance, which it moves in one rotation is called the pitch- and this is what we defined
- 00:32:41pitch here. But since the propeller is moving in a fluid medium it may not move, behave,
- 00:32:49as if it is moving in a solid medium therefore, there may be slip, its actual movement may
- 00:32:55not be equal to P, if I defined P as pitch that is, the distance moved in one revolution
- 00:33:06of this helicoidal surface, the propeller actually need not move P, it may move less
- 00:33:11because it is in a fluid medium, it may slip- this part we will see later.
- 00:33:17Right now, let us just understand that though we are defining the propeller blade as a helicoidal
- 00:33:23surface and defining P as a distance moved in one revolution, in an actual case, propeller
- 00:33:29may not move distance P in one revolution because the medium is not solid, there may
- 00:33:38be many other reasons, but one of the main reasons is it is not solid, to overcome the
- 00:33:43resistance in a solid medium, we are actually applying manual force to move it; in a fluid
- 00:33:50medium what happens as we go along the course we will see- have I been clear ?
- 00:34:03So, most difficult part of propeller geometry is representing it diagrammatically, showing
- 00:34:14its various features. So, if I bring back this diagram again, this
- 00:34:23section that is shown here, this section is what is called an expanded section that is,
- 00:34:31if I expand the helix this is how the section would look. Remember, what I have actually
- 00:34:37drawn is, what I have actually done is I have taken this propeller a at a constant radius,
- 00:34:45a constant radius, it is not a flat line, it is a constant radius, the section shape
- 00:34:51what I have shown here, it is not a straight line it is at a constant R; what I have shown
- 00:34:58here is if that radial arc was made into a straight line, how this section would look-
- 00:35:08do you understand- we expanded this to a straight line, is it not the helix?
- 00:35:13This is a diagonal, it is a straight line. So, this is as if we have expanded it along
- 00:35:20this line and the angle of this line is phi of pitch angle, you see this angle here, phi-
- 00:35:30can see?- this angle is called the pitch angle defined by the P and 2piR.
- 00:35:38And what is pitch angle? You can tell me, tan phi is equal to, tan phi equal to P by
- 00:35:502piR,P divided by 2piR is the tan phi. So, pitch angle phi is tan inverse of P by 2piR
- 00:36:01. So, here you have got this line, which would
- 00:36:08come on the helix if it was drawn in your straight line at an angle to the 2piR line
- 00:36:17phi, and this would be as if the section has been straightened.
- 00:36:22That is not the section of that part where it is cutting
- 00:36:27Yes, it is exactly that, it is exactly that. If I take R here and cut it here, if I take
- 00:36:35this R and cut it here, this is actually a section in three dimensions, but if I have
- 00:36:41expanded it, pulled it out along the helix, then it becomes a straight line, the section
- 00:36:49elongates in length along that line- do you understand?- so, that is that section, it
- 00:36:58would look like this and this is the actual section with which we will be dealing, this
- 00:37:06is called an expanded section- you got it? Expanded section- am I clear, has it been
- 00:37:29understood?- actually, it is on a three dimensional plane, the section is in three dimensions,
- 00:37:34it is as if I have pulled it out to a straight line and that straight line is at an angle
- 00:37:39to horizontal, then that section will look like this.
- 00:37:43Now, what I do is I now move it at that same distance r, I make that line horizontal instead
- 00:37:52of diagonal like this, I make this line like this, horizontal, I made this line horizontal,
- 00:38:01just physically moved it then, I get a line- you see here, can you see this diagram clearly,
- 00:38:10all of you can see it? This is that angle phi, this is the angle phi, here is what I
- 00:38:20have R theta L and R theta T- I do not know whether I have explained this to you or not.
- 00:38:29This distance, this distance here is called r theta L, you see, this is, this distance
- 00:38:39is actually how I would have seen it on the arc- that is, that is the projection, this
- 00:38:50distance is the projection into this plane, in theta equal to 0 plane, projection is from
- 00:38:58here to here- tell me if you are not understanding, this is very important for us to define the
- 00:39:08three areas, that are important to proceed with later on.
- 00:39:25What have we done? We have expanded the cylinder; this is P, this is 2piR , the cylinder was
- 00:39:41like this, in this it was like this, I have expanded it, this is the helix that I had-
- 00:39:55so far so good?- now, when I expanded the helix since, at a particular radius of the
- 00:40:01propeller blade the face I am saying is a part of the helix that would come has a straight
- 00:40:08line here actually, it is not straight will it come as a straight line? So, let us say
- 00:40:15the pitch was coming here, face was coming here now, I am not giving any offset to face-
- 00:40:19let us understand the geometry first- and it has a back like this let us say, this is
- 00:40:26my blade section, but if I look at the propeller blade straight away like this, then this would
- 00:40:37be my point, this is my projected length, my projected length if I do a projection of
- 00:40:47the propeller blade, it is here, but if I expand that line, then the propeller blade
- 00:40:53comes like this, elongated- this can be understood. Sir Yeah.That part will be and that propeller
- 00:41:03is a three dimensional. So, there is a difference there also you are telling that
- 00:41:11We have taken the pitch. We have taken the pitch here, this is the length of the propeller
- 00:41:19blade section, actual length. that is the Yeah. Um.That the arc will be
- 00:41:29a two dimensional curve. This arc is a three dimensional curve, this
- 00:41:34is a helix, the part of a helix, this arc, this arc is also moving, it is part of a helix-
- 00:41:45do you understand?- so, this is, now, as if I have straightened the helix, so this is
- 00:41:54a longer length, which I am actually not seeing, what I am seeing is the projection here, this
- 00:42:01much. So, this is actually the projected length of that section, but this is the actual length,
- 00:42:10if I measure the length, it would be this, what is this, what is this? At constant R
- 00:42:18if I measure, I take a thread put it from here to here at constant and expand it this
- 00:42:24is the length I will get. That is a actual actual length.
- 00:42:30Actual length at radius R- is that clear? So, this is phi and I can say this is theta
- 00:42:45equal to 0 line, what is the, see this is theta equal to 0 line let say, and this is
- 00:42:51R, so what is the length of this arc, projected length? Now, let us say projection means I
- 00:42:58will have a circle and a cylinder at a constant section and I draw a line, what is that arc
- 00:43:07length? R into theta, whatever is a theta, so this distance is therefore, R into theta
- 00:43:15L and this distance is R into theta T, trailing edge this is L, this is T, the projections,
- 00:43:25mind you- is it too difficult? See here, let us make this surface flat for
- 00:43:42the time being, what is the section you will see? You will see this length, if I take a
- 00:43:49photograph, what length I will see? This length and that will be on this arc, so the length
- 00:44:00of this will be R into theta, length of an arc is R into theta, all I am saying from
- 00:44:06standard co-ordinates the leading edge will be R theta L and trailing will be R theta
- 00:44:13T- that is the projection.
- 00:44:18So, now when I draw the propeller outline and come back to this diagram, when I draw
- 00:44:29the propeller outline, if I draw an angle phi here, my section would have come here,
- 00:44:36that I am drawing on a horizontal plane. So, this is R theta T and this is R theta L along
- 00:44:52that diagonal line at angle phi and that when I bring it to the horizontal plane it becomes
- 00:44:58a longer line- do you understand? So, this section is now known as the expanded section
- 00:45:10drawn horizontally- have you understood, I am asking you, you have understood? Good
- 00:45:32But if I have, if I want to draw a projected line, then it is only on that arc I put, if
- 00:45:41I draw at an R, draw theta L and theta T this side I get this L and theta lines and join
- 00:45:48them I will get the projected line- projection is very simple once I know the pitch and I
- 00:45:53once I know the angles, theta L and theta T, I can easily draw the projected outline.
- 00:46:00The expanded outline I have to draw by drawing this phi line, the pitch, and then projecting
- 00:46:07it into a horizontal line, that would give me an outline which is called the expanded
- 00:46:13outline. So, you have got an expanded outline, you have got the projected outline.
- 00:46:22Now, there is a an outline called the developed outline that is- see what we are getting-
- 00:46:34the projected outline is if I had R here and I drew it, if I took the photograph here,
- 00:46:39how that line would look that is, this circle T C and L – is it not- that is why I am
- 00:46:48doing the projected line. Now, suppose I do not actually make it into a straight line,
- 00:46:52but bring this circle to a single plane, this circle is in three dimensions if I bring this
- 00:47:01out to two dimensions, then I will again get a line which is more than the projected line-
- 00:47:08can you understand?- that line is called the developed line, where that will be horizontally
- 00:47:21projected from L and T to give, here in this case we have done Ldash and Tdash, which is
- 00:47:27the along with the offset of the leading edge. It is the horizontal line and it would come
- 00:47:34on another circle, which will be geometrically defined as, if you take P by 2pi this side
- 00:47:41and angle phi here, you will get this center and from there you draw a circle, which will
- 00:47:46automatically give this Ldash and Tdash projected horizontally on this circle to Ldoubledash
- 00:47:52and Tdoubledash if you join them they are called developed outline- have you understood?
- 00:47:59Basically, what I have done if I take a radius R a section if I draw it projected, same section
- 00:48:07I get projected outline, if I that section I bring to a single plane by expanding it,
- 00:48:13not by making horizontal, but in that same circle, then I get developed outline, that
- 00:48:19circular line if I pull it and make it straight, then I get expanded outline.
- 00:48:32Actual expanded outline is not opening the second curvature, well, yes, that is true,
- 00:48:42in two different planes. We will stop now, have a small gap and start again. Thank you.
- 00:49:10We will continue with propeller geometry.
- 00:49:15We have seen there are three outlines that can define a propeller: the expanded outline,
- 00:49:22the developed outline and the projected outline.
- 00:49:25Correspondingly, there are three areas that we can define that is: expanded area, developed
- 00:49:38area and projected area. Now, the area that is covered by the circle with radius R that
- 00:49:55is, propeller radius, R is the radius up to the propeller tip, that is called the disc
- 00:50:02area, A0, which is equal to pi R square or pi D square by 4, if D is the propeller diameter.
- 00:50:18Expanded area normally is represented by AE; developed area AD; and projected area AP.
- 00:50:25So, non dimensionalising this we have three area ratios that is, expanded area ratio,
- 00:50:40which is equal to AE by A0; similarly, developed area ratio is equal to AD by A0; and projected
- 00:50:53area ratio, which is equal to AP by A0. So, this is the definition of area.
- 00:51:04Propeller diameter is given by D, and propeller pitch as we have seen is given by p. Now,
- 00:51:11this pitch will be constant at all radii if the propeller face formed a single helicoidal
- 00:51:24surface.
- 00:51:26But sometimes we may not give a constant pitch across the radius that is, the pitch may vary
- 00:51:35like, if this is the radius R- this is full radius- then your pitch distribution may be
- 00:51:49constant; if it is a constant pitch, then the pitch distribution will be like this to
- 00:51:56the R, this is the pitch, at all radii the pitch is constant. On the other hand, I may
- 00:52:06decide that this pitch distribution is not ok, I can reduce pitch at the root and increase
- 00:52:13pitch at the tip, so in that case I can also give a pitch distribution, which may look
- 00:52:18like this; I can give a variable pitch distribution to the propeller blade. In that case, what
- 00:52:30will be the resultant pitch? If I give a variable pitch distribution, the
- 00:52:40resultant pitch of the propeller, if I want to designate it by a single quantity, then
- 00:52:47in the variable pitch case, resultant pitch, you will, you can see, can be given as mind
- 00:52:57you, the pitch is starting only after the root, the boss, the blade is starting from
- 00:53:04the root till the tip. shape is known as aerofoil section where you
- 00:53:12can see the leading edge is not really sharp, it is rounded and the trailing edge is sharp-
- 00:53:21that is how propeller blades are made- the leading edge has a curvature, but the trailing
- 00:53:26edge is sharp. There is another way of knowing for which is the leading edge- the one that
- 00:53:33is sharp is the trailing edge, the one that is blunt is the leading edge and that is the
- 00:53:40one that will be meeting a water first, so you can also decide which way the propeller
- 00:53:44rotates by just looking at the propeller if it has the aerofoil section.
- 00:53:50Now, as we have seen later, earlier, you can also give some offset to the face from the
- 00:53:58straight line and still it would be an aerofoil section. This is the most commonly used section
- 00:54:06for majority of propellers available in the world. This on the another hand is called
- 00:54:14a segmental section where the back of the propeller section is a part of a circle- unlike
- 00:54:24an aerofoil section you can see it is not part of a circle, it is blunt forward and
- 00:54:29sharp towards the trailing edge- here in the segmental section the back is part of a circle,
- 00:54:40this is many times used where there is a requirement of a, typically these sections are used in
- 00:54:52propellers for trollers where you require not only free running speed, but also some
- 00:54:59amount of pull that one must exert such as, hauling a troll net or something like that.
- 00:55:09In many propellers there is a combination of both aerofoil section and segmental section
- 00:55:18that is, aerofoil sections up to a certain radius and then the section slowly change
- 00:55:23to segmental section- we will see some of these propellers later on.
- 00:55:28Then, what we have is called a lenticular section where the section is symmetrical about
- 00:55:35its central line. There will be a drag in the same direction,
- 00:55:41but lift in the opposite perpendicular direction. So, if you look at this lift, which is going
- 00:55:47like this, most of its component is in the axial direction; if I now compute it, one
- 00:55:56is this direction, one is in this direction, most of it is this way because perpendicular
- 00:56:01to, perpendicular is very, making very small angle to the axis of the propeller.
- 00:56:12Thrust and lift are not same, are not different, the axial component of lift is the thrust;
- 00:56:21otherwise, what is thrust, how do you get this axial force? This lift that I am getting,
- 00:56:29the component of that in the axial direction is what I call an element of thrust by any
- 00:56:35point here, that thrust integrated over the whole blades, all blades, gives me the total
- 00:56:42thrust on the propeller- is that clear? I am also loosing something in the form of drag,
- 00:56:52so, ultimately, the propeller efficiency will be, is a ratio between lift and drag- but
- 00:57:01have you understood how lift is being generated?
- 00:57:04So, let us look at this diagram a little bit. We also know from aerofoil theory that if
- 00:57:13you go on increasing this angle- this angle alpha called the angle of attack- if I go
- 00:57:19on increasing this angle of attack, lift increases more or less linearly like this- as I have
- 00:57:27shown here- that is, I get small lift if the angle is small, and if my velocity angle of
- 00:57:36attack is more and more, I get more and more lift. But very strangely beyond a certain
- 00:57:43lift angle, certain angle of attack- this is angle of attack axis- lift suddenly drops
- 00:57:50that means, you do not get any more lift- this is called the stall angle, it is called
- 00:58:00the stall angle. So, we have to design your propeller that the lift is, the angle of attack
- 00:58:05is within this. Now, when you go reducing the angle, when it is at a particular angle
- 00:58:11to the propeller there will be no lift, so that angle is somewhat this- this is called
- 00:58:16the no lift angle; only when the angle is created with respect to that, start getting
- 00:58:20lift till stall angle; so, our aim should be to design the blade sections so that you
- 00:58:27stay between no lift line and stall angle- am I clear? We will stop here and next class
- 00:58:38we will continue with propeller theories. Thank you.
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