Today, we will conclude the lecture series on propellers. We have been looking at lot of propeller fundamentals, propeller theories. We have looked at propeller theories that provide a basis of propeller estimation, performance estimation, propeller shape estimation, size estimation. One of the theories actually was developed without even considering the propeller shape, blade shape. However, after these coverages, what we can do is, we can look at the propeller blade shape and we can look at some of the typical propeller shapes, blade shapes, aerofoil shapes that have been used in the modern propellers. And then, of course, we will conclude the lecture series with tutorial, which means I will bring in a solved problem for you and then I will leave you with a few problems for you to solve for yourselves. So, this series of problems should help you in understanding the theory that we have covered. Very simple theory is really and it should also help you in creating propellers that you would, if you would like to create a propeller for yourself, for your small craft that you may be making. So, all these is possible with the simple theories that we have done in the course of last three lectures. And today, we will conclude this series of lectures on propellers. Today's lecture is mainly about creating the blade shapes to begin with, before we take up the propeller problems. The blade shapes that we know are made up of aerofoils as we have seen. Now, some of these blade shapes are very peculiar or I would say original to the propeller blade shapes. The aerofoils that are used in propellers are not used in any other applications. They are typically made or designed for propellers only. And hence, we have aerofoil shapes and blade shapes that are typical to the propellers of various kinds. Now, propellers can be of various kinds. As we have discussed, propellers can be subsonic. They can be transonic. We have not got down to making propellers which can work in supersonic flight conditions. So, even today, we do not have propellers that can fly an aircraft through supersonic speeds. It cannot go through the shocks. The efficiency of the propellers goes down very fast. And hence, they are not competitive to the jet engines. But, at subsonic speeds, it is pretty much known that the propellers are more efficient device for thrust making than many of the jet engines. And as a result of that, at low subsonic speeds, even today, propellers are the most preferred form of thrust making device for aircraft flight. Whereas, at somewhat higher subsonic speeds, the turbo fans and the turbo jets have their own place, especially for long distance flights. But, there are many applications of propellers, especially the ones we call turboprops. That is propellers powered by gas turbine engines are used extensively in many medium subsonic to slightly high subsonic transport aircraft, both for cargo as well as for passenger. As theoretically, propellers are indeed the most efficient thrust making device. In fact, the propellers are being now redesigned to operate with transonic tip speeds. And we shall have a look at such a propeller today. So, let us start taking a look at what a conventional propeller looks like. And then, we will take a look at the transonic aerofoils and a transonic, typical transonic modern propeller, what it looks like. A typical propeller, as we have discussed many times, is made up of aerofoils. Now, if you look at this one single blade of a propeller, you can see that along the length of the blade, the aerofoil section or the aerofoil shape changes drastically. Near the root of the propeller blade, the aerofoils are very thick. They could be symmetrical aerofoils as the requirement here is not so much as aerodynamics, but the requirement here is more of structural integrity and the strength of the propeller. As this entire propeller is held at the root of the propeller and essentially, structurally speaking, this entire propeller is a cantilever beam in rotation. And as a result of this cantilever arrangement of the propeller holding, the entire propeller load, the aerodynamic load, the lift and the thrust that we have talked about created by the propeller itself has to be borne at the root of the propeller and that is where all the stresses, strains and the moments are actually finally felt. So, this portion needs to be made very strong so that they can hold the propeller in rotation. This is something which has to be taken care of right in the beginning of the design and as a result of which, in this portion of the blade, the aerodynamics is often sacrificed and the structural strength of the propeller blade at the root is given precedence. However, a little after that, especially from here onwards, let us say, you need to create propeller blade shapes that help in creating lift and which as we have seen finally, help in creating thrust. Now, the aerofoil sections that we choose in these sections are essentially conforming to the local flow. As we have seen in the velocity triangles earlier, the local flow incident on the blade there is typically low subsonic, a combination of forward velocity which we call V infinity and the rotational speed twice pi n r or omega r. Now, at this station near the root, somewhat near the root of the propeller, the local velocity V r is rather small, most likely to be low subsonic and hence you use a aerofoil section which is indeed low subsonic aerofoil. So, the aerofoil section that you choose around here is typically meant for low subsonic usage. They are low cambered, but thick aerofoils which conform to low subsonic application and you need somewhat thicker aerofoil to create a substantial amount of lift which as we know would then create a significant amount of thrust. However, as you move along, you will find that the aerofoils are becoming thinner and thinner and thinner and at the tip it is a very thin aerofoil. So, they become progressively thin aerofoils and as we can as we know from the aerofoil understanding that these are all different aerofoils. These are not the same aerofoils made thinner, these are indeed different aerofoils all together because at the tip, again if we go back to the velocity fields that we were talking about near the tip of the propeller, the resultant velocity V r incident on this leading edge is going to be rather high and this is likely to be high subsonic for most of the modern aircraft propellers. So, you need a high subsonic aerofoil which is normally a thin aerofoil to keep the drag low otherwise the drag would mount very fast. A thick aerofoil which you use near the roots, if you use near the tips would create enormous amount of drag at that high speed and as a result of which the propeller efficiency would be extremely low. So, you need to create aerofoil which has a very high lift by drag ratio. Now, C L by C D of course, as we know is essentially a figure of merit for aerodynamic efficiency of any aerofoil and as a result of which as you go towards the tip from the root to the tip you have thinner and thinner aerofoil. So, that you continue to have high aerodynamic efficiency of each and every of this sections and as a result of which the overall thrust creation is done with higher propulsive efficiency or propeller efficiency. Now, this is the reason because of which you have so many different kinds of aerofoils as you go along the length of the propeller from root to the tip of the propeller. The another thing you would notice is near the root of the propeller the angle at which the aerofoils are set are at high angle. For example, near the absolute root which is actually inside the root the angle is nearly 42 degrees and then near the the next aerofoil which is a proper aerofoil lift creating aerofoil the angle is 39.5 degree nearly 40 degrees whereas, as you move towards the tip of the propeller the angle falls and near the tip of the propeller the angle is as low as 17.3 degrees. So, that is the change of the angular setting of each and every propeller and the aerofoils now become what we call finer and finer setting. So, the root of the propeller is set at what can be called a coarse setting and the tip of the propeller is typically set at a fine setting. So, within the blade itself the propeller aerofoil settings move from coarse setting to fine setting as it moves from root to the tip of the plate. Now, this is also conforming to the inlet flow angle phi which we have seen in the earlier lectures and conforming to the velocity field there that means, a combination of forward velocity and the rotational speed omega r. So, combination of the two create this flow angle situation and then of course, by design you attribute or accommodate a small amount of angle of attack which finally, creates the blade setting angle beta. So, this is how these aerofoils are selected this is how these aerofoils are set at these places and together they are blended into one propeller blade shape which then creates thrust in a more efficient manner. Now, as we have seen choice of these aerofoils setting of these aerofoils together and blending them into one blade shape create a efficient propeller blade which should be efficient during all times of its operation. Of course, as we know today that all propeller blades today are under variable pitch operating controls situation and as a result of which most of the propellers do have a variable pitch controls normally associated with the propeller operation. If you look at it the propeller blade this is the leading edge if you turn the propeller this is also called the leading edge which as you will see probably is a comparatively flatter surface. So, if you look at this propeller blade this is that let us say top surface. So, that is the top surface which as you can see has a curvature whereas, the bottom surface which is the surface which is we call leading surface that is the surface that moves forward in rotation. So, that is the surface that meets the air first and as a result of which you have a comparatively flat surface which from aerofoil parlance that would actually be called often a lower surface or under surface and we have seen that many of the aerofoils used are actually flat under surface. So, you can see here that many of the aerofoil that are used here actually do have flat under surface aerofoil shape. So, when you put them in the propeller that surface often becomes the leading surface. So, probably instead of calling leading edge more appropriate would be to calling leading surface whereas, this is indeed the leading edge of the aerofoils. So, this is the leading edge of each of these aerofoils put together whereas, this would more appropriately we should be called probably leading surface and that is the surface that moves into the air first as the propeller rotates. So, this is how a propeller blade shape is put together created with the help of a large number of aerofoils bigger the propeller more is the number of aerofoils that you would need to put together and blending them into one smooth blade shape. As we have seen many of the propellers in the early era 50 years back the propellers used to be made up of wood because that was the easiest material to give complicated shape like this. But over the years they used aluminium alloys for cast aluminium for giving the shape and later on in modern propeller era they are using composite material to give more complicated propeller shapes in a most accurate manner more accurate the blade shaping is in conformity with this aerofoil shapes more the propeller efficiency is likely to be achieved during actual operation. So, this was a conventional propeller shape I will quickly show you propeller aerofoil which is meant for transonic applications. Now this is the kind of transonic propeller aerofoil which is used these days it can be used in a flight mark number which is close to let us say high subsonic flight mark number and during such a high subsonic flight mark number the flow over the aerofoil as we see here can go supersonic. So, on the surface of the aerofoil the flow would go actually supersonic even though the entry mark number here is high subsonic and hence these are called transonic aerofoils. So, somewhere over the aerofoil shape the flow would indeed go supersonic and it is most likely as it shown in the diagram here is most likely to again come out with subsonic profile. So, somewhere on the blade surface the flow transits from subsonic to supersonic and then again transits back to subsonic and leaves the propeller blade subsonically. So, that is why it is called a transonic propeller and the blade shape that you see here is also created these are typically computer generated aerofoil shapes and they are created for propellers. These aerofoils are not used for any other purpose in any other kind of aerofoil applications they are typically created for propellers and as I mentioned they are computer generated to conform to transonic local flow that is expected to be present during propeller operation. Now, this kind of transonic aerofoil is typically used in the tip area where we were earlier using very thin aerofoils to conform to a high subsonic flow. This is the area where flow is now likely to go transonic in the modern propellers and instead of these thin aerofoils thin subsonic aerofoils the modern designers would like to use such transonic aerofoils where the local flow there the combination of forward velocity and omega r that is the rotational speed makes the flow actually go supersonic over the aerofoil shape. So, this is a typical transonic aerofoil shapes and as we have seen you need more of these aerofoil shapes to make up an aerofoil propeller or part of a propeller. So, most of these aerofoil shapes are computer generated by the designers and then blended into a propeller blade shape a modern propeller would have transonic blade shapes around here, but it would still have subsonic blade shapes in the lower half of the propeller and they would continue to look something like this. That means, they will go even in the modern propellers progressively thicker and thicker as they move towards a root and the root will have to be designed to withstand high stress and strain and the large moment that comes due to the cantilever fixing of the propeller blade. So, that would continue to hold good. However, only the tip sections would now be redesigned to accommodate transonic aerofoil shapes which are now a days generated typically for propeller applications. We can look at a typical modern propeller as you can see here it is made up of 8 blade 8 propellers and each of these propellers is made up of a large number of aerofoil shapes and some of the aerofoil shapes towards the tip of the propeller are likely to be very likely to be transonic aerofoils. Also, one can see here this modern blade shape has used a sweep. This sweep is something which is normally associated with aircraft wings. However, many of the bladed machines are typically the propellers and compressors and fans are using the sweep for a number of aerodynamic advantages and specially when the propellers go transonic the sweeps have certain clear advantages in terms of containing the drag that comes about and as a result of which the propeller efficiency is held at a higher value. So, this is a typical modern propeller with swept leading edge and as you can see it has certain amount of sweep at the trailing edge also and this also uses the transonic aerofoils. So, that these propellers can be called transonic propellers. So, these are the modern propellers that are used in modern aircraft a very modern aircraft and as you can see here it uses up to eight blades to create one propeller for thrust making for aircraft for modern aircraft which fly at high subsonic flight speeds. Now, we can look at some of the problems which we would like to use the theories that we have done in the earlier lectures and these theories would help you in solving some of the problems. Now, before I give you the problems I will try to solve a problem for you and this problem is of a variable pitch propeller and this propeller is a little more conventional propeller. What is states here is it is used in an aircraft which is cruising at 644 kilometers per hour at sea level to begin with and is powered by a three bladed propeller. Now, this propeller is connected to an engine which rotates at 2600 rpm through a 1 is to 2 gearbox. So, the rotational speed is actually brought down by 1 is to 2 ratio which means the propeller speed would actually be half of the engine speed and it is supplied with a power of 1491.5 kilowatts of power at that particular operating condition flight operating condition. It is stated that the propeller is designed with blades of NACA blade airfoil sections. So, it uses the NACA airfoils which we had looked at before. The question is to compute the propeller diameter and the efficiency of the propeller at this operating condition if the propeller is a variable pitch propeller what would be its efficiency at 161 kilometers per hour. So, our problem is that we have a propeller that is a variable pitch propeller. It is of course, powered by an engine and it is flying or cruising straight and level with an aircraft and it is a three bladed propeller. So, we can use and it is stated that it uses the NACA blade section which allows us to use some of the propeller characteristics of NACA airfoil propellers which are three bladed propellers. As we have seen before every kind or every propeller actually should have its own characteristics or characteristics maps as we have seen and we need to use those characteristics to solve these kind of problems. So, this is a variable pitch problem and I will try to solve this problem for you. So, that you can get a feel of how to solve typically a variable pitch problem and later on I will give you some problems which are probably somewhat simpler problems for you to solve for yourself. Let us see how the solution of this problem would proceed. The density of the air at this operating condition that is a normal sea level and that is rho air is given as 1.22 kg per meter cube that is a standard air density at sea level and the flight speed is given as 644 kilometers per hour which translates to 178.88 meters per second. As we know most of our solutions would proceed with velocities etcetera given in terms of meters per second whereas, the normal method of designating flight speed is normally in terms of kilometers per hour. Now, it is given that it is using power of 1491.5 kilowatt which of course translates to 1491500 joules per second that is as per the psi system and the propeller it is given that the propeller rotates at half the engine speed through gearbox ratio of 2 is to 1. So, it is rotating at 1300 rpm which then translates to 21.666 rps that is revolutions per second. So, that is the rotational speed of the propeller. Now, these are the given parameters as given in the problem statement. What we can do is we can look at the first thing the speed power coefficient of this propeller given the parameters that are already supplied. Now, the speed parameter power coefficient is something which we had discussed in the last class and we can use it here for the propeller designation. Now, speed power coefficient as from its definition comes out to be 3.175 that is the numerical value of the speed power coefficient which as we know it does not require the propeller size of the diameter. So, this is one propeller parameter which does not require the propeller dimension for it to be evaluated. So, we have the speed power coefficient as 3.175. So, what we shall do is we shall use the speed power coefficient and use the speed power coefficient plot or graph to arrive at the blade setting from the maximum efficiency consideration. We are assuming that we will solve the problem for maximum efficiency of the propeller for this particular blade setting or for this particular operating condition and the blade setting which we will be arriving at. The other thing is the problem is now going to be solved at a propeller design reference radius of 0.75 R which is often the normal propeller design reference radius which means the propeller blade shapes are often first created at the 0.75 R. Let us quickly go back to the propeller diagram which we are looked at right in the beginning. You see all these blade shapes need to be created by design. The airfoils need to be set at various designations but quite often one starts off with one of the blade shapes which could be somewhere around here which is to begin with representative of the entire propeller. So, this let us say this particular airfoil section which is let us say at 0.75 of the radius of the entire propeller. So, if this is let us say the axis of rotation the radius of the entire propeller is so much and this is let us say at 0.75 of the radius of the propeller. So, this section would be considered the reference radius or reference section of the propeller and for the design purpose to begin with that represents the entire propeller. So, the performance at that section would be representative of the entire propeller. So, if you calculate the values of elemental thrust there that would be an average elemental thrust representative of the entire propeller. So, that is how quite often the propeller design is created propeller design is proceeded that you start off with a representative blade section which is not at 50 percent which is normally at around 0.75 r and that is where normally the propeller reference radius is often created. If you have a transonic propeller which we had just look at the reference radius could be a little higher it could be somewhere around 80 percent of the propeller blade some are over here which is likely to be then a more representative of the propeller blade loading. So, propeller reference radius is often chosen during the design and we are going to solve our problem at that reference radius which is as I mentioned representative essentially of the entire propeller actually. So, we will proceed along those lines. Now, if we look at typical three bladed propeller NACA using NACA airfoils and the blade is being considered at 0.75 r. If we look at this blade section blade characteristics what we see here is the speed power coefficient CS is shown here in the x axis. The y axis on this side is advanced ratio V by N D on this side you have the propeller efficiency eta and we have the carpet plots available of these parameters CS versus efficiency and then CS versus V by N D. The other thing that is shown here as variable is the blade setting angle beta. Now, this angles which are shown here are the blade setting angles beta. Now, as a result of which as you can see here higher the blade setting angle higher are the you can go into the higher advanced ratio that means the higher forward speeds of the aircraft and the propeller which is flying whereas, if you are stuck to a fixed pitch propeller at a lower blade setting angle you cannot move at a very high speed. So, this is a typical propeller characteristic which allows the propeller to move at comparatively higher forward speeds. The efficiency is also shown here with various blade setting angles at the lower blade setting angles as we can see here the range of operation is very small over a very small range of CS and the CS range is extended at higher and higher angles of beta blade setting angle of each of these blade setting angles you can reach fairly good efficiency. Slightly higher blade setting angles can start giving you efficiencies of the order of 85 86 percent at very low blade setting angles the efficiencies are a little lower of the order of 80 percent. So, if you use typical NACA airfoil sections and typical three bladed propeller this is the kind of characteristics that is normally available for that blade or that propeller and if you are now trying to find out how this propeller is going to behave under a particular operating condition that has been specified in this problem you would need to use this characteristic map. Let us use the characteristic map and see where we get our solutions. You see if you calculate the values of the CS which we have found 3.17. So, this is where you start off with and then you arrive at V by N d which is of the order of 2.25 and you arrive at a solution point which is somewhere over here and you are likely to get a blade setting solution of the order of 46 degrees slightly higher than 45 degree which has been provided here. So, if you proceed vertically upwards at 46 degree efficiency curve you could get at this CS and efficiency of the order of 86 percent. So, in this graph what we can see is if you use the parameters given and calculate the fundamental parameter CS and the advance ratio V by N d you can arrive at a suitable blade setting angle for this particular blade section the reference section. So, the reference section of the blade at 0.75 R should now be at 46 degree blade setting angle as we know the blade setting angle would indeed vary from root to the tip of the blade. So, this 46 degree is at the reference blade section at 0.75 R and not for the entire propeller of all the blade sections. So, that needs to be kept in mind and this is a variable pitch propeller. So, this particular blade setting is suitable for that particular operating condition which is specified in the problem at any other operating condition you can choose another blade section through variable pitch mechanism and operated that section to get good efficiency of operation. So, this particular operation now gives us an efficiency of the order of 86 percent. Let us proceed with this problem solving. We get the solutions which is let us say the best match point and as a result of which the extrapolated blade angle you can see that it does not fall on one of the lines. So, you need a slightly extrapolated line which is a 46 degree line. So, it is somewhere between 45 and 50 and close to 45. So, let us say the solution is 46 degree and the best efficiency for that 46 degree again we did not have a 46 degree efficiency line. So, that needs to needed to be created and as a result of which that extrapolated solution gives us best blade angle for the reference section of the propeller at 46 degree and corresponding best efficiency would be 86 percent representative of the entire propeller and the advance ratio there is 2.25. Let us proceed along this from this we can now compute that the diameter of this propeller based on these parameters would be 3.667 meters and as a result of which we get a value of J now the velocity forward velocity we had already calculated 27.77 meters per second as the alternative flying speed that was specified in the problem. Now, we are solving the alternative flying speed where it was specified as 161 kilometers per hour a lower flight speed and that at that low flight speed the forward velocity is 27.777 meters per second and there the advance ratio now is 0.562 given the value of D we have already found. Now, at this flying condition the speed power coefficient C s would now be 0.793. Now, you can use this value of advance ratio and this value of speed power coefficient to find a new solution and we use the graph again what we see here that we are now at a rather low speed power coefficient a low flying condition and at which the advance ratio is also rather low and our solution point is somewhere over here. So, this is what you get when you try to find a solution which is pretty close to the maximum efficiency operating condition of the particular propeller which for which the characteristics is available to us and as a result of this we can conclude the solution by looking at that part of the graph a little more closely. This is where the solution point is and this is where we have arrived at as our solution and we get a blade angle as 29 degree which is slightly less than the 30 degree line which we have over here that is a 30 degree line and as we come along this at the C s of the value that we have found this is what the solution blade setting angle would be that is 29 degree. Now if you proceed along that and go to the 29 degree solution angle you would get an efficiency propeller efficiency of 50 percent. Now this is what you get from this map which is representative of this particular propeller which has been designed and characteristic map created out of that design. So, this is the solution of the alternative flying operating condition that was specified in the problem where we get a blade setting angle now of 29 degree with an efficiency of 50 percent. So, when you are flying here you should be at a blade setting angle of 29 degree with an efficiency of 50 percent. So, it can be seen that at this value of J which is representative of a low flying condition the blade setting angle is 29 degree where the efficiency is rather poor it is only 50 percent efficiency which is a very low efficiency of operation. So, what can be done is if you now set the blade setting at 15 degree you could actually get a efficiency of 80 percent. Now this is possible with this propeller only and the blade setting angle could actually be used to get a higher efficiency and this would have given a speed power coefficient of 1.1. Now what happens is at that value the propeller would go on a over speeding to absorb the power supplied. Now you see we had already specified the amount of power that is available the gearbox ratio that is available and if you use those values as your input power and the result is that you would arrive at a situation where propeller is using need propeller need is less than the power that is being supplied and this would result in a over speeding of the propeller. This over speeding of the propeller is not a good idea the propeller would get a hugely a stressed due to the over speeding and as a result of which the propeller might break. So, the problem statement the alternative operating condition at low flying speed then would require actually a variable pitch mechanism and this is where the variable pitch mechanism and its utility really comes in you can now be used the variable pitch mechanism can now be used and you can now go outside the constant speed operation. So, that you can get a higher efficiency. So, if you continue to use automatic variable pitch mechanism with constant speed you would result in a low speed operation you need to realize that the constant speed variable pitch mechanism which can go on automatic operation would result then in a low efficiency operation. So, you need to choose your operating controls rather judiciously if you just leave it to automatic control as we see in this problem solution you would result in a low efficiency propeller operation of the order of 50 percent efficiency. On the other hand what can be done in this particular operating condition is that you could actually choose a different speed of operation at which the power of the engine would actually be much lower the propeller evidently does not need so much power anymore it can do with much less power and you can choose a lower power setting which means a lower speed of operation of the engine and if you do that at that low speed the power matching between the propeller and the engine would be more appropriate and in that situation you can now choose a blade setting angle of 15 degree at which the CS would be 1.1 and you can operate at an efficiency of 80 percent. So, you see you can have variable pitch mechanism and you can keep the propeller operating at variable pitch normally you would like to do that during cruise during cruise you keep the propeller on automatic variable pitch constant speed operation and propeller would always have a what we call the floating pitch mechanism and it will set its pitch but that is very good during cruise whereas, during low flying conditions during very off design operating conditions you would probably like to choose an engine operation at a lower speed so that the matching between propeller and the engine in terms of power matching also in terms of torque matching is more appropriate and there is no chance of the propeller over speeding to a very high speeds which as I mentioned could result in the breakage of the propeller physical breakage of the propeller. So, you need to and not to speak of the fact that it operates at a very low efficiency. So, the result is under certain operating condition as we see it will be more judicious to go for a speed control control the speed at a lower speed of operation and then choose a propeller blade setting which now as we see can be a fine setting at which you get a good efficiency 80 percent efficiency of operation of the propeller. So, the solution of this problem gives us a glimpse of the variable pitch mechanism which is used in most of the modern aircraft today and we see that the utility of the variable pitch mechanism indeed gives us a lot of handle in terms of operating efficiency of the propeller, but there is a certain amount of control logic that needs to be built in. So, not all the time the engine or the propeller needs to operate or should operate at constant speed and hence the control algorithm or the control law that needs to govern the operation of the propeller and the engine together needs to be built in judiciously. So, that it continues to give very efficient operation during all modes of the aircraft flight. What I will do now is I will present to you a few tutorial problems for yourself to solve very simple problems. So, that you can make use of the theory that we have done in the course of these lecture series and apply those theories to the problem solving. I would say these are rather simple problems and should not have any difficulty in solving the problems wherever we have the problems which are numerical problems the answer to the numericals are actually given. So, you can check your solutions and see whether you are arriving at the correct solutions and as I mentioned you should not have any difficulty solving these problems using the theories that we have done in the course of these lectures. So, these are the tutorial problems that I present to you. I will read out the problems to you one by one. The first problem is of course, a propeller which has a diameter of D that develops thrust T when operating with an advance ratio J and r p m n. Now, this propeller is to be replaced by a pair of equal propellers of the same shape operating at the same velocity V and advance ratio J producing together the same amount of thrust T. So, the idea is to use two propellers obviously smaller in size which would together would produce same amount of thrust operating at same advance ratio that means an aircraft which was being earlier propelled by a single propeller is now being to be propelled by two smaller propellers which have the same shape. So, that they produce the same amount of thrust. Another problem is find out the diameter D prime and the rotational speed n prime of the two new propellers which are obviously going to be smaller propellers and prove that the total power required by the two propellers equals the original propeller power and if that is so if that is so you can use the same engine probably to use two propellers or you can use two smaller engines which together produce the same power. So, it is a very simple problem and you should not have any difficulty solving this problem. The second problem is then aircraft flying at 592 kilometers per hour is powered by a propeller rotating at 1800 r p m. That is a fairly common rotational speed of propeller somewhere between 1200 to 1800 are normal propeller rotating speeds. The propeller is of diameter 3.05 meter and uses NACA 0015 airfoil section which are very standard old NACA airfoils. At the reference blade section at 0.9144 meters from the root the blade angle is 47.7 degree. Compute the local flow angle at that station again a very simple problem. So, if you use the simple fundamental things that we have done you should not have any difficulty finding the local flow angle. The answer is given here and that will also tell you what the local incidence is of that particular blade setting. So, this is again very simple problem. The third problem is an aircraft is propelled by 4.572 meter diameter propeller which produces 35.6 kilo newtons of thrust. Thrust as we see now would be expressed in terms of kilo newtons for most of the aircraft engines including propellers and all jet engines. Now this aircraft is flying at an altitude where the atmospheric conditions are such that the density of the air is 1.03 kilograms per meter cube using momentum theory compute the induced velocity through the disc. Induced velocity is the small v which we have done during the momentum of the actual disc theory and the final velocity of the flow in the far wake which is far downstream of the actual disc or the propeller in the momentum theory and the answers are given here. The fourth problem is the compute the diameter of the flow field in the far wake of a propeller of a diameter 3.05 that means the propeller has a diameter of 3.05 and it is producing a thrust of 8.9 kilo newtons while flying at a speed of 322 kilometers per hour. What would be the diameter of the flow field in the far wake of a propeller? So, that is the problem statement which is given here should be able to find from the propeller theories that we have done. The last problem that I present to you is a 907.2 kg helicopter is powered by 9.144 meter diameter rotor which is as we know is very similar to actually a propeller. So, propeller theory applies there quite largely and when this helicopter is landing it descends at an uniform rate under the sea level conditions and the induced velocity small v as we have done in momentum theory is one third of the rate of descent of the helicopter. Compute the velocity at which the helicopter is descending. A hint is given here for your solution that the rotor upward thrust is equal to the helicopter weight and the helicopter weight is given here. So, you should be able to use the momentum theory now to compute the solution of this problem the answer is given here. The sixth problem that we have is an aircraft while cruising at 724 kilometers per hour is expected to encounter 5927 Newton per hour conditions of drag. The propeller flying this aircraft is of diameter 3.657 meters and is designed with NACA 5868-93 bladed propeller blades of which we have done the characteristics before in the lecture. The engine delivers 1491.4 kilowatts while the propeller runs at 1300 rpm very similar to the problem that we have solved and check if the aircraft propeller is matched for the cruise flight and compute any extra power or power shortfall that may be found. So, you got to check whether the cruise flight is possible and whether there is any power shortfall the answer is given here and you can check your solution with the answers that are given here. So, these are the few problems that you may like to solve and by yourself and check out that the theories that we have done actually lead to reasonable solution of very simple problems that are available in many of the text books. So, this concludes our lecture series on propellers. Next we shall be moving towards various jet engine ideal cycle analysis which will be done by Professor Pradeep and from propellers we will move on to the various jet engines and later on I will come back and I will present to you the engines which are used for rockets and missiles and a glimpse at some of the engines that are used for spacecraft. So, rockets, missiles, spacecrafts is what I will come back to you for in between Professor Pradeep will present to you the jet engines and the details of the jet engine cycle analysis.


What's going on guys got Kyle here relating sports cards, and we are ripping. This is 2022 Panini Phoenix football hobby break number 4 box break number 44. This will be the last break of the morning session guys. Appreciate you We have Brad O with the Eagles Brett E Titans Bryce B has Ravens Dolphins Calum F Giants Dale F has Broncos Derek C has Colts Don F with the Cowboys Eric T Bengals Erica E has the Chiefs Frank G with the Chargers Gary W Packers John F Falcons Jordan B Texans Joshua V has Bucks Justin O has Bears Kevin M is going to have Steelers and Jax Long J is going to have the Commanders Matt G is going to have Cardinals Rams Maximilian H has Lions at Bills Nicholas O with the Niners Pat M or Peter M. Sorry Peter M with the Saints Ross K with the Panthers Ryan B Patriots Steve S has Vikings Steve C with the Browns Valerie P Raiders Zachary D Jets and Zachary W has the Seahawks Good luck guys four left Phoenix 4 box number 44 See some nice hits here. What was the question? A burrito or fried chicken? Yeah, I'm with you.  It's good. So I had fried waffles. I had a chicken waffles and bokeh Got the uh, the blueberry syrup That sounds pretty good. It's pretty good. That chicken waffles and bokeh we had dinner with SGC Pretty good Got a couple of highlights. I'll say and some beers for sure rookie Aidan Hutchinson Uh orange we got devin white number 2 99 on the orange And tom brady fire forge silver It's not base, right? Ty chan the rookie we have pink hot routes chris godwin to the uh bucks number to 175 Silver hot routes is digs For the bills Fried chicken burrito sounds pretty pretty good right now. I'm not gonna lie Dude, I'm gonna have to get something like that for dinner. That sounds really good Does that exist somewhere like it does but I'm gonna have to check out a gavi as well See what they got the 250 derrick henry red. Oh gavi is also good Flamethrowers dac prescott Chick-fil-a does have a breakfast burrito with the chicken nuggets in it. That's kind of a fried chicken burrito It's pretty good too It's one of the one of the better options, I think We got uh purple rookie jordan davis for the eagles number to 199 hot routes, uh chris godwin Oh, it's your thunderstorm one until 10 p.m. That makes sense got our one per box tight shandler and the wave jesson jepperson hot routes trade lance turn mcduffy We got number to 149. This is going to be jumbo material rookie of drake london Nice jumbo patch there for the falcons and sauce gardener On the rookie silver leo chenal Number to 149. We have rpa tray mcbride Rookie tight end for the cardinals Maybe the only tight end for the cardinals right now silver collial mac See I was thinking like regular burrito stuff, but the meat inside is fried chicken. That's what I was thinking All right, boys. This is a little bit too, uh, delicious sounding for right now But now they say mac and cheese mac and cheese fried chicken burrito. Good lord. I mean four spots go to publics right now I can cheese with some uh Yeah, I might have to do that. I might have to make that myself. There's a red contours of uh tea law Is there a tortilla big enough for that number to 199? Oh, yeah, do they sell those at publics? Flamethrowers mat staffer. I got a big tortilla The biggest one possible Robinson We've got number to 15. This is gonna be Jalen waddle. Nice auto there for the dolphins Low number 10 of 15. That sounds amazing steve Nice hit fins See what this guy's saying I think I've seen that before that sounds fantastic.  I'm in I'm sure they add macaroni like why wouldn't you? There's a purple malik willis flamethrowers for the titans To 125 and can he picket silver flamethrowers behind it? Now it looks a little weird, but I probably still eat it steve. I've destroyed it. I think I need it pretty quick There's a pink josh allen nice one there number to 199 for joshi Jamo rookie rising leo chenal that is a rookie purple To 125 and a contours of russ Dangerous mr. Unlimited Gotta be unlimited Good luck on box two We have karsten wince on the light blue to 150 Zach wilson flamethrowers There's a pink marcus mariotta to 199. Yep Contours of maddie corral in the recipe down malik willis purple rookie That is to 125 nice sit there for the titans Hot routes london rookie silver. We got desmond ridder That is number to 10 on the uh The uh Laundry tag the laundry tag number to 10 nice hit for the falcons Fire fabrics to 10 That is nine of 10 very nice hit falcons DJ more on the silver Mamma Mia I was unexpected We've got a wave mr. Biskey.  Oh all in a burrito. Good lord. I'm in Get the rice out. I'm good filler and we have gold fire forged for the niners gonna be um The 75 I guess that's yellow fire forged steve young I sit on the insert Kirk cousins flamethrowers Auto is gonna be a veteran auto nice one here just in jefferson That waddle in the last one jefferson in this one that is four of five on the green. All right minnesota Steve s with the uh four of five j jeta auto. We'll mag that one for you bud Very nice hit on the j jeta Hassan haskens rookie silver That's a spicy meatball as well steve best receiver in the league right there taekwon thorton is the best receiver in the league The 299 we have rpa vilas jones jr.  Or uh divante parker silver mac jones air is cracked icecam tonus rookie for the uh For the cardinals to 50 contours brock lezner Brocks all over panini products right now He's in ufc. He's in wwe He's in uh last year's prism Oh What is this? What is this one? I got like a birthday that sprinkles Sprinkles of roquan smith courtes brought the sprinkles. She did immediately Roquan smith sprinkles those are fire. I could use a cupcake. Those are pretty rare. Got red marcus mariotta to 250 All right. Now I want hot rods a j brown. We're gonna talk about fried chicken burritos mac and cheese burritos Orange tb12 nice one there for the bucks Flamethrower son 99 and hot routes george kittle. That's the first one I've seen Didn't know what to call that one I like it. Is that how dillon got his name? That's how dillon got his name infamous sprinkles Their case hits b. Oh nice. I saw I saw two in a box Oh, really? Unreleased a I saw like four in a case So we've got light blue to 150 flamethrowers of willis Jalen hurts and two boxes left guys We'll close out the uh morning breaks for us Good luck on box three. Yeah, Dylan's off today. I believe No, uh, no sprinkles in the building Oh They've got a archetype rookie that is Kenny pick it And it's rookie there for the uh For the stealers there on the archetype. That's a pretty card uh silver chenny tendall and malik willis rookie rising hot routes drake london To 99 or 199 trelon berksilver Yeah, I think is said kevin The uh archetype It's a great four boxer. Yeah, right. We got jahan dots and blue For the commanders to 35 nice rookie, uh dots in there Dolchich we've got to 50 It's gonna be dual rpa for the cowboys jalen tulbert Some nice patches there Tulbert on the rp8 of 50 Cleo max silver Everything that needs to be there is there purple michael thomas or pink 299 You've got this. Let's go jay Let's go jay 10 bucks are sorted into less than two hours guys. Here we go. Got pink debo samuel hot routes. All right 10 kaser That is to 175 and drew breeze fire forged. You're about to say 10 bucks ain't that bad 10 bucks. That's quick We have a wave christian kirk for the jacks And Derek car there's filler That is a black hot routes to 10 Um chris godwin Nice one there for the bucks That is eight of 10 on the hot routes. Very nice You know, I never had to sort one of those when I was a sorter One of the big breeze You don't Know I know I don't How about a justin herbert auto for the charger spot what at four boxes Ever since courtese walked into this room. That is a silver not numbered herbert. Very nice hit uh charges Charge charges the charges congrats on that one Herbie for the charges my phone needs the charges. Yeah, there's one right next to you. Yeah God silver rookie christian watson 92 Oh, I still got that new phone battery going on. Yeah, I just got the new phone. So it should be good. Last in a while Dude, I'd have to travel for like two days at one point. We got another jumbo relic. It is desmond ridder there to 50 I said on the falcons jumbo patch Yeah, my uh, my old one was not very good It was not very good And there's his teammate drake london He won per box Falcons hits so much in its products. I know I know it is like ridiculous. Uh, brian robinson red rookie To 250 a roge The darkness man Got purple alon kamara. You gotta turn that off. He's got ramshot c5 db There you go. I don't care. Hey, you need to know that. I don't care stay informed You know all the tcu db's The burrito that doesn't exist yet I could show up somewhere You guys got mac and cheese and chicken, right? Okay, whatever.  That's the best From your league forest, dude. We got yellow dallas goddard. Maybe a little under the night To 75 contours polamalu Got red rookie, uh jacob brisker To 250 curt warner fire forge silver Chris alive a rookie. We got pink. That is drew breeze fire forged Saints to 175 flamethrowers ridder. It's raining not near us I just show melbourne It's 149. We've got rpa or sorry just uh just a patch there christian watson For the pack to 149 sake one barkley silver Yeah, it is I thought it was an rpa at first so I was like that thing is Got something going on We've got a brian cook purple rookie for the chiefs number to 125 And jamar chase contours Got filler This is herbert flamethrowers red to 199 Six packs left Good luck. Good luck There's a kyle philips red uh red rookie for the titans. It's 250 trail on berks rookie rising Tornado watch. Uh-oh To 299 we have rpa eric azucanma Where the dolphin's there The silver rpa so everywhere revard flagger lake marion orange Kind of what I was thinking when I saw it like every florida county It's literally all of central florida It's until 10 p.m.  Good luck. We have a wave mark andrew's Josh allen flamethrowers on the back. All right guys. Let me get going on a quick hit recap here Do some of the nicer color in the autos First up. We got sprinkles Roquan smith sprinkles christian watson patch. We got jumbo patch of ridder to 75 or the 50 the 50 Uh drake london patch. We got the laundry tag patch of desmond ridder number to 10 Nice hit a nice break for the falcons nine of ten Got derrick stingley auto. We got jaylon waddle number to 15 on the auto eric ezucanma rpa uh tulbert rpa vealus jones rpa Mcbride rpa. We've got the short printed archetype. Kenny picket there Very nice hit for the stealers beautiful card We've got a justin herbert silverado not numbered for the chargers and we have jay jedda justin jefferson on the green to five Nice hit there for the vikings All right guys that will do it for uh phoenix 4 box number 44


And also a welcome from us. So we are very humbled to be the first session of the day. So we are all from Linux integration engineering. And when I knew that the topic for this DevCon would be cloud and hyperscale, so I couldn't resist and invite these awesome engineers who are fascinating projects to have a panel discussion and talk about how we are doing hybrid cloud. And actually, when we started planning for this, we first had to sync on what hybrid cloud actually is. So we had to look it up on internet, find the precise definition to be on the same page. So it was quite an experience for us. So let's start the introduction. Ondra, please introduce yourself. So hello, I am Ondra, and I am working as an engineer at the image builder project in Red Hat. And yeah, I'm one of those people in our team who are not afraid of touching ops, so I'm here. So I can tell you something about our operations. And if you are wondering what this image builder, it's a tool for building and uploading images. Primarily currently, that's cloud images, but we can do also ISOs, containers, and much more, I think. And we are doing it for REL, for CentOS Stream, and also for Fedora. And we have basically two big operations thing going on. And one of them is our nice CI that runs like hundreds of jobs every day to test that we are building the right thing. And then we have also our production service that's online, and every one of you can try it. So basically you need to go to console.reader.com, then go to insights and image builder, and you can build your own customized REL image. Fedora image is not there yet. But it will be, definitely. And CentOS Stream, and it's just the best way how to get a code image of our stuff. So feel free to try it. And let's go to Michael. Thank you. I'm Michael. I'm part of the CKI team and responsible for infrastructure there. And CKI stands for Continuous Kernel Integration. So we are providing kernel testing as a service. So independent of what other people say, the kernel is actually tested. So we are providing testing for upstream, integrating into the awesome email-based workflow of the upstream kernel developer community. And we're also providing testing for internal Reddit kernel developers that are nowadays living on gitlab.com in merge requests and treating the kernel as a normal software project. And so CKI does everything you would expect from a CKI project for a software project. We are running builds for the kernel, for multiple architectures. We are testing them in labs inside of Reddit, mostly. And then we're also looking at the results of those tests, trying to detect new issues to alert kernel developers about them and trying to figure out what to do with those new issues. Because as the kernel is a bit special, still it means that you might have issues that you know about, but you can't immediately fix. So that's where we are kind of working on the workflow and improving it, making that possible. Okay, thank you, Michael. Okay, hi, I'm Pavel. I'm an engineer and team lead in the copper team. We are working on the copper build system on the underlying mock utility and several other, let's say, packages, maintenance software, maintenance-oriented stuff. The copper build system is a tool for building third-party RPM repositories on top of, like integrated on top of Fedora and the Red Hat Enterprise Linux and other distributions.  But it's also like very easy to consume the content from us, like you just hit the command DNF copper enable and the name of the project and you can start installation. Thanks to our sponsors, cloud sponsors, we have quite some power nowadays. We run even over 300 VMs in parallel today and we could even scale more if we needed. And as such, it's like kind of expected and desired you to use us for continuous builds and for stuff like builds RPMs in pull requests and so on, either using our webhook support or for example, the packet service. I checked today and we have like 17 terabytes of package data, so it's, yeah. Wow, that's impressive, thank you Pavel. Nothing like having notes in front of you and not saying what I wanted to say. I think I did not introduce myself, so I have Tomasz. I also work for Red Hat and you probably see the schedule and there were four people and suddenly there's three. So actually Miro Watker, he got sick and cannot be with us so maybe he's watching, hi Miro. And please get well, we need you. Okay, so we should probably speak about how you are working on your applications. So let's deep dive into clouds. I mean fly up to the clouds. So please describe like what infrastructure do you use and like if it was VMs or containers, maybe can we start with Pavel with you? Yeah, we have two copers. One is public, one is internal for Red Hat purposes and I would like to talk about the FederaCoper one because that's much more interesting. So everything is public. We don't use some private stuff in our lab. We have on-premise machines in the Federa Infrastructure Lab where we run a libVirt. We have, we run machines in AWS, spot instances and on-demand instances just in case something gets wrong. We use IBM Cloud for S390, we use Oregon State University for PowerPC or little NDN and yeah, we start VMs using a separated tool from the copper code some resource allocator which divides our VMs into pools and those pools are kind of homogeneous sets of builders always dedicated to one infrastructure and each VM in that system is tagged using like architecture tags. So when a copper or I mean user or even the copper build system comes and wants to use let's say S390 machine, it says so using the tag and it gets the machine either immediately or after some time when it gets like allocated. So like for saving the budget we like allocate certain amount of VMs in advance so people don't have to wait till we allocate them and we allocate more if there is the amount for them. There's also like prioritizing between pools like we try to use the VMs we have in our on-premise lab because we already paid for it so why to use cloud and then we fall back to other pools like IBM, I mean AWS spot and then we go to the on demand one because they are simply more expensive. Yeah, starting stopping takes some time so we try to recycle VMs but it's kind of like tricky because building RPMs is a privileged operation. Not the building itself but for building RPMs you need to install other RPMs as build dependencies and for that you need to be root. So we kind of give full powers to those VMs to all of our users and as I said, anyone can build in copper and it would be kind of dangerous if we allowed to hack users on each other. So we recycle if it is absolutely like safe for the same users in the same projects but otherwise we shut down the machines as absolutely normally like we start every day like thousands of machines, maybe tens of thousands today. Okay, thank you Pavel. So please don't try to hack other users. It shouldn't be possible. Okay, Michael, please tell us about the kernel CI that is to be also pretty interesting to work on. So yeah, we are also using hybrid resources, both cloud resources and on-premise resources trying to kind of split this depending on the properties of those environments. So if you have cloud environments like AWS or GCP, you have highly reliable infrastructure managed professionally, which can more or less endlessly scale or at least what you would expect. So that's what we also use cloud resources for. So really stuff that needs to be stable. We have an OpenShift cluster running there that hosts our microservices. We have a messaging cluster running in AWS because that's based on VMs, a very stable environment. You're using lambdas as webhooks, really having basically only three megabytes of code as the stuff that can break and no VMs in the middle. And then we also using obviously cloud resources for anything that needs to scale. So if you're building kernels, that might be no build job running when all kernel developers are asleep and then at four at night, basically they actually have their productive times and then they're spinning like hundreds of them, right? So that's only possible if you go to a hyperscaler to do in a responsible fashion. Otherwise you might starve other teams of resources. We are using on-premise resources for other reasons. For example, if you need interesting architectures like IBM S390X, PowerPC, then you might have cloud providers that can give them to you, but it's actually a bit harder to use them when the copper team does, but we don't. So we are falling back on local machines for those. The same goes for the testing aspect of the kernel. So if you're testing the RDMA support, you need an RDMA lab. You need special hardware. So that's something that you will only find on-premise because you kind of built it yourself. And then the third reason for doing stuff locally is again the cost factor where you might have a workload that is long running and it's actually pretty beefy, so you need big machines and they would be really expensive to actually rent from somebody like AWS or GCP. So it depends on we're trying to be both cost effective and mindful of our customers that expect a stable service. Okay, thank you, Michael. Please don't tell us about ImageBuilder.  And yeah, that's a customer facing service and it just needs to be high available. There needs to be zero time redeployment. So it just must work for all of you if you want to build an image. And so we need to do something stable, which is OpenShift, you know, running multiple containers just in case if something fails to have redundancy. And we run it in AWS because that's what our SRE team supports. And the set part of this story is that currently you just cannot build an image in a container for various reasons like it would have to be privileged and you would need to open a lot of paths to it. So it's just not possible currently. So also we are running a pool of machines in AWS and they are doing the actual worklifting. So already it's kind of non-standard situation and we will talk about it later hopefully, right? I hope so. We have time. Yeah, that's it. Our CI is also very interesting because we are running a lot of machines and we would like to run most of the stuff in AWS because it's just, you know, hyperscale you can run as much stuff as you want. But we need also to test these images. And so we need virtualization. And in EC2, it's very hard to have virtualization. There's an option, but it's extremely pricey. So we don't want to go there. So instead we are going hybrid and are using local OpenStack. And then you need to solve all the issues to handle resources into clouds and we use Terraform to abstract it and it eats so much memory. So yeah, it's painful. Okay, so next topic is not painful. You already said OpenShift. So let's talk about OpenShift. So for those of you who don't know it, it's amazing product by Red Hat, like Red Hat OpenShift container platform. It's our flagship product to run containerized applications. And honestly, like even in our project, I can't imagine you would run it on anything else because it's just saved so much time and everything. It's based on Kubernetes. And so let's hear it from the panel. It's how they use OpenShift. On there you have the mic, so you need to start. Okay, all right. So yeah, our production, basically the API layer is running on OpenShift. And for us, I think it's a success story because it does what it should do. Just it hosts the platform in a stable manner, even though the cluster under the application is being upgraded, it just works. And yeah, we have like probes and metrics to measure everything. And so far, I think that we haven't managed to broke production. So that's pretty nice. But also, you did? Not yet. Not yet. Oh, not yet. Yeah, not yet. I haven't checked like in a long time. Anyway, yeah. And what did I want to say? Well, I know. Yeah, that it can be tricky. That's something to realize. Like it's an asynchronous big platform. It can contain, I don't know how many nodes. And sometimes you need to be careful about timing. Basically, from one of our stories, we were killing the pods while requests were still going to the spots, which lowered the success rate quite a lot. So yeah, it's not a great thing. So we need to play with it for some time to understand all of its concepts. So your application needs to be aware of how Kubernetes OpenShift works. So, okay, thank you. Michael, are you using OpenShift? Yeah, before production. Yeah, so the CKI team, so we are running everything we can on Kubernetes and then by extension OpenShift, it kind of makes it consumable. We try to run Kubernetes by ourselves, but it's far more involved after you know what all the pieces are that you need. So OpenShift kind of like really abstracts it away. So, but then there are some limits what you can run on Kubernetes, for example. Kubernetes has some ideas of workloads coming out of what Google designed, Borg for at the time, I suppose. So it has this idea that workloads can get killed and then you can re-spin them up again. It's stuff that can be paralyzed. So we have, for example, long running jobs that need to stay up for a couple of days. So that's not something that Kubernetes really was designed for, can deal with nicely. So we keep those things out of Kubernetes. We have other workloads that don't fit maybe the feature set, but they could be made to work. For example, we are using, we are building kernels. We need to support architectures like SV90X, PowerPC, but the Kubernetes cluster normally is one architecture. So there are some limitations. If you want to build container images, you can't build them for SV90X on an x86 Kubernetes cluster nowadays, maybe that will be fixed. But so we're hitting those limits and then kind of like you always need to, yeah, then kind of like try to solve those problems outside of it. It might be more painful. It would be kind of nice if it would be on OpenShift, but it's not at the moment. And then the third thing we are not putting on an OpenShift cluster is stuff that needs to scale extensively, like build jobs and it's what the corporate team similarly deals with you. You could scale a Kubernetes cluster by putting more nodes in them and then you would put workloads on those nodes, but it's much easier to just spin a VM in a hyperscaler directly and then run the workload directly on those machines. So that's, it's easier and more cost effective and has less failure modes. So there we are some, yeah, not going Kubernetes or OpenShift. Okay. Thank you. And Pavel, can you tell us about your OpenShift story? Yeah, we are not using OpenShift yet. And we are sometimes broke the productions. Maybe that's the reason, but we certainly plan to use it. Like we already have a work in progress pull request for OpenShift deployments and there is yet another pull request from some guy from the outside doing customized for Kubernetes deployment. And yeah, the question, how am I supposed to start my own RPM build system because I cannot use Fedora-Copra one because legally choose or because I have some proprietary stuff I need to build. Such questions come often and often and it, I mean, moving to OpenShift without Infra will not only like simplify our own work but it will also like kind of connect us with the other folks doing the deployments. We will kind of like standardize it. So that's it, yeah. Builders, builders are like the problem still. Like even if we are with the Infra in OpenShift, we will still have to spawn VMs because we need to give our users full privileges. As I said, so with this case I think in, I mean the OpenShift virtualization could like help us a bit but still we need all the architectures and even though we are using multiple clouds now, none of them is using or providing all of the architectures we need. So likely the allocation part and the flexibility part will have to stay with us. Okay, thank you. So about the builders, Pavel, would it help you if OpenShift had support for username spaces? Yeah, definitely, like to some extent it would not probably solve the architecture point of view but having username spaces, I mean, in the mock tool that copper is using, we already support a rootless username space container so you can run mock there and it would like really like change the way the RPMs can be built. We could like move some of the stuff to containers that it would be really awesome. Okay, thank you. I hope we'll get there one day. Okay, next topic. So we are still in the OpenShift area but we already heard like what works, what doesn't so Michael, what's missing for you in OpenShift? It's mostly on the multiple architectures I think. So we are not an application team so we are providing CI pipelines so that might not be the usual case but I think we three have similar issues that we want to provide support for multiple architectures out of a common infrastructure and for us, for example, that means that we want to build container images for multiple architectures and it's possible you can build a multi-arch image that's available in Docker or Builder or whatever and the user doesn't really need to care about the architecture that their machines have. They just put an image and it just works but then actually producing those images is something that's harder to do so I think there's still pieces missing of the multi-arch story and it becomes interesting I think also for customers that for example want to migrate, for example to arm machines or arm clusters or something then they might have actually similar issues that this migration story becomes really hard to implement in practice because you're stuck to the native architecture while you're building your application and actually moving that over is more painful than it needs to be. Okay, thank you. So I'm glad that we have one panelist who works on building images. So Ondra, what's missing in OpenShift for you? So sadly it's not username spaces because we are currently in the way how kernel works. We are dependent on the kernel. So for example, nowadays it's not possible to build a Fedora properly on REL because Fedora uses a special file system. If you can guess the name, I will tell you where you can get cheap butter. And yeah, so for us it's basically support for virtualization and in our case we are running on AWS so there is an option for using virtualization for OpenShift, it's called OpenShift Virtualization or the upstream name is Kubevert, right? And yeah, that would be nice, but in AWS if you want virtualization it's extremely expensive. So in our case if I can like trim, it would be amazing if we can spawn EC2 instances as basically plots. Like the lifecycle would be the same thing and it would be just very nice to integrate it into the whole Kubernetes workflow with transparent networking and things like this, but one can only dream for now I guess. No, you need to file that feature request. Right. Okay, thank you. So like even the audience, how are you doing? Are we too technical? Are we boring you? Or because the next topic I'd like to ask is deployment and testing. So is it exciting for you? Okay, so, so wonder how are you deploy and test image builder? Okay, so I can talk more about the deployment. So our Sari team made us a wonderful workflow for GitOps so we could just store all the configuration for our service in Git and we can, you know, revert, they even run some tests on PR so we know that it will break even before we deploy it which is very nice. And yeah, it benches both the EC2 instances that we have using Terraform, probably, yeah, Terraform and the OpenChiff parts is like a custom pipeline built on Tecton and Jenkins, I think. So that works wonderfully. And yeah, we have staging and production environment for the service which is amazing. The only difference that there is is that a stage is just a small scale, like, I don't know, four times smaller. And that's nice because if we ever had an issue somewhere it appeared in stage and we just fixed stage and everything was on track again. So that's nice. And also it's a rule for all of our production stuff or yeah, all of them is that we try to not have SSH keys there or like any access. So if we want to know like in which state the machine is we need to have a look at logs or at metrics and we push all logs from all of our services into one's plunk instance and it's just super nice that we can see everything there. No, very nice. So Michael, how about you, deployment and testing and staging and production? We don't have staging, we just break production. So yeah, so we have used GitOps as well so everything is somehow managed either by having yamls that can be deployed into OpenShift clusters, Kubernetes clusters and it's heavily templated to be able to abstract stuff like monitoring and logging. I think we ended up at a similar setup. So everybody is a platform engineer, I think, kind of like trying to come to a common layer that kind of encapsulates the common parts, especially if you're on microservices. And then for all the rest we use Ansible. So there are like bare metal machines, VMs and AWS DNS zones that need to be updated and all four of those kind of like miscellaneous things. It's Ansible. So yeah, we had an architect that kind of like started doing these things and before he could get to Terraform he left for the image builder team. So we are kind of stuck with Ansible and they got the cool stuff. Yeah, and then so for testing, we are mostly unit testing on one level. We don't have a staging environment and not because we don't know how to spin what up but it hasn't up to now provided enough value to do it. So we have a partial one, but for most other things we are, because we are running kernel build pipelines, we are going to change components of those pipelines when we are working on them. And so what we can do is spin up cannery pipelines where we take a known good pipeline, basically a kernel revision that we built and tested and we can spin it again, but now with updated components. So before we merge those things so we kind of like replace these individual pieces and then look at it whether it still works right and still gives the same results as before. And that actually works very well. But it's not that we consider that the all end, I think how we deploy is, there are improvements we would like to do, for example, on Kubernetes using something like OpenShift GitOps, Argo CD, like those consolidating things where you also actually check whatever you deploy is actually running in the cluster and that there's something that actually looks at it instead of just throwing it over the wall and hoping that it will all work out. So that's one. The other aspect is that the way we manage secrets is okay, but we have like, I counted was like 300 of them. They're all nicely stored. But then if somebody comes along and says like, oh, you got compromised, please rotate them in the next two hours. I mean, we don't even know where we got them, right? That's not, so the whole secret rotation dynamics secrets rotating on a schedule, rotating them. If somebody leaves on incidents, it's something that we are working on. So that's there's a lot of stuff that needs to be done. Okay, thank you. So Pavel is here from you. Yeah. We also have production and development stack, but still somehow happens that production goes down. I don't know. What do I do? For development, no fancy getups. Unfortunately, we only do continuous builds and builds from PRs and the LinkedIn and stuff like that. For like local development, we have a portman compose stuff so we can run locally the copper stack and test, develop and so on. Yeah, so that would be it. One specific is like building the golden images because we cannot simply, we need those VMs to start very quickly. So we cannot use simply the images that Fedora provides because they are too old. We need to install there some, we need to update it. We need to install some software configured and so on. And that would be simply take too long. Therefore, we built our own golden images and they are based on the Fedora images and we are doing it using Virtsys prep and tools around that, gluing it together with some of scripts and they are very ugly. So, and you can imagine that supporting multiple clouds with golden images, it's, yeah, we are really looking forward for image builder support, but currently Fedora is not in scope with all the architectures that we need, so. Okay, okay, thank you, Pavel. We are actually slowly running out of time. We have about five minutes, so I can't imagine we would be doing this presentation with Miro as well, like we would already run out of time. So final topic, current challenges. You already spoke about some, so do you have some more? Yeah, I think moving to OpenSheet will be one of them because like we are three folks speaking of full-time, it's two and one quarter and it's not too much. So we would like to like minimize the maintenance cost even more, so OpenSheet should help us. We are looking forward for the image builder support and moving this to them. And yeah, all the problems we are talking about are kind of similar, so maybe like take it as a challenge and organize something and do it together, solve the problem in a way for all of us. Yeah, like a panel discussion. Actually, while we were preparing, like we already sink on so much stuff, that was amazing. Thank you, Pavel. Michael? Yeah, so the issues we see next to the other stuff we already mentioned is around scaling. So introducing testing might initially be a problem because people don't like that, but then after a while they kind of like get into the mood and then stuff starts to increase in scope and the amount and so if a service scales, it depends on whether, if it's on-premise fast then we are going, we are hitting scaling issues where we hit resource limits of statically allocated resources like a testing lab for example, that only has a certain amount of machines and if you throw more jobs in this direction at a certain moment, that basically will not work out very well. And on the other hand, if you throw more jobs at a hyperscaler then the hyperscaler is kind of happy about it and will charge you for it. So there will be costs associated with scaling and it will expose, and in our case it does expose then certain maybe assumptions that were not valid of what causes costs and how many costs and all those budgets you needed to formulate in the beginning of the fiscal year might actually exceed it quite easily. And so you kind of need to keep track of the costs that those scaling aspects actually cause and mitigate them. So that's a continuous battle of keeping track of it and working on it to stay within budget. Yeah, thank you. Yeah, so I think that our upcoming challenge is scaling our service because we are currently using the China Auto Scaling Group in AWS but we have the size fixed at a certain amount of machines. So we need to move as we get more customers, we need to of course scale the service automatically. And yeah, this is like a challenge, a complete new challenge for software engineer because you need to collect metrics, decide on which metrics you will scale, how much, and then even somehow validate it before you put it into production. Otherwise, it may happen that you end up with zero machines in production because you failed at making proper script. So yeah, that's the big next challenge and we'll see if maybe we can share some information about it. And I was even thinking that Pavel, you said that it would be nice to share information more. I was thinking during this talk that maybe organizers should deploy OpsConf or something like this, operations. Anyway, that's it from me. Okay, thank you. So Honor says we are out of time. So unfortunately, we can't take any questions right now, but please reach out to panelists and when you see them on DevConf, I'm pretty sure they'll be happy to talk to you. And thank you panelists for taking up the challenge and sitting here and talking about your experiences. Thank you everyone for joining. Please have a round of applause for our panelists. Thank you.


It is interest expense that creates the interest tax shield for a levered firm. Now to determine the value of interest tax shield for the purpose of determining overall value of the firm, we need to compute the present value of all the streams of the annual interest tax yields, how it can be determined, we can see it with the help of an example. We know that a levered firm pays cash flows to its investors more than the cash flows provided to its investors by an unlevered firm and these are the cash flows in the form of interest tax shields that a levered firm can give to its investors but an unlevered firm cannot. So this means that the levered firms cash flows to the investors are the sum of the unlevered cash flows to the investors plus the interest tax shields. This equation can be pictured with the help of a diagram where we see the cash flows of an unlevered firm in the form of a bit depicted in a block colored in green and in the next we have unlevered earnings in blue and the corresponding tax in the pink but if the firm is levered then this tax is split into two forms. A considerable portion is paid to the investors in the form of interest tax shield so that a part of tax paid to the investors of the levered firm in the form of interest tax shield which is not available to the investors of an unlevered firm. This means that the interest payment which are paid to the firms investors reduces the firm's tax obligations and this reduction in the tax obligation which is a gain for the investors of the firm date reduction or saving is termed as the interest tax shield. We know that the cash flows of a levered firm are equal to the sum of the cash flows of an unlevered firm plus the interest tax shield and the law of one price says that if it is true then the same must be true for the present value of these cash flows so modifying little the mm1 proposition with the presence of taxes it can be said that a levered firm's total value exceeds over the unlevered firm's value owing to the present value of the interest tax shield this means that the value of levered firm is equal to the sum of value of unlevered firm and the present value of the interest tax shield. Now this tax saving or the interest tax shield benefit depends upon the amount of debt the amount of interest payment and the debt period. Now how to determine the value of interest tax shield we have an example where we have loan value of 2 billion dollars annual interest payment of 100 million dollars time period of the debt is 10 years and marginal tax rate is 35 percent we have real risk free rate of interest of 5 percent so the interest tax shield will be the product of annual interest payment multiplied by the corporate tax rate so corporate tax rate is 35 percent and the annual interest payment is 100 million dollar the interest tax shield comes to 35 million dollar these are the annual interest shields if we want to determine the present value of these interest shields we need to apply the formula of annuity and that annuity formula is applied here where we have to multiply the annual interest tax shield with the present value of interest factor of annuity at 5 percent for 10 years at this gives us the value of 270 million that 270 million dollar is the present value of the interest tax shield. Note that we have not used the amount of debt in this computation of present value of interest tax shield because from a counting point of view the loan amount is not deductible only the interest expense is allowed to deduct from the earnings and what will happen if we want to determine the interest tax shield with the existence of permanent debt till now we are assuming that the interest tax shields based on interest rates tax rates the amount of debt and the period of debt are certain but in practice these are rarely certain rather these are generally uncertain because firms interest payments vary due to changes in three things like firms policy on its outstanding debt rate of interest on the firm's debt and the risk of firms default in paying interest payment to the debt holders also a firm's marginal tax rate can also influence due to the changes in the firm's tax code or the tax rate and the firm's income bracket so these are the factors that can have a considerable effect on the interest tax shield of a particular firm generally firms try to retain a debt on permanent basis and they like to pay interest there on an annual basis so this means that they exist a permanent sort of debt the firm like to maintain in its balance sheet more realistically taking example of short term debt a firm likes to pay its short term debts with newer issuance of another short term debt this means that this principal amount of short term debt will never be paid rather it will be refinanced once the existing debt is likely to be matured this means that effectively it is a permanent debt generally a large firm a large firm's balance sheet carry permanent debt as in the form of certain amount of debt every year and from year to year it is carried on as a firm's business policy this is known in fact this the firm borrows new debt to pay the existing all or the older debt the assumption behind this debt policy is that the firm maintains a fixed amount of debt on its balance sheet rather than the amount that varies from year to year or from on its every debt contract now we have an example to understand the valuation of interest tax shield in the presence of permanent debt we assume that a firm borrows risk-free debt stabilized by the capital D in order to keep it permanently in its balance sheet the firm's marginal tax rate is the C and the risk-free interest rate is equal to RF now the yearly interest tax shield is the product of corporate tax rate risk-free rate RF and the amount of debt which is D now if we determine the present value of this interest tax shield we need to determine the amount of to discount the amount of interest over the risk-free rate this means that we need to develop a formula carrying the corporate tax rate with the multiplication of annual interest expense and divided by the risk-free rate now the interest is the product of RF or the risk-free rate and the capital D now so cancelling the RF the resulting amount is equal to the C or the capital rate and the debt so simply the present value of interest tax shield on permanent debt is equal to the product of the corporate tax and the amount of debt the this computation assumes that the debt is risk-free and the RF or the risk-free rate is constant throughout the debt period and if we assume that the debt is fairly priced in the open market then the market value of debt is the product of the present value of the interest expenses or the future interest payments now if a firm has constant marginal tax rate then the value of the interest tax shield for a permanent rate debt will be equal to the present value of the corporate tax rate as a product of the future interest payment this means that the present value of the interest tax shield on permanent debt is the product of the corporate tax rate and the future interest payment and by solving this equation we can reduce it to the product of corporate tax rate and the amount of debt or the D now the implication of this new equation is that the product of corporate tax rate and the debt shows magnitude of the interest tax shield this means that for a 30% corporate tax rate this means that for every $1 in the newer amount of debt the firm value will be increased by every 35 cents


yn y ledwedd y 12 mlynedd, mae fyddwn yn cyfrifio'r cyflwys gweithiau ar y cyfrifio'rав)! gael fod yn gweithio'r hyffordd byd fyELL sylwyd. mae'n gorffogol a'i wneud diwylliannau hwn. Ac mae'r hyffordd arno allan o'darnol, yn cyfrifio'r aww, cyfrifio'r aww, fewn cyfrifio'r aww, gan roedd ddweuddfa llwyso ar y bag yn gweithio'r aww, a mae'n holl연 dechrau mewn gwirioneddau mewn oedd yn gyfrifio. After many months of deliberation, swapping to and fro between several clubs in that long end of the bag, one club is about to make way for another. The question is of course which club has come out of the bag, which club is going in the bag and more importantly, what are the reasons for it. Now that is a foreign, it is a DHY foreign and it travels about 200 yards. ac mae'n 7 mwydd ac mae'n cael 200 ysgol. Ac mae'n 3 hybrid ac mae'n cael 200 ysgol. Ac yn fwy, mae'n 9 mwydd ac mae'n cael 200 ysgol. Mae'n cael 200 ysgol ac mae'n cael 200 ysgol. Mae'n rhaid i gyd ymlaenig. Mae'n ddodol y ffaiffau sefydig a'r osod dwi'n rhoi. A'r osod, mae'n rhaid i gael o feithio. Mae'n rhaid i gael sjoc ing compatible wedi'i siplayg o hynny o gilydd o yn cael dangos. ychydig y gallwch yn fawr. 4DHY, mae'n gweithio, ond mae'n gofyn i'r awdol yn ystafell yn yslyf. Felly mae'r ddweud o'r 3DV. Mae'n ddefnyddio. Mae'n gweithio ychydig sy'n gweld y gyfliad o'r 9i yn y gwaith ddiw i'r awdol. Mae'n gweithio i'r awdol yn fawr. Mae'n gweithio i'r awdol. Mae'n gweithio i'r awdol. A dyna, mae'r maswch yn y gwyl fath. Mae'n gweithio i'r awdol. ymdodwch eich cyfrifio sy'n gwneud i'ch gydag ar gyfer o'r ffordd a'r ysgol. A mae'n rhaid i'w ddweud hynny yn gwybod i'r ffyrdd yma yw'r hynny'n gweithio'r clwb gyda teit yn rheidwch gwybod i'ch mawr. Roedd eich gymredu'r rôl. A mae'n gweithio'r gwybod i'ch gwybod i'r gwybod. Roolwch, roolwch. yw ddechrau'r paru gyda'r ninwyd. Felly yw'r ystod ydych chi'n gweld yn y cyffredinol ac mae'n gwybod i gael ychydig i'w ddechrau'r cyffredinol yn y sylwedd y cas o'r cyffredinol yn y dyfodol. Nid yw'n gallu'n cael y 200 yi'r ysbryd mae'n gweithio'n gwrth yma'n ei ddweud a'r bwysig sy'n gweithio gwneud yn y bag. Mae'r gweithio i'w clywed yn eich hun i siwr, ac rwyf yn gweithio gwych iawn i'w bag, sy'n gweithio'n gweithio gweithio o'n gweithio'r gweithio. Mae'r gweithio'r gweithio'r gweithio yn han iswyr datblygu ar gyfer Taelor, mae'r lleif iawn yn gyffredig. Rwyf wedi'i gweithio'r gweithio'r gweithio, mae'n gweithio'r gweithio'r gweithio, a mae Osian Johnson yn gwneud i'w bag. I don't think on every round he plays but certainly on occasions he'll put both a 7 wood and a 9 wood in the bag, I'm not going to do both, but what I will say is it performs incredibly well and I can't compare it to any other 9 woods that are out there because quite frankly this is the only one I've ever hit. Oh that's just ridiculous. Now it's worth pointing out there is nothing to say there is anything wrong with the other clubs that we've mentioned, in fact they all perform incredibly well. The thing and the reason why I've chosen the 9 wood is because of how it personally suits my game and fits into that kind of distance that I'm looking to carry. So if you go back to the dry ball data what you'll see is that 196 is an average carry distance, you'll see a launch angle which is incredibly steep as is the descent angle. You'll also see a spin number that is relatively high for what you're trying to achieve and for me what I'm trying to achieve is playing into a long par 3s or whether I'm playing into a second shot into a par 5 or indeed I'm playing off of a tight par 4. And all the numbers that's put together if you like those elements of data all suit a requirement that I have but that's not to say it'll be the same for you. And you might want other things from your clubs that carry a distance of like I said 200 yards but I've got to say I love the fact that this thing travels so high but also fires out there so well. That's just incredible. We've played there off the turf, no tee, down the middle of the fairway, we're playing a par 5 right now off the tee and there's no reason again. I say a lot to Hannah off camera and then feel I should repeat it back on camera and I just said to Hannah this club is just so good for so many different situations even playing a par 5 off the tee. Why not? It's a safe way of making sure that you get that ball in play and you're scoring a couple of 100 yards down the line or perhaps pop another one in and see how it plays but another 200 yards and we're flicking a wedge in. That seems a safe way to try and at least make par. Well I think we've got to see that as a challenge and see what we can do. It was 500 yards, we're playing slightly into the breeze but let's see what we can do with how far we leave ourselves with third shot by playing two nine woods. Absolutely ripped that. That's got to be within sort of eight or nine iron distance I would imagine but couldn't have hit it any better. The other thing I will say just that came to mind when I hit that, the other thing about the nine woods you can play it in a number of different ways. I've really tried to sort of hit that hard distance was what I was really trying to get there and you can probably hear it from the audio it really cracked and fired out there. But you can also float one a little higher and take a little bit off and it's quite easy to do when you've got a shorter shaft, a bit more control about the club. 96 in and works out sort of spot on with what we've just said 500 yard par five. Probably play that second shot a bit longer than the first in actual fact but certainly 200 yards each as a minimum to cover 400 yards. Leave us 96 in. The shortest club I've got in the bag at the moment we're doing a bit of other testing is, well I'm afraid it's an eight iron so we're going to try and see what we can do with an eight iron. Don't mess this up and two good nine woods. Oh that looks really good you know. You've got the legs kick on a bit. Kick on a bit. Do you know what that's not too bad and it's a fairly easy but a straight forward two puts there we walk off with a par and it's all about having so much control in that nine wood in my opinion. Thank God for the men's putter. We made par. Right we're going to finish the video right here and I'm going to finish off with a shot which is always a bit dangerous really get greedy and the last shot of the day messes up. We're going to stay positive because I've that much confidence in this nine wood we shall see. But the summary is quite simply this video like I said was about seven wood or nine wood. It's about much more than that. It's about making sure that wherever clubs are in your bag that they cover a yardage and they're not all covering the same yardage and particularly at the top end of the bag I think that's a real hard thing not to be doing. But as it happens I'll be dropping a couple of clubs at least and the nine wood will be going into the bag. Right last shot of the day. Don't mess it up and off and God for that. Same thing as we've hit all day. I should let the stale away for shot tracer but same thing as we've seen all day. The ball flight is ridiculously high. It's the only one thing to consider on a particularly windy day. If you play in links conditions that kind of golf then maybe the nine wood is not for you but the type of thing I want from this golf club it really does tick every box and like I said I've not got any information to pass on to you in terms of comparisons to other models because I've only ever tried the tailor-made stealth but this thing is an absolute weapon. I understand why DJ's got one in the bag and it's safe to say that'll be mine. Right now same old thing. This is my sort of findings of playing a nine wood. Lots of you out there will have your own opinions and they perhaps differ from mine so make sure you stick them in the comment section below and as I always say help your fellow golfers make some informed decisions. That's it for me. We've just about got done. The rain was pouring here this morning. We had a nice finish off here at Cardin Park. I'm done and we'll see you all soon.