 Hello again, I am Sohan Soanna and in this video we are going to talk about the aerodynamics of airship. So, we are going to talk about how do we estimate the drag of an airship, we are going to talk about the aerodynamic stability of an airship and we are going to talk about this very peculiar effect that we only consider in buoyant vehicles that is the added mass effects. So, let us start. So, as I mentioned earlier in the previous talk about on the dynamics of airship, I had mentioned that the dynamics of airship are primarily derived from the submarines because they are buoyant vehicles as well and a lot of hydrodynamics is hydrodynamics of submarine is similar to the aerodynamics of airships. Now, in case of aerodynamics, we also consider a little bit about little bit of missile aerodynamics here. Now, it may sound off because missiles are very high speed vehicles as compared to airships. But the reason why we have also considered missiles is because of the tail part. Now, submarines do not have a tail which is as similar to that of an airship, but missiles do. So, that is the reason why some of the aerodynamics bit have been adapted from missile in addition to that of a submarine. Now, let us when we talk about aerodynamics, typically we have aerodynamic coefficients. So, these would be lift coefficient which is Cl equal to lift over half rho V square A where rho is the density of the fluid or air. In our case, V is the velocity at which the aircraft or the airship is flying and A is the reference area. Now, CD is drag over half rho V square A similar to what we have for lift. And then we also have moment coefficient of moment. Now, we have three kinds are basically rolling pitching and yawing moments. So, that would be half rho V square A into L. Now, in addition to the reference area A, we also have the reference length L. Now, that depends on the moment that we are considering. Now, I have a very, very basic equation here. Now, what exactly does A mean? Now, A we call this as a reference area and typically it is a function of the lift generating component. Now, let us look at this issue of reference areas here. Now, in a conventional airplane, the lift generating component is the wing and the therefore the relevant area or the reference area for aerodynamic coefficients would be the wing platform area. So, that is why that is the reason why we consider the platform area for a conventional airplane. Now, in case of airships, the lift generating component is the envelope. So, envelope does not have any area. So, of course, we have the surface area of the envelope, but that does not actually capture the total lift generated by the airship. Now, what is the lift is a function or the aerostatic lift of the airship is the function of the envelope volume. Now, that is why considering envelope volume as a reference would be a much better solution rather than considering the surface area of the airship. But volume is not exactly an area. So, how do we get a reference area from envelope volume? So, what we do is we take this trick. We define this term called volumetric area or the volumetric reference area, which is basically the envelope volume raised to the power 2 by 3. So, volume has the dimensions of meter cube, whereas volume to the power 2 by 3 has the dimensions of the area that is meter squared. So, that is how we are going to define the volumetric area and it makes total sense because it is the envelope volume that generates the lift in the case of airships. Now, there is a empirical relation which could be used. Now, this is required because some of the reports on aerodynamics of airship use surface area as the reference area. However, most conventional reports of most the followed convention is to use the volume over 2 by 3 as the reference area. Now, that is why caution has to be exercised whenever some wind tunnel or aerodynamic data is to be studied. And this is that relation which would convert the aerodynamic coefficient of volumetric drag to coefficient of area based drag. So, this is what that empirical relation looks like. And this empirical relation was tested on, was based on R-101 airship and it has also been verified on skyship 500 and the error percentage that we get is about 0.8. Now, this is a very decent approximation that we can have when we have to compare or when we have to transfer the area based coefficient of drag to the volumetric drag coefficient. Now, in this case volume here is wall VOL, surface area is SA and L by D is something called as the fineness ratio or the length of the airship divided by the maximum diameter of the envelope. So, that is L by D here. Now, let us start with the drag estimation. Now, given an airship envelope with certain components attached to it, how exactly would we estimate the drag? Now, before we come into drag estimation, I want to pose a question. Now, why are airships not spherical? Because spherical airships would give us a lot of advantages. However, it is very unlikely to see a spherical airship. Now, what are the benefits of spherical airship? Basically, when we have a sphere, the total weight of the airship would also go down because the envelope weight is proportional to the envelope surface area. We would also have lower skin friction drag because skin friction drag is also a proportional to the envelope surface area. Now, what exactly is skin friction drag? Now, that is because of the shear stress between the liquid layers. So, there would be this boundary layer formed on the surface of the airship or an object which is in fluid flow. And by virtue of it, we have surface friction. Now, both of this for skin friction drag and for the envelope weight, sphere is a better option because it gives the maximum volume for the lowest value of surface area. So, basically, sphere has a minimum surface area for a given volume. So, it would be better to reduce the envelope weight and also the skin friction drag if we consider a sphere. Also, it is omnidirectional. Now, what I mean by omnidirectional is that the aerodynamic behavior of a sphere is same in all directions because it is symmetric about all the axis, all the axis you can possibly think of which is centered at the center of the sphere. Also, there are certain structural advantages for a sphere. For example, there would be uniform internal pressure. If the envelope is not uniform, then there would be different internal pressures inside the envelope. And another one is that there is no room for kinking. Now, what is kinking? Let us consider an airship in which the internal pressure has dropped, maybe because of gas leakage. So, there is less gas to maintain the shape of the airship. Now, the tendency of the lifting gas is to always go upward. Now, because it is such a elongated airship envelope in a conventional case, what we have is the normally lifting gases would collect in two tips of the envelope, which is the nose part and the tail part. And because of that, we will have two different center of volumes for these two parts of gas because they are separated because of less internal pressure. And that is why what we have is this internal kinking because we have two upward forces and because of that we have this kind of kinking. And this particular phenomenon wherein you have two different center of volumes and two different separate gas bodies acting together, lifting gases being acting together, we have this kink. And this will not happen in case of a spear. Now, in spite of all that, whenever we typically look for an airship, what we see is a conventional, a streamlined shape for an airship which is like this, like a rugby ball. Now, why is that? Now, let us look at the flow of the air around a spear. Now, this is what we would expect to see a laminar flow which is totally attached to the surface and there is basically such a nice flow around it. Unfortunately, in the real world, this does not happen. What happens is that there would be a flow separation. And because of this flow separation, there would be eddies or recirculation in the wake of the airship. So, here we see that there is this recirculation in the flow and these are basically eddies and this is also where the flow separation happens. Now, because of this, we have something called as form drag. Now, form drag is because of the shape of the object. Now, here in this case, we have a spear and the spear would have a lot of eddies or recirculation area at the wake of the flow. It is also a function of the projected frontal area. So, in this case, we for a given volume, we have this frontal area and it is directly proportional, the form drag is directly proportional to the projected frontal area and that is why we have a heavier, we have, we see that the form drag is higher for a spear. Now, let us say for the given volume, what we are going to do is elongate this structure. So, basically, we are just pulling the structure along one axis and what we see is the recirculation area or the flow separation is delayed and that is why we have lesser eddies and therefore, the form drag reduces. When we further elongate or this process is called streamlining, so what we basically get is lesser and lesser area of recirculation or eddies and therefore, lower drag. So, what we have done here basically is that we have found out a way to minimize the drag, but at the same time, we are making the airship go only in one direction or this shape will have minimum drag only in this particular direction. Now, we cannot travel in any other directions and that is why the conventional airships that we see are shaped like this in the streamline envelope shape and they are unidirectional. So, this is the reason why airships are shaped the way they are. Now, let us look at the total drag of the hull of the airship. Now, what are the components as we talked about? So, the first component would be the skin friction drag. Now, this is a function of the total surface area. The second one is the form drag. Now, this is a function of the shape of the envelope and the total drag would be the sum of these two skin friction drag plus the form drag. So, the fineness ratio is again as I defined in the previous lecture is the ratio between the length of the airship and the maximum diameter of the envelope. So, L by D here represents the fineness ratio. Now, the reason why I have defined this is because we are going to require it in the estimation of drag. Now, the skin friction drag to total drag ratio is given by this particular empirical relation, which is about 0.6 over L by D. Now, this is the contribution of the skin friction drag. So, basically if we multiply 0.6 over L by D into total drag, what we get is the skin friction drag and the form drag would be the contribution of form drag would be 1 minus 0.6 over L by D. So, using these two relations, we would be able to calculate what would be the skin friction drag component of the total drag and what would be the form drag component of the total drag. Now, we have still not talked about how do we exactly estimate the total drag of the airship. So, let us talk about the hull drag. So, it is basically the total drag that is going to act on the airship. As I mentioned, we have streamlined the hull now and in a typical airship, it contributes about 50% of the total drag. So, if we have a airship which has a CD or the drag of let us say 1 Newton, then in that case 0.5 Newton would be coming from the hull of the airship. And we can estimate the hull drag using Horner's method. He has given a empirical relation in 1958 and it would give us the axial volumetric drag coefficient. So, remember this is the axial volumetric drag coefficient. So, the reference area for drag calculation would be volume to the power 2 by 3. Now that in this particular equation, the drag coefficient is a function of Reynolds number which is dependent on the density of air or the density of the fluid, the characteristic length of the airship which is typically the length of the airship and also the velocity of the flow. And also we have the kinematic viscosity. And then it is also a function of fineness ratio which is length of the airship of a maximum diameter of the envelope and this is that relation. So, it is a function of L over D, that is the fineness ratio and the Reynolds number Re. So, this is what the equation looks like and now this is based on experimental data and this equation kind of gives us a very good relation or very good estimate for the volumetric drag coefficient. Now let us look at how it looks when we plot it against the fineness ratio. Now the different colored lines here represents the flow at the axial drag coefficient at different Reynolds number and this is what we see. Now what we see here is about 3.5, the fineness ratio about 3.5, the axial drag coefficient more or less remains constant. However, the minimum occurs at this point which is L by D of 4.65 that is when the fineness ratio is 4.65 we get the lowest drag coefficient for all Reynolds number. Now there are drag components of other components as well. So, what are the other components? So, we have the fins typically we have symmetric airfoils for because their function is to dampen the oscillations and also give some level of stability to the airship. Then we have the gondola. Now we approximate this as a box in a flow field. So, we basically assume that it is a box which is kept in a flow field and then we have propulsion units. Now this depends on the way we aerodynamically model this depends on the kind of propellers we are going to use the kind of propulsion units we are going to use and then there are these mooring mass protrusions which is at the tip of the nose of the airship. Now this is a table of drag component wise drag breakdown and this is taken from airship technology by G.A. Kauri and here we see that the barrel contribution is about nearly 50% for each of these airships. Although in the USS Macon it is a little on the higher side it is typically okay to assume that it is about 50% of the total airship drag. Now let us do a small calculation to estimate the drag of an airship which has a volume of 1000 meter cube and a fineness ratio of 4. It operates at a Reynolds number of 10 to the power 8. Now the question is to estimate the drag coefficient of skin friction and from drag on the barrel and also to estimate the drag coefficient of the airship. Now let us see how we can do this. Now the first thing we are going to do is we are going to use the hull drag we are going to estimate the hull drag using Horner's method. Now for a fineness ratio of 4 we get using this equation or even by using this graph what we get at this Reynolds number is about the drag coefficient volumetric drag coefficient about 0.02 approximate value. Now further what we can do is now we have the drag coefficient of the hull. Now the skin friction drag we already have a equation for that. So basically when we do this what we get is 15% for a L by D of 4 and the skin friction drag can be calculated using because we know the CD hull so that becomes the total drag. So we multiply 15% into 0.02 what we get is 0.003 that is a skin friction drag coefficient and the form drag is nothing but 1 minus 0.6 by L by D that is 85% or simply the CD hull minus the skin friction drag coefficient that also will give you the form drag. So that gives us a number of 0.017. Now we have estimated we have done the first part of the problem which is volumetric coefficient of the skin friction and form drag on the bare hull. Now how do we calculate the total drag of the airship? It is basically twice the value of the bare hull that is 2 times CD hull would give us the total drag coefficient of the airship. Now this is how we calculate the drag coefficient. Now the question was to find the drag force on the airship then we would require the density of the flow because the formula for drag is 0.5 rho V square. So if we go back to the first slide that we have so here it is. So here we have drag equal to 0.5 rho V square A into CD would be equal to drag. So if the question is to find the drag then we would need the velocity of the flow and also the density of the flow. The volume is already given so the reference area would be volume to the power 2 by 3. In the next session we will talk about the aerodynamic stability of airships.