Lecture - 50
Subsonic Parasite Drag Estimation
Let us have a look at what method can be followed by a conceptual aircraft design team to estimate the aerodynamic lift coefficients.
(Refer Slide Time: 00:25)
(Refer Slide Time: 00:27)
?? and ?? for configuration. We assume here that some kind of a configuration and layout has already been arrived at by the design team. And now they are interested to go for some analysis.
So we will discuss only about the subsonic parasite drag coefficient estimation in this particular presentation. And the information that is relevant to transonic or supersonic aircraft will be provided in the form of notes. This kind of approach is mostly applicable to transport aircraft.
(Refer Slide Time: 01:01)
The components of the subsonic parasite drag you know will not look at induced drag right now, we will look at it a little bit later. It consists of basically skin friction drag, form drag, interference drag and others. The others would consist of miscellaneous drag due to various items which are mounted on the aircraft and they will drag due to leakages and protuberances.
(Refer Slide Time: 01:32)
There are 2 approaches commonly suggested for estimation of the subsonic parasite drag coefficient. One method is called as the equivalent skin friction method and the other is called as a component buildup method. The equivalent skin friction method essentially looks at a very simplistic approach in which the whole aircraft is replaced by an equivalent flat plate and certain coefficients are specified based on the aircraft type.
And using them you can get a very quick, very basic first cut estimate of the parasite drag coefficient. The logic that is followed in this particular approach is as follows. The parasite drag is supposed to consist of skin friction drag and the pressure drag and the skin friction drag in a well designed aircraft would probably be 90% of the total drag. In a well designed aircraft the pressure drag would be kept less maybe around 10%.
So, since it is a small fraction, we replace its accurate estimation by just a factor X. So the parasite drag will be equal to the skin friction drag plus a small factor of skin friction to replicate the parasite drag. We define the term called as the equivalent skin friction coefficient ??? . And we assume that the ??0 value of the aircraft is equal to this ??? , which is a fixed number for a specific aircraft type into the wetted area ratio or ???? ????⁄ of that particular aircraft.
So there is a list given to what would be the appropriate value of the ??? for various types of aircraft. And the list varies from high speed aircraft to propeller sea planes, which have notoriously high drag values and based on past data and experience, the ??? values range from 0.0025 to 0.0060. So to calculate ??0 using this method is very straightforward, get the ratio of ???? ????⁄ using the chart that Raymer has given in his textbook.
Which we discussed about, when we discussed about the initial sizing, we showed that graph. So from there, you get the wetted area ratio by eyeball parking, how the aircraft looks and multiply by the corresponding value of ??? for a aircraft type. With this you will get a very crude estimate of the ??0 value. In the component built up method, we go into slightly more detail.
We say that the total drag of the aircraft is because of the summation of drag of each component plus drag due to leakages and protuberances, which we will discuss and drag you to certain
miscellaneous items. And for each component, the drag of the component is going to be its skin friction drag plus its form drag plus the interference drag that occurs because of the proximity
of various components.
So for the skin friction drag, we use a similar formula as we use in the equivalent skin friction, the difference is that we have a different value of ?? for different components of the aircraft.
By component, I mean only the main assemblies, the wing, the fuselage, the tail, and nacelles.
So, it is identical in formulation, but more specific in detail. So you calculate the ???? ????⁄ for each component.
And you also then calculate the value of ?? formula or given for estimating ?? for various types of bodies. The form drag is considered to be you can say related to the skin friction drag through a form factor. So once you know the shape of the body, you can get a form factor and again there are formulae available for it and then you multiply that form factor with the skin friction drag.
The interference drag is also considered as a factor applied to the skin friction drag through an interference factor Q. And this factor Q is 1, when there is no perceptible interference between 2 bodies. This will happen when the 2 bodies are actually separated by a large distance or there is no flow field interaction between them or not much flow field interaction between them.
And when they are operating in close proximity when the drag of one, the presence of one affects the drag of the other, then the Q value becomes higher. And miscellaneous drag is the drag of items such as the flap, the landing gear when it is un retracted, the upsweep aft fuselage and the fuselage base area. We will discuss all of these and then finally you have this drag due to leakages and protuberances. Thanks for your attention. We will now move to the next section.
Lecture - 51
Component Buildup Method
(Refer Slide Time: 00:15)
So, the general formula for the component buildup method is as shown here, ??0 =Σ ??? ∗ ??? ∗ ?? ∗ ????? ????+ ?????? + ???&?
where the various components or various terms in the equation are as described.
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So, how do you estimate the flat plate skin friction coefficient this depends on the Reynolds number, the Mach number and the surface roughness and it is a very strong function of the extent of laminar flow, if you have laminar flow over the entire body, then the value of ?? will be quite low. And if you have turbulent flow over the whole body, then it will be much larger.
Now, experience has shown that, when you have a Reynolds number more than half a million, it is very difficult for you to maintain laminar flow.
And at a Reynolds number of 1 million, the turbulent skin friction drag is 3 times the laminar of skin friction drag. So, if you are able to use very smooth skin using a polished metal or using a molded composite, then you might be able to maintain laminar flow over around 15 to 20% of the wings and the tails, but on the fuselage, it is very difficult to maintain laminar flow, maybe 5% of the fuselage perhaps may have maybe not.
(Refer Slide Time: 01:57)
This particular graph shows the variation of the ?? value skin friction coefficient as a function of Reynolds number for laminar flow shown in the blue line so, this line is for laminar flow.
And these 3 lines are for the turbulent flow, because the formulae are a little bit different for the 2. Now, what we notice is that the gap between the skin friction coefficient for fully laminar flow and turbulent flow is quite huge.
And in a simple, you know, typically this is going to be nearly one third. So, if you notice here, for example, if you look at the Reynolds number of around 0.4 million, you know you have 0.002 and 0.006. So, it is a factor of 3, it is one third and this is a huge saving. So if you can maintain laminar flow, it is a very big but if you can, then you have a chance of reducing the laminar flow to a value of nearly one third.
(Refer Slide Time: 03:28)
And this is the reason why many attempts are made to maintain laminar flow. The Piaggio Avanti aircraft is 1 example of a 3 surface aircraft, where the designers have provided special features in the aircraft to ensure that there is a laminar flow of nearly 50% of the wing and one third of the fuselage and for this aircraft a very special NLF wing was designed by the Ohio University.
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The second point that is important is that surface roughness leads to higher value of the skin friction coefficient. So, to take care of the effect of surface roughness, what we do is we use the concept of Re cutoff, cutoff Reynolds number. So, if the Mach number is less than 0.75, then we define the cutoff Reynolds number in terms of l over k where l is the characteristic length of the component and k is the surface roughness.
So, if you notice what we do is we use the value of either the cutoff Reynolds number or the actual Reynolds number in the turbulent flow calculation. So, if you go back and have a look at the formula for the turbulent flow, you can see that the Reynolds number comes in the
denominator and the power is 2.58. So, if Reynolds number is large, then the value of ?? is going to be small. But, if we have surface roughness, or if we have more surface roughness, then what we do is instead of the actual Reynolds number.
We use a cutoff Reynolds number which is a larger value a smaller value sorry and the smaller value gives you a higher value of ?? and this is how you take care of the effect of surface roughness. So, what you do is, you calculate the cutoff Reynolds number and if you find that the cutoff Reynolds number is lower than the actual Reynolds number, you use that number in the formula given on the previous slide and you will get the required ?? value.
If you do not know the value of surface roughness, some characteristic values are given here for typical types of surface that is provided you can notice that the lowest value of surface roughness is for the smooth molded composite, the value is just in a 0.52*10-6 whereas, a camouflage paint on aluminum has nearly 20 times more. So, you can see that the surface roughness is going to make a huge difference in the calculation of the ??.
(Refer Slide Time: 06:26)
Now, to get the value of form factor, because form factor FF is to be multiplied with the value of in the calculation of the skin friction coefficient. So, for bodies which are like a wing, horizontal tail or vertical tail lifting surfaces, this formula in terms of the maximum location of the x/c or location of the maximum thickness and the t/ c thickness to chord ratio and the sweep at the quarter chord and the Mach number these 4 parameters the sweep, Mach number the t/c
and the location these 4 parameters decide the value of the form factor.
So, this (x/c)m is the location (x/c)m is shown here, that is the location of the maximum thickness if we do not know you can take it as 0.3 for low speed airfoils or 0.5 for high speed airfoils, lambda m is the sweep of the maximum chord line, maximum thickness line sorry. And, you
know, if you do not know the value, you can get this value by the simple formulae the form factor for bodies like a fuselage or nacelle which are round, which are bodies that have some diameter is obtained using this particular formula.
Here we use the factor small f, where small f is ? =?√(4/?)????
where ???? is the maximum cross sectional area if we have a nacelle or a smooth store, then we can use this formula where f = l/d, l stands for the characteristic length. Now, formulae are not to be used beyond the Mach MDD Mach drag divergence Mach number.
(Refer Slide Time: 08:39)
They have to be used only for subsonic flow calculations. And then we look at the interference factors Q. This is a measure of what is the effect of the presence of a component to the component nearby. And, if you have an external store such as a bomb or a rocket or a drop tank or any other item suspended below the aircraft, if you mount it near the fuselage, it has got a very high value of Q compared to something that you mount near the wingtip because you move far and far away.
So, with the fuselage as a baseline the value of Q will be 1.0. And for various types of tail, Vtail, conventional tail, H tail you can see there are different values of Q which are recommended.
(Refer Slide Time: 09:28)
Now, for nacelle and store mounting the value of Q factor is a function of how much distance you are from the fuselage vis-a-vis the fuselage diameter. So, if you mount it directly on the fuselage, then the distance of the store is 0 and Q is very high. In other words, it means that there is a 50% increase in drag because of interference. If you mount it in such a way that the location is less than 1 diameter of the fuselage, then it becomes 30% higher or 1.3.
And if you clear the distance equivalent to the fuselage diameter, then the Q value equal to 1 which practically means no interference. For wingtip mounted missiles, we use Q as 1.25. If you have a high or a mid-wing or if you have a well filleted low wing, then we assume there is hardly any interference but if you have an unfilleted low wing you can have it between 1.1 to 1.4.
(Refer Slide Time: 10:34)
Now, one more term to be considered is the leakage and protuberance drag. Now, what is meant by leakage? Leakage is the tendency of the aircraft to inhale or exhale the air through the
various holes, every aircraft has got some scoops mounted so, that the ambient air can be used for cooling of the various devices or equipment inside. And from these at these places, basically
the ambient air is brought to rest and hence, there is going to be a loss of momentum which will correspond to a drag.
There are protuberances on every aircraft there are antennae, there are lights, there are edges of the doors, there are fuel vents there are in sometimes there are rivets, which are protruding all of these are going to contribute to additional drag which we call as the protuberance drag.
So, here what is done normally is a percentage is taken. So, you look at historical information and you assume that bombers will have approximately 2 to 5% additional parasite drag because of protuberances transport.
And turboprops will have larger values of 5 to10% but the fighter which will have many, many appendices and drop tanks and armaments, etc, protruding out they are going to have much larger values say between 10 to 15%.
(Refer Slide Time: 12:05)
Let us have a look at the concept of drag area to take care of the drag of miscellaneous items.
So, drag area is defined as the product of the drag coefficient created by attributed to the particular body or a particular component multiply by its area. So, since drag is ? = ???? therefore, drag area can be called as ?⁄? because ?⁄? will have the same numerical value as
???. So, sometimes we also refer drag area is as ?⁄? value.
So, usually we use S as Sref. So, the miscellaneous drag coefficient ??0 will be the drag area divided by the wing reference area. And what you do is you keep you add the drag area of various components to get total drag area and if you when you divide that by the wing reference area, you will get the ??0 miscellaneous. So therefore, drag area is a direct indication of the drag coefficient. And this concept is very commonly used in the automobile aerodynamics in which case the reference area is Sref or the frontal area. So, for example a bicycle has a drag area of 0.6 to 0.7 square meters.
(Refer Slide Time: 13:37)
Look at some cars so if you have a car like Volkswagen XL I and also notice the rear wheel is actually hidden in the covering you have a very low value of drag area. On the other hand a car like Honda inside which is fairly smooth and aerodynamically shaped will have but exposed the wheels will have you know nearly double the drag area. But if you look at a car like a Hummer which is having a very squarish front area and a very large it will have you know maybe nearly 10 times more drag area compared to a Volkswagen XL 1. So, it is very common to use this concept of drag area in automobile aerodynamics.
(Refer Slide Time: 14:30)
So we can look at miscellaneous drags now, so drag of the stores. So, for estimating the drag of each store that is suspended below the aircraft you might use some empirical relationships given. So ?
⁄? versus Mach number curves are available for various stores and the store suppliers normally provide these curves. You can use them to get the value of ? ⁄? and then add it to the miscellaneous drag, for landing gear drag normally the values are estimated with a comparison from the test data.
So, what you do is you use a component build up method where each component of the landing gear is considered to be creating drag. So, you calculate drag of each and then you take 20% extra for interference between them, if you have open gear wells, you take 7% more drag. Now, one more cause of high drag is the fuselage upsweep which we see many a times in cargo transport aircraft.
So, in these aircraft, normally a door is mounted at this location. So, there has to be a very abrupt change in the angle. So, you have this upsweep angle u and there is a formula available for ?⁄? of the upsweep even the value of using radians you can use this particular area and in this formula A max is supposed to be the area cross sectional area in this particular view.
So, with this you can estimate the value of the additional drag due to fuselage upsweep. So, what is happening here is that the air which is flowing past the aircraft is suddenly made to turn up. And this upward motion of air causes this additional drag called the fuselage upswept drag.
(Refer Slide Time: 16:34)
Flaps and the speed brakes are also huge components, huge contributors to the drag flap drag is estimated by a factor called F flap that is a function of the type of the flap, flap chord ratio this is the extent of the flap, flapped area / Sref area is also the extent of the flap along the span and delta flap is the flap angle, we assume that up to 10 degrees of angle the contribution is very, very minor so, it can be ignored.
So, only deflections beyond 10 degrees are assumed to contribute to the additional drag this particular figure indicates what is meant by the flapped area Sflapped as mentioned here. So, the flapped area is not just the area covered by the flaps, but the area which is under the area of the aircraft which is either ahead or behind the flaps. So, the area that is under the influence of the flaps is called as a flapped area.
So, Fflap there are various so, each of the type of flaps there are separate values suggested for the Fflap. So, it is like a small value for plane flaps smaller value for slotted flaps, because they are more efficient, delta flap is normally specified but if not you have to assume a value from historical information, speed brakes are also going to create a huge amount of drag because they are almost like flat plates which come out and project. So, you can assume delta ??0 to
the flat plates to be nearly 1 to 1.6 times the speed break for frontal area.
(Refer Slide Time: 18:22)
And then you have the base and canopy drag in many aircraft, the edge of the tip of the fuselage is not closed, but there is a base and because of this there is a abrupt disturbance in the flow.
So, this leads to separated flow and hence there will be additional drag because of this and there are formulae available for calculating the value of the ?⁄? of the base as a function essentially of the base area, which is again this is the base area, the area that you encounter on the base of the aircraft.
So, you can have a query in mind that pusher propellers may have low base drag even with high aft fuselage angles and also with the large base areas. The reason for that is that the flow in the area flow in this particular area is manipulated by the presence of propellers in the pusher aircraft. Canopy is also a huge contributor of drag sometimes depending on its shape, whether it is flat or whether it is curved, depending on how it is located.
So, depending on how the canopy is you can create you can assume the value of K and get the value of ?⁄? as a function of the windshield frontal area. Thanks for your attention we will now move to the next section.
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