Lecture – 44
Estimation of maximum L/D
(Refer Slide Time 00:27)
Let us see how we get an estimate for the maximum lift over drag ratio. Once again, we are going to mostly use historical data; Why? The reason is that we cannot do anything better because we are at a stage in design where we cannot get the accurate value of this parameter because we have not even finalized the configuration. All we know is the type of the aircraft
that we are designing.
So, there are certain thumb rules available some guidelines available one simple guideline is as a function of the wing aspect ratio. So, for aircraft which have aspect ratio between 7 and 11 which is the typical value for you know many low speed transport aircraft, the regional turboprops etc, you can assume the (LD)max to be twice the wing aspect ratio based on this
particular graph. However, please note this is only a very crude estimate and maybe this is to be used as a starting value I do not recommend that we should use this value in the calculations.
(Refer Slide Time 01:28)
This is just a very very basic value instead it will be better to go for picking up a value of the (LD)maxbased on some historical data which is actually available. So, some average (LD)max values are available for typical aircraft and for a few select aircraft, which are piston top turboprop type, you can see that the (LD)max is of the order of 13 to 14, 14.2.
(Refer Slide Time: 02:00)
Let us understand what are the drivers of subsonic LD? The subsonic value of LD is very strongly dependent upon the aircraft configuration. In level flight, we go for a condition that lift is equal to weight and hence, the LD
will depend based mostly on the D because the L is almost constant. So, now, if you want to look at a look at LD you have to look at D very carefully.
Now, for subsonic aircraft, there are 2 main components of the drag or D. One is the parasite or Zero lift drag which is a function of the wetted area of the aircraft and the other is the induced or lift dependent drag, which is a function of the wingspan because it is a function of aspect ratio which is span square by area. So, if we want to get a handle on both these aspects, the span as well as the wetted area.
We should consider not just the aspect ratio, but the wetted aspect ratio. The wetted aspect ratio AR wet is defined as the square of the span divided by the wetted area of the aircraft.
And the wetted area aspect ratio is a much better indicator of max LD
as compared to just the proof of this lies in a comparison between Boeing B 47 and Vulcan aircraft.
(Refer Slide Time: 03:40)
Raymer, in his textbook has given this example, it is a very nice example, which shows that you could have a totally different shape, but you may have the same value of maximum LD.
So, here we have 2 of these, these 2 aircraft on your left is the Boeing B 47 which is having a slender wing with large sweep back. And on the right we have a Vulcan which is all wings virtually all wing it is bordering to have actually blended wing body but there is no blending here because there is a distinct fuselage.
So, we noticed that the reference area of the wing in the case of B 47 is 1413 whereas it is 3446. This I am assuming is in square feet because this data is from Raymer textbook. The wetted the wetted area is much larger for this aircraft because there are slender very very slender wings and also there are this fuselage and tail surfaces, the span is not very different
116 versus 90.
So therefore, Swet Sref will be approximately 8 for B 47. And approximately 3 because Vulcan is mainly wing only. So, you have the wetted area, basically, the Sref is going to be the projected area of the wing. And the S ref is going to be the Swet is going to be the area of the top surface
of the wing bottom of the wing. And of course, the other things, the aspect ratio of this aircraft is 9.4, whereas that for the Vulcan is 3, but the wetted aspect ratio for both the aircraft is almost the same.
And hence, the (LD)max for both the aircraft is also almost the same. So, this particular example shows that if the wetted aspect ratio of if the velocity ratio of 2 aircraft is similar, we can expect them to have the same or similar (LD)max values.
(Refer Slide Time: 06:03)
So, Raymer has given a very simple procedure for getting a quick estimate of the (LD)max of the aircraft that you are designing. Raymer says that, although you do not have the configuration designed, you still have some idea about the baseline aircraft that you are going to probably use in your calculations you also have a rough idea of how roughly your aircraft
will look like. So, will it be like this? Or will it be almost a flying wing?
Will it be like F4 or will it be like Boeing 747. So, in this particular chart, what you do is, since you are geometrical calculations have not yet been completed, you can just eyeball the aircraft and use the typical configuration value. So, for each aircraft, there is a point and on this graph. So, for example, your aircraft is looking like this, you can assume that the
Swet Sref value will be approximately 5.
On the other end, if you are looking at something like Cessna skyline, it will be 4 if you are looking at something like 747, it will be maybe 6.25. So, like that, and if it is a flying wing like B 49, it will be just twice the reference area. So, it will be nearly 2.
(Refer Slide Time: 07:41)
So, this way, you can use this particular chart to get a ratio of what is the typical expected value of Swet Sref. And then there is another chart where the wetted aspect ratio on the x xis. This is the wetted aspect ratio that means span square by the wetted area, this is plotted and on the
y axis you have the expected value of (LD)max and there are lines for various aircraft types.
So, for example, you have one line for civil jets, you have one line for aircraft, which have a fixed landing gear, but they are propeller driven, you have another parallel line for retractable prop aircraft, indicating that the retractable prop aircraft normally have a higher (LD)max, the increase in the (LD)max is approximately 2 as you can see, the gap between these 2 lines is approximately 2 you know approximately from 10 to 12 which means, the (LD)max is going to increase by a numerical value of 2.
Similarly, there is one line for military jets, the other line for subsonic jets and high speed jets and then he says there is a poor correlation with the actual data. So, with whatever best information you have, you should be able to get the (LD)max values and you should be able to use it. So, what we notice is that for most of the civil jets which are falling along here, the
(LD)max is between 14 to 20 that is the typical value of (LD)max and for you know lower the lower values are applicable for aircraft with propeller driven aircraft and the fixed landing gear. The (LD )max there tends to be from between around 10 to 12 or 14.
(Refer Slide Time: 09:41)
You can use other information also. For example, here is data taken from Babikian et al from MIT who have plotted the value of trends in the value of (LD)max over the years from 1955 year 2000, and they use the color coding they use symbols like this for the turboprops symbols like this for the regional jets and for other the blue triangles are all the large aircraft.
So, you can see there are some spreads also most of the aircraft are actually falling within this particular band.
In other words, the (LD)max is probably going to be between around 10 to 15 and these trends are increasing and modern day aircraft have (LD
)max bordering between around 15 to 20. So, this is the kind of value and perhaps the limit would be around 22 that would be the max value that you can expect to be generated. But there are attempts being made to increase the (LD)max, Thanks for your attention, we will now move to the next section.
Lecture – 45
Estimation of Engine Parameters
(Refer Slide Time: 00:23)
Let us also look at how do you get the SFC values in cruise and loiter. Again, we have to take records to historical data. The SFC values, this is again the chart from Raymer’s textbook where the equivalent jet SFC values are plotted against the Mach number for various types of aircraft and with this chart you can get a rough idea, but this is just an indication. So, this
chart actually helps you decide which kind of engine is to be used.
Depending on the Mach number we can depending on the cruise Mach number or the Loiter Mach number that you want the aircraft to achieve, you should select the type. For example, this is a nice intersection where low bypass turbofan and turbo jets they roughly have a crossover. So, at Mach numbers beyond around 1.8 it will be better to go for turbo jets because they are going to have a lower value of the SFC.
Similarly, when you go to around 3.7, 3.8 Mach number, you will start seeing that the turbo jets are going to have an increasing trend in SFC whereas then the Ram jets are going to become more economical. So, depending on which kind of Mach number you are going to follow for low speed aircraft you can see up to Mach number of around 0.4 piston prop turboprop are, after Mach number 0.4 you start seeing turbo props becoming better below that the piston props have a much lower. So the lowest SFC is for the piston props, this is the line for them.
(Refer Slide Time: 02:08)
But you know this chart actually helps you decide what powerplant to use typical values of SFC in SI system which is in milligrams per newton second this particular unit milligrams per newton second is used because the numbers which come out are easy to mention and talk about rather than saying 0.000255 or some such very small number. When you work in
milligrams per newton second, you get number like 25, 30, 14, 15 which are easy to talk about.
So, if you do not have any idea about typically what you will be getting you can assume these values, these are realistic numbers and if you have a piston prop or turboprop aircraft in mind, in these aircraft, the typical values of the SFC based on power or called as power SFC in milligram per watt second, tend to be as listed here.
(Refer Slide Time: 03:05)
So, this particular chart is quite useful to start off and this has come from the Ramer’s text book. Professor Scott Eberhardt has plotted the historical TSFC trends for turbofan engines.
And you notice that consistently the TSFC is going to is reducing. So, this indicates that as the year progresses SFCs are coming down.
(Refer Slide Time: 03:29)
But if you look at the data for cruise SFC trending in aircraft, we see that we are now slowly reaching some kind of flattening if you have a bypass ratio beyond 8, so up to 8 bypass ratio they are slowly come down after the bypass ratio of 8 to 10 they start to becoming flat.
Thanks for your attention. We will now move to the next section.
Lecture - 46
Estimation of Design Gross Weight
(Refer Slide Time: 00:15)
So, basically if we just recall now, we started by estimation of the mission fuel fraction for that, we were looking at the 2 segments of cruise and loiter. And for these segments, we use the Breguet equations for the Breguet equations, we needed (LD)max and sfc for that, we looked at some empirical and approximate procedures and now, the total fuel fraction is going to be estimated as WfW0=(1+RFF)(1−WxW0 )
This reserve fuel fraction is normally specified by the regulatory authorities or sometimes also decided by the airline themselves from their own experience and from their own policies from the point of view of safety. Typically, airlines assume 6% or 10%. So, airlines normally carry around 6 to 10% extra fuel to take care of the contingencies.
(Refer Slide Time: 01:24)
So, summing up now, we revisit this particular formula in this formula, Wcrew and Wpayload, they were estimated based on the requirements given by the customer for Wpayload and requirements specified by the airworthiness agencies or the operating procedure or operating norms of the airline empty weight fraction was obtained using the AW0C formulation. Based on the type of the aircraft, w´ f was obtained by calculating the mission segment profile for each mission, many of them were assumed by historical data.
But 2 of them for loiter and 4 cruise were obtained using the Breguet equations. So, therefore, if I replace the w e bar formula by the formula used by us and if I replace the w´ f formula by this formula that we just obtained earlier, you get a large formula which allows you to calculate now,
WxW0 has been obtained by a multiplication of the various mission fuel fractions. Reserve fuel factor is a number which is assumed by the airline.
A and C are the constants which depend upon the aircraft type. So, now, we come up with a slight problem, we basically have an iterative equation because what we want W0 also appears on the RHS because the fraction of the aircraft depends on the W0. And as you oticed, C exponent is negative. So, heavier aircraft tend to have a lower empty weight fraction. So, we end up with an implicit equation. So, what we need to do now is we need so, this number and this number will be available to you as a fixed number. RFF is an assumed constant, W0 is what has been estimated. All you need to do now is following an iterative procedure.
(Refer Slide Time: 03:38)
So, you assume some starting value of W0, typically we assume it 4 times as the payload because payload is typically 25% of the total aircraft weight. So, it is good to assume 4 times the payload as the starting value of W0. First thing you do is estimate the empty weight fraction using the formula AW0 C KVS where KVS=1 for most aircraft because we do not use variable sweep in transport aircraft in general.
Then you estimate the segment weight fuel fractions for some segments like warm up taxi out, climb, descent and approach and taxi in we use historical data. For the cruise and loiter segments we use the Breguet range and endurance formula and using that we estimate the fuel fraction for
the entire mission. And then you just include a reserve fuel factor and get the w f bar which is the WxW0 and then you calculate by at iterating, and you iterate till convergence. So this is the procedure which is used for Initial sizing. Thanks a lot for your attention. If you have any questions, we will use our channels of communication to sort out your queries. Thank you.