Aces High Bulletin Board
General Forums => Aircraft and Vehicles => Topic started by: Stoney74 on June 12, 2007, 12:05:41 AM
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WW, F4UDOA, Tango, et al...
I was looking at NACA Report 824 and was trying to determine some values from the charts. One item was design lift coefficient. Another was pitching moment. I see Cli on the charts but understand how to read it as presented. And, I don't see the pitching moment at all. Furthermore, I'm trying to determine what type of airfoil will be best for a certain Vmax and not Vcruise. Raymer's book suggests designing the airfoil around Azerolift at Vcruise.
Just looking for some guidance I can't glean from the readings...
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Hi,
by far more important for the highspeed behaviour and at least as important for the lift coefficient is the wingshape(aspect ratio, trapezium or squary, the form of the wingtips, swept wings etc).
"Airfoil lift coefficient" is by far not the "wing lift coefficient".
In theory only on a perfect eliptical wing the "Airfoil lift coefficient" ís the same like "wing lift coefficient", other, more squary wings, with smal aspectratio, guns, not covered wheels, antennas, etc minimize the wing efficiency often down to factor 0,5.
As result two wings with exact the same airfoil can have a very different "wing lift coefficient", while the different of the "wing lift coefficient" due to Airfoils in WWII was mainly rather smal.
Though two exceptions are the Spitfire airfoil and the P51 airfoil, where the Spit airfoil was rather thin, while the P51 Airfoil didnt provide very high max AoA´s, so mainly the max lift was not that high.
For highspeed with "normal" asymetric WWII airfoils the aspectratio and swept-wings are most important as well. Although the (semi) laminar flow wing provide a smaler drag at some speeds, the also rather limited critical mach of the P51 show that also this airfoil dont have a that high influence.
The solution to gain higher critical mach´s are smaler aspectratios(He162, Me163, Spitfire), more thin airfoils(Spitfire) and/or swept-wings (Me163, Me262).
Since the wingform, providing the best wing efficiency regading the lift, is most bad for highspeed and the other way around, modern jets often use swing-wings. This provide a high aspectratio and so a high lift factor for slowspeed, but also a smal aspect ratio and swept-wings.
On a wing with a smaler aspect ratio the airmasses can get shifted sideward in a better way. Further more, while swinging the wing backward, the relative thickness of the airfoil decrease, while the swept wings provide a more stable flight(swept wings have a better result than the V position of not swept wings).
Greetings,
Knegel
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Usually profile data is given 2D and there are some formulas to convert it to 3D. Some basic stuff here (http://www.grc.nasa.gov/WWW/K-12/airplane/downwash.html).
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Stoney74,
Funny thing about airfoils. Many WW2 fighters shared the same one. F4U, F6F, P-38, F7F and I believe the FW190 as well all used the 2300 series.
IMHO it is much easier to reverse engineer based on airframe than one section at a time. I like to read the range charts of various aricraft to determine which was most efficient. For instance look at the amount of fuel required to fly a given distance and compare several different aircraft types for instance P-51D, P-38L, F4U and F6F. You can look at fuel required, distance and HP and see which aircraft had the least drag at cruise speed and most efficient engine. The P-51D is truely a marvel in this regard because of the laminar wing.
Also take a look at the F4U document on my webpage. It has Cdo, airfoil type of many aircraft and a detailed drag breakdown of the F4U-1D.
http://mywebpages.comcast.net/markw4/MSWF4UDATA.pdf
FYI, I am not an expert on airfoil design
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While it is certainly true the shape of the wing (looking down from the top) influences the ratio of lift to drag (higher aspect ratios are generally better) I don't think you can argue this is more important than the airfoil shape (the view of the wing from the side).
I am pretty sure the opposite is generally true. Why? Because the aerodynamic properties of wing shape (again looking down) can very nearly be determined from paper and pencil. The properties of airfoils however had to be measured in wind tunnels, that is until fast mainframe computers came along in the mid 1960s. Engineers tend to make fewer mistakes when there is less uncertainties about the calculations...
Getting back to the question asked, go to the website for Loftin's Quest for Performance (a NASA publication) I am prety sure he will point you to two variables - the zero lift coefficient and flat plate area, which is how you calculate static drag.
see http://www.hq.nasa.gov/pao/History/SP-468/ch1.htm
the equations are found in http://www.hq.nasa.gov/pao/History/SP-468/app-c.htm
As for pitching moments, they will tell you something about how the plane will manouver. It won't say much about Vmax or climb rates.
The reference to zero lift coefficient at Vcruise might be a statement about variations in the angle of attack of a plane driven by differences in thrust. Pitching moment might be relevant to that.
-Blogs
Originally posted by Knegel
Hi,
by far more important for the highspeed behaviour and at least as important for the lift coefficient is the wingshape(aspect ratio, trapezium or squary, the form of the wingtips, swept wings etc). ...
Knegel
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greetings F4u - just up for my quarterly breathe of air..
-Blogs
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First, I appreciate the responses so far...
Second, I should have preceded my post with a small bit of context. I'm in the initial stages of coming up with a Formula 1 design for Reno. I've taken a look at all of the most competitive planes--Nemesis (the original DR-9, not the Sport class NXT), Endeavour, Mariah, etc. and their sizes and shapes. The craft that went into the original Nemesis is probably beyond my abilities due to the fact that the guy that designed it worked for Lockheed's skunk works and that it was basically assembled by parts made at Scaled Composites. That being said...
Pitching moment of the airfoil has an effect on horizontal tail size and moment, so therefore, after selecting an airfoil, you make the tail have the area necessary at the proper moment from the CG to keep the plane pitch stable. Therefore, I need to figure out the pitching moments. I see them listed on the airfoil data charts, but don't know how to interpret them.
Second, while most aircraft are designed with range in mind, a race plane is more concerned about speed, so that's why I'm interested in design lift coefficient with respect to Vmax instead of Vcruise. Mostly I'm looking at the 6-series airfoils. So with respect to design lift coefficient, I'm thinking I need to find an airfoil that gives me Alpha(zerolift) at Vmax or close to it.
Thanks again
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I think the distinction between Vcruise and Vmax is not going to be important for you. I say that because the coefficients being used are dimensionless. The airfoil that maximizes lift relative to drag at the cruise, to a first approximation, is going to give you the maximum speed.
The qualification here is that we are looking at the same angle of attack at the two amounts of thrust. The pitching moment is being cause by the lift vector not being pointed straight up. That is caused by (1) the angle of attack of the wing (the lift vector will be perpendicular to the chord of the wing) and (I believe) the difference between the center of gravity and the center of lift, which depends on where the wing is located. There is possibly a third factor, which is any force outside the horizontal plane induced by the source of thrust (on some planes, the propeller is not perpendicular to the direction of flight), and the magnitude of that vector will depend on the amount of thrust. The analogy for a car is how the nose rises relative to the trunk when you slam on the gas.
So if I am right, the pitching moment is going to depend on these three variables and you are not going to be able to derive them from a table of lift coefficients for different airfoil sections.
At a minimum you need an introductory book on aerodynamics, but you really need a trained engineer to help with this.
Two books you might look at are Mair & Birdsall's Aircraft Performance or the older book Airplane Performance, Stability, & Control by Perkins & Hage.
-Blogs
Originally posted by Stoney74
First, I appreciate the responses so far...
Second, I should have preceded my post with a small bit of context. I'm in the initial stages of coming up with a Formula 1 design for Reno. I've taken a look at all of the most competitive planes--Nemesis (the original DR-9, not the Sport class NXT), Endeavour, Mariah, etc. and their sizes and shapes. The craft that went into the original Nemesis is probably beyond my abilities due to the fact that the guy that designed it worked for Lockheed's skunk works and that it was basically assembled by parts made at Scaled Composites. That being said...
Pitching moment of the airfoil has an effect on horizontal tail size and moment, so therefore, after selecting an airfoil, you make the tail have the area necessary at the proper moment from the CG to keep the plane pitch stable. Therefore, I need to figure out the pitching moments. I see them listed on the airfoil data charts, but don't know how to interpret them.
Second, while most aircraft are designed with range in mind, a race plane is more concerned about speed, so that's why I'm interested in design lift coefficient with respect to Vmax instead of Vcruise. Mostly I'm looking at the 6-series airfoils. So with respect to design lift coefficient, I'm thinking I need to find an airfoil that gives me Alpha(zerolift) at Vmax or close to it.
Thanks again
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Thanks for the tips Joe. Obviously right now I'm just making drawings and dusting off some rusty math skills. Before I start putting anything together I'll have some professional advice. IF1 has a technical director that you can send designs to and they'll help keep you safe and within the realm of reality. There are a lot of other resources here locally--a benefit of living in Reno. Regardless, I'll take a look at those books and bounce it off what I already know. I've been pouring through a copy of Aerodynamics for Naval Aviators and have a couple more that I'm going to order from Amazon. I'll add these two titles to my list.
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Finally found what I was looking for. Thanks for the input...
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Originally posted by joeblogs
While it is certainly true the shape of the wing (looking down from the top) influences the ratio of lift to drag (higher aspect ratios are generally better) I don't think you can argue this is more important than the airfoil shape (the view of the wing from the side).
Hi,
as long as there get very different airfoild used, Airfoil and Wingshape are same important, but in WWII most fighters had very similar airfoils.
Unlike to the WWI time, where the scientists just started to gain knowledge, resulting is very big differents.
If you look to the extremes, you will see that the Wingshape and Airfoil are same important.
A squary wing with a Aspectratio of 3 or smaler, but a highly effective asymertic Airfoil, dont will create more lift than a trapezium Wing with a aspectratio of 11, but a flat symetrical airfoil.
I took the Spitfire and P51´s as exception, cause they have rather seldom airfoils in WWII, both with a rather bad influence to the CLmax, but with a good incluende to the drag.
Originally posted by F4UDOA
Funny thing about airfoils. Many WW2 fighters shared the same one. F4U, F6F, P-38, F7F and I believe the FW190 as well all used the 2300 series.
IMHO it is much easier to reverse engineer based on airframe than one section at a time. I like to read the range charts of various aricraft to determine which was most efficient. For instance look at the amount of fuel required to fly a given distance and compare several different aircraft types for instance P-51D, P-38L, F4U and F6F. You can look at fuel required, distance and HP and see which aircraft had the least drag at cruise speed and most efficient engine. The P-51D is truely a marvel in this regard because of the laminar wing.
I dont think you can see much due to this, cause you never know if the engine, the propeller or the airframe is responsible for the low fuel consum or high cruise speed.
Imho, Stall speed, Vmax, climb ratio and critical Mach are values to work with, in combination with wing load, span load, wingarea, aspectratio, powerload etc.
btw, i doubt the P51 Airfoil was a the main factor for its long range. Rather the very clean surface condition, the very streamlined fuselage, the thrust producing radiator system and a very good fitting aragement between engine, reduction gear, propeller and speed of smalest drag was the cause for the high speed and low fuel consumption.
The rather low critical mach number of the P51 dont give a hint that the airfoil was a main factor. Tests did show that the smalest pollution did disturb the laminar effect anyway, and the P51 anyway only had a semi laminar wing.
The P51 was a masterpiece of a clean construction, from the Spinner to the tail, all is smooth(without wax) and the wheels are covered.
The Vmax different between 109G10 and K4 show what covered wheels do.
Greetings,
Knegel
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I should be more careful. If you are taking the plane into the transsonic regime, wing planform (what you call wingshape) is going to matter a whole lot.
Below the transsonic region, however, the properties of a wing's planform can be determined on paper and so engineers are not going to choose wildly inefficient shapes. They will choose different shapes, but the effects tend to be second order compared to things like dihedral and twist - hence the huge debate over the Spitfire wing shape.
With airfoils however, much less was known until NACA's pathbreaking experimental research. That is one reason why engineers were so conservative about selecting airfoils.
In any case, none of this helps Stoney74. Fortunately he has already found what he was looking for.
-Blogs
Originally posted by Knegel
Hi,
as long as there get very different airfoild used, Airfoil and Wingshape are same important, but in WWII most fighters had very similar airfoils.
Unlike to the WWI time, where the scientists just started to gain knowledge, resulting is very big differents.
If you look to the extremes, you will see that the Wingshape and Airfoil are same important.
A squary wing with a Aspectratio of 3 or smaler, but a highly effective asymertic Airfoil, dont will create more lift than a trapezium Wing with a aspectratio of 11, but a flat symetrical airfoil.
...
Greetings,
Knegel
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Originally posted by joeblogs
So if I am right, the pitching moment is going to depend on these three variables and you are not going to be able to derive them from a table of lift coefficients for different airfoil sections.
Well, the pitching moment of the airfoil section has an influence on the sizes and moments of the horizontal stabilizers. Some airfoils have higher pitching moments, which either require a larger horiz. stab at the same moment, or a smaller horiz stab at a larger moment...or so I've come to understand it. Pitching moments at different lift coefficients are listed on the airfoil charts. That was the catalyst for the original question. Design lift coefficient is also listed as a part of the airfoil number. (From what I've read) The design lift coefficient is the lift coefficient at which the airfoil section produces the least drag. In the airfoil nomenclature, i.e. a 64415 airfoil, the third digit (4 in this case) is the design lift coefficient in tenths. So, for this airfoil section, the design lift coefficient is (.4). It relates to cruise speeds in a manner that you should try to match the airfoil that is best suited to the cruise speed desired. So, in order to determine the proper tail sizing, it seems you have to know the pitching moment of the airfoil at its design lift coefficient to ensure pitch stability at Vcruise (or Vmax in my case). Other characteristics of the airfoil will effect stall speeds, Clmax, pressure distributions, etc.
Again, this is initial information, and not something I'm hanging my hat on. Merely a starting point on what, if carried to fruition, will be a long, detailed process.
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Originally posted by joeblogs
I should be more careful. If you are taking the plane into the transsonic regime, wing planform (what you call wingshape) is going to matter a whole lot.
Below the transsonic region, however, the properties of a wing's planform can be determined on paper and so engineers are not going to choose wildly inefficient shapes. They will choose different shapes, but the effects tend to be second order compared to things like dihedral and twist - hence the huge debate over the Spitfire wing shape.
With airfoils however, much less was known until NACA's pathbreaking experimental research. That is one reason why engineers were so conservative about selecting airfoils.
In any case, none of this helps Stoney74. Fortunately he has already found what he was looking for.
-Blogs
Hi,
also at slow speed, specialy while flying with high AoA´s the planform make a huge different. To understand this influence and to create a effective planform is at least as difficult as to create a good airfoil. Actually one dont work perfect without the other.
Typical fighters in WWII had a wing aspectratio between 4,6 and 8,8, this make a huge different, at least as big as the flat Spit airfoil to the wide spreaded 2300 airfoil.
The 1st good airfoils, based on exact researches got used already in the FokkerDr.1 and D.VII and D.VIII. The Götingern University made this researches, resulting in the "Göttingen Airfoil", which did provide a much superior handling(stall character).
I guess the constructors was so conservative while selecting airfoils, cause mach related problems was new and the used airfoils was already close to perfect(good mix between good lift and smal drag) for speeds below critical mach.
Since most planes in WWII had rather smilar airfoils, the influence to the max CL is rather smal.
As i wrote in my 1st post, aspect ratio, trapezium or squary, the form of the wingtips, swept wings etc are the more important factors in WWII( "etc" also include dihedral and twist, simply all not airfoil related influences).
Greetings,
Knegel
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What is intersting about the evolution of airfoils is that we started with very thin wings when speeds were quite slow. Fokker and some of the German aerodynamicists figured out a thick wing was much more efficient at those speeds.
We then went through a 20 year period where wings were pretty thick, but speeds had nearly tripled. By then, a thinner wing was more efficient, but it took a lot of wind tunnel tests to convince people it was worth engineering thin, but strong wings. Then came laminar flow...
Originally posted by Knegel
Hi,
The 1st good airfoils, based on exact researches got used already in the FokkerDr.1 and D.VII and D.VIII. The Götingern University made this researches, resulting in the "Göttingen Airfoil", which did provide a much superior handling(stall character).
Knegel
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JoeB!!
Hope you are well, I have been a passive reader on the boards lately. Always enjoy your post, keep'em coming.
Knegel,
I think their are many factors that contribute to the P-51's range performance. But keep in mind that the range chart in the manual is for a standard service aircraft with Wing racks attached so it was not in an optimal condition. The 109 was full of bumps, protrusions etc as was the Spit. The P-51 was designed to be a "clean" aircraft from the jump. Take a look at the results of the postwar Bendix Air Races where essentially stock P-51's raced from Cleveland to LA at speeds averaging over 400MPH. Frankly amazing for the time IMHO.
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Hi F4UDOA,
in no way i would disagree to this, thats why i wrote:
"The P51 was a masterpiece of a clean construction, from the Spinner to the tail, all is smooth(without wax) and the wheels are covered."
Hi joeblogs,
yes, the diefferent steps of development and knowledge are very interesting. Its sometimes suprising what "simple" unknown things turned to be a real wall.
I realy wonder how simple some "walls" from today can get cut down, if we only would know how. :)
Greetings,
Knegel
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Originally posted by Knegel
I realy wonder how simple some "walls" from today can get cut down, if we only would know how. :)
I'd say these guys are doing it every time they complete a new project. Case in point here (http://www.scaled.com/projects/proteus.html)
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Stoney:
Sorry, I am late to the party as usual :)! I was out of town last week on business and didn't browse the forums. Just saw this thread and wanted to respond.
Firstly, best of luck on your endeavor to build that aircraft! That's really exciting! I don't think I would be ever bold enough to tackle something like that! I don't design planes for a living so make sure you take anything I say with a grain of salt!
As to your question, it appears you've answered it yourself. NACA 824 contains charts that give you airfoil pitching coefficient, Cm for airfoils at both c/4 (quarter chord-point: 1/4 of the chord distance from the leading edge) or AC (aerodynamic center). CMc/4 varies with CL while CMac is the point along the airfoil where CM doesn't vary with changes in angle of attack.
I'm not sure which sets of equations you are referring to for your calculations in estimitating longitudinal stability. I'm not at home right now so can't reference my books to look it over. However here's one equation on the web from Stanford that's useful:
(http://brauncomustangs.org/upload/CMeqn.gif)
The equation and it's explanation can be found at the following webpage:
http://adg.stanford.edu/aa241/stability/staticstability.html
Basically the equation represents the entire CM of an airplane about it's center of gravity (cg). A conceptual way to describe the equation is basically:
Airplane Pitching Moment = Moment(from wing lift) - Moment(from tail lift) + Moment(at Wing AC) + Moment(fuselage)
From this equation basically you just need the CMac of the wing, which NACA 824 gives you. Of course like gripen said you'll have to account for 3D effects if you want a more accurate estimation.
Tango, XO
412th FS Braunco Mustangs
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Originally posted by dtango
However here's one equation on the web from Stanford that's useful:
(http://brauncomustangs.org/upload/CMeqn.gif)
The equation and it's explanation can be found at the following webpage:
http://adg.stanford.edu/aa241/stability/staticstability.html
Basically the equation represents the entire CM of an airplane about it's center of gravity (cg). A conceptual way to describe the equation is basically:
Airplane Pitching Moment = Moment(from wing lift) - Moment(from tail lift) + Moment(at Wing AC) + Moment(fuselage)
There is also a moment caused by powerplant(s) ie thrust line and also the propwash tends to change things.
I have been designing RC-planes since 80s and in practice we set the needed incidences (thrust line, wing, tail) by experience due the complicated nature of the issue. However, those formulas certainly give some clue. I think that in the case of the full scale airplanes, the fine tuning of the incidences is still done based on wind tunnel data and flight tests despite powerfull computer aided design tools available today.
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Originally posted by dtango
Of course like gripen said you'll have to account for 3D effects if you want a more accurate estimation. [/B]
This is all extremely preliminary information I'm looking for here. Right now I'm just basically looking at sizing. I've got a long road of different steps to take before I even start drawing up plans, much less making parts.
It'll be a while before I have the potential to pull a John Denver...
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Yep agreed gripen. I thought about posting the nastier form of the longitudinal stability equation which accounts for thrust and other vertical offsets when I got home. That lasted about 2 seconds ;).
Stoney- keep us posted!
Tango, XO
412th FS Braunco Mustangs
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Any of you guys know a reference for the NLF series of airfoils?
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Stoney:
Try the UIUC Airfoils Coordinate Database for starters:
http://www.ae.uiuc.edu/m-selig/ads/coord_database.html
Search for NLF. There's an assortment of natural laminar flow airfoils there. Hope that helps!
Tango, XO
412th FS Braunco Mustangs
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Generally a good approach to the design process is to study the other designs for the same purpose first. I see developement of an aircraft as an evolution; you learn from your's and other's doings and a bit by bit you can improve the design. Radical approach tend lead to the enermous amount of problems which are impossible to see before the proto is built.
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The original Nemesis, the most successful IF1 racer in history and now a resident of the Smithsonian, used a NLF airfoil. That's why I asked.
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Ah, you are in right track; you don't need to invent the wheel :)
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Next topic for discussion:
Canopy profile...
Mariah, currently the perpetual champion in the Formula 1 Gold Class has a bubble type canopy profile. Nemesis had a fast-back type configuration. Hoerner states a fineness ratio of 3.7:1 is the most aerodynamic shape for a protrusion. Given that, and my planned canopy height of 10 inches, a 3.7:1 fineness ratio supports a bubble type canopy approximately 37 inches long. Kent Paser, author of Speed With Economy created a fast back canopy configuration for his plane. Is there a way (without a wind tunnel) to determine which configuration produces the lowest drag? Seems to me a fast back configuration gives a fineness ratio much higher than 3.7:1. Personally, I'd prefer the bubble canopy since the visibility would be much better. Anyone?
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Stoney:
That's a tricky question with an equally tricky answer. Here's my understanding:
You can use the component buildup method to estimate subsonic parasite drag of each component of the aircraft which you then build up to the total aircraft parasite drag. With that in mind you may be able to use this method to assess the drag of different canopies.
The first key relationship is:
Dp = f*q
This equation basically says that parasite drag equals to the equivalent flat plate area of the aircraft multiplied by dynamic pressure (.5, air-density, velocity-squared).
For the component buildup method you basically find equivalent flat plate area (f) for the entire plane by finding (f) for each of the components and sum them up. Essentially the greater the total (f) the greater the parasite drag. The equation for f for each component is:
f=Cf*FF*Q*Swet
where
Cf= skin friction coefficient (how smooth or rough the surface is)
FF= component form factor
Q= component interference factor
Swet = wetted area (total area exposed to the air)
Let's ignore Cf, Q, or Swet for now and assume they are they same for each canopy. With this assumption you can see that form factor FF then determines parasite drag. The larger the value of FF, the greater the drag.
Without getting into the details of the FF equations the relationship between form factor (FF) and fineness ratio is the following:
(http://adg.stanford.edu/aa241/drag/images/image2.gif)
Diagram from Stanford:
http://adg.stanford.edu/aa241/drag/formfactor.html
In the diagram above K is the form factor. You can see that the greater the fineness ratio, the lower the form factor. The lower the form factor, the lower the parasite drag. That's why the fast-back canopy is said to be less draggy than a bubble canopy because as you have said the fast-back canopy fineness ratio is greater than the bubble canopy.
So it appears you have your answer. The fastback canopy is less draggy.
Well... here's the tricky part. Our assumption that we can ignore Q and Swet is not accurate because they may not be the same between the two canopies so you will need to factor these variables as well.
Interference factor, Q ranges between 1 to 1.5. You'll have to to look up resources to helpy you estimate Q for the canopies in question. Wetted area, Swet you'll have to calculate for each as well.
Oh, there are several different equations for FF for different parts of the airplane. Also there are different rules of thumb to use on scaling each equation depending on the shape of each aircraft part. Here's the FF equation for canopies and fuselages for your reference:
FF = (1 + 60/fr^3 + fr/400)
where fr (fineness ratio) is:
fr = l/d or fr= l/(sqrt[(4/pi)*Amax])
where
l= length
d= max cross-sectional diameter
Amax = max cross-sectional area for non-circular shapes
Tango, XO
412th FS Braunco Mustangs
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Awesome Tango!
I'm setting up a spreadsheet to start running the numbers. I'll be back with the results...
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Apparently, wetted area is a major factor (assuming I did my math right).
I had to estimate some of the wetted area for the top because I couldn't get my CAD software to draw the contours I was looking for. As a substitute, I computed the area by approximation, using the areas of the triangle shapes that encompased the approximate shape I wanted.
Here's the equations and then the numbers I used:
Flat Plate Area (f), Fineness Ratio (fr) and Form Factor (FF) per the equations Tango posted
Wetted Area: 3.142(pi)*[Atop+Aside/2]
where Atop = the 2D area of the top of the drawing and Aside = the 2D area of the side. Got this equation from Raymer's book.
I iterated 6 basic sizes. All were 10 inches high and 10 inches wide of varying lengths: 3 ft long, 4 ft, 4.5 ft, 5.0 ft, 5.5 ft, 7.0 ft. The 7 foot length is approximately the length the assembly would be if the canopy was a fastback type configuration. The 10 inch height of the canopy occurs at a distance of two feet on all 6 sizes. The front and back slope away at fairly smooth contours, with the front more blunt, and back more shallow (i.e. half-teardrop shape).
3' f = 1691 in.^2
4' f = 1395 in.^2
4.5' f = 1404 in.^2
5.0' f = 1446 in.^2
5.5' f = 1461 in.^2
7' f = 1596 in.^2
Obviously the least drag is created somewhere close to 4' rather than at the longer lengths. Took me a couple hours, but interesting none-the-less. Next up is drawing the fuselage out. After that I'll put a 3D model together and post it.
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Raymer posts this simpler pitch stability equation is his RDV design book:
Xnp = ((Cla)Xwing - Kfuselageterm + Ktailterm(Xtail)) / (Cla + Ktailterm)
where Xwing = "Location of 1/4 chord Wing MAC"
and
where Xtail = "Location of 1/4 chord Horiz Stab MAC"
Do the units for this location of 1/4 chord matter? Also, what location? Is it the location along the MAC directly, or from the CG datum?
I'm using this equation for some simple comparisons between two drawings. He's got a much more complicated equation in his textbook that I'll use once I start narrowing down my options...
Thanks,
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Hiya Stoney:
I'm out of town at the moment (once again) with no way to reference my books so don't know how Raymer derived that equation hence the significance of some of those terms in the equation.
That being said to answer your questions:
(1) I'm not sure about the units. I'm guessing the units don't matter as long you make sure you're using the same units for Xwing and Xtail. Pitching moment (Cm) is dimensionless so if the equation is pitching moment then the units mathematically drop out. Not knowing what the other terms in Raymer's equation are I don't know how the units drop out.
(2) 1/4 chord wing/h-stab MAC - that's the distance from the leading edge for each lifiting surface in question, wing or tail h-stab. 1/4 chord point (or c/4) is essentially very near the mean aerodynamic center (MAC) of the lifting surface at subsonic speeds. This has been demonstrated experimentally for cambered airfoils.
(http://adamone.rchomepage.com/aerodyncent.gif)
(I made an earlier statement in this thread that Cm_c/4 varies with aoa. This is only true at high aoa's where separation of airflow with the airfoil occurs. Otherwise the pitching moment at c/4 is nearly constant since it's close to the aerodynamic center of the airfoil.)
The key property of 1/4 chord point (or airfoil aerodynamic center) is that pitching moment at this point is constant and doesn't change with aoa. This makes it a very useful reference point because it is a fixed position and simplifies the math for stability.
Here's some more helpful information on the topic: (be sure to read further down)
http://adamone.rchomepage.com/index5.htm
Hope that helps!
Tango, XO
412th FS Braunco Mustangs
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Sorry, I didn't mention it...
Xnp for Raymer is the equation for neutral point, and then used for the static margin.
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Ah, should have been more obvious to me :) - Xnp.
Raymer's equation doesn't appear to be expressing location of neutral point (Xnp) as a % so that means the unit of length remain so whatever units you are using for Xwing and Xtail need to be the same and are carried through the calculation.
Tango, XO
412th FS Braunco Mustangs
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tango check pms bud;)
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For those interested, my first concept drawing.
(http://i125.photobucket.com/albums/p61/stonewall74/AJ-1.jpg)
Length is 16.5 ft. Span is 24 ft.
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While we're on the topic, I'd like to know if there's anything I could use against the WWII Aircraft Forums (http://www.ww2aircraft.net) guys who state that the 190 split flap is more efficient than the F4U's slotted flaps.
In addition, he states that the Spit14 can outturn a 'flapped' Corsair.
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Wrong thread Buddy.
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Something's eerily familiar with that concept...
Mig-3?
Maybe you had similar objectives in mind with the Mig-3 when designing that concept?
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Actually, I started out with a 16.5 foot line. Added a 10 in. long spinner, then an 8 inch long prop extension, the engine, the fuel tank, the cockpit, the empenage, etc. That gave me the side profile. From there positioned the wing (the geometry was done prior to) on the fuselage at an approximate point to get the 1/4 chord point of the wing at about the CG of the aircraft. Once all those box-outs were placed, it was a matter of smoothing out the transitions, minimizing wetted area, and conforming some of the geometry to the International Formula One design formula. The cockpit interior is 18 inches wide just to give you a sense of scale.
Biggest influences were the Lancair Legacy, John Sharp's Nemesis, and the Arnold AR-6.