Landracing Forum
Tech Information => Aerodynamics => Topic started by: robfrey on November 04, 2013, 07:57:44 PM
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Aircraft designers do drag build ups all the time by adding parts separately. If done correctly, you can expect accuracy within 3%.
Now it is time for you to leave this Cd stuff behind and start talking flat plate drag equivalence. This is a much better measurement
system for figuring out the total force needed to over come drag created when moving a body through the air at a particular speed. This is much more relative to what we are doing.
The correct way to measure aero drag is this formula.
Stagnation drag + Separation Drag + Wetted Area Drag = Total Aero Drag.
The hardest things for us car guys to grasp is that frontal area was not mentioned anywhere in the equation. This is why you could double the width of your tail-fin (if for some reason you wanted to) and it will not double it's drag.
It sound like you are on the right track back not being afraid to drag those tail feathers through the air. Heck we have two giant tail fins on our car at a full 18% of cord.
Written by Interested Bystander
Rob,,
That the frontal area is not mentioned explicitly in your equation doesn’t mean frontal area has no bearing on the performance. Your second sentence essentially says that drag is independent of the frontal area--which is obviously incorrect.
While a drag coefficient is really a fudge factor allowing useful results to be easily extracted from the characteristics of the shape and fluid properties, your expression is made up of quantities that are very hard to determine.
If you think your equation is so superior, please explain, for example, what “stagnation drag” or “separation drag” is and how to predict it. Can you do so without involving frontal area? (And can you do that for non-streamlined shapes?). Your terms seem like alternate expressions for pressure drag and skin friction.
Al’s wing: Any aero appendage is going to add drag and therefore negatively impact performance unless its effect allows the vehicle to sufficiently overcome a stability and/or traction barrier.
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This thread is definitely more relative to Streamliner and Lakester aero drag.
I am still just a student of this science and do not claim to know everything
Ok where to start-
I stand by my statement about how to arrive at total aero drag.
You see, all aero drag fits into one of the three types if drag.
My reason for starting this conversation is to take the science that currently exist and apply it to what we are already doing.
This is just going to clarify and try to unify the the terminology a bit.
I do get a bit frustrated when everybody keeps talking as frontal area is the only thing that matters.
A torpedo shaped Streamliner that is. 40' long will have more drag than a Streamliner what is 25' long with the exact same frontal area.
This is because wetted area drag has increased as has separation drag. This is because air will start to separate and tumble along any surface that runs parallels with flow. The smother the surface, the less this happens but it still happens.
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Rob - That MUST have been "INTERESTED OBSERVER" -
He, like the Limeys say "Knows the sums", where I, dropped engineering for art.
Not that yers truly isn't an aero enthusiast,
The AFD drag car we built with Arivett Bros. for Roger O'Dell that Ed Vickroy drove ran numbers at the world finals that National Dragster named "Run of the year" in '92 (over Bernstein's 300) had a tunnel, plus flip ups and tire wipers in front of the rear tires a la Indy cars of the era. And a single element rear wing
With Don Enriquez driving at a later racer, the tunnel broke loose and so did the rear tires while the tunnel slid to a stop glued to the track!
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Rob, I'm not very knowledgeable about all of this, but I have been reading up on it a bit.
It seems to me you are basically quoting some basic principles of fluid dynamics? On something streamlined like a submarine, I thought you would call it the 'wetted area coefficient', but on a vehicle streamliner, I thought it was a volumetric drag coefficient?
I'm with Interested Observer, as I'm real interested in how stagnation drag and separation Drag compare to skin friction and form drag. What about interference drag?
Can you please explain this concept more thoroughly? I've read up on all of this, but I'm still struggling to get my mind around all of it! :?
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Rob, Nevermind!
I googled flat plate drag equivalence, and started reading up on it. When I found myself reaching for my calculater, I said to heckjwith it, I'll just visit Rob and he can explain it to me! LOL! :-D
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The frontal area and Cd method of figuring aero drag shows its shortcomings when one wants to decrease it. It is hard to quantitativly analyse the effects of proposed changes.
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Stagnation drag happens when oncoming air
runs headlong into an object and can't decide which direction to go. Places for stagnation drag include: the grill, Headlights, leading, windshield the leading edge of a Naca 66-018 airfoil, front side if tires on a lakester., or anything that would cause pressure to rise in front of a moving object., basically I guess it could be described as air "packing up" on the leading edge of an object moving though the air.
Separation drag happens when the flow of air becomes unattached to a object. This pulling away of the air creates a low pressure area. Examples would include, the back of a semitrailer, rear exposed chute tubes, the backside of the tires on a lakester or even the exposed backside of the tires on our Streamliner. These little patches of exposed tire are one of the biggest drag items on our car. We worked hard to minimize this. Also anytime you have an aft facing taper that is not transitioned smoothly enough from a straight section the flow will become detached creating drag. I think that it is safe to say that if a body section is creating a pressure change, either positive or negative, it is consuming energy, thus creating drag. I have yet to find an air compressor or vacuum pump that consumes no energy.
Wetted Area Drag is all the skin that is exposed to the moving airstream, The more surface area, the more drag. Simple analogy is a garden hose. The longer the hose the more energy is needed to maintain the same flow rate. This is when things got interesting for me. All wetted area does not have the same drag. The area that is in laminar flow has only about 1/3 of the drag as areas in that are not in laminar flow. Consequently, we fought hard for laminar flow.
I contend that all the drag that you all have been speaking about falls into one or more of these camps.
I now stand ready for cross examination. LOL.
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Rob, Nevermind!
I googled flat plate drag equivalence, and started reading up on it. When I found myself reaching for my calculater, I said to heckjwith it, I'll just visit Rob and he can explain it to me! LOL! :-D
Better yet, visit Eric. Just wrap your head with duct tape first as you know.
When I was getting my education, my brain hurt almost every night from overload.
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Interested Bystander, I stand corrected. Sit that way too. It was interested observer.
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Hmm it seems like we are just talking about the various pools of drag
ie types
but those of us that are trying to go faster are trying to wrap our minds around what goes in to these collective pools and how to influence that pool..
Ms Liberty original tank nose was too blunt--ie a sphere =stagnation drag--
therefore she now has a nose that looks like the wicked witch's
My 30" dia. tank made my car have to be longer than if I had used my 33" dia tank---so I could get stuff in----whoops there goes more into my surface vs my cross section===it just the formula---we still have to build SHAPES and assemble them that have the smallest total collective pool of DRAG :-o that still stays the same chose parts and shapes that collectively add up smaller vs BIGGER---brought to you by hopefully and newly through its first INSPECTION!!!! :-D
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Rodfrey,
So the thought that you could dimple the side of a car like a golf ball and make it go faster and or get better fuel mileage is false then.
Richard
P.S Not trying to be smart just something I know is out there.
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My $0.02 is this:
Using the frontal area calculation that the automotive world lives by is a good rough measure or attempt at comparing two shapes against each other. I'll use reductio ad absurdum to present examples.
Let us assume we are running three objects through the Fa formula and calculate the HP required to move each of these objects 100 MPH. The results of which are as follows:
Object 1: .4 HP needed
Object 2: 78 HP needed
Object 3: 8,000 HP needed
What did we learn from this? Well, Object 1 is the most aerodynamic since it needed the least amount of HP. Object 3 is the least aerodynamic because it needed 8,000 HP to achieve 100 MPH. But what are these objects? What shapes do they represent?
This formula is good for a rough comparison of both known and unknown shapes to each other, but it doesn't tell you how to make them more aerodynamic. The reductio ad absurdum portion of this exercise is that object 1 is a sparrow, object 2 is a car and object 3 is a locomotive.
Now, if we look at the method that uses flat plate equivalent alone, it is not that far from what the Fa formula tells us. The difference is that the resulting numbers are compared not to each other, but to a 1 square foot flat plate placed perpendicular to the airflow. It really just changes the anchor point of reference from object-to-object to object-to-flat plate. Neither of these methods alone gives you the ability to identify and quantify explicit areas of drag.
The second part of the method Rob makes reference to is the build-up calculation. How I believe it works: If you take each discrete shape that is interfacing with the air and calculate the flat plate equivalent, THEN add all of those together, you have a total drag number for the object. The advantage to this is now that you have these details and an anchor of FPE, you can start to analyze for improvements. You can now compare the wheels to the windshield to the spoiler to determine which areas of the shape are yielding the most drag so that you can focus on those areas. If the fuselage is 12% of the total drag, but the parachute tubes are also 12% of the drag, you may want to look at the parachute tubes first.
Here's the other part of Rob's statement, what kind of drag is it? If the parachute is a cube bolted to the top of the car, you have both stagnation and separation drag. Placing a more aerodynamic shape on the leading portion of the cube will help, maybe not ideal, but you can reduce the stagnation drag. Maybe because of packaging or money, that is all that can be done, but at least you know where the drag is and what it costs. You can also measure the improvement from 12% to %12 - x when you reduce the stagnation drag.
Rob references tires and the stag/sep drag they cause. Not much you can do about the shape of a tire, it will be what it will be, but you can look at the shape of fairings and ways to present the tires to the air. These shapes can all be calculated and added together to give you a reference of what the air should be doing with the shapes you have chosen. It will also give you some reference within your own design to know where your problems are and where to focus your efforts.
This isn't a new concept or a new idea that is being proffered, it is how the aviation world has worked for years. It is just being highlighted that it can also work in areas outside of aircraft design.
Sparky - I like your concept of pools(buckets, classes...) of drag, knowing which kind and how much is in each bucket as well as what you can do to correct AND MEASURE THE RESULTS of your changes is how you make your shape better.
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Rodfrey,
So the thought that you could dimple the side of a car like a golf ball and make it go faster and or get better fuel mileage is false then.
Richard
P.S Not trying to be smart just something I know is out there.
Richard,
In certain circumstance dimpling can have a positive effect on wetted area drag. You would not count all the extra area caused by dimpling because the air is not following each dimple in and out of the surface of the vehicle. Again, this fits into one if the three categories of drag.
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Rob et al,
You are correct that it is useful to characterize and be aware of the sources of and magnitudes of drag generating fluid behavior, but it is another thing to completely discount the usefulness of the Cd approach, which rolls all your component drags into one figure of merit, and then, in addition, to completely dismiss the importance of frontal area. Those were my primary points.
My secondary point is that trying to predict those components is exceedingly difficult. Not everyone is prepared to deal with pressure distribution, boundary layer, and Reynolds number calculations. (Although CFD is well on the way to handling this, it, too, is not a trivial undertaking). I notice you didn’t offer quantitative examples of separation drag calculations.
While I would certainly defer to Eric on these matters, I would be surprised if he didn’t generally agree with the above, and if you or he can cite preferred reference sources or materials that can further illuminate the utility of the drag component approach, I am sure all here would be interested. Probably for Eric these drag questions call up an almost intuitive, reflexive response, having been immersed in it for decades. For others, not so.
P.S. (having now read bbarn’s addition)
I would have no issue with the “flat plate” equivalence approach--but it is no different than adding up the drags of the various features and comparing them one to another to see their relative significance. The difficulty is in determining each of their drags and how they arise out of the different modes of drag creation--shape, skin friction, etc. We may be getting confused here about the drag of components and the components of drag.
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IO,
I agree 100%. I'm just trying reiterate the idea that frontal area is important but it's not everything and shape does matter.
I by no means have all the answers and certainly do not want to come across as a know-it-all. I'm just trying to share what we have learned which I believe is the reason for this forum. :-) Cheers!
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This is fun..
Reminds me of what Rich Fox told me years ago. I was telling him of this computer program that predicted acceleration rates, I went on telling him how FAST I was going to go…. He listened quietly.. then casually said…”A… Dalton… why don’t we all meet at the Motel 6…. And RACE our computers… it WOULD be so much CHEAPER..”
Similarly, I was speaking to Charley Markley.. Again.. there I was..”yea Charlie.. I need 300 mph in the first mile, then 400 in the quarter, and we will go out the back at 500….” A long pause…. And he said.. “ well don’t you think you should go 400 first…”
You know … I’m a slow learner… As my partner Jackson says…” we will be smarter 12 months from now” and we are learning.. The basics.. get to the other end … faster than the record twice.. in a row..
Be sure your tires aren’t rubbing the frame.. only dial up hp needed.. and don’t overpower the given course condition .. it ruins $1500 of tires.. fast.
I heard rumor Jack Costella was quoted as saying… My cars don’t go through the wind, they go under it.. that’s probably true.. :-)
Well .. “ My car won’t be going through or under the air.. When the wind hears us coming, it will get the heck out of the way” :cheers:
Bob
All should watch jack’s intro video at http://www.jackcostella.com/
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Let us discuss a little further, I think IO and Rob are on to something in their dialog.
Fa in and of itself is not a useful number, it doesn't convey any meaning or measurement other than ft2. It doesn't describe a shape or how it interacts with the air, it only conveys a number.
Here is an example that illustrate the issue:
Let us assume we have two objects that have an Fa of 1937.5 ft2, which one of them is more aerodynamic?
You can't tell from these numbers alone...or can you? (<-Legit question, I don't think you can, but maybe I missed something)
The two objects I have used here is a 747 and a building where the dimensions are 20ft wide and 100ft tall. Both of these can fly, but only one can do so efficiently!
It is not until you introduce the Cd with the Fa that you get something useful. The Cd describes how the air is moved around the object with an Fa(x), and from that you can determine the general aerodynamic properties of the shape. (FYI, the drag coefficient of that 747 I used above is 0.03 (http://www.withouthotair.com/cC/page_273.shtml (http://www.withouthotair.com/cC/page_273.shtml)).
IO is correct in his statement about FPE as well: "the difficulty is in determining each of their drags and how they arise out of the different modes of drag creation--shape, skin friction, etc.". It may be a completely cost prohibitive endeavor to remove and measure each component of a standard vehicle to measure it's contribution to drag. Think about the challenge of measuring the frontal area and the drag coefficient of a fender, hood, bumper, windshield, door handle, tires, hub caps, antenna, mirror... not to mention the fact that you are missing the aerodynamic interaction of one part against another.
Here I think is where the real differentiators are: In the world of aviation, you are not incumbered with certain details like, will it fit under existing bridges, how well will it parallel park, will it fit in the average parking garage, I don't need a rear view mirror, tires only need to be sticking out when I am on the ground, all other times they are out of the airstream....
The world aviation engineers have to work in have different requirements because they have different goals. You don't see many passenger cars with a ~2000 ft2 frontal area that seat 400+ and drive cross country in 4 hours. Conversely, you don't see many airplanes that you can hop in and go 3 miles from home and run through the drive-thru to get your kids french fries either!
Back to IO's comment. I think in a door-slammer situation, you are not likely going to do an entire buildup using the FPE method to determine total drag, it is not economically feasible. I do think though that if you are talking about "Specialty construction" or building adaptations for your door-slammer, there is great value in knowing the FPE, if for no other reason, you can get your drag, Reynolds, wetted... if you base your build on known shapes.
If you are like me, looking at this link http://en.wikipedia.org/wiki/Drag_coefficient (http://en.wikipedia.org/wiki/Drag_coefficient) will yield nothing but an aggravation -- unless the subject interests me, then I'll devour it as best as I can. You can skip reading the whole thing, just look at the top right side and the pictures/shapes they have. I am not sure the accuracy of these numbers, nor am I implying they are reliable, I am only illustrating that your basic shapes can be estimated, some work has already been done, there may be more accurate sources for Cd's as well.
I know for sure that the numbers presented in that link are not precise, because there are many "streamlined" shapes (foils) to choose from, velocity, size, AOA... all contribute to the drag. Some foils are more effect at different velocities and AOAs and produce less drag than represented in that table. If you are talking about a foil, get a copy of "The Theory of Wing Sections", it has what you need to calculate foils, lift, drag, by AOA, by velocity...
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Don't forget...
We don't have all day to get to the perfect speed. We aren’t racing to terminal velocity. Well ok some are. Fast cars not so much. The dragsters in NHRA are going 320 mph in 1000ft today, and we are trying for 500 in 5 miles. Hmm. We are racing on an island of salt. We don't have more than 6 miles tops ... if that. Fyi , my own calculations put the terminal velocity of the Turbinator at over 700 mph, but then again, we only have 6 miles.
This is fun stuff. Interesting and NOT Nascar.. bs.
Real Innovation Real Racing Let the Innovators loose.
:cheers:
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When I'm trying to understand this I too think like Sparky in terms of pools or areas of drag. Frontal area, overall surface area (skin drag), coefficient of friction for wheels/tyres and so on. Anything that you can categorise (even the density of the air) that will stop you going as fast as you think you ought to. I've been lucky enough to work with Richard Noble's aero guru Ron Ayers over the years and he's helped to clarify my understanding of this area - at least to some extent for a layman like me. I've learnt one general and one very specific lesson from Ron.
One is that when you move into the whole computer model, CFD, wind tunnel correlation world for vehicle design then you need to keep an open mind and understand what the numbers tell you rather than simply using them to subjectively support your original theory. That's because as you learn more about what's really going on as opposed to what you assume is going on, some things are counter-intuitive and at first you think "that can't be right". An example. Prior to SSC almost everybody talked about how the whole subsonic/transonic/supersonic airflows at Mach 1 would lift the nose of the car. You only have to look at a pic of a shockwave on the front of a fast jet to understand why that was a common belief. While that is a danger, it also turns out that at around Mach 0.9 (670ish mph) the compressed and accelerated air shooting out of the back of the car underneath at getting on for Mach2 tries to lift the "back" of the car. So if you haven't got a method of producing down force (ie a tail) then you are in for a spot of low level aerobatics. Who would have guessed that let alone been sure of it without CFD and rocket model test data allied to an open mind? The Budweiser Rocket and SoA had rear end lift off at around these speeds. Coincidence? Maybe.
The more specific lesson is one I've mentioned before and that's wake drag. Literally the drag caused by the plume of salt or dirt kicked up by a vehicle traveling fast. Look at the latest pics of NAE at Alvord (or SSC at Black Rock for that matter) and you'll see huge plumes of dirt. That plume - still attached to the vehicle and getting bigger until the stuff at the back settle down again - effectively increases the overall vehicle aero envelope and drag. Which is why on JCBDieselmax Ron used carefully crafted tunnels underneath the body and around the wheels to stop the plumes forming in the first place. Looking at the latest Mormon Missile and a couple of others it's seems they too have picked up on this but I wonder how many carefully crafted aero envelopes designed with low CDs to slip through the air ignore it. That's now another pool or area of drag on my list.
As I said, I'm no aero expert but I know a man who is so it's a subject that is as fascinating as it can be baffling until you slowly fill in the gaps in your knowledge. I'll stick to being a keyboard jockey I think.
Cheers
Robin
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Robin UK - I think the wake drag you are referring to is the separation drag Rob is referring to. I think a good example of this is a canoe vs. a row boat. Think about giving two good stokes in a canoe and the same two strokes in a traditional row boat (blunt/flat rear), which one will go further on the same thrust?
The difference is the canoes shape lowers the separation (wake) drag to be less than the row boats drag.
Mental exercise: Take the row boat and the canoe, scale them so they have the exact same frontal area and repeat the test...what would the difference be?
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Good reference books for this discussion.
"Race Car Aerodynamics, Design for Speed" by Charles Katz: Get the second addition, good book on everything from streamlining, wings, ground affects, all applied to cars.
"Competition Car Aerodynamics" by Simon McBeath: Mostly related to formula and sports racing cars but good reading. Mr. McBeath also has a monthly article on aero in "Racecar Engineering" magazine.
"The Leading Edge" by Goro Tamai: My favorite aero book, I know it is about solar powered car aero but it all applies to what we are interested in and it is very informative and well written.
"Fluid Dynamic Drag" by S.F. Hoerner: Not available in a current printing (I think) I down loaded from the net, over 450 pages on almost anything aero you can think about. Well done but heavy reading.
" Theory of Wing Sections" by Abbott and Von Doenhoff: This is "the" book on wing design and aero, very technical but a great reference for picking wing sections.
"Personal Aircraft Drag Reduction" by Bruce Carmichael: This is the book that the "flat plate" aero design comes from that Rob is talking about. Carmichael is one of the leaders in the development of the NLF, Natural Laminar Flow, school of aero design. This is the basis of the design for Rob's Project NACA 6600 car. Great reading with discussion of many projects using NLF.
Plus there is a ton of NACA , NASA and SAE papers on aero that are available on the web.
Read all or any of these and your "ignorance of aero will be diluted"
Rex
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Carmicheal's book is just plain awesome.
It's a great compilation of his work and many others. I just can't say enough about it. Highly recommended reading.
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I think I subscribe to the Comic Book of Aero---like BB example---show me the pictures :roll:
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Same here Sparky, luckily Carmicheal's book is full of illustration.
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Good reference books for this discussion......"Personal Aircraft Drag Reduction" by Bruce Carmichael: This is the book that the "flat plate" aero design comes from that Rob is talking about. Carmichael is one of the leaders in the development of the NLF, Natural Laminar Flow, school of aero design. This is the basis of the design for Rob's Project NACA 6600 car. Great reading with discussion of many projects using NLF....
I have a number of the books listed, but not the Carmichael one. If I remember right all give equal weight to A (in our case frontal area) and Cd (the total Cd of the object) such as in the reference mentioned above...
http://en.wikipedia.org/wiki/Drag_coefficient
Does Carmichael not give the frontal area equal weight in figuring drag force or does he use a different method to figure the total Cd of the object and then gives equal weight to frontal area when figuring the drag force.
I also think the Leading Edge is one of the best sources although some of the math is over my head,
Sum
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Masters of the Wind..
How many thousands of pounds of jet thrust does it take to make the dirt of the earth, blow in the wind?
The answer my friends, is blowing in wind, the answer is blowing in the wind.
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"Race Car Aerodynamics, Design for Speed" by Charles Katz----Joseph Katz--- Maybe
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At SW 2013 I was in the 911 pit talking to Donny and I said something about how slick, lose the salt was and his team mate turned and said "That's why 911 weighs 6400 lb."
No wing of coarse
Richard
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Prof. Joseph Katz. Car guy. Helped me with my project. He's at SDSU. Thanks Joe. :cheers:
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"Race Car Aerodynamics, Design for Speed" by Charles Katz----Joseph Katz--- Maybe
This is a great book and I've always wanted to meet Dr Katz as he has been a great asset to so many racers. I did think his book focused more on generating downforce than minimizing drag. I thought it to be a better book for SCCA racers than SCTA racers. Learned a lot from this book though.
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Sum,
From what I remember, Carmicheal does not bother with Cd at all. Can you confirm this Rex?
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Carmichael does talk of Cd; mainly wetted area and in conjunction with Reynolds numbers though.
Strojnik's books are an interesting read as well.
Also recommend Mike Arnold's AR5 videos.
jon
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"Race Car Aerodynamics, Design for Speed" by Charles Katz----Joseph Katz--- Maybe
This is a great book and I've always wanted to meet Dr Katz as he has been a great asset to so many racers. I did think his book focused more on generating downforce than minimizing drag. I thought it to be a better book for SCCA racers than SCTA racers. Learned a lot from this book though.
It is the challange we face in our chosen Motorsport, and Dr Katz Book book reflects this as most Motorsport is about Down Force. It really helped me get my head around fundamental Aero and the way it it works on Vehicles.
"The Leading Edge" by Goro Tamai is about cheating the wind but not at the speeds we are aiming for. Again it helped me to understand Aero concepts, but I am still no Scientist.
This discussion is great, it's of great interest running a relatively Low Power Bike.... Aero is everything.
Pete :-D
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Just a comment by Ron Ayers regarding the drag contribution of skin friction on the JCB car. He said that over 70% of the total drag at over 300 mph was contributed to skin friction. So things like fit, finish, body joint design and skin stiffness, which is especially critical on cars with flat sides or top, have a huge affect on the aero ability of any streamliner. Most top fuel bodies are made from .050 mag sheet and if you watch them at speed they are vibrating in and out at such a frequency and magnitude that there is no possible chance that they have attached air flow and attached flow, either laminar or turbulent is what you must have to be aero. If you look at the skins and inter support work on Marlo's liner you can see that Jim recognized this and provided a lot of support to prevent any skin deflections, I also think that he used .071 and thicker aluminum for skins which all help. (it also allowed him to really make the skins smooth and fit well by lots of filing with the "hungry file")
Rex
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0.050 sheet magnesium is certainly light but it burns and then it's hard to extinguish.
Regards, Neil Tucson, AZ
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It must be some sort of fire resistant alloy. A person would be nuts to use the pure magnesium.
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Jon,
I just ordered the first of the AR 5 DVDs. Can't wait to receive it! I will ask for some of the others for Christmas.
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Just received the first of the Arnold AR-5 videos. First one is titled "Why is it so fast", it is a great video! I highly recommend it!
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I spent time in the wind tunnel at the CSIR working as a subcontractor to a major manufacturer.
You won't believe some of the small insignificant things that affect aerodynamics.
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NHRA funny cars paint a fire resistaint coating inside the body, a few liners have done the same.
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Glen,
Tell me more about those paintable fire resistant coatings.