Teardrop calculation

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internetscooter
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Teardrop calculation

Post by internetscooter »

I am wondering if anyone has come across the maths behind the perfect aerodynamic shape - the teardrop (assuming speed is below the speed of sound)?

Googling finds lots of vague info describing why it is good but I want to find something a bit more precise. Ideally I'd want a formula I can put into a spreadsheet, throw some numbers at it and have different teardrop graphs pop out.

It should be possible to "tune" a body shape to a particular speed and internal size requirements, so a teardrop of a particular width has the correct length.

Paul

BTW This is something interesting I found:
Image
Paul
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David Leikvold
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drip drip

Post by David Leikvold »

0.04 goes a long way to explaining why the Jarman Stewart belly tank goes so well with a virtually standard motor. Looks like all the effort Doc and Rev put into keeping the tank length standard was worth it.
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grasshopper

Post by Dr Goggles »

..for what it's worth my calculations tell me that we had no wheelspin . You're thinking "calculations?"....well,sitting up the front makes it harder to feel what the arse end is doing. The revs weren't flaring, the speeds matched the revs we were pulling and we weren't standing on it early.when we do it will break loose obviously but the point I'm making is the evidence demonstrates that we have a very clean shape.....we can thank the guys who drew the original slipper tank for the Canberra for that, ta.We just stuck with it :wink:
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Post by internetscooter »

I "think" I have just worked it out, after hitting the RMIT library and getting a book on Fluid Dynamics.

The teardrop shapes aren't simple and there are a number of ways to calculate them. The thing to look for is "symmetrical airfoils". The following website lets you pick the type of airfoil design (which is the teardrop maths itself) and then calculate the final shape by applying the parameters. There are lots of other cool tools to play with :)

http://www.mh-aerotools.de/airfoils/javafoil.htm

This is a screenshot of a non-symmetrical design but it gives you the picture
Image

Paul
Paul
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round

Post by David Leikvold »

The perfect teardrop is also circular throughout its cross section (Alan Fountain's car being the best example of that). I wonder what difference it makes if you vary that cross section in the interests of practicality. For example the JS tank has a flat bottom where it was originally attached to the wing tip and a canopy added and an air scoop too, all of which alter the cross section. They've all been subtle changes and well executed so their effect would be minimised. If someone was planning a streamliner the game would change significantly. The teardrop would have to be stretched to become more like an aircraft fuselage or more like Lucky Kaiser's bike just to fit everything in, all the time moving further and further away from that delicious 0.04 number. Frontal area is important too, I wonder if a teardrop tank with flattened/narrowed sides would be any better than a full width one? Almost seems like a rocket powered belly tank with razor blade wheels and tyres might be the go :wink: . Now that really would be an E ticket ride!!
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Post by Dr Goggles »

The B52 tank isn't a tear-drop yes it has a circular cross section,, a "tear-drop" has it's widest point at one third of the way along it's length.........here's the body of Al Fountain's tank( thanks for the pic Drewfus)

Image

and yes you're right about scoops and stuff, frontal area is the killer( put your hand out the window of the car at 60mph and twist it around to feel the change in force) as is destroying the rear taper....
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Post by internetscooter »

Dr.G if you experiment with the javafoil applet you'll probably find a shape that exactly matches your lakester as the shapes are based on airplane standards. Then you can play about with some numbers and calculate the Cfd.

I think there might be one for Al Fountain's tank too.

The Cfd is for free air, being on the ground effects the performance.
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Lynchy
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Post by Lynchy »

..for what it's worth my calculations tell me that we had no wheelspin . You're thinking "calculations?"....well,sitting up the front makes it harder to feel what the arse end is doing. The revs weren't flaring, the speeds matched the revs we were pulling and we weren't standing on it early.when we do it will break loose obviously but the point I'm making is the evidence demonstrates that we have a very clean shape.....


Dr G - doesn't that just prove that you didn't have enough horsepower? Don't take that as a criticism, just an observation. Or rather, that the body is clean enough to go faster with more power. Wheelspin will occur when traction is broken due to not enough weight on the tyre or the tyre breaks loose when the body hits the aero wall, actually a combo of the two.

So the good news for you guys is that you've got more to go.

Lynchy
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Post by Dr Goggles »

ipso facto....


That's exactly what I meant Lynchy.

Even with what power we had the car was still accelerating, there are sedans out there with three to four times as much power running in the 170-80 range ............and spinning, they won't go much faster than that because they are "hitting the wall"

If we had 500hp, .....and a motor that held together at 8000,

They're easy to find , just hard to pay for...........


It's all in the aero. :wink:
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Post by grumm441 »

Lynchy wrote:
..for what it's worth my calculations tell me that we had no wheelspin . You're thinking "calculations?"....well,sitting up the front makes it harder to feel what the arse end is doing. The revs weren't flaring, the speeds matched the revs we were pulling and we weren't standing on it early.when we do it will break loose obviously but the point I'm making is the evidence demonstrates that we have a very clean shape.....


Dr G - doesn't that just prove that you didn't have enough horsepower? Don't take that as a criticism, just an observation. Or rather, that the body is clean enough to go faster with more power. Wheelspin will occur when traction is broken due to not enough weight on the tyre or the tyre breaks loose when the body hits the aero wall, actually a combo of the two.

So the good news for you guys is that you've got more to go.

Lynchy



Don't worry
We have a whole lot more HP for that little motor just lying around
G
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I make it work
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Post by Rob »

I read somewhere that a tank needs to be a given distance from the ground at it's lowest point to reduce/minimise drag. I can't remember if that distance was a factor of girth or length though. :?

Cheers,
Rob
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Lynchy
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Post by Lynchy »

If we had 500hp, .....and a motor that held together at 8000


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get a cuppa.

Post by Dr Goggles »

Rob wrote:I read somewhere that a tank needs to be a given distance from the ground at it's lowest point to reduce/minimise drag. I can't remember if that distance was a factor of girth or length though. :?
Cheers,
Rob


much debate over this one Rob....and let me say that I'll be surprised if the argument is ever settled. The fact is the easiest way to do it would be punching in the speeds , and chassis dynoing some genuinely "streamlined" cars. Fact is there's a shortage of people interested in building on the "pure" side. Witness that the majority of big time streamliners ignore some of the most basic tenets. Generally they are dictated by what the builder wants to put in them.Ours is an equal folly because we wanted it to "look" right and let the volume of the tank dictate what we used........it ain't long enough for a V8 AND a gearbox .......
That said , obviously most builders make a serious effort to clean up their shapes once they have a basic idea of what they are going to build. We spent a lot of time on getting the exhaust out the rear(critical) lining up the axles and minimising the steering and brake gear and hiding the chute........going for drums on the rear instead of discs.....

anyway here is a post that REv put on landracing .com a few years ago when they were debating the "high or low" ride height thing on our build diary there........................

I am writing this reply to you and to whoever else is interested or wish to chuck their two cents in.

Apologies for the usage of the high falutin metric system.

For those who missed it Rex pointed to a page in Goro Tamai's "The Leading Edge" discussing the manner by which drag quickly increases below a certain ride height and cited some figures which seem to threaten our design's efficiency.

I must admit that this area has had both the good Doctor Goggles and myself ponderous as to the correct direction to take so I went out and found a copy of the book. Below is a history as to how the bottom is as it is at present.

Our main Aerodynamics text to date has been "Race Car Aerodynamics" by Joseph Katz, Ph.D which I can recommend for its readability and information.

The difference between the two texts is that Katz's book focuses on methods of maximising downforce due to aero effects whilst minimising drag whereas Tamai's focus is about eliminating downforce altogether.

Tomai's book is written primarily for solar cars where energy conservation is a priority and traction issues marginal. As the title suggests Katz's focusses on racecars which have different criteria (eg cornering and acceleration issues).

Upon reading Katz and understanding the traction difficulties on salt, we found ourselves considering all sorts of thoughts of ground effect devices but for a number of reasons were reticent to embrace them.

Firstly we did not wish to destroy the traditional style of the belly tank so we were reticent to go too far with a diffuser etc.

Secondly, we are building against the clock so we wish to keep it simple for its first years out then can tune the shape against a base model.

Finally it is a bit of a black science when you don't possess a wind tunnel and you could do a lot of work that makes the Dodge thing slower.

We were cheered up by the fact that the So-Cal Lakester belly tank wannabe (So-Called belly tank?) turned up sporting a similar method that we considered. Rex mentioned that it hasn't performed well yet but in its defence Bonneville has seemed to be pretty rough of late and not conducive to ground effect technology. Neither is several inches of water so the jury is out for me on that one.

My understanding of how it works by looking at it is a splitter at the front to stop air creeping under and provide some downforce at the front, then has a difuser at the back to accelerate the air that is underneath so that a low pressure zone is acheived by the Benouli affect pulling it down. It doesn't seem to have skirts so I would imagine that it sucks more in from the side rather than the car down causing drag inducing vortices... correct me if I am wrong. (anyone GM?)

Anyway, for the above reasons we have decided to not have any ground effects for March and have addressed the issue of traction by making it HEAVY. (No replies please Propster).

Our intention was to get the car as low as possible for stability and to acheive the goal of having the axles on the centre line this put the diff in the widest point of the car and meant body panels could sit over each appendage minimising cutouts, oh yeah it looks cool too.

A number of cars at the salt are really low and perform well so we assumed that the drag due to ground proximity was minimal. For example one car we have enjoyed watching develop is John and Paul Brougham's belly tank which has put in multiple 200mph runs over the past couple of years at Gairdner and is very low (see image). Admittedly it is a little TOO low as it bottoms out a bit at the moment but larger Goodyear Eagles are on their way! Both John and Paul have been very helpful in providing us with much info along the way.

The Brougham tank does have a curved base though where we are proposing a flat base. Our favorite tank was the Hooper tank (the flat head killer) (see image) and part of its charm is the low flat base, as is Xydias' original SoCal and we made the decision early to go down this path.

So what height is the best height?

On page 118 of Tomai is a graph outlining the best ground clearance heights for certain shapes to ensure lack of drag due to ground effect.

Rex indicated the row entitled, ?torpedo shape with an oval width / height of 1.25 and length/height of 3.6. has a H/l of 0.3 min. to 0.05 ; that is a minimum ground clearance of 126mm to 210mm for ours (our car being 4.2m metres long.)

Currently we are around 40mm so that looks way under.

But our w/h is 0.88 / 0.81 = 0.92 and l/h is 4.2 / 0.884 =4.75 and extremely tapered. Tomai's calcs are predominantly to be used for a solar car of width of 2metres and 400 to 700mm thick and of fairly uniform shape for the length.

A better zone of the graph therefore to look at is:

?Torpedo with flat bottom with various cambers and width=height? which is worked out as a ratio of height to breadth at a Hmin ratio of 0.15.

For our car that makes 121.5mm (a whole 3.5mm lower!!!!) but at least it confirms that we are at the lower end of the scale.

The fact the whole shape is tapering I assume will lower the impact as well....?

The mention of "Camber" refers to the amount the centreline axis of the shape is above the chord from tip to toe expressed as a percentage. (Bloody ?camber,? couldn?t the nerds have used a term not already in the automotive lexicon???)

The curve of the centerline of our car caused by the extra tank on top and chopped bottom helps counter the drag caused by proximity to the ground by increasing the distance traveled over the top of the car and hence similarly accelerating it helping equalize pressure.

The book says the ideal amount is between 3% and 6%. I worked out ours to be 4.7% (yay). Apparently the best shape to have is a slight ?S? shape in this camber. Ours is that slight S shape so that seems helpful.
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BOB ELLIS
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Post by BOB ELLIS »

The basic formula for land speed racing is,

hp+m=mph.
Where hp = Horsepower
m= Money
Therefore , Horsepower + Money = MPH!

Or in the case of a doorslammer like ours,the formula changes to..
hp +m+m+m+m= "Broke the motor"

Another handy formula from my cousin Albert, E=mc2.
Where E = Enjoyment of racing.
m= miles travelled to the event,
c = cartons of beer consumed at the camp.

Therefore, if you travel along way,and drink alot of beer with some old mates,it don't matter that you broke the motor,you still enjoyed yourself!
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Lynchy
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Post by Lynchy »

very good call Bob!!!
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