Aerodynamics

[Killrob]

[size=150]Aerodynamics[/size]

Aerodynamics are an important aspect of car design and as such, probably also of importance in your game.
As using the search function has revealed only a tiny bit of information on how you want to tackle this
aspect [1] of the game, I would like to pose the question: how are you going to implement it?

This post is written out of sheer curiosity, but also to get you thinking about this topic a bit now that you
are almost done with the soon-to-be-awesome engine designer part (yey! ). And maybe, even give some
new pointers towards some things that could be considered in a perfect world with infinite amounts of time
for development.

In the discussion around engines and fuel consumption the following was mentioned/stated:
“… This will then get used with the weight and rough aerodynamics of a car …”

It seems to me from the little I have read here, that the aerodynamics will be an integral part of the car body
designer. So here comes a heap of questions to stimulate discussion:

[size=150]Questions / Considerations[/size]

a) What parameters do you offer for direct and indirect tweaking by the user?

b) How is the car’s total drag coefficient [2][3] approximated? Is its frontal area calculated from
the size of the parts? Is the drag coefficient the sum over the partial coefficients of the different body parts?

c) Is there any synergy between parts in regards to aerodynamics (negative or positive)?

d) Is the under-works/chassis (umm, don’t know the correct term, the bottom surface of the car closest
to the road) considered part of the aerodynamics package of a car? It is very important for faster cars, able to
create enormous amounts of down-force, and with it, cornering capabilities.

e) Are you going to consider turbulence created by rugged features of a car? The rear end of a car for
example, creating under-pressure right behind the car, which in turn creates a force opposite to its direction
of movement. Mirrors are another example where the formalism in [2] can be misleading because their front
is nice and round… which is a misconception in general: the back-side is often more important than the front,
example: the shape of falling water drops forming an equipotential surface.

f) Will there be some kind of “wind tunnel” feature where the effects of different designs/parts can be
established? Of course I understand that writing a wind-tunnel simulation probably would be a matter of a few
years in itself.

I think this is it for now. Keep up the excellent work, not only with the game, but also the much appreciated
openness towards the community!

/Killrob

[1] Aerodynamics in your game will be over-proportionally important as compared to real-life car
manufacturing because gamers will be inclined towards building sports-cars or faster cars just because of
their inherent coolness factor. This makes it an aspect even more worth considering in at least some detail.
[2] en.wikipedia.org/wiki/Drag_equation
[3] en.wikipedia.org/wiki/Aerodynamic_drag

[Deus_ex_Machina]

wow

somehow i thik i like you.

new here, thinking about things, AND using the search function… thumbs up

not really a solution, but if u limit the sale figures of sports cars it will reduce the severity of the problem…
underworks… martin brundle calls it both the floor and the undertray…

i like your suggestion about the wind tunnel.

[Drake]

Good questions, It is good to see someone asking some technical stuff on here.

@Killrob

c) Is there any synergy between parts in regards to aerodynamics (negative or positive)?

I do know from the thread I had started about Engine Configurations that parts can Indirectly affect aerodynamics. Since the game calculates the size of the engine, the height is an important factor in how aerodynamic you can make the front end of a car. So a Flat4 or Flat6 are not very tall, so you could make the front of a car more aerodynamic. Also I am hoping they will give us the option to mount our Inline engines in Slant positions… That way they aren’t as tall and can allow more aerodynamic body at the expense of taking more width and possibly higher maintenence costs.(less room to work on things means more labour costs)

As for the other stuff, the Devs should be able to answer that.

[Daffyflyer]

Im 98% sure you’ll be able to slant mount engines (unless we find some horrible reason not to)

Interesting thoughts about aero.

There will be some form of aero calculations, as previously stated for fuel econ calcs.

How sophisticated we can make it depends on how hard it turns out to be, but we will certainly aim to implement a fairly accurate system, and thanks for the information (we are no aero experts, so anything we can get will help )

[zeussy]

I have given aero some thoughts,

I think a good initial approximation could be calculated using the front area of the car (so smaller and lower the better) with how aggressively the gradient of the surface of the car changes.

So if you have a flattish bonnet, that suddenly changes gradient to a quite steep windscreen (think 4WDs) as that has an aggressive change in gradient that is bad for aero. Where as a car that is just one big gradual sweeping curve (I hate to say it, but the Prius) that is good for aero.

[Daffyflyer]

Probably also a similar thing with the drop off at the back (wake drag)

I was thinking for added objects like mirrors, vents, wings etc. it would just be a flat “This bit adds/takes away X amount of drag” but not really interacting with the aero properly as it’d be too complex.

I wonder if we can work out a simple way of calculating lift also, I would think that would mainly be based on how much air can get under the car, but probably also the curve of the top of the car (wonder if Zeussy will cry reading this!)

[Killrob]

@Deus ex Machina

not really a solution, but if u limit the sale figures of sports cars it will reduce the severity of the problem…

Yes, indeed. It is not necessarily a problem at all, specifically not to game balance due to the important
point you mention here - a limited amount of potential buyers for certain kinds of cars.

[quote=“Drake”]

[quote=“Killrob”]
c)[/quote]

Is there any synergy between parts in regards to aerodynamics (negative or positive)?

I do know from the thread I had started about Engine Configurations that parts can Indirectly affect
aerodynamics. Since the game calculates the size of the engine, the height is an important factor in how
aerodynamic you can make the front end of a car. [/quote]

Ahh I see, it seems promising that things like the size of internal parts is considered as constraints on the
size of the car body!

[quote=“Daffyflyer”]
There will be some form of aero calculations, as previously stated for fuel econ calcs. [/quote]

[quote=“zeussy”]I have given aero some thoughts, I think a good initial approximation could be calculated
using the front area of the car (so smaller and lower the better) with how aggressively the gradient of the
surface of the car changes.[/quote]

[quote=“Daffyflyer”]Probably also a similar thing with the drop off at the back (wake drag)
I was thinking for added objects like mirrors, vents, wings etc. it would just be a flat “This bit adds/takes
away X amount of drag” but not really interacting with the aero properly as it’d be too complex.[/quote]

I see your thoughts are moving in a good direction. I’d like to make some points to provoke additional
though:

**1) **While the front and its gradient is very important, the back is even more so. For example: a car with a flat,
Bentley-esque front, but a perfectly aerodynamically shaped rear end, creates less drag than when it’s the
other way around. The gradient does matter too as you correctly point out, but I want to remark that “flatter”
is not necessarily “significantly better” if coupled with other parts. Let me clarify my meaning: Say you have a
very smooth gradient front, but a back of equal gradient; in that case making the front even smoother won’t
help the overall aerodynamic performance much, because the optimal shape is closer to

*backgradient = frontgradient/2 *

(I pulled that one out of my ass considering the front-/back- gradients of a falling water drop).

**2) **The “optimal” gradients depend on speed! Captain Obvious speaking… While a Hummer may be almost
perfectly aerodynamic at a speed of 5 m/s, it certainly is not at 50 m/s. Let’s see what “optimal” means in this
case: a bulky car will at any non-zero speed experience more drag than an aerodynamic car, but there is a
break-point where the formalism from my reference [2] departs from the simple speed^2 dependence:
when turbulence becomes the dominating contribution to drag. This point may be good to consider in your
maximum speed calculation, as well as in your fuel-consumption calculation at cruise speeds.

**3) **Your approach for added objects is perfectly fine, adding flat amounts of drag for different parts will be a
good enough approximation. Questions that arise then are: you mention the “amount of drag”, drag is a force
that is a function of speed; what speed are you going to calculate the drag for (also consider point 2 in this
question, makes it veeery tricky!)? My approach would be to give external parts at least three parameters:
frontal area A, aerodynamic efficiency Cd (baking in the turbulence thing?), weight m and maybe even a fourth
one: downforce, while the latter can be very tricky to estimate. I think that covers most aspects, including
but not limited to mirrors having more of an effect on a small car as compared to a big one. For not considering
the synergy between parts too much: I’m totally on your side there, this is way too complex to do.

[luncheonticket]

[quote=“Killrob”]
**1) **While the front and its gradient is very important, the back is even more so. For example: a car with a flat,
Bentley-esque front, but a perfectly aerodynamically shaped rear end, creates less drag than when it’s the
other way around. The gradient does matter too as you correctly point out, but I want to remark that “flatter”
is not necessarily “significantly better” if coupled with other parts. Let me clarify my meaning: Say you have a
very smooth gradient front, but a back of equal gradient; in that case making the front even smoother won’t
help the overall aerodynamic performance much, because the optimal shape is closer to

*backgradient = frontgradient/2 *

(I pulled that one out of my ass considering the front-/back- gradients of a falling water drop).[/quote]

I want to add a small comment to this, if I may.

While what you say is generally true, you have to take into account the Kammback/Kammtail effect. This means that you can abruplty interrupt a teardrop shape at the back (the exact point eludes me, I’ll have to take a second look at my books) with no negative drag effects. This is the way lots of past and modern hatchbacks are designed.

[Killrob]

[quote=“luncheonticket”]
I want to add a small comment to this, if I may.

While what you say is generally true, you have to take into account the Kammback/Kammtail effect. This means that you can abruptly interrupt a teardrop shape at the back (the exact point eludes me, I’ll have to take a second look at my books) with no negative drag effects. This is the way lots of past and modern hatchbacks are designed.[/quote]

That’s an important comment indeed, and a very valid one! I would like to point my German-perfectionist-bastard (and physicist ) finger at your formulation though: “no negative drag effect” cannot be correct (while you probably mean the right thing). Wikipedia probably states it correctly here:

“Wind tunnel tests showed that a true tear-drop shaped body offered only a slight improvement in efficiency…”

It would be awesome if you could find something about this in your books! From my feeling I would assume that the possible point of cut-off entirely depends on the maximum speed of the car. The faster it is, the more teardrop you need… but that’s just a “feeling” and not based on hard facts. The cut-off itself always remains a compromise though.

[Deus_ex_Machina]

en.wikipedia.org/wiki/Kammback

eblog.mercedes-benz-passion.com/ … rturkheim/ the picture of the SLR u see what happens.

[luncheonticket]

[quote=“Killrob”]

[quote=“luncheonticket”]
I want to add a small comment to this, if I may.

While what you say is generally true, you have to take into account the Kammback/Kammtail effect. This means that you can abruptly interrupt a teardrop shape at the back (the exact point eludes me, I’ll have to take a second look at my books) with no negative drag effects. This is the way lots of past and modern hatchbacks are designed.[/quote]

That’s an important comment indeed, and a very valid one! I would like to point my German-perfectionist-bastard (and physicist ) finger at your formulation though: “no negative drag effect” cannot be correct (while you probably mean the right thing). Wikipedia probably states it correctly here:

“Wind tunnel tests showed that a true tear-drop shaped body offered only a slight improvement in efficiency…”

It would be awesome if you could find something about this in your books! From my feeling I would assume that the possible point of cut-off entirely depends on the maximum speed of the car. The faster it is, the more teardrop you need… but that’s just a “feeling” and not based on hard facts. The cut-off itself always remains a compromise though.[/quote]

What Mr. Kamm exactly said was that ‘drag begins to increase after the rear of a car’s cross-sectional area is reduced to 50 percent of the car’s maximum cross section (maximum cross section = frontal area)’. This means that boundary layer separation and therefore turbulent flow starts to appear on a tapered tail after said point, increasing drag. These appears more forward on the car profile the higher the ‘angle of attack’ of the wing-like profile is (due to the 50% area rule), so to have laminar flow almost back-to-back you’ll have to design a vehicle that is unreasonably long:

(the example is an airplane wing, but you get the idea). For this very same reason is why planes stall when on high angles of attack.

So, since turbulent flow at the back is mostly unavoidable, a convenient solution is a Kammback/Kammtail. This allows to design a car of reasonable length and packaging characteristics while at the same time having low-ish drag.

The boundary layer characteristics also depend on the Reynolds number so yes, maximum speed would also be a factor on choosing the cut-off point. However, IIRC 50% was a pretty good ballpark figure since (again, IIRC) the Reynolds number doesn’t change much at the speeds a production vehicle achieves (the Reynolds coefficient is VERY high in real-size cars, so its order of magnitude stays within 10^6 at speeds between 50 and 300km/h) so separation of the boundary layer would happen at approximately the same point regardless of speed.

Then again, I’m pulling this out of memory (not to say out of my arse ) so I’ll need to check my books and uni notes to be 100% sure. I’ll go to fetch my books from my parents’ place this weekend so I can be more accurate.

@Deus ex Machina

the picture of the SLR u see what happens.

Well that picture pretty much sums up what happens. It’s too bad that’s not a Kammtail:

Here, a brick with a Cd of 0.25 (Audi A2). Of course the Kammtail is not what causes such low drag, but it doesn’t harm at all does it?

[machalel]

All good information, but make sure you don’t lose sight of the other factors that make a big impact: Lift/Downforce

Sometimes if you attempt to get the best aero efficiency, you will introduce unwanted lift. It can be better to ‘cut’ off the rear, and sacrifice some drag to get some downforce. A famous example of this is the Porsche 917 Long-tail vs Short-tail Le Mans Car (en.wikipedia.org/wiki/Porsche_917). The long-tail version had better drag characteristics and a higher-top speed, but also had severe handling problems at high speed, whereas the short-tail version was more ‘cut off’ at the rear, which gave it worse drag characteristics, but much better downforce.

Anyway, here’s a few more pics

[Killrob]

Very good point machalel, there are some horrible examples of lack of downforce at higher speeds. Maybe one should talk more about aerodynamic efficiency than pure drag but still, it’s the drag that determines the maximum speed… if you crash or not is a different question Maybe the aero-calculations would give you two modifiers: total drag and effect on handling.

Good pics btw! But none of them really shows the critical volumes… it always looks nicer in promotion shots to show the nice curved lines and not the turbulence. Just saying: those pics are not implying that there is no turbulent wake (well d’uh, I’m Captain Obvious today).

Edit: On a different note… did you guys ever considered that most of today’s compact cars (like Ford Ka) are more aerodynamic in reverse gear than in normal driving? xD

/Robert

[Deus_ex_Machina]

ummm, is there someones hand and arm visible @ the rear wing of the porsche?!?

[machalel]

hahahaha, it does look like an arm! but I don’t think so.

[luncheonticket]

Almost all production vehicles have some degree of aerodynamic lift at high speeds, except for maybe some of the fastest and most expensive exotics. The manufacturers usually tend to err on the side of low drag instead of low lift when choosing a compromise since it’s more advantageous (high lift is only bad for high-speed handling while high drag is bad for top speed, fuel efficiency and emissions).

However, they are making great advances nowadays, achieving low drag figures while keeping lift to a bare minimum (or as I said, even managing to create some downforce).

@Killrob True, but that is true for most cars. However, lift is higher!

[aknot]

I happen to know a little about aerodynamics and feel I might help a little out, hoping you guys can use these formulas…
First of all: I’m going to leave out friction of airflow along the side of the car, since it only matters for long things like trains, not for cars. I won’t be looking at turbulences, since barely possible to calculate. This can be assumed, as long as the rear of the car has a perfect edge and the scurface of the car is perfectly even. I’d guess we get around 10%-20% less than what we should.

Edit: First I had it totally wrong, everything was crap, so now I hope I finally have it right…

Lets get started:

At the front of the car air particles/molecules collide with the car’s body. They then fly on in a different angle, roughly in the direction of the next convex edge. The change in momentum of those air particles are equal to the change in momentum of the car, which equals drag force and downforce/lift combined.

I will need the hight difference to the next convex edge, and I call it h. I will also need the lengthy distance from nosetip to said edge and call it x.

For dF i got:

dF = * h * rho * dA * ds/dt * v / ( cos(alpha)x + sin(alpha)h) = rhodAv^2 * h/(cos(alpha)*x+sin(alpha)*h)

horizontal component
dF_h=sin(alpha)*dF
and vertical: dF_v=cos(alpha)*dF

Where alpha is the angle of the outline of the car (so the angle counts, not so much its gradient!! Though that causes turbulences, as do concave edges…)

dF_h can be calculated for all heights and widths and added up to total drag.
dF_v will add up to total downforce/lift

But we are only half way through, since we need to have a look at the rear too.
Here we get a drag force because of an area of underpressure behind the car.
I took a few more minutes to work out the underpressure from the euler-equations. Since that was somewhat more complicated than the above I leave the mathematical details out and present my solution:

delta_p = p_0 * (rho * (v * sin(alpha) )^2) / (2*p_0 + rho * (v * sin(alpha) )^2)

where p_0 is enviromental pressure (100kPa), rho the density of air (1.29 kg/m^3) and v the velocity.

The actual drag force is the area of the plane we are looking at times the underpressure…
F=A*delta_p and has the direction of the normal onto said plane, therefore:
drag = -sin(alpha)*F
lift = cos(alpha)*F

I think I got it right; I usually do…

To implement this I’d simply divide the front area into lets say at least 1000 little squares, calculate front and rear drag influencies and add all of them up (as if you’d calculate with 1000 molecules)…
If you have any questions or need further explanations ask me, if I don’t answer fast enough you can bug me by writing to aknot@mailfish.de
Greets

[aknot]

sorry folks, have to add something:

If you have a rear part like the Nissan or the Mercedes (coupés and notchbacks) and your speed is not too high then the air beeing sucked down along the rear window (generating lift through underpressure) hits that rear end and generates downforce again. The faster you are, the lower the air pressure behind the rear window, the fewer air flows onto the trunk and the rear spoiler, and guess what, the less downforce and the more lift you have.

[Killrob]

Hey aknot, this is really good stuff I mean I’m a PhD in physics, but don’t know nearly as much about this so I just want to say well done, it makes sense! You’ve been studying some fluid dynamics I take? I guess I’ll have to kidnap you if I run into problems with the aerodynamics calculations in my own game. What I find especially interesting is your lift/downforce considerations. So that’s why the Audi TT had such big problems keeping its ass on the road when going 200+ km/h haha.

One area where “sides” or “flat” areas matter is the underworks, although they are poorly developed for most “normal” cars, but they definitely contribute to the drag through friction and causing turbulence.

Another question: turbulence… would you say that when it kicks in it behaves more like v^(2+x) where x is a positive number, or still just as v^2? For now I’ve settled for something around v^3 which seems to give reasonable results… but I’m a nub, so no telling if it actually makes sense, chaos is hard to calculate xD