Thanks, hardingfv32, strad.
I couldn't find anything about the effective force on the wheel in that paper. Of course, I'm into the aerodynamic pithecanthropus group in this forum, always erectus.
Anway, I found this graph in the paper. So, I thought, hey, lets give it a try.
This graph is definitely funny. The huge area of great speed on top of the wheel, well, doesn't exist. There is a huge buildup of air in front! In top front, if you get my drift, aerodynamically speaking.
I haven't realized
that, after 40 years of thinking about racing.
The top front of the wheel goes against the wind! Like Bob Dylan!
So, I took the picture in that paper that showed air speed around the wheel. Like all pictures made by aerodynamicists, it uses a colour palette designed by old hippies.
Psychodelic wheel showing airspeed. Red is 20 m/s, yellow is 15 m/s, green is 10 m/s, cyan is 5 and blue is zero. Lucy in the sky with diamonds...
I copied and pasted it into AutoCad (yeah, I know. I still have my slide rule, so what?) and made arcs around the wheel, in blue, cyan, green, yellow and red, according to the colour of the air on the edge of the wheel. I apologize profusely to those who are trying to read this post in the middle of a hangover. Don't. You could make a T-shirt with this picture and many people would ask you if you like mandalas.
There are arcs here, even if you don't see them
Then I deleted the picture and scaled the image to 66 cm in diameter. This is what I ended with:
I'm just sitting here watching the wheels go round and round. This is the air speed around the wheel. Red is fast, blue is slow (stagnant)
So, I calculated the pressure on each arc. Easy. The drop from atmospheric pressure is equal to the density of air times the difference of the square of velocities halved. This is what I got after typing that simple formula and looking up in AutoCAD the length of each arc.
Assumptions I made (boring! boring! skip this part! go to the next image!): at 0 m/s of air speed, pressure is 101 kPa. The drop in pressure is (where rho is air density, v2 and v1 are speeds in meters per second):
Delta P = rho/2 * (v2^2-v1^2)
For example, for 20 meters per second, I get a pressure of
P = 101000 Pa - 1.2 kg/m3/2 * ((20 m/s)^2 - (0 m/s)^2) = 100520 Pa
The force of air is simply the length of each arc multiplied by the width of the tyre, to get the area in square meters and then multiplied by the air pressure.
Force on each arc. Wheels are 0.335 m wide, that is, Formula One front tyres
So, it was very simple to draw a line from the middle of each arc to the center of the wheel with a length proportional to force. Like this.
Now magenta enters the picture (yuck!). Each line pointing to the center is proportional to the force in the segment of the wheel
Then, I added all the forces as vectors, that is, I moved each line to the end of the previous one. End result of forces is this:
Downforce! It's alive, Igor, it's aliiiiive!
The white arrow in the previous image shows a downforce of... lemme see... more or less... what? 8.3 kilonewtons? That's like 800 kilos on each tyre? Oh...my... I discovered the new ground effect!
Unga, unga! (that's pithecanthropian for "eureka!").
Why? After doing all this it dawned upon me that I considered that there is no air pressure UNDER the wheel. At all.
If I have made the same analysis with a static wheel, not moving at all I would also have gotten a downforce!
However, the more I thought about it, the more it seemed plausible. The patch is effectively sealed from atmospheric pressure, that's undeniable, at least to me and at least for the moment.
The net force of the air "on top" of the wheel must be compensated by an increment in pressure from the asphalt on the patch, sure, the wheel is not going to sink into the ground, but this patch force is not caused by air! So, my conclusion is that the air is always exerting downforce on any wheel of any car, even when parked.
If this is not true for some reason, then at least is a good quiz for Aerodynamics 101...
"Explain why air doesn't exert downforce on a parked car".
This conclusion must be so wrong in so many ways that I decided to include a blue segment under the wheel.
I made it horizontal, as the patch, and measured its length. Then I added one more line to the graph. This is the "alternative ending", assuming that somehow the air "filters" under the tyre and actually exerts pressure (which at the moment I doubt
).
Either the car sinks or the car floats! There is no middle ground in this post! Colombia is passion! More exclamation signs!!!!
The problem (huge problem!) I have is the magnitude of the force. It's 6.3 kilonewtons. That's like 600 kilos! I refuse to believe the air pressure caused by air speed equals 2.5 Tons for the four wheels.
I apologize in advance for the many hands that must be palming the many foreheads of as many aerodynamicists in the forum.
Anyway, guys, please, explain to me all the wrong assumptions I made in the Pithecanthropian language instead of explaining them in English, will ya?
Raise one finger for "you're wrong", two for "your so wrong" and three for "I cannot believe how wrong you are".
