Calculating the force by the undertray

[mep]

I couldn't find anywhere a way how to calculate the force which is generated by the floor of the car, so I tried to do it by myself and now I whant to know if I am on the right way.


I found one formula for horizontal streaming:

p + 1/2*rho*v² = konstant

rho is density of air =1,22Kg/m³
konstand is air pressure when the car does not move
konst.=1bar =100 000N/m²

I put this to
p =konst. - 1/2 *rho *v²
and for kons.=1 bar
so I get
p=100 000N/m² -1/2*rho*v²

Now when the car moves we have a lower pressure on top of the car and a more lower pressure under the car. The difference should be the pressure which presses the car to the ground.
So I calculated the pressure over the car at 16,66m/s (60km/h) and under the car, where the speed is higher because of the venturi like shape of the floor.

top of car
po=100 000N/m² - 0,5*1,22Kg/m²*16,66²m/s²
po=100 000N/m² - 169,3N/m²
po=99830,7N/m² =0,9983bar

under the car
here is the speed higher because of the reduced area
you can calculate the speed by V1/V2=A2/A1
I took the factor 1:2 so we have a speed of 33,32m/s

pu=100 000N/m² - 0,5*1,22kg/m²*33,32m/s²
pu=100 000N/m² - 677,23N/m²
pu=99322,7N/m²

The difference is now
dp=507,9N/m² = 0,005079bar

Lets say we have in average this pressure difference over the floor and
a floor surface of maybe A= 1,5m². So we can calculate the downforce by:

F=dp*A
F=507,9N/m²*1,5m²= 761,85N =76kg downforce

Sounds good, but there is one think I started to wonder about.
If the car drives faster is the speed over the car faster and so the pressure reduced. The speed of the air under the car gets also faster but in the same relation even after taking it into square. So the downforce doesn't depend on the speed of the car. So something I didn't got right.
But I didn't tried it with figures maybe i should.

edit: I am quite shure it is right.

Is is right that the pressure over the car in motion is lower than on a standing car?

[jddh1]

The pressure over a car in motion from air is higher because the speed of the air over it is higher (Re number increases and so on). Case in point: Look at the McLaren front wing. The top wing goes down under pressure in high speeds and then it lifts up as the car slows down. It's quite clear in TV images actually.

[mep]

The top wing goes down under pressure in high speeds and then it lifts up as the car slows down

Of course goes the wing down. It wouldn't work propable if not.

Now I tried it with higher speed figures and I got a higher result.
So the downforce does depend on the speed. Now I'm quite sure that the way of the basic calculation is right.

I used the law of Bernoulli for horizontal streaming for this.
It says that the higher the speed, the lower the pressure.
So the pressure over the car should also be less than static pressure.

[miqi23]

Mep, get your self a good Aerodynamics book suited for starters. They tend to explain things quite easily and perhaps a good internet search can be fruitful as well. There are loads of things out there on the internet, sadly I do not remember any at the moment, however I will post a few if I remember in the future!

Anyway, Bernoulli is good for explaining certain aspects of aerodynamics but fails to explain Aerostatic changes which is caused due to the loss of Dynamic Pressure. A wing can be explained with regards to bernoulli, but how would you explain the increase in front down-force of a car when a Splitter is used?

[mep]

Can you please get a bit more detailed.

[Ogami musashi]

if you want a very good site that goes into details about aerodynamics

http://www.desktopaero.com/appliedaero/ ... eface.html

This a demo version of a cd textbook but in fact you have all contents, just some interactive features are missing.

This is most accurate is know but it requires quite a good level as the primary goal of this textbook is to explain and show the full model of Navier stokes.

It explains bernouilli, corrections for compressibility and surface pressure gradients.

Aside from bernouilli you'll discover that pressure decrease with curvature because conservation of energy requires that the particules stay on track, thus to stay on track with the curvature the pressure at the surface needs to decrease (this is the explanation, erm, one of the, of the front splitter downforce) so that the above pressure pushes it onto the surface.
If the curvature is too much (=if the gradient is too high) there's loss of energy (transformation in drag).

This site will provide you all the equations you need, just that it will really require to have a good maths level and aerodynamic background.

Hope this helps.

[Carlos]

viewtopic.php?p=57931&highlight=&sid=f456e0b907826ce3b045b456a450cfaa#57931

mep - This is our Books,softeware,links thread with a lot of CFD content.

May I ask anyone that can to post it as a "sticky" and maybe move/pin it to Off Topic Chat. Thanks in advance.

EDITED

[syguy]

Mep, your calculation and reasoning in applying Bernoulli's theory over a car are correct. The static pressure over the top of a moving car is lower than the ambient static pressure. The downforce on a racing car comes from the static pressure difference between the upper car surface and the lower car surface. As long as the lower car surface can induce a higher air velocity under the car (therefore a lower static pressure than the upper surface) the resulting force due to static air pressure will be downwards, hence the use of diffusers.

Mep, also as you said, with increasing air velocity the force you calculated will increase. Your calculation is equivalent to a lift coefficient:

Lift = 1/2 * rho * V² * Area * CL

Where CL (Lift Coefficient) = R² - 1 and R is the area ratio you mentioned and took to be 2.
Of course my use of lift coefficient is this case is really a downforce coefficient.

Now Bernoulli's theory is only a starting point for such calculations. I believe Colin Chapman discovered ground effects performing a similar analysis, so you are in good company. However, to better estimate reality requires acknowledging viscosity effects. Say hello to wind tunnels and CFD…

[mep]

Thanks a lot syguy.
Your post gave me a lot of courage back.
Maybe you are the first one who really read what I have written.