Calculating dowforce of a wing

[no1schuifan]

Hey, sorry if this is posted in the wrong place. Can anyone give me some guidance on how to calculate the theoretical downforce of an upwards curved spolier. Any help will be much appreciated :)

 

[no1schuifan]

The context to this question is i wanted to work out the theoretical downforce produced by a diffuser on a car. So can anyone help me in working out the pressure difference underneath a car with and without a diffuser. For additional info, I've set the diffuser at 0.15 rad and 4.3cm(w) 0.7cm(h) 5.7cm (l). This is for a model car hence the use of cm.
So first of all how could i work out the change in dynamic pressure underneath the car due to the volume change of the diffuser? is this possible? Any help as said before will be greatly appreciated. Thanks in advance.

 

[rcgldr]

My guess is that this is one of those real world cases where the aerodynamics are too complicated to mathematically model well. Even with the high end software available to aircraft designers, considerable time is spent with models, wind tunnels, and prototype testing.

If you could video tape the car along a fixed path where you could calibrate the change in height of the model due to downforce on the suspension, then you could compare this to the amount of force required to produce the same amount of suspension compression in a static (non-moving) situation.

 

[no1schuifan]

Ok i guessed so much :(. Thanks for your help though. The reason I'm doing this is for a school project, I've built the wind tunnel and model so i have the dowforce produced but i thought if i could validate the results through a bit of theory it'd improve my project.

 

[Nick89]

If you built a wind tunnel then you might be able to see (use smoke) at what angle the air is deflected by the wing. You can then use fluid dynamics (conservation of momentum) to calculate (very roughly) how large the down force is. It probably won't compare very well, but at least you've got a simple theoretical model.

 

[xxChrisxx]

To get a real idea of acutal downforce you'd need a full CFD model (which I realize is out of the question). But as Nick said you can use conservation and Bernoullis eq to calcualte the pressure under the floor and above the car. You can then assume the car is a flat plate (ish) to get an area.

Diffusers are tricky business because it's not as clear cut as an aerofoil. It is also fairly unlikely that your diffuser will generate any downforce at all unless you run a very low ground clearance. Its also acutally not the diffuser that creates the downforce its the area under the car in front of the diffuser that does the job.

There is no way you'd be able to practically measure the downforce from a moving car and get useful results. However as you've built a wind tunnel, all you need is the air moving over the car at the speed the car would be going :P.

What sort of model is it you are making, and how low are you running it etc?

EDIT: Just reread your name OP. You are a fan of Dick Dastardly, oh dear.

 

[no1schuifan]

Dick Dastardly...you mean the greatest driver ever :P

I've studied Bernoullis equation quiote intensively but how could i use the conservation of momentum in my calculations?

My setup at the moment is a nitro engine turning a fan of pitch 2.5cm. The tunnel tself is 1m long and the wind speed at approx. 12ms-1. My model is 1/18 size and the ground clearence s about 2.5mm. I've measured the downforce produced by a simple diffuser at 0.15rad at 12m/s and the DF produced was about 0.05g so yeh very small.

 

[rcgldr]

I don't know how Bernoulli would apply, since it can be considered a over-simplified, no work peformed, form of

http://en.wikipedia.org/wiki/Navier-Stokes_equations

Then the problem becomes determining the actual equations, and then doing some form of numerical integrations since generally they can't be solved directly. From what I understand it's not usually possible to determine the actual equations for a real world model, so again some simplification is required.

The other issue you're dealing with is low air speeds. You'd need a relatively large wing to generate significant downforce at low air speeds.

 

[xxChrisxx]

Oops I didnt read what he put properly, I just meant that the mass flow is conserved.

 

[xxChrisxx]

Jeff just how is he going to solve the navier stokes eq... (EDIT: as you say it requires numerical methods to compute). Bernoulli's is perfectly valid for this type of thing as it doesn't require hyper accurate answers, its a simple way of determining the pressure acting under the car with a nice simple eq. Hes working with low speed incompressible flows so... : /

On saying that I've forgotten the most important question, of what level are you working at schuifan? What is the aim of the project?

 

[rcgldr]

Bernoulli's is perfectly valid for this type of thing as it doesn't require hyper accurate answers, its a simple way of determining the pressure acting under the car with a nice simple eq.

Bernoulli prinicple explains a relationship between static pressure and speed in a work-free environment. I don't understand how Bernoulli principle is used to calculate lift, drag, and turbulence caused by a solid moving through the air and in this case with ground effects. For example, there are stagnation zones fore and aft of an object that move at the same speed of the object, yet their pressures are different. How is this handled with Bernoulli prinicple? A program like xfoil is useful for wings, but this model car with a diffuser is more complicated. I don't see a simple solution.

Measuring the amount of downforce via suspension compression seems straight forward. The treadmill might be able to help measure the drag. Attempting to measure or calculate speeds and/or pressures seems very complex.

 

[xxChrisxx]

What do you mean by work free environment? How is the flow being worked?

The idea isn't to use bernouillies to model the pressure distribution over the length of a moving car (as that's not really possible) and there is simply no way he can get the detail he needs to compare or validate the distribution with a home hade wind tunnel.

He wanted a simple and easy way to find a ball park figure for downforce for comparison. Now admittedly this does require some assumptions that strech reality. Basically treating the car as a rectangle or flat plate with zero angle of attack and using the pressure differential either side and treating the car as static. This won't give you a distribution but the OP only mentioned he wanted a figure.

 

[rcgldr]

What do you mean by work free environment?

Bernoulli principle is based on the assumption that conversion between pressure and kinetic energy takes place without any work being done, so that the total mechanical energy of the affected air remains constant.

How is the flow being worked?

In the real world, whenever a solid moves thorugh a fluid or gas, work is done. After the solid passes through a volume of air and after the affected air's pressure returns to ambient, it will have non-zero velocity, reflecting the work done by the solid.

But at the exit, the velocity is greater than free stream because the propeller does work on the airflow. We can apply Bernoulli's equation to the air in front of the propeller and to the air behind the propeller. But we cannot apply Bernoulli's equation across the propeller disk because the work performed by the engine (by the propeller) violates an assumption used to derive the equation.

http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

There are differences between a prop and wing, but how is the basic principle here any different for a prop, rotor, or wing, other than the amount of work done on the air?

One main difference is the amount of induced wash is much greater for a prop or hovering helicopter because the induced wash is in the direction of travel with respect to the air flow. A helicopter in forward motion experiences less induced wash, but a forward moving
helicopter and a wing experience some induced wash as air is accelerated downwards and backwards from above and in front of the rotor or wing.

The other main difference is the magnitude of the pressure differential for a prop or rotor is typically higher than a wing (except for a high load situations, such as an F16 pulling a 9 g turn).

He wanted a simple and easy way to find a ball park figure for downforce for comparison. Now admittedly this does require some assumptions that strech reality. Basically treating the car as a rectangle or flat plate with zero angle of attack and using the pressure differential either side and treating the car as static. This won't give you a distribution but the OP only mentioned he wanted a figure.

I still don't understand how you're proposing to calculate pressure differential and/or speeds based on a zero AOA flat body or flat pate experiencing ground effects with a diffuser.

Instrumenting the model car in the wind tunnel with some wires attached to strain gauges would probably get reasonable results.

 

[xxChrisxx]

I think you either you or I am majorly failing to appreciate the circumstances of the OP.

When he says school project I get the impression that this is super low budget high school job. This is also a homemade windtunnel, which I doubt is going to be built to the point where it gives a reliable and steady flow (much less calibrated) he's going to need a strain gauges, pitot probes etc which I also doubt he has acess to at a high school level. This is akin to me saying to him 'just do a full 3D CFD model' when he has acess to neither software nor budget.

Now I could be wrong which is why I asked what level he was working at. If this is a Uni level project then all of these problems go away as the level of equipment and control available to him is higher. However if this is a uni level project, it does beg the question that why on Earth does the OP just not bang a simple CFD model in.As to the other points above I'm moving house so all my books are packed, once things settle down i'll crack them out and be answer your main points Jeff. (Well that and it'll give me time to research whether I'm talking tosh or not).

 

[rcgldr]

For wires and strain gauges, fishing line and a very light type of fishing or hanging mail scale could be used to measure drag. Noting how far the suspension compresses would help estimate downforce.

 

[xxChrisxx]

Thats more like it, nice low tech solutions. :D

It also depends on how the model is built, if there is no suspension couldn't you just plonk it on some scales?

OP: is it a fully scaled car with working suspension etc? (so many questions!)

 

[no1schuifan]

Sorry i haven't replied for a while, I've been in Germany on a physics trip. In answer to your questions, I'm 17 and the project is being carried out at high school. The model does not have suspension either, it has a curved upper surface to produce downforce and then a flat floor onto which i change the diffuser at the rearand is attached to a set of scales to measure the downforce. I just feel i need some theory/mathematical analysis to validate my result. BTW I'm greatly apprecating all your help. Thank you

 

[no1schuifan]

This is really basic but say a theoretical downforce of 2.7N is produced, what would be the reading on the scales of this was the case? Would it be 270g?

 

[xxChrisxx]

To be honest you've got to put in the report that there is no really meaningful calcualtion that you can actually do. Aero is a black art becuase it's semi empirical in nature.

I'm still reading up on what you can possibly do, my inital thinking was to treat it as two separate flows (above and below the car). Giving two separate pressures acing on an area. Similar to the force experienced by a roof with a wind blowing over it and a steady pressure in side.

Treating the diffuser and underfloor as a ventrui tunnel, and using bernoullis and continuity to calcualte a pressure drop. On reading more however this by itsself wouldn't be useful as it doesn't acutally tell you the underfloor pressure. I'm starting to think there is no way of calcualting it without at least some empirical data.

I'm sorry I couldn't be more help, I've kind of exhausted my knowledge of fluid mechanics and any answer you'd get from my method is likely to be meaning less anyway.

 

[no1schuifan]

No worries, thank you for all your advice though. I just have a couple mch more simpler questions. Firstly, in the bernoull equation: Static pressure + dynamic pressure = constant . What exactly is the static pressure- is it atmospheric pressure? Also, how does this shows that velocity is proportional to pressure?

 

[xxChrisxx]

Static pressure is just what it says on the tin, the pressure when the fluid isn't moving. In open atmosphere static pressure is atmospheric, however this isn't always the case. Such as in the diffuser, the pressure recovery of the diverging nozzle accelerates the air under the car. The static pressure of this will be below atmospheric.

So static pressure is usually measured, by a bourdon tube or something similar.

Dynamic pressure is the pressure due to the velocity, it is measured by a pitot tube. The total pressure is a combination of the two.

All Bernoullis states is that as flow accelerates (it its dynamic pressure rises) its static pressure must drop to maintain the conservation of energy.

 

[no1schuifan]

Ok thanks. How could i represent an increase in mass of the car as a force. For example, is the mass increased with a certain angle diffuser by 0.1g how could i deduce the down force from this as the units aren't the same as N?

 

[rcgldr]

Firstly, in the bernoull equation: Static pressure + dynamic pressure = constant.

This only occurs in the ideal (imanginary) case where an exchange between pressure and speed² occurs without performing any net work on the fluid or gas. In a real world situation, the pressure and or speed isn't going to change unless there's some mechanical interaction causing the change (such as a solid moving through the air), so the total pressure is changed, and how this is distributed between static and dynamic pressure depends on the mechanical interaction.

Take the case of a propeller, and consider the shape swept by the path of the propeller to be a disk. For the flow across the disk, the speed stays about the same, but the pressure jumps from below ambient to above ambient, and the air then continues to accelerate aft of the propeller. The concept is convered in this NASA link:

But at the exit, the velocity is greater than free stream because the propeller does work on the airflow. We can apply Bernoulli'sequation to the air in front of the propeller and to the air behind the propeller. But we cannot apply Bernoulli's equation across the propeller disk because the work performed by the engine (by the propeller) violates an assumption used to derive the equation. :

http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

What exactly is the static pressure?

The static pressure is the pressure of the air as sensed by an observer moving at the same speed as that air. The total pressure is the pressure sensed after slowing down the air to the same speed as the observer. The dynamic pressure is the total pressure - static pressure.

In the case of the propeller, the static pressure is lowest just fore of the propeller disk and highest just aft of the propeller disk. The dynamic pressure is relative to speed², and is highest well aft of the propeller, at the "exit velocity" as described in that NASA link above.

More about car aerodynamics and diffusers at this link. Note that the diffuser result in vortices, which make it difficult to use Bernoulli to approximate the lift and drag factors. Generally wind tunnels are used, because the math and the ability to predict turbulent flow is very difficult.

http://mhest.com/spotlight/automobiles/articles/Race-CarAerodynamics.pdf

It is possible to sense the static pressure of moving air with a static port. The port is a flush mounted tube where the tube opening ''hides" under a thin boundary layer of air that doesn't move with the moving air just outside the thin boundary layer. Because of viscosity, the air transitions from moving at the same speed as the static port to the speed of the air beyond the boundary layer, but the pressure sensed at the port opening will be very close to the case where the static port was moving with the outside air. The tube is connected to a chamber with a diaphram used to calculate altitude in an aircraft. It also provides a static pressure reference for the pitot tube which is pointed into the direction of the air, and senses the total pressure, and the difference total pressure - static pressure = dynamic pressure, which is related to speed ², and this is used to indicate the air speed on an aircraft (not a true speed, but more of mass flow speed, since it's sensitive to the density of the air at various altitudes). Sometimes the pitot and static port are combined into a single device.

http://www.grc.nasa.gov/WWW/K-12/airplane/pitot.html

http://en.wikipedia.org/wiki/Pitot_tube

http://en.wikipedia.org/wiki/Pitot-static_system

http://www.luizmonteiro.com/Learning_Pitot_Sim.aspx

 

[no1schuifan]

Thank you very much that was extremely helpful. think I'm going to give up on the theoretical validation for now :(. Just one final question: How do i convert the mass reading to down 'force' ?

 

[xxChrisxx]

What do you mean by mass to downforce?

If you mean you've put it in some scales, or something that gives a reading in kg. The force is m*g.

It may be a good idea to support the front of the car and then use the scales for the rear, and vice versa to get an idea of downforce distribution. Edit, this will require some fiddly balancing act to get the inital distibution correct.

 

[AIR&SPACE]

Well, it depends.

If you have a symmetric foil, that satisfies Thin Airfoil Theory then

Lift per unit span = density_air * (Velocity_freestream^2) * Angle_of_attack*chord*pi
and the coefficient of lift is
C_L = 2*pi *Angle_of_Attack

whereas if you have a cambered airfoil, that satisfies T.A.T, AND you happen to know the equation of it's camber-line, (in the form dz/dx) THEN

$$C_{L}$$ = (2*pi)*[ a.o.a + $$\frac{1}{pi}$$$$\int$$ $$\frac{dz}{dx}$$ (cos$$\theta_{0}$$-1)d$$\theta_{0}$$ ]

and that integral is "from 0 to pi"

Then, of course, L= (1/2)*density*Velocity^2*Area*C_Lift

You may be able to find airfoil data for NACA foils that has it in the form z/c so then you need to find dz/dx from that.

So, yes. You CAN do it. So now it is up to you to do it.

and I should point out that x is the distance on the chord, z is "altitude", and y is going into the wing.


source: Fundamentals of Aerodynamics, 4th ed. John D. Anderson

 

[xxChrisxx]

Air&Space, he's looking at the effect the diffuser will have, not just the wing profile.

 

[AIR&SPACE]

Air&Space, he's looking at the effect the diffuser will have, not just the wing profile.

I'm just giving him "guidance on how to calculate the theoretical downforce of an upwards curved spolier."

The diffuser part has been pretty much hashed out, but no one has given him the means to CALCULATE the downforce (lift) of the upwards curved spoiler. As long as the spoiler is such that it meets the Kutta-Jukowski Condition and it meets the requirements of T.A.T then this is an appropriate answer.

I would say he's also looking for the effect the spoiler would have, not just the diffuser.

 

[rcgldr]

In the case of wings for Formula 1 cars, the designers are willing to sacrifice a high amount of drag for more downforce. At around 160mph (depending on setup), overall downforce is around 2.5 g, while drag is about 1g. The "wing" is usually multiple sections, with the last section angled upwards at 40 degrees or so. The standard math used for airfoils don't work well with multi-section wings or the diffusers that rely on turbulent effects.