So I've been thinking a lot about servo torque and how to accurately gague how much is necessary given a worst case scenario (i.e. full deflection, full throttle). I know there are servo torque calculators out there, but if I calculated it myself I know it would be done right and to my specs. The following is for a given 3D type airplane. Large control surfaces, relatively slow speed, huge throw! And, since I'm an aspiring engineer, I find this "fun." I think I might be the only one who does, but I press forward nonetheless. Here's what I was thinking:

-Create a parametrization for, say, and elevator half deflected at 60 degrees. This is pretty simple, it's just a portion of a plane with the proper dimensions angled at 60 degrees and above the xy plane.

-Then, use a vector field (some call them force fields, flow fields) of (50,0,0). This assumes that the wind is traveling (relative to the plane) at a speed of 50 miles per hour horizontally and more importantly perpendicular to the z axis.

-Then just do a flux integral with these. This will give me the amount of air hitting th surface when going full throttle at 50 miles per hour at a 60 degree deflection.

My question is, how heavy is air? If we were doing this in water, I could multiply by the density of water per cubic foot or whatever and get how much mass is crossing hitting the surface each given second. But what about air? What do I use for air?

Thanks guys! This will be great once I get this figured out. Definitive servo torque needs!

Reid

Air (dry) at 1 atm of pressure, 60F is 1.225 kg/m3 (g/L)

Air (dry) at STP is 1.2929 kg/m3 (g/L)

Tim

rplumbo,

What you need to do is a surface integral of pressure. You won't quite get that the way you describe it. I see two ways to get started on this problem. One is to find some measured coefficient of pressure data for a deflected control surface, and use the flight speed and area to approximate the force. The other is to make a bounding assumption, like the drag on a flat plate perpendicular to the oncoming flow. The data needed for the second approach can be easily looked up. For the first, I am not sure.

banktoturn

Remember that a flux integral is a surface integral just evaluated over some vector field. But, is it not valid to say that the pressure applied on the surface is equal to this integral (where airspeed equals 50 mph) multiplied by the weight of the air hitting the surface per second? The surface integral gives me the amount, the density of air that TimR has provided would give the weight right? Thanks for the input so far guys! Keep it coming!

Glad you discovered RCU Tim!


Reid

Before you dive into the calculus, be sure to get the basic physics correct. You have to account for the change in momentum of the air flow. You need to know the flow in, and the flow out (direction and speed of both). With that info you can perform your momentum balance (or force balance if you prefer to look at it that way.)

The flow out is the tricky part - to get a useful answer you'd have to simulate the fluid flow. (This is where you open the proverbial can or worms.) If you did that, then you'd also have pressure distribution data and you could easily compute the net force (as banktoturn noted).

Have you considered existing airfoil simulation software? There is some free stuff floating around. For example, xfoil.

If you can describe the surface (tail surface plus deflected surface) and if you can get the software will spit out a pressure distribution, then you're home free.

If you get that far, please add boost tabs and tell me if they really have any meaningful effect .

Reid,

Unfortunately, it is not as simple as integrating the mass flow rate projected on the surface ( that is how I understand your description ). While this seems intuitively valid, it won't give the correct pressure, and determining the actual pressure is more complicated. One could build on your approach, and end up with a full fledged computational fluid dynamics program, which would be fairly expensive to run. Since this is a lot of effort, it is probably more feasible to start with some experimental ( or previously computed ) data. I think I would be inclined to use the flat plate approximation, since most of the data I've seem for deflected control surfaces is for surfaces that are 1) smaller than typical 3D control surfaces and 2) not deflected as much as typical 3D control surfaces. If you represent the deflected control surface as a flat plate with the same area as the frontal area of the deflected surface, I would think that you would get a loading which is higher than the actual loading. Then the geometry of the hinges and control linkage would let you determine the mechanical advantage, and hence, the required servo torque, with some safety margin.

banktoturn

Just how important are the fluidic properties of air at 50 mph on a highly deflected 3D type control surface?

Relatively (in air) slow speed, high deflection angle, large surface... it would seem that his computation might not be completely accurate, but close enough for gov't work. Or, are the factors not taken into account significant for what he wants to model?

Tim

It is not a matter of the fluid properties, its more basic than that.

You can't just consider the fluid "hitting" the surface, you also have to consider the fluid moving away from the surface. The difference represents a change in momentum that you are interested in. i.e. mass flow in at a particular speed and direction versus mass flow out at a different speed and direction.

If we left a piece of steel out under a faucet and knew the water velocity of the water and the parametrization of the piece we could calculate the amount of water that's hitting the surface at any given time or over a given interval. Or if we had rain and the parametrization for a windshield and we wanted to know how much rain is hitting the windshield. These, we could do and they'd be simple to do. Why can we not apply this to air? Or can we apply this to air and is it the "weight" of the air piece of this puzzle that we cannot apply? So conservation of momentum and fluid flow aside wouldn't this work and wouldn't the answer just be favored to the safe side anyway? The air will flow over the surface, not just hit it and stop like my flux integral assumes, butit would intuitively seem that the flow wouldn't apply any extra pressure. Is this right? I'm not an aerospace engineer quite yet. Fluid dynamics comes Junior year.

Thanks!
Reid

Nothing about the faucet or the rain on windshields are different.

Okay... the windshield is extreme, because in that case the water
pretty much stops dead its tracks... If the air flow were to stop "dead in its tracks" then we'd call it stagnated, and you'd be able to measure the "stagnation pressure" with a pitot tube and estimate your air speed. In that case, all the airs kinetic energy (speed) is all converted to potential energy (pressure) so pressure goes up... at least that is how I think about it. Mr. Bernoulli had something to say about that as well.

If you wanted to know the force on the steel under the faucet you'd also need to know the momentum change of the water.

Simplify this for a moment. Rather than a wing, image a tube with air blowing through it. If you bend the end of the tube to redirect the air then you must apply a force to hold that tube in place. You could calculate the force because you know the change in direction of the air exactly, and you know the flow rate exactly. It's easy because you know everything.

The wing is same, except it's hard to get a handle on all the parameters you would require in order to do the calculation. Exactly how much air was redirected? Exactly at what angle? In principle, what you propose is not wrong as an estimate, but I think you really need to factor in where the air is going, not just where it is coming from in order to model the physics correctly.

Perhaps you could simply add a term that accounts for the air as it leaves. Say, it comes in at zero degrees, and leaves at the angle at which the surface is deflected. That will give a rough idea of how the forces vary as you move the surface.

Here is my unsolicited advice for your studies: Never set aside fundamental laws of physics! Three things you can always depend on: energy is conserved, forces balance, and F = ma (integrate w.r.t time to get momentum law).

Keep it up, you're getting there.

50 MPH with 60 degrees of deflection. I'd have to say you will have horrible flow separation as well. That would yield a horribly complicated flow field. It would be a lot more complicated than flow through a curved tube. I'm not sure you will get the accuracy you are looking for. You can always guestimate.

If you get a chance, take some CFD classes if your school offers any. You'll be able to input geometries and compute pressure distribution fields on anything you want.

Here is one I did a while back in school. The pressure distribution on an Eppler 423 at Re = 300,000 and at 5 degrees angle of attack. I don't have the scale with it. The file has been converted so many times that it isn't as pretty as the day I made it.

Reid & TimR,

Unfortunately, as intuitively appealing as it is, the "weight of fluid" method simply is not a workable model of the way air exerts pressure on a solid body. There are several simplified ways of approximating the force, but that isn't one of them.

banktoturn

AQ500, I was not proposing it would be like flow through a tube. I used that as an obvious example of why you can't just consider the flow into the system.

This was generated by javafoil. See: http://www.mh-aerotools.de

If you can get software such as this to dump the pressure distribution you can put a number on the net force applied to the control surface.

Note the streamlines (lines of constant speed). When I ranted about change of momentum, I was taking about this. The change in velocity (speed and direction) of the flow represents a change in momentum.... which can only be caused by a force.... the lift and drag. That was I was trying to get you to recognize. But you are likely better off sticking with the pressure distributions as has been noted.

Reality will be more complicated that this picture. As mentioned, the flow may separate, etc, etc, etc,.

JimTrainor,

I'd be a little suspicious of the pressures out of Javafoil for big surface deflected 60 deg., especially on the low pressure side. This raises an omission I made before. To get the force, you need to integrate the pressure difference between the two sides.

In normal English, streamlines are the paths that massless particles would travel in the flow. They are not lines of constant velocity.

banktoturn

I'd be suspicious too, hence the caution in my post "Reality will be more complicated..."

I recall writing simple software to this in 2-D a long time ago... my recollection was that we followed the lines of constant speed and called those streamlines.

Isn't it the same thing? If you follow a path of constant velocity there will be no flow perpendicular to that path... hence that is the path a hypothetical particle will follow....

I think the term velocity is being used loosely here... I would normally consider it a vector. Perhaps speed should be used... dunno.

Anyway... it's just a model...

I misread the post above about the pipe. It would be nice if everything was staright forward. The change in momentum could be used to fin the force of lift on the entire stab if you knew all of the variables. I think it would be nearly impossible to calculate the load on the control surface itself off of the force of lift off of the entire stab.

Banktoturn is right. There is no particle movement across or perpendicular to the streamlines. The velocity along a streamline is not constant. We can consider the flow we are dealing with as incompressible with little error. A higher velocity can be noted from the streamlines being closer together because mass is conserved and density remains nearly constant. To get more mass through the same area the velocity must increase. You can kind of see this on your plot. On the upper surface of the airfoil the lines are stacked closer together while on the bottom they are further apart. The higher velocity yields a lower static pressure and the oppisite for lower velocity. Thus we have a pressure differential and lift.

Also if we are going for pure accuracy, a 3D model needs to be used.

you're right... nearly impossible to calculate using any sort of change in momentum. . Stick with the pressure distributions. I was climbing that tree to point out a flaw in the initial assumptions.

So whats the home message for rplumbo? Get the pressure distribution and compute the surface integral over the control surface? Gee... that sounds interersting... might try it myself.

Well, that was refreshing.... the joys of RCU.

So, rplumbo... what do you think?

p.s.
I'll have to dig through some old books to get streamlines straight (not that I've been convinced I'm wrong or anything )

In what form will the pressure distribution be? I assume it will be some sort of vector field? Or will it be a function? I think we can all do either, they're not tremendously difficult. Did I read mention of a program that will spit this out? Will it spit out a function though?

We're getting there. All this and I already have my servos. Long live the literati, er, maybe the matherati.

Thanks!
Reid

Well.... I am no expert, but if I were to do this I'd look into xfoil (http://raphael.mit.edu/xfoil/) and see if you can setup a geometry that mimics the deflected control surface - as javafoil can do.

Buried in the software's data structures is the information you need. Once you can get at it, you may need a bit of theory to extract the pressure distributions. Here's a sampling: http://www.mh-aerotools.de/airfoils/...tributions.htm

You won't find any functions though... just numbers that you must be numerically integrated.

It would be any interesting exercise.... perhaps a lot of work, however. You might have to modify the software to spit out the data you need... could get messy. The accuracy would be limited when the deflections are really high.

You started down an interesting road here... I am really interested in what would happen if such an analysis was done with the addition of boost tabs. Check this out:

http://www.geocities.com/roger_forgues/Boost-tabs.html

.... look at figure 3.

I found out a couple of new things. I was talking to my Physics professor yesterday and asked him about this. He agreed that a simple flux integral wouldn't give the exact relationship; however, he did say a standard flux integral would give an overestimate that wouldn't be too far off. He explained it this way. The most pressure would be if the air hit the surface and stopped. The flowing of the surface would not add to the pressure, and it may in fact reduce the pressure. So a flux integral of the worst case scenario, the air hitting the surface and stopping, multiplied times the mass of the air will give a reasonable overestimate. He also said the Navier-Stokes differential equations were designed to to almost just this, but the Navier-Stokes equations are millenium prize problems, meaning no one really understands them. Here's a link:

http://www.claymath.org/Millennium_P...escription.pdf

Good to know!
Reid