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# Gliding object - Wind tunnel procedure?

## Gliding object - Wind tunnel procedure?

(OP)
Hi experts!

I am trying to qualify the flight performances of a non-powered aircraft in CFD. I have no idea about how it is done in a real wind tunnel, but to calculate the Cl and Cd coefficients of the aircraft, I had to provide an incidence angle (which I assume to be 0° without any thrust), and I had to provide an initial value for the speed - as in the wind tunnel (which I choose arbitrary then, close to what I think it should be from experience) + the weight and surface that I know.

My intent is to determine
-the maximum glide ratio (based on the drag polar curve I guess https://en.wikipedia.org/wiki/File:DargPolarAL.png)
-the coresponding forward speed (based on the glider polar curve I guess https://en.wikipedia.org/wiki/File:GliderPolar.png)

I am however confused by several aspects:
- Without any thrust, does a gliding object has an incidence of 0°? So how can I deduce the best glide ratio from the drag polar curve which requires different incidence angles to be built ?
- How do we connect the glider polar curve to the drag polar so I can determine the corresponding forward speed?

So to sum up, my question would be : with the possibility to get the Cl and Cd coeffs of my entire gliding object for a given initial angle and speed, what would be the procedure to calculate the maximum glide ratio and corresponding forward speed.

Thanks in advance for any clarification.

### RE: Gliding object - Wind tunnel procedure?

I think a glider is almost always running at a _small_ negative incidence angle, except for a flare to a positive incidence angle just before landing, and a positive incidence angle when it's being towed.

(No real expertise claimed here.)

Mike Halloran
Pembroke Pines, FL, USA

### RE: Gliding object - Wind tunnel procedure?

There are several great book on [GOOGLE] 'sailplane design'...every aspect... unless of course Your powerless aircraft is a winged space plane...

Regards, Wil Taylor

o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

### RE: Gliding object - Wind tunnel procedure?

This subject is always thoroughly covered in introductory aerodynamics textbooks, so I recommend you start there.
Mike's suggestion sounds intuitively correct, but isn't. The glider must develop lift. Its wings are at a positive angle of attack. It needs this angle of attack, and forward velocity, to maintain an amount of lift that is _equal_ to its weight. Its flight path forward is largely the forward velocity, however, there is also a small velocity downward which is its descent rate. The rate of descent is whatever energy value is necessary to overcome the energy lost to drag.

STF

### RE: Gliding object - Wind tunnel procedure?

Try
Fundamentals of Sailplane Design by Fred Thomas
"Grundlagen Fur Den Entwurf von Segelfluzeugen"
Translated by Judah Milgram.
Available from College park press , Maryland.

You are judged not by what you know, but by what you can do.

### RE: Gliding object - Wind tunnel procedure?

Thank you SparWeb for the education.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Gliding object - Wind tunnel procedure?

Frame of reference is important.

A glider's "thrust" is a component of its lift that is pointed opposite to the drag.

For this to happen, the fight path must be downwards relative to the horizon.

### RE: Gliding object - Wind tunnel procedure?

(OP)
I don't know this book you are referring to - but ordered, thanks.
I however read many extensive pdf files here and there describing the physics of the glider flight. Not a mathematician but I guess I understand most of it. However I am still not able to build a CFD procedure.

I make myself more clear:

I am looking for the optimum glide for a non-powered flying plane and the corresponding forward speed at this incidence + if possible the stall speed.

To achieve this, I have to first build the drag curve and the lift curve in respect to the angle of attack.
> first issue, I have no idea what reference speed I should choose for this. This document http://ewp.rpi.edu/hartford/~ferraj7/ET/Other/Refe... use a specific speed without explanation. This one http://maecourses.ucsd.edu/callafon/labcourse/hand..., as an exercise ask to plot these curves for a set of 3 different speeds. Are lift and drag ratio independent from speed so I could choose any one? (I am not supposed to know the span of speed covered by my aircraft between stall and structure damage).

Second, by coupling with the attack angle I can construct the drag polar curve (Cd over Cl). This curve allows me to determine graphically the optimum glide through tan(theta) value. Doable.
> no way to do it by any formula, my profile is not a standard one and is pretty complex.

Third I would need to determine the corresponding forward speed and sink rate.
> The only curve I know for this is the polar curve. I am not sure this curve can be drawn from experimental values (CFD wise). And even if it's the case, any angle of incidence drawn from the origin would cut the curve in 2 locations. One at lower speed but with a high angle of attack, one at higher speed with a lower angle of attack. I suspect there might exist a mathematical formula to link Cl, Cd (so theta and alpha) and the forward speed/sink rate.

Thanks for any tip or comment!

### RE: Gliding object - Wind tunnel procedure?

The reason only one speed was used is (aside from time involved) that there was no desire to deal with Reynolds number effects on the test results. Since they are coefficients, the results can be scaled with reasonable accuracy over a reasonable range around the test condition.

You can see this in the second experiment, where the point of the multiple velocities is to be shown in Part 1, question 6.

### RE: Gliding object - Wind tunnel procedure?

(OP)
Maybe a drawing is more clear :)

- From an initial speed (how to choose?), I can determine the Cl and Cd for a range of attack angles
- From these 2 graphs I can draw the Cl/Cd over attack angle and determine the angle which would represent the best L/D ratio
- With this angle in hand I can now compute the drag over speed and define the minimum drag speed.
- Finally, I can recompute Cl and Cd with the proper speed and find the incidence angle from the polar graph

Does this makes sense? The only unknown parameter is the initial speed (most probably defined by a 3.10e5 Re number or so if I understood well)

http://files.engineering.com/getfile.aspx?folder=3...

Thanks again.

### RE: Gliding object - Wind tunnel procedure?

i think there are two different things being talked about.

L/D_max is one thing, D_min is another. the AoA for max L/D is different to AoA for min D.

I think I would fly my glider at L/D_max (which defines Cl) at a speed so L = Wt.

Thinking further I think you start with a flight path (1deg nose down, 2deg ?, ...) which will
1) define L as %age of Wt, and
2) define the AoA offset (ie the glider can pitch with respect to the flight path)

Now draw Cl and Cd vs AoA, and determine AoA for L/D_max.

At this AoA (or Cl) how fast do you need to go so that 1) is satisfied ?

### RE: Gliding object - Wind tunnel procedure?

(OP)
Hi rb,

In this page http://www.free-online-private-pilot-ground-school..., if you look at the paragraph between fig 5 and 6, it says "Note that the maximum lift/drag ratio, (L/D max) occurs at one specific angle of attack and lift coefficient. If the airplane is operated in steady flight at L/D max, the total drag is at a minimum.". I am not saying that your statement is wrong. The fact is that I read this in other pages so I took it as an interesting starting point.

As this appears to be a multi variable problem, I wonder if an iterative approach would not be the solution - this would concur with your further approach as well. And this is very easy to program on top of CFD.

### RE: Gliding object - Wind tunnel procedure?

https://www.grc.nasa.gov/WWW/K-12/airplane/glidvec...

The glider reaches a state of balanced forces for each angle of attack of the wing, which is respect to the flow of air around the wing, not to the horizon.
There is thrust induced by the horizontal components of weight and lift.
During balanced glide, that thrust has the same magnitude than drag, and lift has the same magnitude than the vertical component of weight.

Each angle of attack of the wing is commanded by the elevator, which makes the tail an airfoil with some negative angle of attack (in order to balance other forces generated by lift, CG location, etc.).
If you force the nose down via elevator, the glider gains speed until reaching a new state of balanced forces.
If you force the nose up via elevator, the glider loses speed because the induced drag increases (refer to the mentioned Figure #5).

Reproducing those exact conditions in a wind tunnel could be difficult because the direction of the airflow is always perpendicular to the vector weight.

### RE: Gliding object - Wind tunnel procedure?

He's using CFD.

In a wind tunnel the weight is tared out anyway because the model won't have the correct mass or mass distribution to represent the full sized aircraft unless a lot of effort is expended. If required the force balance could be rotated so that the Lift direction was no longer perpendicular to the flow or just do the rotation transform on the data to simulate the glide slope.

### RE: Gliding object - Wind tunnel procedure?

(OP)
Thanks @Lnewqban

The most simple but comprehensive presentation I found is this one : http://www.rjplancaster.net/documents/PrinciplesOf...
But as we can deduce from slides 12, 13 and 34, we have to much variables for solving the equation.

Lift is proportional to alpha and V2
Drag is also dependent on alpha and V2

I tried to bind, link and combine all equalities I have between mg/L/D/Cl/Cd, I still thinking that an iterative approach is the only one to solve this equilibrium problem.

I expected something simple and done by aerophysicists since ages!

### RE: Gliding object - Wind tunnel procedure?

(OP)
Hi guys,

Back on my investigations after a short break.

Here is what I managed to have so far:

Using DOE (design of experiments) features of some cloud computing services, I measured the L/D ratio for a complete matrix of speed and AoA.
Among all the measures, there is a specific speed (V0) for which L/D is maximum. This gives me the AoA of my flying object (alpha) and thus the glide angle (gamma, L/D=1/tan(gamma)).

I am not sure to understand clearly @rb1957 procedure about calculating the forward speed, but this is the last variable I am missing now. My experiments gave me a speed of V0 corresponding to my L/D max. Considering that I have a non thrusted object (similiar to a paper aircraft or a glider), does this means that if I drop it from a certain altitude, it will fall down and accelerate until it reaches, V0, alpha and gamma configuration naturally?

If we put some ballast in a glider, it goes faster but keeps the same path. What makes me more confused is that a CFD simulation never asks for any weight at all. On which basis is calculated this V0?

Thanks!

### RE: Gliding object - Wind tunnel procedure?

(OP)
I guess the answer is simply in this Lift equation:
https://www.grc.nasa.gov/WWW/K-12/airplane/lifteq....

Extracting V. But it doesn't take in account the wingload (ballast addition which increases forward speed).

### RE: Gliding object - Wind tunnel procedure?

not sure why you'd go to a K-12 (kindergarden-12) description of lift when you have much better sources (any textbook). I'm surprised you went to this source for this basic information (and it seemed to be a revelation to you).

You say you've done a bunch of virtual experiments and obtained the C/Cd surface. I think ('cause I don't know) that important design decision for you is the wing setting angle (the angle between the wing reference plane and the glider axis). This will set (I think) the glider max L/D, speed for max L/D, and glider max speed (and probably a bunch of other performance parameters too).

Have you read and understood the books we've suggested? There is plenty of information out there to help you.

I'm surprised that more weight makes a glider go faster, unless there's another effect that balances this advantage (lower max L/D ?) ... but then glider compete in weight categories, don't they ?

### RE: Gliding object - Wind tunnel procedure?

RB1957,
I'm surprised that more weight makes a glider go faster, unless there's another effect that balances this advantage (lower max L/D ?) ... but then glider compete n weight categories, don't they ? When you add weight to a glider , all it does is to shift the polar curve to the right, and down a bit. the min sink increases a bit and the best L/D speed also increases. This is why competition sailplanes carry Jettisonable water ballast, when the thermals get weak they dump the water to improve the sink rate.

You are judged not by what you know, but by what you can do.

### RE: Gliding object - Wind tunnel procedure?

You sort of have a how long is a piece of string? problem. If the aircraft is already designed that simplifies it but I'm not sure where you are. Neglecting updrafts (thermals, or how sailplanes sail) A maximum distance glide will be at L/Dmax and a max endurance glide at minimum sink rate, which, I'm not sure they are the same. If, through CFD you determine L/Dmax for the aircraft in a trimmed, gliding state (where L is the aircraft weight + trim force from the elevator)....

Oh wait, I found this max distance and endurance glide states defined. :
http://www.dept.aoe.vt.edu/~lutze/AOE3104/glidingf...

*Make sure the simplifying assumptions suit your case*

This will give you sink rate and velocity for the two states and the flight path angle. If you're putting it in a wind tunnel, remember to solve for at put it at the appropriate AOA to the free stream.

My qualification: 1 course short of mech/aero double major 20 years ago.

### RE: Gliding object - Wind tunnel procedure?

@berkshire, I was remembering that as I wrote it, and it makes sense (I think) increasing max L/D speed and increasing sink rate. and of course gliders don't have to pay the price (or at least the full price) to carry the extra weight ... not when they get towed to release altitude.

### RE: Gliding object - Wind tunnel procedure?

(OP)
Thanks for sharing the doc.

As L/D varies both with AoA and speed, I am using at the moment a dichotomic approach to first determine the AoA with a guessed speed, and then refine it by playing around with different speeds. The final values give me the L/D, so the gliding angle. The speed is experimental and given by the CFD simulation. I have to confront this value to the theoretical one but as I said CFD doesn't ask for any weight value.

### RE: Gliding object - Wind tunnel procedure?

ok, AoA for L/D max is slightly affected by Re, but there is an L/D max at a specific Re (close 1E5 by the look of it) and so a specific speed for L/D max.

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