Reynolds number ???

[Gonzalo]

Thanks to the thread “Tell me what makes it fly” I have learned about lift more than I thought it could be possible. Now I wonder what it the next step to improve my poor knowledge about aerodynamics … Maybe to understand what the Reynolds number is?

Regards

Gonzalo.

[vintage1]

You really like to punish the brain don't you.

My understanding is not complete here, but I will make a start. Others will do better.

Once people started to realise that all wings are not created equal, and that air and water are not 'perfect fluids' (if they were we wouldn't stall, ir possible even fly at all) they wanted a way to simulate air flow and test fluid dynamics in scaled down models in tanks and in wind tunnels.
But they discovered that teh airflow wasn't the same at all in teh model, not at the same speed anyway. So some clever chaps scratched their (heads mostly) did a lot of complicated maths, and decuided that it would be possible if you applied variuous scaling factors to the model, to get the flow pattern about right between the model and full size, and that would stall in teh same way - more or less, and give a figure for lift and drag that was similar to the full size.

The key was to make the result of a calculation about size, fluid viscosity and density, and flow speed the same on the model as on the full size. They called this the Reynolds number. Fo reasonably non turbulent flow this gives very good results, but IIRC it failsto give good results both at transonic speeds and indeed at speeds below stalling.

This numvber was extended to provide another key bit of information, as it was found that certain types of airfoil performed better at one reynolds number than at another and vice versa., but in general an airfiol, no matter what size it was, performed similarly if the reynolds number was kept the same. I tghink you do this by keepin teh airspeed proportional to te square root of the scale, from rusty memory, but don't take my word for it.

It also works with boats and water.

[Ollie]

http://www.centennialofflight.gov/essay/Dictionary/Reynolds_no/DI114.htm

For standard air pressure and temperture, for an airfoil:

Re = 6380 X velocity (ft/sec) X chord length (ft)

[JMP_blackfoot]

http://www.centennialofflight.gov/essay/Dictionary/Reynolds_no/DI114.htm

For standard air pressure and temperture, for an airfoil:

Re = 6030 X velocity (ft/sec) X chord length (ft)

Metric (I assume Peru is metric as is most of the rest of the world) :
Re = 70000 x Chord length(m) x Velocity(m/s)

[Igwe Aneke]

If you really want to improve your knowledge about aerodynamics i really advise you to buy either Basics of R/C Model Aircraft Design by Andy Lennon (http://www.amazon.com/exec/obidos/tg/detail/-/0911295402/ref=pd_bxgy_img_2/102-1309720-6756946?v=glance&s=books) or Model Aircraft Aerodynamics by Martin Simons (http://www.amazon.com/exec/obidos/tg/detail/-/1854861905/qid=1098359920/sr=8-1/ref=pd_csp_1/102-1309720-6756946?v=glance&s=books&n=507846).
Note: Andy Lennon's book is (much) easier to read and understand.

[Ollie]

My mind was off. English units for 6030 was wrong. I edited number to 6380 for English units.

Thanks, for metric version.

Model Aircraft Aerodynamics
by Martin Simons uses metric units.

[Antonsoarer]

Thanks to the thread “Tell me what makes it fly” I have learned about lift more than I thought it could be possible. Now I wonder what it the next step to improve my poor knowledge about aerodynamics … Maybe to understand what the Reynolds number is?

Regards

Gonzalo.

Gonzalo,
In simple terms think: Bigger Chord and or Speed means higher Reynolds number which means you move away from a Bee swimming in thick water-like air to a Jumbo flying with low drag and high lift in...erm well... air :rolleyes: Our models tend to operate in the area of low or erratic efficiency (high drag and low lift) between these extremes

There are some big steps in efficiency between the two extremes (it’s a non-linear world) mentioned above. Also note that speed will track wing loading for a glider so higher wing loading doesn't always mean worse performance!

Tony.

[10cent]

Reynolds # is just one of many "dimensionless numbers" that help describe and predict fluid motion. To acurately scale down a full size plane (in this case) you would actually need to hold more than one dimensionless parameter constant. The number of dimensionlesss parameters needed depends on the situiation being scaled or modeled. If you really want some brain food I would recommend finding a used Fluids book at a university store or something and checking out the chapter on "dimensionless parameters and scaling" or "modeling".

It gets kind of tricky and I haven't tried to fully apply it to scaling a model as yet but it would be a fun puzzle...maybe over the winter I can try to whip up some scaling parameters...hmmmm :rolleyes:

[10cent]

:cool:

I found a pdf that explains the system of acurate scaling in fluid flow quite nicely...I think...I'm at work so I just skimmed it. Anyway, the Buckingham Pi method is the standard accepted approach and here it is:

www.me.ttu.edu/classes/ME3370/StudyGuidepdf/ChV.pdf

enjoy

[Gonzalo]

If you really want to improve your knowledge about aerodynamics i really advise you to buy either Basics of R/C Model Aircraft Design by Andy Lennon (http://www.amazon.com/exec/obidos/tg/detail/-/0911295402/ref=pd_bxgy_img_2/102-1309720-6756946?v=glance&s=books) or Model Aircraft Aerodynamics by Martin Simons (http://www.amazon.com/exec/obidos/tg/detail/-/1854861905/qid=1098359920/sr=8-1/ref=pd_csp_1/102-1309720-6756946?v=glance&s=books&n=507846).
Note: Andy Lennon's book is (much) easier to read and understand.

I just ordered the books. I really want to improve my knowledge about aerodynamics and if possible be able to design my own models.

[Gonzalo]

Now I understand that if we build a scale model (lets suppose by a factor of ¼), and want it to perform similar than the real plane, we have to maintain the Reynolds number the same by increasing the velocity (4 times in this example).

But … What do we mean with “perform similar” Guess that between other things it means that lift and drag forces will be proportional, in our example if:

Lr(V) and Dr(V) are the lift and drag forces on the real plane at speed V

And

Lm(V) and Dm(V) are the lift and drag forces on the model at speed V,

Then

Lr(V) = K * Lm(4*V) and Dr(V) = K * Dm(4*V) being K the same proportional parameter for both the lift and the drag forces.

My next question is how do we calculate K? Is it related to the scale factor of the lineal dimensions (1/4 in this example) or to the wing area (1/16 in this example)?

Also if Vs is the stall speed for the real plane, then the stall speed of the model is 4 * Vs. Since scale models are not flying at X times the speed of real planes, does it means that scale models fly closer to stall?

Regards

Gonzalo.

[Ollie]

Assuming that the Re number is the same for full scale, the models must fly faster. This assumption is wrong for equal Re when models fly slower for full scale!

The Re for models have much smaller Re numbers compared full scale Re numbers. The best airfoils for models have worse performance, poor lift and more drag compared any full scale Re airfoils. The wing loadings of models must be very, very much lower compared to full scale wing loadings.

[flieslikeabeagle]

Gonzalo, I think it means that scale models are always flying at Reynolds numbers less than the full-size plane.

This is why the best airfoil for a scale model is not necessarily the best airfoil for the full-size aircraft.

As to drag and lift, my understanding is that both of them are proportional to the square of the velocity, to the area of cross section, and to the drag (or lift) coefficient.

If the wing is scaled to a quarter the length and a quarter the thickness, it has one sixteenth of the cross sectional area. The velocity is four times higher, so the square of the velocity is sixteen times higher. Multiply the two factors (one sixteenth and sixteen) together, and you find that your quarter-scale wing is developing the exact same lift and drag as the full size wing!

This is the other reason why models fly at smaller Re than full-size planes - you don't want to make as much lift or drag as the full-size plane, since you have less weight to lift and less power to drive the model with.

I know relatively little about aerodynamics, so if I made a mistake here, experts feel free to jump in and correct me. But I think I'm right.

-Flieslikeabeagle

[10cent]

beagl is on the right track. Did anyone check out pg 7-9 on that pdf I posted earlier? (Yeah, I know it was boring and I don't blame you). Anyway, for a model to acurately behave like the full size plane you would need to hold both geometric and kinetic similarity. That means that you need to hold both the Re the same and the fluid flow rate over the wing the same...which means that a perfectly scaled model (assuming we can't fly in syrup) would need some seriously high speeds to generate similarity. It just isn't practical. Then if you add in trying to hold those constraints for all the control surfaces etc.... :confused:

Anyway, the long and the short of it is I don't think it is possible from a r/c standpoint to build a model that flies just like the full size plane. I'm probably overlooking something but that's my best guess.

I think the plan for scaling is to scale the geometry then find a wing that makes it fly ok.

[Sail 'n Soar]

Assuming that the Re number is the same for full scale, the models must fly faster. This assumption is wrong for equal Re when models fly slower for full scale!

The Re for models have much smaller Re numbers compared full scale Re numbers. The best airfoils for models have worse performance, poor lift and more drag compared any full scale Re airfoils. The wing loadings of models must be very, very much lower compared to full scale wing loadings.

You will never have the Reynolds number of your model equal to that of the full scale unless your model is very large and your simulating your lightly loaded full scale flying either very high or on Mars. There are two important aspects of Reynolds numbers relative to our modeling. The first is that the drag coefficients will be higher and the second is that the max CL's will be lower. You compensate for the higher CD's by flying slower and not trying to fly 3,000 miles without refueling. You compensate for the lower CL's and lower scale speeds by flying at lower wing loadings.

I don't really think you need to go any deeper into the theory than that. Unless you already have a siginificant technical background with good higher math skills, I think you will be wasting your money on any university aero text. The over simplifications of most undergraduate texts give you just enough knowledge to be dangerous without the practical experience to put things into proper perspective.

[flieslikeabeagle]

..this may be a good time to bring up "cubic wing loading". Does anyone know the scaling concept behind this parameter? I can see that what it does is make the wing loading number higher as the wing gets smaller, telling you that for similar performance, the wing loading needs to be smaller for smaller wings. But what is the theory behind this?

-Flieslikeabeagle