How do i calculate reynolds number?

[dude_joel]

G'day everyone
I've looked around and can't find any threads related to what Reynolds number is, how to calculate it, explanations of the equations required, what effect Reynolds number will have on an aircraft etc.
most Google searches provided me with equations for fluid dynamics or a pipe and didn't go into aircraft so they leave a lo of questions unanswered.
I think a thread devoted to this would be very useful on this forum.
Thanks
Joel

[ciurpita]

here's a decent web page, Re is proportional to airspeed and wing chord.
http://www.zenithair.com/kit-data/ht-87-5.html

in general, the drag of an airfoil will have higher drag at lower Re (lower airspeeds and/or lower chord). it seems that over the range of airspeeds that model sailplanes can be flown, there is a significant increase in drag at slower airspeeds.

wingtips that shrink down to narrow chords have low Re and significantly higher drag coeficients. but fortunately, there's not much area and the drag penalty washes out.
http://ciurpita.tripod.com/rc/rcsd/drag2/drag2.html

[Ricardo RW]

Wow Greg, those web pages are wonderful, your site is really full of treasures!! Thank you for sharing.

[HELModels]

Here is a simplified way to calculate Re:

6380 * airspeed(ft/sec) * average chord(ft) = Re for a wing

6060 * airspeed(ft/sec) * average chord(ft) = Re for a stabilizer

[biber]

Why do you have different formulas for wings and stabs?

Do they work in diferent media with different kinematic viscosities? :rolleyes:

biber

[CloudyIFR]

You can also take 9360 * airspeed(mph) * (average chord * 0.0833333)

This assumes standard a day.
Which is Temperature 59 degrees F (15 degree C), pressure 29.92 inches mercury (1013.2 millibars) and sea level altitude.

Curtis
Montana

[biber]

For quick estimations I always use 70000*chord*airspeed*s/m².
That gives the local Reynolds number (if you put in an average chord, you get an average Re).
Put in chord and airspeed in SI units, i.e. metres and seconds.

To do the maths in non SI I'd boil down CloudyIFRs formula down to:

780*airspeed*chord/whatever_cloudy_does_measure_chord_in/mph

biber

[HELModels]

Why do you have different formulas for wings and stabs?

Do they work in diferent media with different kinematic viscosities? :rolleyes:

biber

Sarcastic Drunkard. It came from a respected source. Maybe one you dont respect, but it has worked for many modelers. The difference comes into play when the profile drag for stab, wing is calculated.

[MarkusN]

Sarcastic Drunkard. It came from a respected source. Maybe one you dont respect, but it has worked for many modelers. The difference comes into play when the profile drag for stab, wing is calculated.
With all due respect, that source is in error. There can be no different formulae for Re if chord and speed are entered in the same units. Unless they are talking different viscosities or air densities, but that does not depend on tail or wing.

Your formulae are close enough in result to still give useable numbers (after all Re is not a value that goes proportionally into a next equation), but they don't make sense next to each other.

[BMatthews]

I have to agree. The only way the tail would use a different equation is if the tail is operating in a different airflow situation. Depending on the model I suppose that is possible but unless the wing's flow is slowing or turbulating the flow over the stab that isn't going to be the case. For most designs I think it's fair to say that the stab is working with a slightly redirected flow due to downwash but isn't going to be in the turbulent trail of the wing outside of some particular angles of attack.

Found a couple of interesting sites. The first is an info page from some Xfoil related site....

http://home.earthlink.net/~x-plane/FAQ-Theory-Reynolds.html

The link to the Stanford site calcualtes your wing's (or stab's) Rn quickly and easily. Too bad they don't indicate the formula the calculator uses...

http://aero.stanford.edu/StdAtm.html

The Martin Hepperle site shows us the Re = v * l * 70000 formula but I noted that this does not allow for altitude changes. Just for giggles I compared a 0.8 foot section at 40 feet/second at sea level and 4000 feet (the praires of Nevada where I motorcycle toured this summer) to see the difference. 203522.79 vs 184719.53. So there's quite a change with altitude. Something to keep in mind and for me an indicator that I'd rather trust the Stanford site calculator that likely uses the full on formula shown on Wikipedia of

[HELModels]

With all due respect, that source is in error. There can be no different formulae for Re if chord and speed are entered in the same units. Unless they are talking different viscosities or air densities, but that does not depend on tail or wing.

Your formulae are close enough in result to still give useable numbers (after all Re is not a value that goes proportionally into a next equation), but they don't make sense next to each other.

Before you discount it as incorrect, you should ask about the context. If you are looking at the graph I am looking at, then it makes sense to correct for stab or wing. Doing that puts you on a curve for wings and a curve for stabs. The curve shows profile drag vs. reynolds. I acknowledge it was out of context, but it isnt wrong, just specific to an atypical application.

The original poster can request a copy of the source if he wants. It works great for designing a model.

[HELModels]

The profile drag vs. reynolds graph is based on some theory and validated by real low reynolds data collected by Hoerner, ARC, Gottengen, NACA. What little I know tells me the stab graph is for symmetrical sections at Cl = 0, while the other curve is for flat bottom foils at Cl = 0.7. The formulas I listed are very specific, that I admit. Context is everything.

[MarkusN]

Context is everything.Exactly. In fact I was ASSuming as much. (That your formula comes out of some context.)

Still, speaking about Re proper it does not make sense to have different formulae for different applications. Re is defined as velocity times typical length (chord, in the case of wings), divided by kinematic viscosity.

A formula that has different factors for different wing shapes most probably makes some assumptions about chord distribution and then attempts to calculate some "mean Re".

[biber]

HELModels, I didn't think I was too harsh, but just wondered where your formulas came from and why there were two of them.
Instead of a clear answer, where you got that stuff from and what context applies,
I got called names, thank you for that.

As you say, the formulae have to be taken in context and you refuse to openly share it,
so what was your initial post worth in your own currency?

However, Reynolds business is anything but linear and a change of some percent in Re is mostly not an issue.
To get a noticable effect you watch out for factors like 3/2 or a doubling or lets say 2/3.
So you really have to know just a rough scale.

biber

[adam_one]

Well, here it goes:

Re = (air density/air viscosity) * air speed * wing chord

Air viscosity is measured in kilograms per meter per second.
Standard value is: 0.0000179 kg/m/sec.

So, a wing with a chord of 1m at an airspeed of 1 m/sec with the standard air density and viscosity will have the following Re:
(1.225/0.0000179) * 1 * 1 = 68459
Thereby, a simplified formula may be obtained as follows:
Re = 68459 * V * L
Where V is the airspeed in m/sec and L the wing chord in meters.

But since the wing chords of model aircraft are often much less than 1 meter, one may get a Re value close enough for modelling purposes by using the following simplified formulas:

Re = speed in kilometres per hour * wing chord in centimetres * 189 (Metric units).
Re = speed in miles per hour * wing chord in inches * 770 (Imperial units).

.

[HELModels]

Apologies to all.

Biber, I was being slightly sarcastic about the name calling, but read your avatar. I admit I dont know much and made a dangerous addition to a straightforward discussion.

Peace

[biber]

That's fair enough for me.
Had there been a smiley, I wouldn't have mind,
but without a hint the ironic part escaped me at that moment.

I guess, by the further posts of other users, the Reynolds number issue is solved now, anyway.

Peace to you

biber

[dude_joel]

wow, opened a can of worms here...
what does the reynolds number mean for an aircraft?

[Neil Stainton]

Wing or stab? :)

As people said, it is the ratio of inertial forces to viscous forces. The lower the number the more guey (sp) the fluid looks to the structure. It is not something that has any obvious meaning in itself, but by looking how airfoils operate at differing Re you can choose one that will work well for your application.

Neil.

[MarkusN]

It doesn't really "mean" anything for the aircraft. Comparing geometrically similar flow problems (E.g. the flow over a wing section) having the same Reynolds numbers will make sure that results will be comparable.

So if you want to apply wind tunnel data to your desingn, it would be good if you had data for the Reynolds number of your intended application, or at least close.

The definition of Re: Re ist the relation of mass forces to viscous forces in a Flow. Thus:

High Re: predominantly inviscid (friction free) phenomena in the flow (large scale aircraft). Turbulence, eddies.
Low Re: predominantly viscous phenomena in the flow (Steel ball in honey). Laminar flow, no turbulence.

In the model world usually: High Re: Will fly OK. Low Re: Open a can of (technical, in this case) worms.

[nmasters]

I don't mean to contradict MarkusN, but low Reynolds number does mean something to an airplane. Low Re means earlyer stall. As the dynamic forces become weaker the viscos effects become more important. Stall is a viscos effect as is induced drag. The result of this is that a slow little model will have a poorer glide and earlier stall than a large fast version of the same airplane.

--Norm

[HX3D014]

I don't mean to contradict MarkusN, but low Reynolds number does mean something to an airplane. Low Re means earlyer stall. As the dynamic forces become weaker the viscos effects become more important. Stall is a viscos effect as is induced drag. The result of this is that a slow little model will have a poorer glide and earlier stall than a large fast version of the same airplane.

--Norm
Norm

Have you ever heard of a stall occurring for a given AoA just because the Velocity increased

or a chart indicating the stall angle for given speed.
IE
Vertical axis would be AoA
Horizontal axis would be Velocity
and the plotted points would be the Stall point with correlation to each.

Bryce.

[JetPlaneFlyer]

Norm

Have you ever heard of a stall occurring for a given AoA just because the Velocity increased

or a chart indicating the stall angle for given speed.
IE
Vertical axis would be AoA
Horizontal axis would be Velocity
and the plotted points would be the Stall point with correlation to each.

Bryce.

The graph norm posted shows lift curve and stall point for different speeds (i.e. Re). Exactly how stall angle is effected varies in detail between one airfoil and another but in general stall occurs earlier at lower Re.

I guess the exception to this may be an laminar flow airfoils where laminar flow turns turbulent at higher velocities, which may result in an earlier stall?

Steve

[HX3D014]

The graph norm posted shows lift curve and stall point for different speeds (i.e. Re). Exactly how stall angle is effected varies in detail between one airfoil and another but in general stall occurs earlier at lower Re.

I guess the exception to this may be an laminar flow airfoils where laminar flow turns turbulent at higher velocities, which may result in an earlier stall?

Steve
will check that out now.

In particular, I was not after the Re component, but just a given set of standards where the only variable is the Velocity.
and the effect on stall point of that.

So (for a very rough example)
same day same location
same airfoil same chord length
just find stall AoA at 10kts
then on the same day same location etc etc
Just find stall AoA at 20kts
then find stall AoA at 30kts and so on.

Looking at the graph now.

(The example came from a book on helicopters and was describing the effects of velocity on stall angle)

Bryce.

[slipstick]

But since the only variables in Re are airspeed and chord, if you maintain the same chord length then changing the speed IS changing Re. Or have I missed something important ;)?

Steve

[nmasters]

in general stall occurs earlier at lower Re.

I guess the exception to this may be an laminar flow airfoils where laminar flow turns turbulent at higher velocities, which may result in an earlier stall?

Steve
That would be a Mach effect not a Reynolds number effect. The velocity around the leading edge can be higher than at the minimum pressure point on the upper surface. It's possible to get compression and transition right at the LE because of this. That's why you should always set the Mach number to some realistic value when analyzing with software. In the absence of Mach effects laminar flow can be maintained indefinitely on a clean surface as long as there's a favorable pressure gradient. The highest transition Re I remember reading about was 25,000,000

[HX3D014]

But since the only variables in Re are airspeed and chord, if you maintain the same chord length then changing the speed IS changing Re. Or have I missed something important ;)?

Steve
My mistake there.

the chapter was actually titled
Effect of Increasing Airspeed on Stall Angle

To quote a portion of the chapter;
"The separation of air occurs more readily when flow velocity increases"

The graph shows AoA up the left
and True Airspeed (KTAS) along the bottom
and the plotted lines are titled "Stall (Separation) Boundary"
the plotted line is starting around 15deg at 0 (KTAS)
13deg AoA would be at about 200 KTAS
11 deg AoA would be at about 320 KTAS
9 deg AoA would be at about 400 KTAS
7 deg AoA would be at about 460 KTAS
to
1 deg being at about 610 KTAS

I think the graph is not actually representative of any particular Airfoil data, but just a Representation of the Principal for illustration purposes.

So I am looking for any data derived from a given set airfoil parameters to peruse.

Bryce.

[JetPlaneFlyer]

So I am looking for any data derived from a given set airfoil parameters to peruse.

Bryce.

Bryce,
When i get home this evening I'll run you off some comparitive Cl and Cl/Cd graphs over a range of Re.

Any particular airfoil, or will a good old Clark-Y do?

Steve

[HX3D014]

Bryce,
When i get home this evening I'll run you off some comparitive Cl and Cl/Cd graphs over a range of Re.

Any particular airfoil, or will a good old Clark-Y do?

Steve
try somthing symetrical. and of about the same chord length of a Rotor blade (Full Scale)

here is a diagram which shows the blade tip stalling first. but theoreticaly it should have a slightly lower AoA due to rotatioal velocity and maybe even washout.
http://www.globalsecurity.org/military/library/policy/army/accp/al0966/al0966b0025.gif
http://www.globalsecurity.org/military/library/policy/army/accp/al0966/le3.htm

http://books.google.com.au/books?id=Q27ho2szWCoC&pg=PA94&lpg=PA94&dq=retreating+blade+stall+diagram&source=bl&ots=NqlcIGbUlI&sig=k7SDSEIoh2Vh_HAH4qKejeGhzaM&hl=en&ei=PcTASe_BIZ3gsAPVuZwx&sa=X&oi=book_result&resnum=11&ct=result#PPA102,M1


Bryce

PS;
I think I understand the effect of Velocity on the Re #
is it a direct multiplication.
so if you reduce the Velocity by 10% you get a Re # 10% smaller.

if so, then the lower Re #’s stalling more readily than larger ones (where V was the only difference in the Re#) seems to contradict the rotor blade tip stall discoveries.

[fnev]

Sorry, because of the equations and my ignorance, this is the best I can do:

Re formula with all the variables involved:

http://fnev.smugmug.com/gallery/7642973_bLqmD#493904645_qo4u3

[nmasters]

Re formula with all the variables involved:

http://fnev.smugmug.com/gallery/7642973_bLqmD#493904645_qo4u3
AAAAAARRGGGGGGGGGGG... :eek: Sutherland's constant... I wrote a little spreadsheet (http://www.rcgroups.com/forums/showthread.php?t=975623&page=3) that would have worked a bit better if I had used that along with the "simplified" standard atmosphere model. Oh well, less than one percent error at 12,000 ft altitude isn't bad and the lift of my test cases came out right.

--Norm