Nerd needed. Reynolds/Cl-max calcs

[blue up]

Well, not exactly a nerd, but if there is anyone here who Reeeeealy understands the calcs needed to take a known wing profile and use it to come up with a predicted stall speed then I'd be eternally grateful for their help and guidance.

Gttingen 535 characteristics (http://library.propdesigner.co.uk/html/gottingen_535_characteristics.html)

This is the wing profile, a very draggy profile that is reputed to produce an almost unstallable wing. I've played around with some calculators on the internet for my 364kg homebuilt but have not been able to come up with one solid, incontrovertible figure for a clean stall.

Clutton FRED - FRED (http://cluttonfred.info/fred#.U5GDCrlF0iQ)

•Wing span: 22 ft 6 in (6.86 m)
•Wing chord: 5 ft (1.52 m)
•Wing area: 111 sq ft (10.32 sq m)
•Length: 16 ft (4.88 m)
•Aspect ratio: 4.5
•Empty weight: 550 lb (249 kg)
•Maximum weight: 800 lb (363 kg)
•Cruising speed: 71 mph (114 kph)
•Maximum speed (Vne): 100 mph (162 kph)
•Stall speed: <40 mph (<64 kph)
•Rate of climb: 350-400 fpm (1.8-2.0 m/s)
•Take off run: <300 ft (<91 m)


The suggestions I've had are that the Reynolds number is about 1.5 million and the Cl-max comes out above 2. Does this make sense?

Thanks, in anticipation!

[Mark 1]

My quick 'back of the envelope' calculation.

Assume ISA sea level atmosphere so:

Rho=1.225 kg/m^3
Mu = 1.983*10^-5

64 km/h ~=18 m/s

Lift required at 1G = 363 * 9.81 = 3561N
Dynamic pressure at 18 m/s = 0.5 * 1.225 * 18^2 = 198.45
So 3561 = CL * 198.45 * 10.32
∴ CL = 1.738

Re = 1.225 * 18 * 1.52 / 1.983*10^-5 = 1.69*10^6

Does that sound about right?

[John Farley]

Blue up

My gut says I would not expect to see a Cl max of over two for a wing that had such a low aspect ratio. Mark 1's number seems to support that.

[blue up]

That all makes sense. I wasn't sure if I was missing out any fudge factors anywhere along the line. Previous reports for the aircarft have given a pseudo stall at anywhere between 25kts (IAS) with power on and 31kts (IAS) at idle.

Bearing in mind that I'm new to all this, do vortex generators have the effect of increasing the Cl-max or is their performance improvement found elsewhere? I couldn't work out if they merely allow a steeper AoA and therefore a shift along the existing CL curve.
Also, by moving the C of G aft on a conventional aircraft I assume you keep the same CL but reduce the effective mass that the wing is supporting as it turns the tailplane into a lifting surface.

(Apologies for the poor use of terminology. Steeeep learning curve!)

Thanks for the calc, Mark 1. I guess I was in the right ballpark.

John Farley. I couldn't find anything published on how aspect ratio affected Cl-max but what you said makes sense.
PS At age 10, I wanted to be you when I grew up. :ok:

[John Farley]

http://img.photobucket.com/albums/v145/johnfarley/CH11F1_zpsf1d98a55.jpg

These are just general trends.

[Owain Glyndwr]

Just to flesh out John Farley's comments:

A good rule for low speed unswept wings is that lift curve slope is proportional to AR/(AR+2); in the absence of anything better to a good approximation you could use this scaling for the CLmax also.
The Gottingen 535 data shows a sectional (2D/infinite AR) CLmax of about 2.25. Scaling this to an AR of 4.5 gives a CLmax of 1.56.
With 800lb and 111 sq.ft wing area this would give a stall speed of 62.3 ft/sec (68 km/hr or 37 kts).

[John Farley]

Thanks Owain

[blue up]

Thanks, everyone.

You've been a great help. It looks like I'll need to go on a diet and/or make the airframe do likewise. Not much surplus to lose on either!

[WeekendFlyer]

Just one caution I would add - don't take a 2D aerofoil section lift coefficient and use it directly for a 3D wing. The 2D CL is always higher than the 3D CL, sometime much higher, unless you have an extremely large aspect ratio. Also any real 3D wing aerodynamics such as sweep, taper or washout will reduce the whole-wing CL.

As a rough guide, typical light aircraft will have a CLmax of about 1.4 clean, and about 1.8 with plain flaps. To get CLmax above 2 you need some complex high lift devices such as leading edge slats, slotted flaps and possibly vortex generators. However, vortex generators are usually a fix, applied if things don't quite work out as expected with the basic wing profile and high lift devices.

Can I recommend you get a good textbook on the subject? This is the one my degree students use:

Fundamentals of aerodynamics - John David Anderson - Google Books (http://books.google.co.uk/books/about/Fundamentals_of_aerodynamics.html?id=CaBTAAAAMAAJ)

[John Farley]

Weekend

You might like to read Owain's post. I think he agrees with you!

[Owain Glyndwr]

John,

You are right - I do agree with Weekend's comments - at least in principal. I would agree that a CLmax of 1.4 is more usual for GA aircraft, but the sectional CLmax of the Gottingen 535, at least as shown in the cited reference, is significantly greater than that of more usually used airfoils so I was content to let it run as 1.56 CLmax as a ballpark figure.
To be more precise would entail calculating the span loading to establish the relationship between peak local CL and the average wing CL - something for which I have neither the time nor the inclination.
I would say though that on reflection, taking trim losses into account, 1.56 should be regarded as an upper limit.

[John Farley]

Owain

I must say one look at the 535 shape and I was back to the late 1940s and winding up a rubber motor!

[Owain Glyndwr]

John,

You and me both! I never did understand how that rubber model with the pot-bellied fuselage (Jaguar was it?) managed to win the Wakefield!

[blue up]

http://i82.photobucket.com/albums/j279/foggythomas/t-shirtdesign.jpg (http://s82.photobucket.com/user/foggythomas/media/t-shirtdesign.jpg.html)

http://i82.photobucket.com/albums/j279/foggythomas/goingforaweighing.jpg (http://s82.photobucket.com/user/foggythomas/media/goingforaweighing.jpg.html)

[Mark 1]

The FRED supposedly ran out of pitch authority before it could reach a true 1G stall, but quoted speeds are prone to all sorts of potential errors:

Was the pitot static system calibrated? static errors especially can yield large errors at low airspeeds.

Was the measurement made at zero thrust? - Idle settings can vary considerably.

Lift can also be generated from the fuselage and tailplane, though it's hard to imagine the Fred is particularly effective in that respect.

Aerofoil data generally applies to a semi-infinite wing as the wind tunnel set-up tries to avoid span-wise flow and end effects.

So there are a lot of real world effects that need to be considered in calculating stall speeds.

VGs should reduce stall speeds by keeping the flow attached at high Alpha thus increasing Cl(Max) but their effect varies considerably between different aerofoils.

[blue up]

I'd need to lose 2 kts from the theoretical figure from Owain above so VGs might be a graet help. Mine is also 22 lbs lighter than the 800lbs figures. I could ditch the radio, the exhaust silencer system and a few smaller items.

Having VGs on the underside of the tailplane ought to be worth trying. Also, a stronger rubber band for the engine.