Hi,

Does anybody know how the Reynolds number is used during an aircraft design process? :spinnyeye

Thanks,

Reynolds number (Re) is basically the most important parameter for aircraft design, at least when you're traveling slower then Mach 0.7 or so. Above that, then both Reynolds and Mach numbers are the most important. You don't really use it directly in formulas like you do Cl or Cd, it's more of like, Re kinda dictates what you can expect the airflow to do over a body. I'm really not sure how to explain it, try reading a beginning text on aerodynamics. Introduction to Flight by John D Anderson is a good place to start. There was also a big thread on Reynolds number here a while back, that might explain things better.

Thanks for the input Daniel,

I've read some few books on the subject and my conclusion so far is that Re is a sort of a non-dimensional number resulting from several variables, such as the air viscosity, airspeed, air density and the wing chord.
And that is based on a formula that looks like:

Re = (air density/air viscosity) x airspeed x wing chord

It seems rather straightforward at first sight, as one gets the idea that with a small model, the air density/viscosity is much more a dominant factor, whereas a full-sized aircraft exhibiting much greater airspeed and wing size, mass inertia becomes more dominant.

As far as I understood it's a mathematical explanation, e.g. why a small-scale model behaves differently in the air compared with the full-sized counterpart.

But I still have no idea how the aerodynamicists actually use the Re number along with other dimensions or on its own as a useful designing "tool".

Cheers,

The most important factor in considering the effect of Reynolds number is that not only does a given aerofoil offer different performance factors at differing Re numbers, but different aerofoils show 'different differences' (if that makes any sense) so that you can that such an such an aerofoil is fine above a given Re number but poor bleow it, whilst another aerofoil may be worse than the first one at higher Re numbers but better atlower ones. This is why, for example, R/C pylon racers don't use the same aerofoils as lightweight F/F gliders.
Mike

Ok, I think I understood your point.
Referring to the formula and assuming the same weather condition (the same density/viscosity) the Re will increase as the airspeed and/or chord increases. There is no reference to the airfoil type, however different airfoils may produce different airspeeds at the same motor thrust…
So, one may say that the higher the Re number is, the better aerodynamics characteristics we get?

Cheers,

That's pretty much it. Another trick to help "see" how the airfoil works is to look at the polars for a number of Re's such as we see a lot these days for glider airfoils.

At lower lift coefficients and higher Re's and speed you're working the higher Re curves down near the low drag area. But as you pull that model back towards higher lift and lower speed the lift coefficient goes up while the Re goes down and you sort of "step" to each of the next curves in turn as the Re shifts downwards and the Cl upwards. So for a single model design the Cl vs Cd curve is a single curve that cuts across the other "windtunnel" curves in a way that describes the model under consideration.

It also raises the point that you can't consider only the one curve for an airfoil when applying it to a given model. Saying that you want one airfoil because it has low drag at high speeds ignores the fact that you have to slow it down during landing. At that point the lower Re curves become significant and if there's any bad charactaristics then you wind up with a model that "likes to be landed hot" without ever realizing the real reason started by ignoring that low Re portion of the curves and choosing a bad airfoil in the first place.

Here's a relatively representative polar for a series of Res... note the extreme change in drag at the lower values, as Ben noted.

smaller the better

The most basic formula for local Reynold's Numbers is this:
((Air density)*(Airspeed)*(Chord))(Absolute Viscocity Coefficient)

Where the absolute viscoscity coefficient = 1.7894x10^-5

The units are standard SI. This will give the Reynold's number at the trailing edge.

Reid

Hi,

Thanks a lot for your responses.
So, one may say that a given airfoil has different Re depending on the weather and on the airspeed, but a larger airfoil has definitely a larger Re than a smaller one, providing the same weather and airspeed.

A larger Re produces a thinner boundary layer, which means less drag and better stall characteristic.

Please correct me if it sounds untrue.


Cheers,

Yes, I agree that one easily may get such a conclusion at first sight.

But according to statements found in some books, the Re applied to a wing chord is not the same as the Re inside the boundary layer itself.
When the airflow meets the wing, a stagnation point occurs at the leading edge (LE) where Re is zero. There the flow is divided to pass above and below the wing.
As the boundary layer flow moves along the wings surface, the Re varies and at every point is proportional to the distance measured around the airfoil between the actual point and the LE.
Thus the Re in the boundary layer increases as the distance from LE increases.
Since the boundary layer flow has to travel longer way from LE to TE with a thicker airfoil, the thicker will have higher Re inside its boundary layer than the thinner one assuming the same airspeed.

Cheers,

adam_one,

The Reynold's number, as you say, is a dimensionless quantity that characterizes the flow. It has many applications, and can be a complicated topic. In the context of wings, higher Reynold's number generally means greater resistance to stall. This means that the maximum lift is higher at higher Reynold's numbers, since you can operate at a higher angle of attack before stall occurs. Higher Reynold's number also generally means that a flow will become turbulent sooner than a low Reynold's number flow, which means that a low Reynold's number wing is more likely to suffer from laminar separation, which causes other performance differences between high and low Reynold's number wings.

For full scale aircraft, Reynold's number is probably not used in the design process per se, because it is almost always the case that the Reynold's number is known to be in a 'safe' range for all flight conditions, and there is not much variation in performance for the moderate variations in Reynold's number. For model aircraft, this is not always the case, and we my need to be more aware of Reynold's number in the design process. For example, a sailplane with a very high aspect ratio wing, which is desirable, may end up with such a small chord that the Reynold's number of the wing moves down below a critical value. This can also happen with wingtips of tapered wings, or stabilizers which are smaller than main wings. All these issues arise because the range of Reynold's numbers at which model aircraft is in the neighborhood of a critical Reynold's number, where performance changes drastically. If you find that part of your wing will be operating at a problematically small Reynold's number, for example, then you do indeed have a design decision to make, to deal with the potential problems.

banktoturn

Banktoturn, thanks for the valuable info.

I think the picture is gradually becoming clearer to me.
As I understand it, a thin airfoil with a sharp LE will stall at smaller angle of attack than a thicker one with a well rounded LE.
I think this is a fact that may often be overlooked when choosing a profile to a model aircraft.
This is particularly important with small models since they fly at much lower Re numbers than the full-sized counterparts.

Cheers.

A futher note on Reynold's number while I am at the keyboard this morning. It becomes important when selecting wind tunnels to be used in the advanced design process of airplane development.

There are a lot of wind tunnels about the country, some designed for low speed (landing, takeoff gear down situations), some transonic (Mach number between .5 and 1.3) and others polysonic (Mach number between .5 and 2.5 or so). The average low speed wind tunnel is larger than the high Mach number wind tunnels. Occassionally there are some really nice ones like those at the Air Force's AEDC facilities that have 16 ft sections. Most supersonic tunnels though are in the 4 ft section size.

It has been found that for each of the flight conditions to be matched that the higher the Rn of the tunnel the better quality the data is. There is also a wing span to tunnel span ratio that should be maintained (based on previous test experience). So the model to be tested is a balance of these things (with the budget constraints thrown in) with the desire to maintain the highest Rn possible.