Anders wrote:
First, I'd like to say that I am no professional aerodynamicist, and the
following text may contain errors. I'd be happy if someone points them
out!

About Reynolds numbers:

Let's say you're a pioneer of flight, and you want to build an airplane
that can fly. How big a wing do you need? To answer this, you could
simply build a wing, put it in your pioneer-wind tunnel, and measure
the forces on it at the speed you think your airplane will be able to
attain with the pioneer-engine you have available. Let's say the wing
wasn't big enough. Now, what do you do? You have to build another one!
And another one... etc, until you get it right. You don't wan't a too
big wing (weight!), and not a too small (can't fly!).

Anyway, this quickly grows old. Someone said: Why can't we predict how
much lift a given wing will have without building the darned thing
every time?

So someone set out to build lots of different wings, and tried to see
if there was some kind of pattern to the amount of lift different wings
gave. Let's see, this one over here is 1m wide, and gives 1N at this
speed, but that one over there gave 2N at the same speed. Hmm, why..
oh, it's twice as wide, but identical otherwise! Okay, lift seems to
increase linearly with wingspan! And people built lots of wings, and
thought hard, and came up with a formula:

Lift = chord * span * CL * Velocity * Velocity * airdensity / 2

Whe
chord = Width of wing, from leading edge to trailing edge
span = Length of wing, from tip to tip
velocity = The relative forward speed of the wing in relation to the
air
air density = The weight of air, per volume (1.2kg / cubic meter)
CL = Lift Coefficient, (varies with angle of attack, and reynolds
number!)

Anyway, this worked pretty well.

The was just one problem! When you build a 30 cm (1') wing, and it
gives 10N of lifting force, you'd expect the same kind of wing, but 3m
(10'), to give 100N (if it has the same chord), at the same speed! But,
this did not occur! Rather, it turned out, that when you take a small
wing, and make it many times bigger, or run it many times faster
through the air, the above formula doesn't work anymore.

When does it work? Does speed have to be the same? Does chord have to
be the same? No! It works when the Reynolds number is the same!

So, if you build a small wing, and run it in a wind tunnel with a
different medium (perhaps water), and this makes the reynolds number
the same as it will be when your real aircraft flies its real mission,
you can expect the lift equation above to 'work'.

So, the Lift Equations allows the lifting force from a wing to be
predicted (very handy when constructing aircraft). But the lift
equation only works when supplied with a CL measured at the same
Reynolds number as you'll be flying at! So you need the Reynolds number
in order to be able to use the lift equation!




Building on your response, I should mention that lift coefficients are
sometimes based on cross section area perpendicular to the wind, rather
than on chord times span. The former gives bigger numbers than the
latter method. So a flat board perpendicular to the wind was sometimes
given as Cl = 1 to 1.2, whereas a flat board at zero incidence might be
given as span times chord and make the contrast between the angle of
attack of a flat board for AoA = 0 versus AoA = 90 look even look bigger
than it already is.

Brian W