You may know from hard experience
that having to push the rowboat through the water with any
worthwhile speed is not all that easy. Since a rowboat displacees
its total loaded weight in water, you have to move that water
bodily aside to get the boat ahead. Water, at say 62 pounds per
cubic foot, has a good bit of density. Thus it is somewhat
reluctant to move aside just to let you through. Here we come up
against the water's inertia, a kind of laziness.

The Air's Viscosity

Like air, water also has viscosity
or stickiness. While you are moving your rowboat through the
water, the flow of the water creates skin-friction on the wetted
hull-surfaces. Thus while rowing you have to overcome two
different kinds of forces. There's the inertia, caused by the
water's density, and the friction, caused by its stickiness.

Let's say you are moving the boat
through the water at a speed of only one mile per hour. So little
water is now moving aside that most of your energy goes to
overcoming the skin-friction force of the water.

Then you start rowing at a speed
of ten miles per hour, the bow-and stern-waves show that you are
spending most of your energy moving the water aside. You now have
to overcome the inertia of the water caused by its density rather
than overcome the friction caused by the water's stickiness. Thus
when going slow, the ratio of friction-work to inertia-work is
high. When going fast, the ratio of inertia-work to friction-work
is high.

The Air's Density

Now when you go out flying, you
want your airplane to glide smoothly through the air. The air
should flow over wing- and fuselage surfaces with a minimum of
disturbance. While air is not nearly as dense as water, (GIVE
FIGURE) it does have a certain density. Thus the air is also
somewhat reluctant to move aside so your airplane can get through.
Thus with your airplane as in the row boat, you also find you are
up against the two important characteristics: density (inertia)
and viscosity (stickiness).

The British scientist and Engineer
Osborne Reynolds discovered these two main parameters years ago
during his research into the flow of liquids in pipes. He found
that laminar flow or turbulent flow depends only on the ratio of
the inertial forces over the friction forces. This ratio of
viscosity over density scientists call the "kinematic
viscosity." For air at the standard temperature of 59
degrees Fahrenheit at Sea Level the value for this ratio is

This standard numerical value for
the kinematic viscosity, actually the ratio of viscosity over
density, and the resulting value for the kinematic viscosity,
forms the first part of the famous Reynolds Number formula.

Reynolds also showed that we must
take two other factors into account. The first is the velocity or
speed with which the air moves over the surface. For your
airplane, this is its flying-speed. The second factor is the
length dimension of the surface. For the wing, for example, this
is the local chord-length. For other parts, it is just their
length dimension.

Our calculation of the ratio gives
us a simple four-digit number. We can use it without ever having
anything to do with the actual values of either the density or
the viscosity. Let's see how we get that number:

Speed
x Length

Reynolds Number =

-------------------------------------------------

kinematic
viscosity

This is the same as multiplying (Speed
x Length) by the product of

u / (1.0 / 0.000156927),

which gives us the number 6372.
The complete formula is

Reynolds Number Re = 6378 times V(fps)
times L(ength) in feet. It's that simple!

Density and Viscosity

The density, viscosity, and the
kinematic viscosity all have in some way the unit (ft) in them.
Therefore, in the formula, speed V and length L are respectively
in feet per second and in linear feet.

For airspeed in miles per hour,
because one mph = 1.46667 fps, we use the number

6378 x 1.46667 = 9354.

For airspeed in knots the constant
is 10767. For the dimension in inches, like for the chord-length
of model airplane wings, the number to use with speeds in mph is
9354/12 = 780.

Here's a simple example for a wing
with a 10 feet chord at 100 mph

flying speed, at Sea Level and
"Standard Day" conditions.

Re = 9346 x 100 x 10 = 9346 x
1000 = 9,346,000.

Per 100 mph of flying speed at sea
level, the RN is roughly equal to 1 million per foot of length.
Thus we can calculate the Reynolds Number for any chordwise
position on the wing or any lengthwise point on the fuselage, and
for any specific flying speed and density altitude. In general,
for full-scale airplanes the nearest 100,000 or even half million
figure will do.

In flight the wing's Reynolds
Number is of course continuously growing. It starts at zero at
the stagnation point in front of the wing's leading edge. While
the air flows aft, the Reynolds Number continuously increases to
its maximum value at the trailing edge.

With his famous formula, Osborne
Reynolds gave us the master key to practical aerodynamics. His
work makes it possible for us to make a direct, practical
comparison of the boundary layer flow. On the wings and on other
parts of our airplanes. Without it, modern aerodynamics would not
have been possible. Our hats are off to him!

The Practical Significance of
the Reynolds Number.

The resistance experienced by a
wing in flight is a function of the Reynolds Number. Normally,
the Reynolds Number is the decisive factor in the air-flow in
determining whether the inertial effect or the viscous effect
wins. Let's take a look at what the Reynolds Number values
roughly tell us about airflow and drag.

If the Reynolds Number is large,
the viscosity effect is small. For the for us practical values
the inertia or density forces dominate, and the parasite drag
increases with the square of the velocity. However, although the
viscosity is unimportant, it may still affect the very thin
boundary layer, leading to the creation of turbulent flow.

Thus the importance of the
Reynolds Number is that it tells us the type of flow we can
expect. It tells you whether you can hope for having laminar flow
over the wing and other parts of your airplane. A low Reynolds
Number gives laminar flow while a high Reynolds Number gives
turbulent flow. For both a laminar and a turbulent boundary layer
increasing Reynolds Number gives lower skin friction drag.
However, because of the higher energy loss in the boundary layer,
a turbulent layer always has higher skin friction drag.

The Critical Reynolds Number.

Near the wing's leading edge the
Reynolds Number is relatively low.

Especially on a smooth wing
surface, the boundary layer flow will be laminar at first. With
increasing Reynolds Number, further downstream at some chord-wise
location it reaches the local critical Reynolds Number.

This is when and where the
boundary layer transitions to turbulent flow. The value at which
it does so we therefore call the transition or critical Reynolds
Number. This is the most important factor in determining
transition to turbulence.

The change from laminar-flow
conditions to turbulent-flow conditions at the critical Reynolds
Number is not definite. The ranges of the Reynolds Number under
which laminar- or turbulent-flow conditions exist depends much on
the shape and (mostly) on the surface finish. It also depends on
such factors as the initial steadiness of flow, absence of
vibration, etc.

On the average (poor) wing surface
usually it occurs at Reynolds Number values of at least 100,000,
and from there up to 500,000. Under ideal conditions it is
possible to maintain laminar-flow conditions for relatively very
large values of Reynolds Number. However, such boundary-layer
flow conditions are unstable. Keeping them stable is the big
trick.

The fastest homebuilt airplanes at
present obviously have accomplished this, as shown in their very
high speeds on relatively low power.

Frictional Resistance (Profile
Drag) and the Reynolds Number

The profile drag of a streamlined
body varies with the Reynolds Number.

At higher Reynolds Number values
the air flow is turbulent. Larg local fluctuations in the
airstream velocity occur close to the surface. The irregularity
of the turbulent-flow conditions results in much higher energy
loss than if the flow were laminar. This accounts for the
increased drag accompanying turbulent flow.

In these turbulent flow
conditions, some of the pressure force driving the flow speeds up
the eddies. Thus the effect of the viscous (sticky) surface flow
on the wing's aerodynamic characteristics is to create a drag
force. This drag force will consume a good bit of horsepower.

Low Minimum Drag

Low minimum drag at high Reynolds
Numbers is the most important aerodynamic characteristic of an
airplane. With laminar-flow conditions retained up to higher
Reynolds Numbers, the drag will be very much lower.

The state-of-the-art GlassAir,
Lancair, and Questar fiberglass homebuilt airplanes are good
examples of this. It requires extreme degrees of accuracy of
surface finish and laminar

flow conditions. Difficult to
achieve, even more difficult to keep. Even slight disturbances
like small particles of dust or insects cause the flow to become
turbulent. Up goes the drag.

Although skin friction is not the
only kind of resistance, it forms a large portion of the total
drag. Extreme care in manufacturing a very smooth surface made it
possible to keep laminar flow at very high Reynolds Numbers.

The aim is to find some method by
which we could avoid turbulent flow altogether. Replacing high-drag
turbulent-flow by low-drag laminar-flow at high Reynolds Number
reduces the horsepower and fuel requirements a good deal. The
improvements in both speed and economy of power are very
worthwhile.

Some Reynolds Number Figures.

The Reynolds Number for full-scale
flight varies from about 2,000,000 for small slow-speed airplanes
to 20,000,000 for large high-speed airplanes. Here are some
figures for a couple of light airplanes, at 75% cruise speed. We
use the formula Re = 9324 x V(mph) x Av.chd.(ft).

VP-2

9346 x 87 x 4.815

=

3 904 248

BD-5

9346 x 200 x 2.235

=

4 167 828

Cessna 150

9346 x 108 x 4.800

=

4 833 562

Cherokee Cruiser

9346 x 124 x 4.857

=

5 615 547

T-18

9346 x 173 x 4.130

=

6 661 905

Questair Venture

9346 x 280 x 2.62

=

6 856 226

Questair Venture

9346 x 345 x 2.62

=

8 447 850

RV-4

9346 x 175 x 4.780

=

7 799 526

Bonanza V35B

9346 x 181 x 5.400

=

9 113 278

As you go up in altitude, the
density of the air decreases. Because of the lower temperatures,
the viscosity increases. All this only slightly changes the
Reynlds Number.

For any altitude and temperature,
under standard atmospheric conditions the air's density and
viscosity are constants. Thus when calculating the Reynolds
Number for flight at altitude, we must use the proper figures.