camber at 40 percent chord, 12 percent thick- 
ness at 30 percent chord)--a fairly typical 
“conventionaal” airfoil section. The lift curve 
show a steady increase in cl with increasing 
RN. However, note that a>maller change in 
cr occurs between Reynolds Numbers of 6.0 
ad 9.0 million than occurs between 0.1 and 
3.0 million. In other words, greater changes 
in CI occur in the range of Reynolds Num- 
bers zhere the laminar (low energy) boundary 
layer predominates. The drag curves for the 
section show essentially the same feature-the 
greatest variations occur at very low Reynolds 
Numbers. Typical full scale Reynolds Num- 
bers for aircraft in flight may be 3 to 5@O million 
where the boundary layer is predominately 
turbulent. Scale model tests may involve 
Reynolds Numbers of 0.1 to 5 million where 
the boundary layer be predominately laminar. 
Hence, the “scale” corrections are very neces- 
sary to correlate the principal aerodynamic 
characteristics. 
The very large changes in aerodynamic 
characteristics at low Reynolds Numbers are 
due in great part to the low energy laminar 
boundary layer typical of low Reynolds Num- 
bers. Low Reynolds Numbers are the result 
of some combination of low velocity, small 
size, and high kinematic viscosity RN= ( 3 
Thus, small surfaces, low flight speeds, or very 
high altitudes can provide the regime of low 
Reynolds Numbers. One interesting phenom- 
enon associated with low BN is the high form 
drag due to separation of the low energy 
boundary layer. The ordinary golf ball oper- 
ates at low RN and would have very high 
form drag without dimpling. The surface 
roughness from dimpling disturbs the laminar 
boundary layer forcing a premature transition 
to turbulent. The forced turbulence in the 
boundary layer reduces the form drag by pro- 
viding a higher energy boundary layer to 
allay separation. Essentially the same effect 
can be produced on a model airplane wing by 
roughening the leading edge-the turbulent 
NAVWEPS DD-RDT-80 
BASIC AERODYNAMICS 
boundary layer obtained may reduce the form 
drag due to separation. In each instance, the 
forced transition will be beneficial if the reduc- 
tion in form drag is greater than the increase 
in skin friction. Of course, this possibility 
exists only at low Reynolds Numbers. 
1,n a similar sense, “trip” wires or small 
surface protuberances on a wind tunnel model 
may be used to force transition of the boundary 
layer and simulate the effect of higher Reynolds 
Numbers. 
PLANFORM EFFECTS AND 
AIRPLANE DRAG 
EFFECT OF WING PLANFORM 
The previous discussion of aerodynamic 
forces concerned the properties of airfoil sec- 
tions in two-dimensional flow with no consid- 
eration given to the influence of the planform. 
When the effects of wing planform are intro- 
duced, attention must be directed to the ex- 
istence of flow components in the spanwise 
direction. In other words, airfoil section 
properties deal with flow in two dimensions 
I while plonform properties consider flow in 
three dimensions. 
In order to fully describe the planform of a 
wing, several terms are required. The terms 
having the greatest influence on the aerody- 
namic characteristics are illustrated in figure 
1.28. 
(1) The wing r?rc11, S, is simply the plan 
surface area of the wing. Although a por- 
tion of the area may be covered by fuselage 
or nacelles, the pressure carryover on these 
surfaces allows legitimate consideration of 
the entire plan area. 
(2) The wing ~ptia, 6, is measured tip to 
tip. 
(3) The avcragc chord, c, is the geometric 
average. The product of the span and the 
average chord is the wing area (6X6=$). 
(4) The aspect ratio, AR, is the proportion 
of the span and the average chord. 
AR=b/c