NAVWEPS OO-BOT-80 
BASIC AERODYNAMICS 
forward stagnation point the local velocity 
is zero and the maximum positive pressure re- 
sults. As the flow proceeds from the forward 
stagnation point the velocity increases as 
shown by the change in streamlines. The 
local velocities reach a maximum at the upper 
and lower extremities and a peak suction pres- 
sure is produced at these points on the cylinder. 
(NOTE: Positive pressures are pressures above 
atmospheric and negative or .ruction pressures 
are less than atmospheric.) As the flow 
continues aft from the peak suction pressure, 
the diverging streamlines indicate decreasing 
local velocities and increasing local pressures. 
If friction and compressibility effects are not 
considered, the velocity would decrease to zero 
at the aft stagnation point and the full stagna- 
tion pressure would be recovered. The pressure 
distribution for the cylinder in perfect fluid 
flow would be symmetrical and no net force 
(lift or dragj wvuid rcsuit. Of course, thr 
relationship between static pressure and ~eloc- 
ity along the surface is defined by Bernoulli’s 
equation. 
The flow pattern for the cylinder in an actual 
fluid demonstrates the effect of friction or 
viscosity. The viscosity of air produces a thin 
layer of retarded flow immediately adjacent 
to the surface. The energy expended in this 
“boundary layer” can alter the pressure dis- 
tribution and destroy the symmetry of the 
pattern. The force unbalance caused by the 
change in pressure distribution creates a drag 
force which is in addition to the drag due to 
skin friction. 
The streamline pattern for the symmetrical 
airfoil of figure 1.7 again provides the basis 
for the velocity and pressure distribution. 
At the leading edge the streamlines are widely 
diverged in the vicinity of the positive pres- 
sures. The maximum local velocities and 
suction (or negative) pressures exist where the 
streamlines are the closest together, One 
notable difference between the flow on the 
cylinder and the airfoil is that the maximum 
velocity and minimum pressure points on the 
airfoil do not ,necessarily occtir at the point of 
maximum thickness. However, a similarity 
does exist in that the minimum pressure points 
correspond to the points where the streamlines 
are closest together and this condition exists 
when the streamlines are forced to the great- 
est curvature. 
GENERATION OF LIFT. An important 
phenomenon associated with the production 
of lift by an airfoil is the “circulation” im- 
parted to the airstream. The best practical 
illustration of this phenomenon is shown in 
figure 1.8 by the streamlines and pressure dis- 
tributions existing on cylinders in an airstream. 
The cylinder without circulation has a sym- 
metrical streamline pattern and a pressure dis- 
tribution which creates n-0 n_et lift. If the 
cylinder is given a clockwise rotation and 
induces a rotational or circulatory flow, a dis- 
tinct change takes place in the streamline pat- 
tern and p’ess.~re &str~‘“u~~oii, The vriocitirs 
due to the vortex of circulatory flow cause 
increased 104 velocity on the upper surface 
of the cylinder and decreased local velocity on 
the lower surface of the cylinder. Also, the 
circulatory flow produces an upwash immedi- 
ately ahead and downwash immediately be- 
hind the cylinder and both fore and aft stagna- 
tion points are lowered. 
The effect of the addition of circulatory flow 
is appreciated by the change in the pressure 
distribution on the cylinder. The increased 
local velocity on the upper surface causes an 
increase in upper surface suction while the 
decreased local velocity on the lower surface 
causes a decrease in lower surface suction. As 
a result, the cylinder with circulation will 
produce a net lift. This mechanically induced 
circulation-called Magnus effect-illustrates 
the relationship between circulation and lift 
and is important to golfers, baseball and tennis