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LIFT
Airfoils
More streamlined shapes have less drag (See Slide 3 for airfoil images)
Drag on a Sphere
No Turbulence
Recall for Laminar flow (no turbulence) the streamlines around a sphere would be
irrotational and symmetric
The front of a sphere would feel high pressure drag force due to the wind but…
This drag force would be equal and opposite to the high pressure thrust (negative drag)
behind the sphere (similar to the force of gravity vs. the normal force)
Net result: a sphere feels no drag force

Turbulence
However, when the Reynolds number is large enough, vortices begin to form
The vortices stay attached until Re becomes large and then detaches from the sphere and
break down to turbulence (View photos)
Vortices have all types of different sizes and different flows and appear at different
lengths behind the ball
Breakdown of the vortices= turbulence Energy has to break down to smaller and
smallers scales, acting as a drag force and slowing it down
The vortices (and later turbulence) greatly decrease thrust on the ball=net drag
Richardson’s Rhyme: “Big whorls have little whorls that feed on their velocity, and little
whorls have lesser whorls and so on to viscosity” Large vortic structures breakdown to
smaller and smaller vortec structures, eventually into individual molecules which create
viscosity
Flow Separation
Drag on a sphere is caused by flow separation over its rear face The less the flow
separartes, the less the drag
Minimizing flow separation decreases drag and keeps the flow laminar
E.g The Golf Ball
Why covered with dimples? To make it go farther
The pressure difference which causes the drag on a ball occurs in a thin region near the
ball called the Boundary layer
Dimples
A smooth sphere has a laminar boundary layer that separates and causes a large wake
behind the sphere causes friction and the air sticks to the ball longer
A dimpled sphere has a turbulent boundary layer that speeds up flow around the sphere
and decreases the wake Increases the boundary layer, decreasing the friction on the ball
and keeping the flow around the ball longer
Less energy into resisting turbulence and more into moving forward
CFD example (computational flow dynamics), allows numeric examination rather than
just trial and error
Reynolds Number for Spheres
Chart represents drag coefficient vs Reynolds number
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