I understand that golf balls have dimples to reduce drag, ultimately
increasing accuracy and distance.  Could these same principles be
applied to  smaller sized objects? Specifically gumball sized objects?

The reason for the dimples in a golf ball is to increase distance, but
not due to a reduction in drag.  When a golf ball is hit, backspin in
imparted, so a lift force is generated.  This is the same kind of
force that makes a curve ball curve.  The dimples increase the lift
force, increasing distance.

Coby1man, you are correct that the dimples reduce drag to increase
distance.  This seems counterintuitive, but it's true.

Airflow around the ball can be of two types, laminar or turbulent (for
better definitions than I could give, try googling "define: laminar"
).  Laminar flow is associated with slower speeds; turbulent flows
come about at higher speeds.  Turbulent airflow imparts less drag on
the ball than laminar flow does.  For a particular object, there is a
speed at which the type of flow turns from laminar to turbulent.  The
speed at which this transition occurs depends on several things,
including the surface roughness.  An object with a rougher exterior
will transition to turbulent flow at a lower speed than the exact same
object with a smoother surface.  The dimples increase the roughness,
decreasing the speed at which the transition occurs, so even duffers
like myself can get the ball going fast enough to take advantage of
this.  Golf companies do and have done lots of research on
aerodynamics and dimple patterns, to get the most out of this
principle.

As far as your original question goes, the speed required to reach the
transition from laminar to turbulent flow depends also on the size of
the object.  A larger object will transition to turbulent flow at a
slower speed than a smaller, similarly-shaped object with the same
roughness.  So if you go to smaller and smaller objects, i.e.
gumballs, higher and higher velocities will be needed to get to that
transition.  If your gumballs are rough enough and velocities high
enough, this could come into play.

Another approach to reducing drag is a sharp trailing edge, which
induces (by discontinuity in outline) the transition from laminar to
turbulent flow in the wake of the object.  Again it is somewhat
unintuitive; one might guess a sharp leading edge has more of an
effect on drag reduction, but a "blunt" nose is often the design of
choice.

Of course with a more or less spherically symmetric object like a golf
ball, the sharp trailing edge idea doesn't "compute".

Who's up for some gumballs with spoilers?

--mathtalk

rfitch- so how fast are we talking about?

on a gold ball there a alot of dimples and the dimples are very
shallow.  For the gumball to to work would you simple scale down and
keep the number of dimples or would you keep the dimple size width the
same and reduce the number of dimples?    Im assuming that the answer
might be in between ?  the large number of dimples would have a
stabilizing effect while at a certain point if the dimples are too
small the aerodynamics begin to work differently?
and if anyone is wondering I am thinking about gumball cannons....

A well-hit golf ball travels at 50 m/s.  The Reynold's number of flow
around a perfectly smooth golf ball at this speed is 100,000, so there
is no way the flow can be laminar.  The dimples do have an effect on
the location of the separation of the turbulent boundary layer, and
this is what causes the lift. To learn more about the lift force on a
golf ball, check out

http://math.ucr.edu/home/baez/physics/General/golf.html

I've looked into the matter a bit further and would like to make some
corrections.  While the overall flow around the ball is turbulent for
any reasonable speed, the same is not true for the flow within the
boundary layer, which is a thin layer of air around the ball in which
the average velocity of the air changes rapidly with distance from the
surface of the ball.  There is indeed a significant drop in the drag
coefficient when this boundary layer undergoes a transition from
laminar to turbulent.  For a smooth sphere, this transition occurs at
a critcal Reynold's number of approximately 500,000.  (The Reynold's
number is defined as Ud/v, where U=velocity, d=diameter, and
v=kinematic viscosity).  As the Reynold's number increases further,
the drag coefficient goes up again.  v for dry air at 20 deg. C is
.000015 m^2/s, and the diameter of a golf ball is .04 m, so with no
dimples, the transition would occur at a velocity of around 190 m/s. 
If it was possible to hit a golf ball this fast, the dimples would
cause the drag to increase, not decrease.  However, at the more
realistic velocity of 75 m/s, the Reynold's number for a smooth golf
ball would be 200,000.  Adding the dimples gets you to the critical
Reynold's number, and causes the boundary layer to go turbulent.  For
a smooth gumball (say 1.5 cm in diameter), the Reynold's number is
sub-critical (the boundary layer is laminar) for all sub-sonic
velocities.  There are two reasons not to get into super-sonic
velocities 1) I don't think your gumball gun will shoot that fast, and
2) the aerodynamics is different.  Dimples in the gumballs are likely
to be effective if the speed of the gumballs is greater than that of a
golf ball by the same factor by which the diameter is less.  That is,
since a gumball has a diameter of about 1/3 that of a golf ball, the
speed should be 3 times greater to take advantage of the same effect. 
This puts you in the range of 200 m/s, which is quite fast.  So unless
you have a very powerful gun in mind (if it's pneumatic, it should
have a barrel at least several feet long) the dimples will not help
you.

Thank you so very much!!  I really appreciate teh time and effort
behind your answers.

i know that this is far beyond the parameters of the original
questions but I am kind of determined.  So you are saying that dimples
would not help reduce drag in a gumball sized object but my final
question would be is there anything that would? withour dramaticaly
modifying the spherical shape..

How does turbulent flow make for a lower drag force? You would think a
laminar flow would have a higher drag force, than a turbulent flow? i
dont kno coudl some plz explain?

Here's a gross oversimplification.  If the flow across a surface is
laminar, then we can picture the effective size of the object being
increased by the size of the "boundary layer" next to the object. 
This boundary layer is the zone in which the airspeed must vary from
zero (relative to the object) at the boundary surface (no slip
condition) to the ambient airspeed (relative to the object) at the
outside of the boundary layer.

If the flow is turbulent, then we can picture the airflow "flickering"
around the edges of the object, so that its effective size is no
longer uniformly extended in all directions at the same time.  The
effective "cross-section" of the object is thus reduced (relative to
laminar flow) and so too the drag.

For a more rigorous treatment we should explore the energy dissipated
by the object into the air flowing past.

regards, mathtalk-ga