Re: Why do longer Skis/Snowboards go faster than shorter ones?

Greetings, Case:

Unfortunately, there is no single/simple Answer for your Question.
At least three major factors play a part, and any one of them,
by itself, could be the crucial difference.

First, while you specified the lengths of the skis and snowboard,
you did not specify widths.  The total amount of friction between
these devices and the snow depents partly upon the total amount
of surface area that contacts the snow.  A snowboard that is wider
than two skis could easily have more total surface area in contact
with the snow, and more total friction, and thus be slower.

Next, there are the various varnishes and/or other coatings that are
applied to skis and snowboards, to reduce friction.  If the coating
on the skis is better quality than the coating on the snowboard, then
again the latter will experience more friction, and thus be slower.

Finally, there is air resistance, and at least two different aspects
of it come into play here.  For the first, consider the position of
the body taken by someone on skis, as compared to the position of
the body taken by someone on a snowboard.  The former is facing the
oncoming air, while the latter is posed sideways.  By inspection, it
is obvious that the latter offers less air resistance than the former
-- but the person directly facing the "wind" can crouch in such a
way as to reduce air resistance a great deal.  The snowboarder can
crouch, also, but SAME sideways surface area is still presented to
the "wind"!  Thus, if the skier can crouch enough, air resistance
will always be greater for the snowboarder -- who thus is slower.

For the second aspect of how air resistance is a factor in the
Answer to your Question, I need to begin by digressing into an
explanation of something known as the "Square-Cube Law".

********************
First noticed/described by Galileo, the Square-Cube Law
associates the strength and mass of an object with its size.
For example, consider a fat mouse:  It has pretty skinny legs
to support the weight of its plump body.  Now consider the big
legs that an elephant has, to support its body.  If you simply
enlarged a picture of a mouse to be the same size as an elephant,
you would plainly see that the mouse's legs are comparatively
much skinnier than the elephant's.  Why?

Well, if you started with a mouse having height/width/length
dimensions of X, Y, and Z, and simply doubled it to 2X, 2Y, and
2Z, then any area-related measurment of the mouse goes up by a
factor of 4 (or 2 times 2, because only two dimensions are
used to compute areas/squares), while any volume-related
measurement of the mouse goes up by a factor of 8 (2 times 2
times 2, because all three dimensions are used to compute
volumes/cubes).  As it happens, the strength of the mouse's legs
is an area-related thing (think "cross-section"), while the
overall mass and weight of the mouse is a volumne-related thing.
You know that the weight of the mouse must be carried by its
legs, of course.  So, if the ordinary mouse easily carries its
mass around on skinny legs, what of the double-sized mouse that
has 8 times the mass but only 4 times the strength in its legs?
They might break under the load!

As a result, all through Nature, larger animals have EXTRA
thickness in their legs, to increase their cross-sectional
areas, to thus have the strength to carry larger body weights,
with the elephant being today's extreme example.  (Yet the
Square-Cube Law has applied all through Natural History, and
the giant dinosaurs had legs of a thickness to put trees to
shame.)

There are plenty of other physical phenomena that are linked
in some way with the Square-Cube Law.  Several years ago I
decided that it can explain the traditional complaint that
parents have, about how their little kids run them (the
parents) "ragged".  See, the average little kid is about
half the size of the adult, and so has only one-quarter the
strength -- but also has only one-eighth the weight.  The
kid has twice the strength-to-weight ratio as the adult!
Trying to keep pace with the antics of little children is
something that no ordinary adult will EVER have an easy
time attempting, thanks to the Square-Cube Law.
********************

Now let's apply the Square-Cube Law to skiers and air
resistance.  Suppose Person A is half the size of Person B:
The math is easier to figure that way, but the essence of
the results apply to any two people of differing size, if
overall proportions are maintained.

The surface area presented by Person A is 1/4 the surface
area of Person B, so Person B will experience 4 times the
air resistance as Person A (ALL other things being equal).

Next, please note that air resistance is a Force, as in the
equation F=ma (Newton's Second Law of Motion: Force equals
Mass times Acceleration).  To figure how a mass accelerates
in response to air resistance rephrasing the equation as
a=F/m, and plugging in appropriate values.  (Person B has
eight times the mass of Person A, remember.)

So, for Person A, we shall use unitary values of Force and
Mass (exactly as in the prior rephrased equation), while
for Person B, the equation is (1/2)a=4F/8m.

Now, since air resistance attempts to SLOW DOWN a skier,
the results of this figuring is that we discover that air
resistance acts to slow Person B, the larger person, at
less than the rate at which it could slow the smaller
Person A (one-half the rate, in this particular case).

THAT is the second aspect of how air resistance can be
a factor associated with your Question.

One more factor, about which I don't know enough, involves
the change in friction between ski and snow, as the weight
of the skier increases.  Generally it is thought that
pressure can cause a thin layer of ice (and presumably
snow as well) to melt, forming water that acts as a
lubricant.  Thus the heavier skier might have yet another
advantage over the lighter, speed-wise, due to more
water/lubricant being present.

But I don't know that for sure, and anything else I might
add here would only be speculation, so I can only hope
that the things I do know have Answered your Question
satisfactorily.