I wouldn't start with “how short”,
but rather with "how little bottom surface”. And with regards to that, it's
probably something a little less than 0.4 meters squared, but it will
depend on the conditions. That's a rough empirical (and a
quasi-theoretical) minimal surface area required to achieve the
proper level of the force of planing. It's not the only (empirical)
requirement however, as conditions do matter. For example, guns tend
to be longer, but very little of the bottom tends to be wet at any
given time. They're not only long because they catch the waves they
are designed for better, but they're dynamically more stable in terms
of user their friendliness. (Other strategies are available here, especially if you're being towed in.)
But people are pushing that frontier back too.
But it's my guess, that by 'how short'
you've assumed a lot more. (Likely obvious to most, but not to me
apparently.) That is, perhaps you've assumed that you've got to be
able to catch waves with a certain minimal level of ease. If so then
the minimum surface can increase, it depends on the strategy
employed. If the choice is to increase length, it's not because it's
required during surfing, but because it's required during
'catching'. The two [catching and surfing] are virtually two
different sports. But even then the limit is likely to be around 0.4
to 0.5 meters squared (see Tom Morey's a.k.a Y, 'The One', a fin-less
chip of a thing, slightly larger than your average skimboard.)
What tends to push board to be longer,
among other factors is that there is a minimum width which works for
us humans, and it's somewhere in 50 cm (20 in) to 58 cm (23 in)
range, give or take. It's amazing how little this width (usually appearing as the maximum width
of the board) varies over the full range of surfboard classes. Well excluding SUPs,
which seem to be breaking new ground(?) by pushing the full meter
barrier(?).
I'm not saying that the only way to
make a board that catches waves easier is to make it longer, just
that there is this standard, or constraint if you like, that tends to
make you go either thicker or longer, or both. This same standard
also constrains you when you try and go shorter.
Neither, by the way, am I saying that the only reason to go longer is to make catching waves easier.
The minimum surface area will change
with conditions, but collectively I believe it's in the 0.4 meter
square plus or minus range for the average mid-range kind of
conditions experience worldwide, the constraining dimension being
that 50-58 cm give or take, maximum width of the board.
kc