Welcome to the Deep Dive. So today we're getting
into something that is a pretty fundamental shift
in logistics. It really is. For almost a century,
right, moving packages was all about discrete
math. You know, nodes and edges on a graph. The
class that transportation brought. Exactly. But
that model just completely collapses when you're
talking about, say, Puck's drone fleet in Milwaukee's
historic third war. Oh, it's a combinatorial
explosion. You can't. The old models for trucks
and set routes, they just, they break down. You
have a massive swarm in continuous airspace.
So it stops being a math problem. It stops behaving
like a series of individual calculations and
starts behaving like a physical substance, like
a fluid. So they threw out the old formulas,
things like the Bobula -Forsyth calculation.
Yeah, that's just for optimizing a single object,
like a bullet. Here they turn to the Navier -Stokes
equations. To create what they're calling laminar
logistics. Right. And what's so fascinating is
they stopped trying to optimize the drone itself
and started optimizing the flow of the whole
fleet. The city is now mapped as a, well, a porous
medium. Okay, let's unpack that central analogy
a little bit. When you say pressure, you're not
talking about air pressure. No, not at all. Think
of it as logistical potential or demand urgency.
So the Milwaukee public market, which is always
busy, that's the high pressure source. It's the
perpetual source, yes. And a customer order,
say, from the Corcoran lofts, that instantly
becomes a low pressure sink. The drone fleet,
the fluid, just follows the steepest pressure
drop. It's physics. And every fluid has friction.
Exactly. Which here we call viscosity. Viscosity
maps directly to the energy cost of complexity.
So not just physical friction. No, it's operational
friction. You lose energy from, say, Sharp, inefficient
turns, those are high -viscosity movements, but
also from regulatory constraints. Wait, regulatory
friction? How does an FAA rule act like molasses?
Okay, so take the FAA's Part 107 rule visual
line of sight. An operator has to be able to
see the drone. Right. We can assign areas where
that's tricky, like near the Italian Community
Center during a big event, an extremely high
viscosity value. The solver's job is to minimize
that viscous dissipation. So the path it calculates
is naturally smooth, efficient, and compliant.
All by itself. All by design. No need to pre
-program no -fly zones in the traditional sense.
I love that. And it's not just drones in the
air. This is a hybrid fleet, right? Multi -phase
flow. That's the term. Drones are the low -friction
air fluid, the free stream. The ground droids
are the ground fluid stuck in the high -friction
boundary layer of the street. And they can switch
between them. Yes, through the condensation maneuver.
If the air viscosity gets too high, maybe a sudden
gust of wind off Lake Michigan or restricted
airspace, a drone can land on a droid at, say,
Catalano Square. It transfers the package. So
the mass moves from the air phase to the ground
phase. And completes the last mile, even when
the air is basically prohibitive. It's incredibly
resilient. Which brings up the big question,
right? If it's all based on physics, how does
it handle, well... chaos what happens when a
fire truck just you know blocks broadway yeah
that's the beautiful part a traditional system
would frantically try to recalculate thousands
of individual paths it would be a mess a huge
processing lag for sure but the fluid model it
handles turbulence instinctively the blockage
is like a wall appearing in the flow Physics
dictates that a pressure wave instantly propagates
backward through the fluid. So the drones react
before they even get there. They slow down and
divert organically based purely on the change
in flow dynamics. It's true self -organization.
And what about that FAA line of sight rule we
talked about? How does it make a drone physically
stop? That's handled by what's called a visibility
scalar field. As a drone nears an area where
that visibility factor drops to zero, the effective
viscosity in the calculation approaches infinity.
The fluid just freezes. It literally freezes.
Flow into that non -compliant area stops. It's
a physics -based enforcement mechanism. So the
real genius here, it seems, is the shift in perspective.
You're not tracking individual particles anymore,
that Lagrangian view. Exactly. You stop caring
about the particle and start managing the total
flow field, the Eulerian view. Yeah. The system
becomes completely self -aware. It's incredible.
And if you think about the bigger picture here,
the Navier -Stokes model takes things that used
to be seen as just obstacles. like wind, or the
urban canyon effect, where tall buildings degrade
GPS signals. It maps them. Signal degradation
becomes signal viscosity. It uses these forces
not as problems to avoid, but as known terms
in the equation to find the truly optimal path.
Which leaves you with a final thought. It does.
What does it actually mean for our infrastructure
when physics problems from centuries ago become
the most elegant, self -organizing solutions
for our most modern logistics challenges?