Understanding how fins generate lift is a big part of improving their design.
And the truth is, when you strip it right back, it's pretty simple.
It has everything to do with the foils.
The curved surfaces on the sides of your fins accelerate water-flow, which you can see in the CFD image below.

See the way the streamlines change to orange as they curl around the leading edge? - That indicates the water there is running faster.
At the same time, the inside surface of the fin redirects the flow.
See in the CFD image below how the angle the water-flow is running at changes between the front and the back of the fin?

In this simulation the water is being shot at the fin at an angle of 16 degrees.
As you can see it exits the back of the fin a lot straighter than it enters.
If you look at the fin from above, you get a good perspective of the total picture.

The flow gets curled around the foil - which is sitting on the rail-side of your board and on the other side of the fin it gets pushed inwards.
When fluids run faster they have lower pressure than when they're running slower.
That's the science behind why airplane wings can make planes fly through the air, or birds can soar on the wind without flapping their wings.
Wings and fins use the same physics, it's just that air is a fluid made up of tiny stuff you can't see while water is made up of other tiny stuff you can see.
And where the lift being generated by a wing is used to create flight, on a surfboard it is pushing your rail into water.
The feeling of the fin pushing your rail into the wave and the rail pushing back is what we, as surfers, describe as drive.
There are a few articles on the internet, for example, this one on Surfline which suggest only side fins create lift.
That's wrong.
The water flow still gets accelerated by the foil on a centre-fin through a turn.
It's just that because both sides of a centre fin are fully convex, like in the picture below, you get less lift because the water is redirected less sharply.

When you move to using foils with a flat inside surface, like in the picture below, the water gets redirected more than on a symmetrical foil.
This means you get more lift, but also more drag when the fin is running straight through the water.

And when you add concave (like in the picture below) you get more lift again.

The trade-off, and there's always a trade-off with design, is when you add a lot of concave you might get a lot lift through your turns but you'll also get a heap of drag down-the-line.
The same thing is true if you make the fin thicker but leave the inside surface flat - you get more lift because the water flow gets accelerated more around the bigger curve on the outside.
But you still get more drag when you're running the board down-the-line (although a lot of data from the Australian Maritime College's water-tunnel and our CFD indicates the trade-off is less drastic than using concaves).
None of this is new science the surf industry came up with.
The foils on fins have always been inspired by aeronautics.
When I talked to Bob McTavish about making the first modern fin with George Greenough, at Alexandra Headlands on the Sunshine Coast in the 60s, he said he'd read basic texts about airplanes.
The result was that even during the D-Fin log era, in the 1950s, Bob was placing the thickest point on his fins a third of the way along the base.
The foil doing that creates is a National Advisory Committee for Aeronautics (NACA) four series - like the one pictured below.

NACA was the precursor to NASA and between 1915 and 1958 its engineers made huge advancements in the science of airfoils and flight.
During the end of the twin fin era Mark Richards introduced flat-sided foils to Australia, I believe he learned the trick in Hawaii although I'm not sure who came up with it.
The early twin fin pioneers were also the first surfers to start using toe-in (where the fins point in towards the nose).
Flat sided foils then dominated side fins until the 90s when Naval Architect Andy Dovell began collaborating with FCS co-founder Bill McCausland.
Bill and Andy eventually used a $1 million Commonwealth Grant to test dozens of different foil and fin combinations in the water tunnel at the Australian Maritime College, near Launceston, in Tasmania.
A lot of the data that project generated remains the most reliable information available today (although FCS is now corporate-owned and all of the people involved in the project have either moved-on or being forced-out).
The fin that came out of Bill and Andy's work was called the H2 - or Hydro Fin 2.
The foil Andy Dovell eventually put on the fin was actually designed by Professor of Aerodynamics Michael Selig and John Donovan who works at Boeing.
It was a foil designed for hand-propelled gliders, model planes that aerodynamicists love making for fun.
As you can see in the image below, the Selig-Donovan 7043 airfoil was a lot thicker than the standard but because it was designed for gliders it had really low-drag down the line.

FCS never publicly disclosed the fact they'd grabbed a foil developed by people outside of the company - something that only became apparent through my research.
My personal opinion is this happened because shortly before the H2 was launched Macquarie Bank conducted a hostile takeover of FCS - forcing out Bill McCausland who is a legend and was a trail-blazer in terms of introducing real fluid dynamics to fin-design.
These days FCS is part of the Gowings corporation and it would be great to see the new owners recognise Bill as part of the company's heritage.
Around the same era, in California, a man named Curtis Hesselgrave began working with Futures founder Vince Longo.
Curtis was a windsurfer and close friends with Chuck Ames (True Ames Fins).
Together with Bob, George and others they'd used texts written by engineers at NACA to improve windsurf fins throughout the 80s and 90s.
As Curtis, who has sadly now passed away, explained to Californian shaper Christian Beamish in this article he eventually got hold of the NACA foiling algorithm from NASA.
This let him design foils specifically for side fins.
Vince Longo, a mechanical engineer, then used early CAD software and CNC routing to take the foils one step further - experimenting with extreme amounts of concave and twists.
The result was Vince's Reverse 3/2 fins where Vince studied NACA catalogues to find different foils that would match in with a fin that twisted inwards at the tip.
The two big fin companies labelled the airfoils they were using as the Vector foil (Futures) and "Inside Foil Technology" (FCS).
In my opinion, the way that using airfoils on side-fins has been hysterically over-marketed leads to a lot of surfers paddling out expecting a crazy increase in performance.
And the feedback from the average guy is often just - "I couldn't really feel any difference."
The fact is, when you see the data on how different they are, you realise the effect is real but subtle and you need to make big changes to create big differences.
That's where what we are doing is a little different.
We use two-dimensional computational fluid dynamics and more modern foils to match the foil to the fin we are trying to make - a trick learned from Belgian surfer, windsurfer, engineer and all-round legend Hans Robeers.
We then test our foils on different templates in the surf, or in 3D CFD.
And later this year we'll be testing three of our designs in the Cavitation Research Laboratory tunnel at the Australian Maritime College - giving us the most reliable data available.
Ultimately, while there's a lot we know about fins and how they work this is really just the start of the journey.
But being able to control how much lift and drag different fins create is the key to making truly better fins.