Speed on stilts: How do hydrofoils work?
Designing the ultimate boat for the Bond baddie.
Holding steady onto the wood frame of the water-taxi, I reached down and dipped my hand into Bangkok's oily waters. A crazy thought occured: If I punch the water hard enough, will it let me fly?
We all know what to expect of a James Bond chase scene, especially if it's on water. Bond will be in an elegant wood-panelled dream machine and the villains… well.
The villains frequent jet skis and black speed boats, barbarous creations favouring power over grace. But if they're really good, they'll be in a hydrofoil.
A hydrofoil has the brutal efficient look, but it also has something else; a cheeky transformative aspect as it rises above the water, neither plane nor boat… and you won't get away from it!
But what makes it work, what keeps it stable?
And if they're so good, why aren't they everywhere?
Let's take a trip through fast ferries, funky surfboards, foil-riding frigates and pedal powered oddities…
1: Drag, displacement and density.
Pedal boats are not generally known for their speed. You think of holiday pedalos off the coast of Sardinia with the kids, barely moving while you sweat under the Mediterranean sun to the tune of a splash-splash-splash from behind you. The boat yields momentum to friction and makes a half-arsed job of it, creating just enough chop to flick salt water onto your sunburn.
But see a person on a Jetcycle hydrofoil pedal boat and you'll notice a few things: Firstly the slickness of the design, second the driving position, lying well-back in a recumbent cycling pose. And thirdly, should you follow the rider for long enough in your eye, as his speed picks up over 5 or 6 knots, the whole skinny polished creation will rise up over the waves and, infuriatingly smoothly, speed away. You'd be forgiven a little jealousy.
Indeed, the top speed of a hydrofoil pedalo like that is about 20 km/h, just a shade away from Olympic rowing speeds, and many human-powered hydrofoil craft are drastically quicker again.
By what sorcery is this done!?
A traditional boat floats by displacement, meaning that it reaches equilibrium when the weight of the water displaced by its hull equals the weight of the vessel. This means the average density of the portion of the ship that's submerged must be lower than the density of the water it travels through: Ships aren't as heavy as they seem!
Sadly, that means that a ship unavoidably needs a massive wetted surface area on its submerged hull, with corresponding wake and frictional drag losses. This is bearable when the ship is moving slowly, but a real bind when it's going fast.
A hydrofoil on the order hand extrudes small wings, hydroplanes, underneath the hull that generate lift. Think like an aeroplane's wings, or a penguin’s, and think flying not sailing.
What this means is that for low or medium speeds a hydrofoil craft is actually worse than a normal displacement ship in almost every way, as there isn't sufficient velocity for the lift from the hydroplanes to perform their magic trick… but as the speed climbs, something special happens. The lift generated from those lifting hydroplanes, all on their own, starts to equal the weight of the vessel pushing down. When this happens, the hull will rise out of the water, drag will suddenly drop and speed picks up significantly.
With that big, draggy hull lifted out of the water the hydrofoil has become a different type of craft altogether, for water is 830 times denser, and 50 times more viscous, than air. With the bulk of the vessel now flying serenely over the waves, suspended on stilts in thin and yielding air, you can really move!
But how do you keep this speedy, stilt-walking beast stable?
2: Stability on stilts
Here's a hydrofoil wind surfer doing his thing. Yes, I know, why not make one of the hardest things you can do even harder by adding a hydrofoil to it? There's no helping some people.
Whoops, over he goes… hydrofoil stability, as it turns out, isn't straightforward.
A regular everyday boat is mostly kept stable by the same displacement buoyancy forces that keep it afloat: If one end goes up, buoyancy forces reduce but weight does not, and the other way around if one end goes down. With a well-designed hull this should give a measure of well-damped static stability. That doesn't apply to sideways (sway, surge) or yaw forces, but for a ship in motion hydrodynamic forces and good old fashioned drag will help out there.
Things are different for a hydrofoil: Once the critical speed has been reached, buoyancy forces are no longer significant, and hydrodynamic stability takes over. Once again, think ‘aeroplane’.
We'll start with heave stability. On a regular boat this is simplicity itself, as buoyancy must balance with weight, so any deviation gets corrected for. For a hydrofoil this is more complex, and more crucial too: If the ‘foils rise too high in the water they'll start crashing from wave to wave, making for a bumpy and dangerous ride. Too low in the water and the hull re-enters and you need to increase the power to get it out again.
3: Heave-Ho!
There must be an easier way to control the craft's vertical position in the water, and there are. Two of them, plus a third that doesn't work.
We'll dismiss the third one first. A foil's length is called its ‘chord’, and if hydrofoils are close to the surface, within their own chord length, the surface of the water will distort around them. For an example of this effect I always think of the seal-hunting killer whales on David Attenborough's incredible Frozen Planet, that used the surface distortion around their own bodies, as a group, to create waves that would wash cute hapless seals off the pack ice and into waiting cetacean jaws. They're complete bastards, killer whales, but smart ones.
Anyway, when it's a hydrofoil and not a killer whale, and you're not hunting for seals, the effect of bringing your foil too close to the surface is that it distorts the surface and lift plummets, which drives the foil back down again. In principle this should work to stabilize a hydrofoil craft, but life and the sea isn't a millrace, and waves exist, so to allow for this you'd need absolutely enormous foils, which wouldn't be efficient at all.
So to control for heave we either need active control or surface-breaking foils. Surface breakers adopt elegant U or V shapes, breaking through the surface at their extremities. On a surface breaking foil, if one end of the boat dips more deeply into the water then there's more foil generating lift, which pushes the boat back up. Likewise if it's too far out of the water then less foil is underwater to generate lift and so it dips back down again. It's a robust, passive way to create stability, but interacts with waves and so makes for a bumpier ride.
Fully submerged foils, by contrast, are wonderfully smooth but lack passive stability and so must be actively controlled by flaps and a control system that senses the boat's position (or just a bloke with quick reactions). This is a low resistance option that's good for high performance racers and fast moving military boats alike, such as the imposing Pegasus class patrol boat, a gun and missile-armed 48 knot speed machine fielded by the US Navy between 1977 and 1992.
You're not getting away from that!
4: Going faster… and faster! Surge control.
Like a helicopter, which is unstable for a whole bunch of different reasons, a hydrofoil has a weird relationship with speed. In most boats, drag (and the thrust you need to sail) rises in a steep curve as you go faster and faster, so to get more speed you need to add more thrust.
This is inverted on the hydrofoil because when it reaches something called the take-off speed it, well, takes off and starts behaving differently. In this weird regime you can accelerate even while reducing the power level of the engine, before things settle down again and sanity is restored.
The graph above shows the oddness of this. There are two distinct drag/ speed curves that you move between as you take-off and ease the hull out of the water. This means that at a given power level (points E and D on the graph) you can either be sailing normally at a low speed or flying fast on foils, depending on whether or not you've first achieved takeoff. Obviously the second state is better for fuel efficiency and getting to where you need to go, so if you've got foils it makes sense to use them.
5: Pitch control and fancy surfboards.
A wave rises, a surfer paddles to keep up with the rising swell of water behind him and is swept forward. As the gentle gradient becomes a hill, then a towering crest, the surfboard rides down and he stands.
Then the board rises on a knife-edge, beneath which a hidden wing lifts surfer and board together. Slicing out of the collapsing wave, the surfer starts a strange bobbing motion, rhythmically kicking down with his legs and instead of slowing down… he speeds up!
Hydrofoil surfboards are but one innovation in this strange nautical marketplace, but like every other hydrofoil craft they must obey the laws of static stability or become unusable.
The foil, like a plane's aerofoil, is a lifting body, and just like an aeroplane the hydrofoil needs a centre of lift that's behind its centre of gravity. Let's explain.
An aeroplane has multiple lifting surfaces, but added together they create a centre of lift (CoL). There is also an average position of all the mass in the aircraft, which it will naturally rotate around: This is the centre of gravity (CoG).
That's the average position that lift works through, but the quantity of lift depends on the velocity of the aircraft and the angle of the aerofoil into the wind: The higher the angle, the higher the lift. To a point.
Now put these two things together…
If a pilot inputs a sudden pitching motion that brings the nose up, he will change that angle of incidence, and the lift. If the CoL sots behind the CoG, then that lift will act against the direction of the pitch, damping down the motion and keeping it in check. This is known as being statically pitch-stable. If the CoL sits ahead of the CoG, then the opposite happens: The pitching motion feeds on itself and unless you intervene loss of control will surely follow.
As with aircraft, so with hydrofoils. You can in theory still control a pitch-unstable craft, but it needs either a computer control system or a pilot with reflexes like a startled cat. Best, then, to keep it stable.
Plus if it's stable then you can use the foil-surfer's kick-off move to accelerate you through the water, which is some trick.
6: We be rollin’: Roll & sway stability
We’ve all been there, weaving a drunkard’s path down a narrow corridor on a sea ferry crossing, focusing on the walls ahead of us so that we don’t think about the sea around us. As we furiously try to acquire sea legs in a mere two hour crossing we find ourselves speeding up & slowing down, and giving strangers way too much personal space for fear that our unsteady walk will smash us into them, sending pre-cut sandwiches and smoothies flying. God forbid you have children with you too.
A ship’s response to waves from the side is important, but unavoidably imperfect as it bobs and sways between peak & trough. It’s easier when the ship is very, very large of course, and also if it has ship stabilizing fins protruding from its keel, sometimes actively controlled to create damping forces. In principle this should be a hydrofoil’s strength, isolated as it is from the vagaries of buoyancy-derived bobbing.
Again we’re faced with a design choice of passive or active stabilization. Passive stabilization in roll or sway can be provided by canted, surface-breaking fins, as lift always acts at right angles to the lifting foil, and a pair of canted fins can therefore be used to create a corrective force automatically; remember that a roll will partially lift one foil out of the water (reducing lift) and push the opposing foil further in (increasing lift).
A design point that’s worth noting is the centre of roll, which is defined by the angle of the inward canted foils. This must be above the craft’s centre of gravity, otherwise the damping effect from the foils would be negative and the boat would rapidly capsize! This is why you won’t see many hydrofoils with extremely vertically-orientated foils.
Sway stability is slightly different, but again works to the advantage of surface-breaking foils, as their angle sets up a corrective force that resists side-to-side sway, though at the expense of generating an opposing rolling motion. What you don’t want is a craft where these two forces can interact and come into resonance, creating an oscillating swaying-rolling motion that would inevitably result in some of the passengers rushing to the side to feed the fishes. Once again there is an aerospace analogy of this, which is Dutch roll in some aircraft. Unpleasant.
On fully submerged hydrofoils you don’t have anywhere near as much passive damping in roll & sway, though if you tilt the foils you will get some. For fully submerged systems you will once again rely heavily on active control, either manually or by computer; a trade-off that buys you a smoother, better ride if you can pull it off.
7: Scaling it up: Size & power!
So we’ve shown how a hydrofoil can remain stable, but the key remaining questions we all want to know are:
How fast can it go?
How big can it get?
As you have probably noticed, aside from a few pleasure craft, specialist racers and James Bond baddies, hydrofoils are not exactly plentiful. One part of this is the extra complexity of these vessels, but another is certainly the limitations on size, for which we will refer to the Square-Cube law…
The key factor restricting hydrofoil size is the fact that as a vessel grows, the mass that you must lift increases as a cube (third power) of its length, width or height, while the lifting area of the foil can only scale with the square (second power). This means that if you keep on turning the Bigness Dial upwards, the foils will eventually outgrow the boat well before you can get the dial to reach ‘Huge’.
Now, in theory you could accommodate that by just increasing the cruise speed as well, since lift scales with the second power of velocity, but eventually you reach a limit here too, as ramping up the velocity creates sharp static pressure drops that can lead to cavitation; a spontaneous boiling of water into localised steam bubbles that then instantly and violently implode. Cavitation doesn’t just impede on the lifting efficiency of your craft, but is also well capable of structurally eroding metal or composite foils, which isn’t exactly ideal.
So, we have a maximum size and a maximum speed, meaning that you won’t be seeing any massive hydrofoil cruise ships anytime soon. However clever designers can give you a bit of leeway with the application of some sneakiness: Vertical strut length, for example, doesn’t scale with vessel size but with wave height, so they don’t grow much. Secondly, you can change the hydrofoil structure, evening-out the size of front & rear foils through a tandem design and making the best use of available space. So some sizeable creations have been built.
A notable example is the USS Plainview, a two hundred foot long fast submarine hunting ship that weighed in at 310 tons, making it the biggest hydrofoil ship constructed. One can also look to the Boeing 929 Jetfoil, a 104 ton fast ferry that can carry 350 passengers at an impressive 45 knots (52 miles per hour). Neither of these could be thought of as ‘small’, and yet compared to their traditionally-hulled equivalents they are: The ferry I used to emigrate from the UK to Ireland a decade ago was a fifty thousand ton behemoth operated by Irish Ferries, the Ulysses, carrying up to 2,000 passengers and over 1,300 cars. It’s just as well: That day the seas were very high indeed, and the big ship soaked up the punishment like a champ.
On such scales, hydrofoils simply cannot compete.
But for those small, fast-moving niches where you might want to fly through the water instead of float, they can be nice.
8: Seaplanes
Hydrofoils are a strange, small niche, but I shall leave you with one that is even smaller, but perhaps most intriguing of all.
In-between the world wars there was a flourishing of optimism around the possibility of shrinking our brave new world through international flight. Amidst the turmoil and turbulence of the post-war boom and the great depression grew a strange fancy: That flying machines could cross the oceans in an eyeblink, faster and more comfortably than anything that had come before.
Perhaps, just perhaps, you could cover the Atlantic in a day rather than weeks, with a brandy and a cigar? The movers and shakers of the two great Atlantic powers could move-&-shake through the wonder of the aeroplane. Leave the proles to the ships and the Germans to their Zeppelins, for surely a gentleman should traverse the seas by flying boat!
It made sense at the time. Aircraft simply could not reliably cross that trans-oceanic gulf, and some flavour of nautical muse had rendered all designs of long-range passenger craft as flying boats, able to take off and land in-harbour and, one hopes, with the over-ocean security that only a sturdy hull could give you. It was a fragile moment in history, unconstrained by the modern-day indignities of security scanners and long airport queues. A flying boat was true freedom, one with a view, and a cigar.
The first trans-Atlantic passenger flight was the Dixie Clipper, a Pan-Am flying boat that left Port Washington for Lisbon & Marseilles by way of the Azores. Twenty-two paying passengers, some of whom had booked years earlier, saw a new dawn of travel come into being on that flight.
It was not to be.
Two months later NAZI Germany swept into Poland, and the world awoke from its frail dream. By the time the war ended, the march of aeronautical technology had moved on, more aerospace than aeronautical it seemed, and the flying boat was retired. A new age was ushered in by De Havilland, then Boeing & Airbus, as the miracle of flight was commodified for the masses.
What has this got to do with the hydrofoil?
I have written previously about a new vista opening itself before the conservative aerospace world: Electric aviation could be a nothing, or it could be an everything, depending on where technology takes us, but for now it’s absolutely an incubator for clever ideas!
And perhaps the return of the flying boat.
An American start-up, Regent, aims to re-introduce the flying boat as a low-cost, zero carbon alternative to local waterborne travel by marrying electric motors on a distributed-propulsion architecture to a ground effect craft, hugging close to the surface of the sea to boost its flight efficiency and stretch its legs. This curious combination of technologies is something special; a niche uniquely well-adapted to electric aviation, and how would such a beast take-off and leave the water smoothly? With a hydrofoil of course.
So godspeed to Regent, because with new-fangled battery-electric power they might be able to revive two glorious old monsters in a single flourish and send them flying into the sunrise: The flying boat, and the hydrofoil. One side flying through water, and one just over it.
And if the twenty-first century can reach back and rescue an old glory from the early twentieth, I’d like to take that journey myself, with a brandy and a hopeful gleam in my eye, and look forward to a new century.
We’ll get it right this time.
Papers used in this article include Hydrofoil Overview-A Brief Tutorial, John R. Meyer/ The absolute stabilization and optimal control of hydrofoil watercrafts, C.G Constantinescu