The physics of hydroplaning
by Mark Palmquist
There are 3 kinds of lift:
• buoyancy lift
• dynamic lift, submerged foil
• dynamic lift, surface skimming
Buoyancy lift relies on creating a hole in the water. No dynamic motion is necessary. To create the hole a boat hull will displace water sideways and downward. Lift is equal to the weight of the water displaced. Buoyancy lift of a hull grows in a linear fashion with every additional cubic inch/cm of submersion. A boat hull traveling through a fluid pushes water out of the way. The water rushes to fill the hole left by where the boat was earlier. Most of the water goes sideways, around the hull, and a small amount goes underneath the hull. A bow wave and a stern wave are created when the hull is moving forward. Bow and stern waves dissipate energy and create drag and can create a speed limit for the hull based on the square root of its length of water line. Water flowing around the curved sides of a displacement hull create lift perpendicular to the center of curvature. The lift on the left and right of a canoe shaped body cancel each other out. So most displacement hulls produce no dynamic lift unless the bow is lifted above the stern and water is deflected downward at the stern. A boat with a wider stern will generally create more dynamic lift than a boat with a pointy stern, however, the pointy ended boat will be faster in low speed conditions.
A boat at rest produces no dynamic lift. Both forms of dynamic lift are speed dependent and grow with the square of the speed. If you double the speed, the lift goes up 4x. Underwater dynamic lift works by bending water slightly downward off the trailing edge of a hydrofoil, essentially an underwater, horizontal wing. The shift of the water flow downwards produces an equal and opposite lift upwards based on the laws of conservation of momentum and pressure differential. To minimize drag, the angle at which the water is bent downwards is typically between 2-4 degrees and the wing aspect ratio is relatively large. Both the upper and lower surfaces of the hydrofoil are underwater, generally about 0.5-1 meter below the surface. As the speed of the hull increases, the lift can increase more than needed, so a hydrofoil’s angle of attack usually requires active angle adjustment. Less angle of attack (AOA) is needed at higher speeds. Reducing the AOA also reduces drag to a minimum.
Skimming lift works by deflecting water downward off a relatively flat, inclined plane. The leading edge must be higher than the trailing edge to produce a deflection. The ideal angle of incidence is generally 4-6 degrees (for a hull with zero dead-rise like a windsurfing board) This creates a hole in the water behind the trailing edge of the skimming surface that grows with speed. The faster the speed of the skimmer, the larger the hole. Just like displacement lift, skimming lift is equal to the volume of the hole, but with much less wetted surface area. Just like with a double sided wing, increasing the width of a skimming surface increases its lift/drag ratio. An ideal skimming surface is 2-3 times as wide as it is long. If you watch expert skim boarders, they typically travel with the boards oriented “sideways” when crossing a swimming pool or river. This limits the amount of water that escapes around the edges. With skimming lift, it is not as important to lower the angle of attack at higher speeds because the skimming surface self regulates by lifting further out of the water so only a small area near the trailing edge is wet at high speeds. To illustrate this, a human needs a water ski with about 5 SF of surface area to hydroplane at 9 knots but only needs 0.25 square feet to hydroplane at 44 knots.
The heeling force on a sail grows exponentially with increasing wind speed. A 41% increase in wind speed doubles the heeling/pitching force. Hydrofoil and hydroplaning lift also grow exponentially. Because of this, dynamic lift can limit or eliminate heeling if the lifting surface is positioned far enough from the center hull to counter the rotational torque created by the sail rig. If the wingspan is roughly equal to the height of the CE from the water line, then the wing has no problem limiting the boats heeling to within 12 degrees.
How does hydroplaning compare with hydrofoiling?
All current sailboat speed records in the past 15 years have been with sailboats incorporating skimming hulls (Yellow Pages Endeavour, windsurfers, kiteboards, Sailrocket 2). The only hydrofoil boat to hold the speed record was Hydroptere. It held the record for less than 1 year in 2009.
Underwater foils are subject to underwater turbulence and skimming hulls are subject to surface waves. The skimming disc crossbeams are designed to flex allowing the disc to step over most waves while maintaining positive lift at all times. The wings of a wingmaran also flex over most waves and slice through the larger ones.
Wingmaran Architecture:
The architectural layout of a wingmaran is similar to the AC75,
with dynamic lift to the lee of, and in front of the CE.
The AC75 incorporates hydrofoil lift.
The wingmaran incorporates hydroplaning lift.
What is the speed potential of a wingmaran?
Every wingmaran that has been built and tested has attained speeds in knots 10% greater than the boat's length in feet, so the wingmaran 15 should go 16.5 knots, an 18’ wingmaran can attain 21 knots, and a 50 foot long wingmaran is predicted to go 55 knots. With a more efficient rig, the speed could be even higher. Testing is underway to determine the effects of waves on the performance of hydroplaning wings and hydroplaning outriggers. Should large waves be an issue, suspension systems can be incorporated.
How does the wing eliminate heeling?
Comparing the rotational force leverage arm of the sail and a leeward skimming disc outrigger (or hydroplaning wing)
Torque= distance x force x angle of attack
Assuming the angle of attack of the sail and the hydroplane are similar,
Lift Force= surface area x fluid density x velocity^2 x lift coefficient
Assuming the center of pressure of the sail is 10 feet up and the hydroplane is 5 feet out,
The distance arm of the sail is 2x the hydroplane
Assuming a sail area of 100 sf and a hydroplane area of 4.7 sf
The surface area of the sail is 21.2x the hydroplane
Assuming the sail is a double sided airfoil of zero thickness and the disc is a single-sided inclined plane
The lift coefficient of the sail is roughly 2.25x the hydroplane
Assuming the boat and wind are traveling the same speed on a beam reach, the apparent wind speed over the sail is 1.41x greater than apparent water speed under the hydroplane,
The sail has a 1.41^2= 2x fluid velocity advantage
Assuming the sail is bending air and the hydroplane is deflecting water and the density of water is 850x more than air,
The disc has a 850x advantage over the sail
The sail's advantages 2 x 21.2 x 2.25 x 2 = 190.8
The hydroplane’s advantage = 850
The hydroplane has a 850/190.8 = 4.45x rotational torque advantage over the sail's heel/pitch torque
What this means:
The sail's lift is dynamic.
While a buoyancy outrigger has more buoyancy lift it has no dynamic lift.
Linear buoyancy falls behind a sail's dynamic lift causing more of the outrigger to get wet with increasing speed creating more drag. This limits the top end speed of all catamarans and trimarans (unless they are lifted dynamically).
The hydroplane’s lift is dynamic. It grows at the same rate as the sail's lift.
However, because the hydroplane has a built-in rotational torque advantage, the wetted area of the hydroplane will actually decrease with increasing hull speed.
The only dynamic advantage that the sail has over the hydroplane is apparent fluid flow.
Apparent fluid flow is greatest when tacking into the wind and least when going down wind.
Coming out of a tack, when the boat is traveling slower, the wind has a dynamic advantage for a short while until the boat accelerates.
The key is to tack quickly, or, let the sail out, fall off, and then as the boat accelerates, pull the sheets back in.
This is what windsurfers must do to keep from being pulled on top of the sail.
As long as wind speed is not 4.45x greater than the boat speed, the boat won't capsize.
In most cases, your boat will be traveling faster than the wind.
A light weight wingmaran, with a modern sail rig, should be capable of traveling at least 2X the speed of the wind, in which case, the leverage arm of the hydroplane is still 2X. So the faster you go the less likely you are to capsize, and the more weight is shifted to the hydroplane but without pushing the lifting surface down. So a wingmaran does not have the same tendency to heel and pitch forward like most other monohulls, catamarans and trimarans, and total wetted surface area decreases with increasing speed, unlike non-foiling monohulls, and non-foiling catamarans and trimarans.
How does a wingmaran compare to other boats that lift up on foils?
Wingmarans have not yet been raced along side other boats that are lifted up onto hydrofoils, however, the cost associated with making a Wingmaran will be much lower than the cost of a monohull, catamaran, or trimaran with 2 or 3 lifting hydrofoils with control mechanisms. Testing in large wave condition is on going. At Palmquist Marine, we are dedicated to exploring the benefits of the use of hydroplaning lift on sailing craft to limit heeling, lower drag, and increase speed.
Fluid hitting a plate
Aspect Ratio
The graph below illustrates the relationship between lift/drag ratio and aspect ratio of the planing surface. This is why a horizontal wing is better than a surfboard. Surfboards have aspect ratios lower than 1 and wings have aspect ratios greater than 1.
Source: A Lifting Surface Approach to Planing Boat Design by: Eugene P. Clement Sept, 1964 (Dep. of the Navy)
Angle of attack (AOA)
The graph below shows that the best angle of attack for producing the lowest drag/lift curve is around 4-5 degrees for zero deadrise and 5-6 degrees for 10-20 degrees of deadrise.
Also note, there are 2 kinds of drag acting on a planing surface, the wetted area (viscous drag) and the frontal area (pressure drag). The sum of the 2 types of drag form a saddle at the ideal angle of attack. This ideal angle does not change with speed. So the wingmaran’s wing can be at a fixed angle and does not need adjustment.
Source: Hydrodynamic Design of Planing Hulls
By: Daniel Savitsky 1964 Office of the Navy
Dynamic Lift Chart
The spreadsheet below shows the relationship between speed and dynamic lift on the Skimming Disc Outrigger.
At about 8 knots the skimmer supports the weight of an adult. But look how the lift grows with increasing speed. Dynamic lift is exponential.
The Constant K was determined to be 1.2 based on knowing that a skimboard supports 80Kg at 8 knots.
Reduced wetted area and drag
The wings of the wingmaran and the skimming discs are similar to the underwater part of the speedboat's hull. Everything above the water creates aerodynamic drag, so it's removed.
Comparing lift: Static float vs Dynamic skimmer
The graph below illustrates the relationship between lift generated by a buoyancy float and lift generated by a dynamic skimmer. At some point the float can no longer support the shift in weight caused by the heeling action of the sail and drag will slow the boat down. The speed limit of any small trimaran is based on the overall width, the buoyancy % of the float, the sail area and the ability to shift crew weight to windward. The advantage of the wingmaran is that the wetted area drag does not increase with increasing speed so the speed limit is extended. The other advantage is that the weight of 2 skimmers with 1 cross bar is less than the weight of 2 large floats with 2 crossbars.
At low speeds, the wingmaran has a speed advantage over a trimaran because it weighs less. And at around 7 knots the skimmer will already match the lift created by a large trimaran float with 220 lb of buoyancy (100Kg). At no point does the heeling/pitching of the mast overcome the lift of the skimmer. The only vulnerable period is when the boat is stalled and the wind is blowing over 20 knots, however, I have been in these conditions and have not capsized yet. You simply take your time sheeting in the main sail and the boat will continue to accelerate. Once you reach 7 knots the boat becomes very stable.
