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Every boat has a chine. The chine is the transition from the bottom of the hull to the side. I guess a boat with no chines would be one with no sides, e.g. a surfboard or a flat piece of plywood (which would probably perform better than some of the mass-produced kayaks out there, come to think of it....)
At any rate, a soft chine allows a gradual transition of a kayak from straight up (primary stability) to edging (secondary stability). Theoretically, there are an infinite number of possible angles, so it's easier to adjust the angle of the kayak to changing conditions. On the other hand, the kayak is never really stable at any given angle.
A hard chine tends to give a kayak good secondary stability; you chunk over onto the side and the relatively flat surface gives the boat more stability when it's on edge.
One disadvantage of a hard chine is the kayak may not be as fast because the maximum hull speed is lower. Maximum hull speed is when the boat planes (rides on top of the water) on its bow wave. With hard chines, the two relatively flat surfaces (hull and side) tend to make the boat plane sooner, so the boat rides up on the bow wave sooner and loses speed. At least that's how I understand it. Corrections? Clarifications?
P.S. My husband says another category of chine is the chines of freedom flashing (with apologies to Bobby Dylan).
I am not a marine architect and the following is my personal observation. So be warned.
If you visualize a cross section of a kayak hull that is comprised of four straight lines that represent four planes making up the hull near the cross section. Two of the lines are a shallow vee that represents the bottom of the hull. On each side of the section are nearly vertical lines that intersect the bottom lines, these lines represent the sides of the hull. This shape would represent an extreme hard chine hull. If you trace a large radius curve connecting the bottom lines and the side lines, this would represent a soft chine hull. The areas between the two shapes at the chines, extended, constitute volumes. Since these volumes are at the extreme distances from the center of the boat they are somewhat equivalent to sponsons.
As the kayak is leaned, the sponson like volume on the high side is lifted out of the water and the sponson like volume on the low side is driven fully into the water. Since the center of buoyancy of the section is the centroid of the submerged area, subtracting the sponson area from one side or adding it on the other shifts the center of buoyancy to the low side. The righting moment is the product of the distance between the center of gravity and the center of buoyancy, and the buoyancy force. The lateral shift of the center of buoyancy therefore increases the righting moment, this increase in righting moment is referred to as secondary stability.
In hard chine boats, there is still some radius to the chine curve, and in soft chine boats the transition curve from bottom to side does not extend from keel to gunnel, in fact it has a relatively small radius. The result is that the differences in volumes at the chine areas is relatively small, so the difference in righting moment is also relatively small.
The effect of the hull shape on speed has two factors, wetted surface area of the hull and the dynamic shape factor of the hull. The difference in the ratio between wetted surface area and volume for hard chine and soft chine boats is minimal (almost insignificant.) The difference between shape factors is greater, but still pretty small. The sharp transition between the side planes and the bottom planes has little effect on drag where the axes of the angles are parallel to the flow of water past the hull, but where the chines sweep up near the bow, the axes of the angles are no longer parallel to the flow. To some extent the water has to make an abrupt change in direction to flow around the sharp angles; this causes disruption in the smooth flow of water which is called turbulence. The energy required to create this turbulence is subtracted from the energy available for propelling the boat forward. The important thing to remember is that the effect is so small that it will probably not be noticed by most paddlers.
I would characterize the Tempest as having soft edged hard chines. This is also true of the NDK Romany and Explorer.
This is often noted as being a reassuring compromise. However, where and how the volume is distributed as well as rocker, seem to have much more to do with the feel of a hull than its chine profile.