Manfred Curry was born in Germany in 1899, emigrated to the US and became a citizen of that country. He died in 1953, just in time to witness the birth of our beloved FD. He actually sailed in one of the prototypes of the boat.
Curry was, and probably still is, the most successful German born yacht racer. He bagged more than 1000 victories. But even more than through his yacht racing, Curry’s legacy lives on because of his work as a sailing-aerodynamics pioneer and through his inventions. It was Curry who first introduced a jib that overlapped with the mainsail. He, very successfully, first used this jib in a regatta near the Italian town of Genoa in the 1930’s. As a result of this success the ‘Genoa’, as it was henceforth called, remained there to stay.
Curry’s true ticket to fame, however, was his invention of a device that nowadays is featured in multitude on almost any sailing boat: the cam cleat. In German, and also in the Dutch language, this cleat bears the name of its inventor: Curryklemme. Of course, Anglophonic sailors cannot stomach the thought of referring to a German and consequently never use the term. Rather would they honor Briggs Swift Cunningham II, who invented nothing less that the hole in the sail that proudly bears his name. The French, for whom the world ends at the frontiers of their beloved ‘Hexagon’, refrain from ever mentioning Curry’s name; they irreverently call the cleat a ‘taquet coinceur’. And the Italians? Well, are they aware that the Roman empire ceased to exist some time ago?
Simple as its principle may seem, Curry’s cam cleat is a much cleverer device than meets the eye at first sight. Its secret lies in the geometry of its two jaws each of which is shaped like a part of a mathematical object called the logarithmic spiral. This spiral, shown in Fig. 1, has a number of distinguished features: it is a self similar graph, which means that from whatever distance it is viewed, it always looks identical. Secondly, if we look at the angle at which any part of the spiral intersects a straight line extending out from the origin to infinity, we see that this angle is always the same, as is immediately clear from Fig. 1. Likewise, the spiral intersects any circle at the same angle. This angle is called the pitch of the spiral. The spiral forms a constant-angle curve and it is this property that gives cam cleats their essential properties: they hold a variety of rope diameters and their holding power is independent of this diameter and they always hold tight, independent of the force on the rope. Also, the cleat is insensitive to the precise direction of the pull of the rope.
A special logarithmic spiral is one with a pitch of about 170. This so-called golden spiral is closely related to the Fibonacci series and the Golden Ratio, both favorites in mathematics as well as in renaissance art. The pitch of the jaws of Curry’s cleat is slightly bigger, typically about 200
Fig. 1. A logarithmic spiral with a pitch of 100.
Nature seems to have a preference for mathematical beauty and, indeed, logarithmic spirals appear all around us: for example in the shape of the shells of certain mollusks, in tropical storms (see Fig. 2), and in spiral galaxies. An interesting technical application is the so called ‘friend’, a device inserted into vertical cracks by rock climbers as protection against falls. The friend is basically an inverted cam cleat (see the drawing at the right of Fig. 2).
Fig. 2. Examples of logarithmic spirals in nature and technology: Nautilus shell, tropical storm and the cams of a ‘friend’, a device used as fall protection in rock climbing.
How cam cleats workLet us have a look at exactly how the cam cleat manages to prevent a rope from slipping. Firstly, let us ignore the fact that the jaws of the cleat have a jagged inner edge and that the rope is fluffy and compressible. Now look at Fig. 3. The beak of the cleat is represented by two logarithmic spirals. Of course, in a real cleat the jaws form only a segment of the spiral, but as long as the rope diameter is in the right range this does not matter. If we analyze the forces on the rope and the cleat, we see the following: the rope is held taught by a tension force T. If the rope is not to slip, each cam of the cleat must supply half this force as a reaction force. This reaction force originates from the axel of the cam. Looking at Fig. 3 we see that the torque exerted by this pair of forces tends to make the blades of the cleat rotate. This rotation is prevented because the rope pushes back on the cams. The balance of torques requires that the size if this so called ‘normal’ force N be just ½T times the ratio of the two lever arms. This ratio is 1/ tan a, where a is the pitch of the spiral. For a = 200 the ratio is slightly bigger than 3 and it does not depend on the width of the gap between the jaws. The rope will stay put if the friction force that the cleat can supply is large enough. It is a well-established fact in physics that the maximum friction between two objects is just the normal force multiplied by a constant called the coefficient of friction. This friction coefficient depends on the two materials and to some extent on surface roughness. Thus, we find that our cleat works if the friction coefficient between our rope and the material of the cams is bigger than tan a or about 1/3. It clearly is. Even if we were to replace the rope by a wooden rod, the cleat would still hold it. If you have a cam cleat in your tool box you can try it at home if you don’t believe me. The cleat will not hold a polished steel rod: The friction coefficient between this material and the aluminum of the jaws is below 1/3.
Fig. 3 Forces on the blades of a cam cleat: The ratio of the normal force N and the tension and friction forces T/2 is set by the non-rotation equilibrium of the blades. This ratio depends only on the pitch α of the spiral and is equal to tanα.
You don’t have to be a rocket engineer to reinvent the wheel. It appears though that it helps if you want to reinvent the cam cleat. In 1978, a guy called Ray Jardine who was an aeronautics engineer, as well as a keen rock climber, invented the already mentioned ‘friend’, a spring loaded camming device for rock climbing based on the logarithmic spiral. These devices are designed to withstand shock loads of a falling climber which can easily exceed 10 times his body weight. As with our cleats, friends, in principle, always hold, because the friction coefficient between the aluminum blades and the rock exceeds the tangent of the pitch angle of the blades (which in this case is about 140). The normal force exerted by the rock on the cams can be several tons. Climbers can be fairly confident that the device does not slip and they can only hope that their friend can withstand the huge forces without breaking apart. Fortunately for them, most of the time their hope is vindicated.
Anyway, the next time you sail and you pull in the sheet of your genoa and lodge it firmly into its Curryklemme, spare a thought for Herr Dr. Manfred.
Curry was, and probably still is, the most successful German born yacht racer. He bagged more than 1000 victories. But even more than through his yacht racing, Curry’s legacy lives on because of his work as a sailing-aerodynamics pioneer and through his inventions. It was Curry who first introduced a jib that overlapped with the mainsail. He, very successfully, first used this jib in a regatta near the Italian town of Genoa in the 1930’s. As a result of this success the ‘Genoa’, as it was henceforth called, remained there to stay.
Curry’s true ticket to fame, however, was his invention of a device that nowadays is featured in multitude on almost any sailing boat: the cam cleat. In German, and also in the Dutch language, this cleat bears the name of its inventor: Curryklemme. Of course, Anglophonic sailors cannot stomach the thought of referring to a German and consequently never use the term. Rather would they honor Briggs Swift Cunningham II, who invented nothing less that the hole in the sail that proudly bears his name. The French, for whom the world ends at the frontiers of their beloved ‘Hexagon’, refrain from ever mentioning Curry’s name; they irreverently call the cleat a ‘taquet coinceur’. And the Italians? Well, are they aware that the Roman empire ceased to exist some time ago?
Simple as its principle may seem, Curry’s cam cleat is a much cleverer device than meets the eye at first sight. Its secret lies in the geometry of its two jaws each of which is shaped like a part of a mathematical object called the logarithmic spiral. This spiral, shown in Fig. 1, has a number of distinguished features: it is a self similar graph, which means that from whatever distance it is viewed, it always looks identical. Secondly, if we look at the angle at which any part of the spiral intersects a straight line extending out from the origin to infinity, we see that this angle is always the same, as is immediately clear from Fig. 1. Likewise, the spiral intersects any circle at the same angle. This angle is called the pitch of the spiral. The spiral forms a constant-angle curve and it is this property that gives cam cleats their essential properties: they hold a variety of rope diameters and their holding power is independent of this diameter and they always hold tight, independent of the force on the rope. Also, the cleat is insensitive to the precise direction of the pull of the rope.
A special logarithmic spiral is one with a pitch of about 170. This so-called golden spiral is closely related to the Fibonacci series and the Golden Ratio, both favorites in mathematics as well as in renaissance art. The pitch of the jaws of Curry’s cleat is slightly bigger, typically about 200
Fig. 1. A logarithmic spiral with a pitch of 100.
Nature seems to have a preference for mathematical beauty and, indeed, logarithmic spirals appear all around us: for example in the shape of the shells of certain mollusks, in tropical storms (see Fig. 2), and in spiral galaxies. An interesting technical application is the so called ‘friend’, a device inserted into vertical cracks by rock climbers as protection against falls. The friend is basically an inverted cam cleat (see the drawing at the right of Fig. 2).
Fig. 2. Examples of logarithmic spirals in nature and technology: Nautilus shell, tropical storm and the cams of a ‘friend’, a device used as fall protection in rock climbing.
How cam cleats workLet us have a look at exactly how the cam cleat manages to prevent a rope from slipping. Firstly, let us ignore the fact that the jaws of the cleat have a jagged inner edge and that the rope is fluffy and compressible. Now look at Fig. 3. The beak of the cleat is represented by two logarithmic spirals. Of course, in a real cleat the jaws form only a segment of the spiral, but as long as the rope diameter is in the right range this does not matter. If we analyze the forces on the rope and the cleat, we see the following: the rope is held taught by a tension force T. If the rope is not to slip, each cam of the cleat must supply half this force as a reaction force. This reaction force originates from the axel of the cam. Looking at Fig. 3 we see that the torque exerted by this pair of forces tends to make the blades of the cleat rotate. This rotation is prevented because the rope pushes back on the cams. The balance of torques requires that the size if this so called ‘normal’ force N be just ½T times the ratio of the two lever arms. This ratio is 1/ tan a, where a is the pitch of the spiral. For a = 200 the ratio is slightly bigger than 3 and it does not depend on the width of the gap between the jaws. The rope will stay put if the friction force that the cleat can supply is large enough. It is a well-established fact in physics that the maximum friction between two objects is just the normal force multiplied by a constant called the coefficient of friction. This friction coefficient depends on the two materials and to some extent on surface roughness. Thus, we find that our cleat works if the friction coefficient between our rope and the material of the cams is bigger than tan a or about 1/3. It clearly is. Even if we were to replace the rope by a wooden rod, the cleat would still hold it. If you have a cam cleat in your tool box you can try it at home if you don’t believe me. The cleat will not hold a polished steel rod: The friction coefficient between this material and the aluminum of the jaws is below 1/3.
Fig. 3 Forces on the blades of a cam cleat: The ratio of the normal force N and the tension and friction forces T/2 is set by the non-rotation equilibrium of the blades. This ratio depends only on the pitch α of the spiral and is equal to tanα.
You don’t have to be a rocket engineer to reinvent the wheel. It appears though that it helps if you want to reinvent the cam cleat. In 1978, a guy called Ray Jardine who was an aeronautics engineer, as well as a keen rock climber, invented the already mentioned ‘friend’, a spring loaded camming device for rock climbing based on the logarithmic spiral. These devices are designed to withstand shock loads of a falling climber which can easily exceed 10 times his body weight. As with our cleats, friends, in principle, always hold, because the friction coefficient between the aluminum blades and the rock exceeds the tangent of the pitch angle of the blades (which in this case is about 140). The normal force exerted by the rock on the cams can be several tons. Climbers can be fairly confident that the device does not slip and they can only hope that their friend can withstand the huge forces without breaking apart. Fortunately for them, most of the time their hope is vindicated.
Anyway, the next time you sail and you pull in the sheet of your genoa and lodge it firmly into its Curryklemme, spare a thought for Herr Dr. Manfred.
Dr. Gizmo
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