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Talking about surfboard weight and acceleration
From a conversation on the subject today:Firstly it needs to be mentioned that objects of greater mass do accelerate faster due to gravitational attraction than lighter objects even in a vacuum.This is because the force of gravitational attraction between objects is proportional to the combined mass of the two objects. The increase in acceleration and top speed due to this is insignificant but still exists, I mention it because I think that it is best to be as clear in our understanding as possibleSecondly and more importantly, Terry Hendricks' analysis assumes that drag due to air is insignificant, but this is most certainly not the case.I presume that you are aware of the fact that denser objects and larger objects of the same density both experience a thrust/drag advantage ( I use the term thrust loosely here to include the force of gravitational attraction) over smaller and less dense objects. This can be seen with gliders: scale model gliders do not travel as fast as full sized ones, due to the fact that mass ( and thus thrust) increases with the cube as size increases whereas surface area ( and thus drag) increases only with the square.In the case of surfing the drag due to air friction is certainly significant.
A 70 pound surfboard using its mass to accelerate against a 35 knot offshore windFor example the air drag on a standing surfer is, at a speed of 15m/s, approximately 70 Newtons, which is ( assuming a situation where an surfer and board with a mass of 800 Newtons is at terminal velocity ) 11.4% of the total drag equation.Now, if we add 200 newtons of thrust to the equation we now have a total thrust of 1000 Newtons and have increased thrust by 25%, however the air drag is not increased.Calculating the result including the increase in drag due to wetted surface area, we find that we have an overall thrust advantage of 1.55% or 15 Newtons, thus the surfboard and rider will acceleate to a higher speed with the added mass.Surfer 1Mass 800 NewtonsAir Drag 70 NewtonsWetted surface drag 730 NewtonsTotal Drag 800 NewtonsVelocity 15 Metres/ secondResult Terminal velocitySurfer 2Mass 1000 NewtonsAir Drag 70 NewtonsWetted surface drag 912.5 NewtonsTotal Drag 984.5 NewtonsVelocity 15 Metres/secondResult 15.5 Newtons of remaining thrust( board accelerates)There are many other interesting examples which can be calculated. For example taking surfer1 and surfer2 above, if we:1) Take a free fall drop, at a given velocity during such a drop surfer2 has a 200 Newton or 25% increase in thrust with no extra drag penalty ! This is because in a vertical there is no wetted surface drag and no lift requirement. . .. at a given velocity drag is not related to mass in this case. What this shows is that added mass gives a greater thrust/drag advantage as the glide path steepens or the surfboard loses altitude.
The same 70 pound board, during the same session. Suprising as it may seem none of the other boards in the water ( which were all lightweight) were able to make a wave in these conditions.These examples are assuming that mass is added without altering the shape or dimensions of the board and rider ( thus increasing their overall density) . If board and rider are simply scaled up in all respects, maintaing the same density then there is a smaller drag reduction to be gained.Here's a question:If two identical yachts ( except that one is scaled up to twice the size of the other) are sailing directly downwind, then the larger yacht will sail faster. Why is this the case ? When sailing downwind air drag increases the speed of the boat rather than reducing it, so the air drag advantage should be reversed. . . and if drag due to planing lift is proportional to mass, then there seems to be no reason for the larger craft to sail faster, and yet it does.
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A 70 pound surfboard using its mass to accelerate against a 35 knot offshore windFor example the air drag on a standing surfer is, at a speed of 15m/s, approximately 70 Newtons, which is ( assuming a situation where an surfer and board with a mass of 800 Newtons is at terminal velocity ) 11.4% of the total drag equation.Now, if we add 200 newtons of thrust to the equation we now have a total thrust of 1000 Newtons and have increased thrust by 25%, however the air drag is not increased.Calculating the result including the increase in drag due to wetted surface area, we find that we have an overall thrust advantage of 1.55% or 15 Newtons, thus the surfboard and rider will acceleate to a higher speed with the added mass.Surfer 1Mass 800 NewtonsAir Drag 70 NewtonsWetted surface drag 730 NewtonsTotal Drag 800 NewtonsVelocity 15 Metres/ secondResult Terminal velocitySurfer 2Mass 1000 NewtonsAir Drag 70 NewtonsWetted surface drag 912.5 NewtonsTotal Drag 984.5 NewtonsVelocity 15 Metres/secondResult 15.5 Newtons of remaining thrust( board accelerates)There are many other interesting examples which can be calculated. For example taking surfer1 and surfer2 above, if we:1) Take a free fall drop, at a given velocity during such a drop surfer2 has a 200 Newton or 25% increase in thrust with no extra drag penalty ! This is because in a vertical there is no wetted surface drag and no lift requirement. . .. at a given velocity drag is not related to mass in this case. What this shows is that added mass gives a greater thrust/drag advantage as the glide path steepens or the surfboard loses altitude.
The same 70 pound board, during the same session. Suprising as it may seem none of the other boards in the water ( which were all lightweight) were able to make a wave in these conditions.These examples are assuming that mass is added without altering the shape or dimensions of the board and rider ( thus increasing their overall density) . If board and rider are simply scaled up in all respects, maintaing the same density then there is a smaller drag reduction to be gained.Here's a question:If two identical yachts ( except that one is scaled up to twice the size of the other) are sailing directly downwind, then the larger yacht will sail faster. Why is this the case ? When sailing downwind air drag increases the speed of the boat rather than reducing it, so the air drag advantage should be reversed. . . and if drag due to planing lift is proportional to mass, then there seems to be no reason for the larger craft to sail faster, and yet it does.
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