Thread: Planing?
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Old 11-23-24 | 10:15 PM
  #384  
tomato coupe
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Originally Posted by Darth Lefty
All right. Here is my criticism of the concept. In order to store energy, movement is required. A bike frame - even a noodly one - is stiff. Now that we have a bowyer in the conversation, imagine a bike frame strung like a bow. How far could you pull it back? How far would the arrow go? Not far, because the bike frame cannot store very much energy, because it's stiff. A spring that barely moves is storing barely any energy. When you pedal a bike you are putting in a force similar in magnitude to pulling a bowstring. This is enough to sometimes bend some bikes enough the wheel rubs the brake pad. That's like a millimeter, or a fraction of a degree. A bow, which is actually flexible and does return a lot of energy, lets the arrow slide about two feet. A spring moves in proportion to the force and stores energy in proportion to the movement squared. A spring that is 2x stiffer stores a quarter of the energy for the same force. A bike frame that is 100x stiffer than the bow stores 0.001% of the energy. It's just not enough to change the resistance profile enough to account for a 4% much less 12%.
You've got the right idea, but some details are wrong. The displacement of a spring is equal to the applied force divided by the spring constant. The energy stored in the spring is equal to 1/2 times the spring constant times the displacement squared, which is 1/2 times the applied force squared divided by the spring constant. So, if you double the spring constant the spring will store half the energy if the force remains the same.

F = k * x –––> x = F / k

E = 1/2 * k * x * x –––> E = 1/2 * F * F / k
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