Recap
In the last installment of this two-part series of articles we discovered that cutting at full speed and with the correct form and angle generates a speed, at the tip (kissaki) of the Katana, of about 40 km/h. While this might not seem, at first glance, a particularly exciting speed, when related to the sword's main objective, which is cutting, we are going to discover something extremely interesting that will change the way you see and practice Iaido forever! Force, pressure and acceleration When evaluating the efficiency with which any blade is cutting, and not counting directly more metallurgic elements like hardness, flexibility and sharpness, the key element is the "specific pressure". This can be defined as the amount of pressure (measured in Kg) that the blade can generate on its smallest surface (the edge). We have to therefore go on with a few more calculations to understand exactly what that value is. To do that, first of all we have to discover the force and acceleration that we apply to the sword when doing a proper cutting movement. Force (F) is obtained by factoring mass and acceleration, and the latter can be calculated by dividing the speed by the time of the cut - and once again we see how important of a factor speed is. We calculated in the previous article that the speed is at about 40 km/h, which converted back in m/s equals to about 11.2 m/s. Taking the standard measure of time for a cut time duration (0.35 s) we will then discover the acceleration: Acceleration: 11.2 / 0.35 = 32 m/s Now that we know the acceleration, we can calculate the actual force applied to the blade, by factoring in the mass of the sword. Let's take as an example a 0.9 kg sword (which is actually on the lower end of a real folded steel Katana, that can easily go over 1 kg, even up to 1.2 kg). Force: 32 * 0.9 = 28.8 N (for Newton, the measurement unit of forces). Notes and approximations Before going on with our calculation, to determine the actual specific pressure that this Force will apply at the moment of the cut, I'd like to point out a few approximations: in reality we are calculating the acceleration of the tip of the sword factored with its mass which should be considered at the balance point of the blade, but this partially re-balances for not accounting for the user's arms mass. There are also implications related to the type of hit (rigid or elastic and in which portion), so we should account also for the kinetic energy of the sword and then proceed in calculating an energy rebalancing at the moment of the impact to really precisely calculate the forces in play but, as we will shortly see, the amounts and dimensions even approximated are so significant that there is not a real need to go to such detail. Specific Pressure Now to finally calculate the specific pressure that is generated at the moment of the cut, we need to try and estimate the surface of the working edge of the Katana. First of all let's say that the Katana is not really used for all of its lenght, but for approximately the half of it, so for 37.5 cm (0.375 m), if we keep the example of a 75 cm sword. To estimate the dimension of the sharp edge it's much harder, as it depends on a few factors difficult to approximate, but to better visualize still the overall amount of the forces we are talking about, let's assume that the edge will have the same size of a common sheet of paper, about 0.05 mm, so 0.00005 m (please note that the edge of an actual fully sharpened folded steel katana might be much smaller than that!). Therefore the surface area of the edge at the moment of the impact will be of 0.375 * 0.00005 = 0.00001875 square meters Conclusions Finally then we can calculate the specific pressure by dividing the Force (F) by this above obtained surface because: Pressure = Force / Applied Area and so: 28.8 / 0.00001875 = 1.536.000 N/m2 Because 1 Newton is equal to about 9,81 Kg, the final result is: 156.628,41 Kg/m2. One hundred and fifty six tons on a square meter!!! We are in front of an extreme and astonishing value: take your body and then throw on it 150 tons of anything and you'll be totally flattened in an horrid mix of blood, meat and bones. Now take that value and put it on the edge of the sword that is cutting you and you'll be very politely and neatly divided in two. This article is based on the work and calculations of Davide De Vecchi, who is fully credited for the original material.
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