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Post by Deleted on Nov 20, 2007 18:45:21 GMT
Today I got the idea of trying to calculate how fast a sword tip of a longsword is moving during a cut and with what power. Not sure if this is right, but here is my attempt.
I recall that an average guy can throw a baseball at about 50 mph. Lets be conservative and say you can move your hand forward at 40 mph as you pull back on the handle with the other hand. So the sword handle is moving at 40 mph and the handle gives us an 8 inch diameter. Now how about the tip on a 3 foot blade? Using the circumference formulas I calculated the size of the arch that the hand is making based on an 8 inch diameter and compared it to the arch of the 36 inch blade. 25 inch circumference vs 113 inch. I calculate that the tip is traveling 4.52 times the distance in the same time. Hence if your hand is moving at 40 mph the tip is moving at 180 mph.
So if the sword tip weighs 1 lb and is moving at 180 mph you multiply to get a momentum of 180 pounds per some unit. If the sword is more blade heavy say 1.5 lbs at the tip, then the momentum might be 270 lbs per some unit on the edge.
I'm not sure this is all correct, I am putting it out here for us to consider and refine.
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Post by Brian of DBK on Nov 20, 2007 18:55:03 GMT
In my hey-day I could throw a baseball over 80 mph...does that mean my sword is going 350 mph?
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Post by ShooterMike on Nov 20, 2007 19:43:58 GMT
Tsafa, I think your calculations may prove to be a bit off since the weight of the sword and the way it moves is quite different than a pitching motion with a baseball.
However, I have a chronograph that measures speed in feet per second (fps). I need to shorten the length of distance it measures (shorten from 36 inches to 18 inches) so I can measure the actual speed through a cut. Just realize that it is always variable since you accelerate the blade into the cut with the fastest speed within the last 6-8 inches before the impact with the target.
Anyone have a handy conversion formula for translating fps into mph or kph?
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Post by Deleted on Nov 20, 2007 19:49:58 GMT
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Post by Deleted on Nov 20, 2007 20:01:04 GMT
Mike, I am very eager to see the results of your test. I hope you get a chance to do them today. If you can do about 20 of them and we can get an average.
Thanks for that link Darkintruder. I think that the one that applies is:
Feet per second x 0.6818 = Miles per hour
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Post by ShooterMike on Nov 20, 2007 20:04:11 GMT
Sorry, can't do it today. I will have to reprogram the chrono and mount it on a shorter 18 inch rod. Also have to have the lighting conditions just right to catch a sword blade...and I'm at work until dark. ![:(](//storage.forums.net/forum/images/smiley/sad.png)
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Post by Deleted on Nov 20, 2007 20:04:54 GMT
Ok. When do you think you can do the test?
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Post by ShooterMike on Nov 20, 2007 20:07:20 GMT
I tested a swing before. I posted it somewhere else, but basically...my fastest swings were 270-280 fps. I could never get to 300 fps. Using your conversion numbers that's 185 to 190 mph.
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Post by ShooterMike on Nov 20, 2007 20:08:40 GMT
So HEY!!! Your numbers are right on!!! I accede to your superior wisdom. ![:)](//storage.forums.net/forum/images/smiley/smiley.png)
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Post by Deleted on Nov 20, 2007 21:29:13 GMT
Holy sh1t !!! I never expected that to actually work out so beautifully. You made my day.
If you get a chance, try that experiment with an axe too. I want to see the variance. I don't expect much on the initial blow. I think the variance would be in initiating successive blows.
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Post by septofclansinclair on Nov 20, 2007 23:07:55 GMT
This could be an interesting physics sidenote. I mean, a sword is basically - what? A type 2 lever? We should get a math major down here...
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Post by Deleted on Nov 21, 2007 1:08:10 GMT
Mike, if it not a bother, could you so some more tests for me please.
Please find out what the average speed is of your thrusts.
Also throw a baseball to see what you pitching speed is. Lets see how this compares. Thanks
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Post by ShooterMike on Nov 21, 2007 1:40:44 GMT
Mike, if it not a bother, could you so some more tests for me please. Please find out what the average speed is of your thrusts. Also throw a baseball to see what you pitching speed is. Lets see how this compares. Thanks There are a couple of challenges to this. A chronograph uses two electronic eyes. One starts the timer and one stops it. Then the onboard computer takes the time measurement in microseconds and calculates the speed based on that time. The problem is that it's designed to measure the speed of a projectile in flight. If the object (like a sword or axe) speeds up or slows down between the eyes, the reading isn't accurate, just an average. The eyes on my chrono are set 36 inches apart. But it gets a little more complicated, because I have the high-end Oehler 33P, which actually has two sets of eyes that are spaced out 18 inches. The two sets of readings are averaged together for the final results. However, if the two sets of readings are more than 20-30 fps apart (like if you accelerate the blade over the chrono) it thinks the readings are screwed up and discards the measurement. I ran into this problem a lot while trying to measure my sword swing. I would get a reading about once out of every 5-10 swings. And it won't measure anything slower than about 200 fps. So I don't think it would be possible to measure a thrust since I can't keep a reasonably constant thrusting speed over a 4 foot distance. And in any case, if I thrust over the first eye the blade wouldn't let it see the line of sight being broken since the blade length would obscure the eye. I don't have a baseball, but I think I have a golf ball. Would that do for starters? Kind of complicated and I probably haven't explained it well. But suffice to say that any testing must resemble a projectile. If you ever make it over here with your bow, I can chrono your arrows... ![;)](//storage.forums.net/forum/images/smiley/wink.png) ;D
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Post by Deleted on Nov 21, 2007 2:06:08 GMT
Mythbusters the show did an episode where they were trying to cut swords in half (*rolls eyes*) and they actually measured the speed and power of a sword cut with ballistics gel so that they could accurately as possible have their machine hitting with human speed and power. If you get your hands on that episode, it is on youtube, you can get a rough estimation of how fast you can actually swing a sword. I can tell you though that a sword tip moves alot faster than 180 mph.
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Post by Deleted on Nov 21, 2007 3:12:18 GMT
Ok... here we go... feel free to point out any flaws, it has been a while since I have had to do this.
Momentum (P) = some mass (m) times a velocity (v).
You have the right idea but the weight of the sword tip you assumed to be 1.5 pounds is actually a force, not a mass. The English unit for mass is a SLUG and can be found by dividing the weight by the acceleration due to gravity (32.2 ft/s2). In this case, the mass of the 1.5 pound sword tip would have a mass of 0.0466 lb s2/ft or 0.0466 slugs. Assuming this sword tip was moving at 270 ft/s, we now have what is needed to calculate the momentum of the tip:
Momentum = mass * velocity P = mV P = 0.0466 lb s2/ft * 270 ft/s P = 12.58 lb s
With all that fun math done, what do we have? We have the momentum, but what does mean? In the case of swords, my first thought for the use of momentum would be to solve a question such as:
If you swing a sword with a tip weight of 1.5 lbs at a velocity of 270 ft/s and strike a 10 lb pumpkin, what is the resulting velocity of the sword and pumpkin assuming the sword sticks in and stays lodged in the pumpkin?
To summarize the answer, we start with 1.5 lbs moving at 270 ft/s. Once the sword sticks in the 10 lb pumpkin, the system of the 10 lb pumpkin plus the 1.5 lb sword is now 11.5 lbs.
You can kind of forget about converting the weight to mass because it ends up getting canceled out being on both sides of the equation.
Momentum 1 (P1) = Momentum 2 (P2) m1 * V1 = m2 * V2 1.5 lbs * 270 ft/s = 11.5 lbs * V2
V2 = (1.5 lbs * 270 ft/s) / 11.5 lbs
V2 = 35.2 ft/s
It might be more useful to find the FORCE (F) with which the sword strikes it's target. The idea of impulse now come in to play along with momentum. An impulse is force exerted over some unit of time. For this we use Newton's second law.
Force (F) =mass (m) * acceleration (a). F = m * a
An acceleration is a change in velocity over some change in time a = (V2 - V1) / (t2 - t1)
We can substitute this in to the above Force equation to get:
F = m [(V2 - V1) / (t2 - t1)]
We found out the change in velocity from the above momentum solution. We also have the mass from the start of the problem. All we need now is the time it took for the blade to change from 270 ft/s to 35 ft/s. This is a good place to make an assumption. Let's assume the impact that caused the change in velocity to be 0.5 seconds.
Plugging in all of our known values:
F = 0.0466 lb s2/ft [(270 ft/s - 35.2 ft/s) / 0.5 s]
All of the units should cancel out nicely resulting in a Force of 21.8 lbs.
What's that? Only 21.8 lbs of force? That doesn't sound like much. We have to remember that that force of 21.8 lbs is applied over a very small area. Time for another assumption. Let's assume that the force was applied over a length of the blade equalling 1 in and that the thickness of the blade is 0.020 inches (about the thickness of my finger nail).
A force applied over (divided by) an area is a pressure.
The area = 1 in * 0.020 in = 0.02 in2
The pressure equals 21.8 lbs / 0.020 in2 = 1090 lbs / in2 or 1090 psi.
This is the reason Japanese blades are curved. It applies the same force over a smaller area resulting in a higher pressure.
We can use the same force and same blade thickness but assume a smaller length of blade contact due to curvature. Let's assume a blade contact length of only 0.25 in.
21.8 lbs / (0.25 in * 0.020 in) = 4360 psi
The smaller the area the force is applied over, the greater the pressure.
Just think of the pressure truely created by the very fine edge of a sharpened katana...
Well, there goes 1.75 hours of my evening.
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Post by Brian of DBK on Nov 21, 2007 3:20:03 GMT
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Post by ShooterMike on Nov 21, 2007 3:52:52 GMT
Mark, you are the man!
But I would add one thing. BACKSTORY: Because I shoot at a pretty high level of competition I'm used to dealing with very small units of time. The time interval between shots fired at a target are called "splits" as in the split time between shots. Most top level, or even mid-level shooters with some experience can judge split times, just from the sound, to within 0.02-0.03 of a second. For instance, my splits on close targets are typically either 0.18 or 0.19 of a second. It goes up to 0.21-0.22 for intermediate range targets.
All that to say, my opinion, based on this experience in dealing with minute fractions of a second, is that the change in velocity happens in about 0.15 to 0.20 of a second. You used 0.5...a full half second, which is like...forever to me! ;D
How would the impact pressure change if you assume 0.15 second for deceleration?
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Post by Deleted on Nov 21, 2007 3:57:18 GMT
--Mike, I don't know about the golfball. I think too light and the speed will go way up. I picked baseball because it has more mass and because it is easy to go to a carnival and see how fast you can pitch a baseball, so it will be easier to relate to. Maybe you can find a tennis ball. I think that is closer. Another idea would be to throw a number of different objects. A rock, golfball, shoe, knife, cellphone, lol. Then we'll consider the results.
On the thrust test, how about if you used a long 2x3 board. That way you have more surface area and a longer grip. The velocity should be the same cause a thrust comes from the body.
While your testing all these things also try some swings with a single-hand sword. Well... since your setting it up, bring some friends over and swing anything you can get your hands on, including your golf-clubs. Lets see what kind of speed we get. We will need to record the handle size (if there is any leverage action) and the length of the object swung from the tip to your hand.
--Bloodwraith, my mathematical calculations have been confirmed by Mikes practical test. So that is two independent methods coming up with a similar result. Mike plays around with guns, and I am sure he has used his chronograph before to measure bullet velocities. He most likely has compared his measured bullet speeds to the manufactures stated figures. I have a lot of confidence in Mikes technical skill in using the machine.
There is also the practical consideration. Consider my momentum calculation. If a 180 lb man stepped on your foot, not big deal. If a 180 lb man man stepped on you foot wearing an ice-skate that would likely break some bone. Now imagine if that ice-skate had a sharp edge. I think that type of force over such a small area is enough to do serious damage.
Edit: I found the episode. The samurai is slicing at 48 mph. The slice is naturally slower then a tip cut.
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Post by Deleted on Nov 21, 2007 4:41:13 GMT
Wow, pretty cool torture tests...I could've told them the myth was false, though. Course, then we wouldn't have cool videos to watch. Was the katana they were using a Paul Chen PK? It looked that way. I also think I I.D.'d a Valiant Viking sword. That katana's got an amazing temper to bend the way it did!!!
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Post by Deleted on Nov 21, 2007 11:22:01 GMT
Mark, I forgot to thank you for taking the time to work out those equations. Thanks Buddy.
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