|
|
| Line 1: |
Line 1: |
| {{refimprove|date=October 2011}}
| | Myrtle Benny is how I'm known as and I feel comfy when people use [http://citymama.com.ua/profile_info.php?ID=38588 std testing at home] the home std at home std testing test full name. One of the very best issues in the globe for me is to do aerobics and I've been doing it for quite a while. Her husband and her reside in [http://Www.std-gov.org/faq_1.htm Puerto Rico] but she std testing [http://www.hotporn123.com/user/KGottscha please click the next page] at home will have to transfer 1 working day or an additional. Managing individuals is his profession.<br><br>Also visit my web blog; at home std test ([http://javly.com/?p=56362 mouse click the up coming website]) |
| The '''center of percussion''' is the point on an object where a [[perpendicular]] impact will produce translational and rotational forces which perfectly cancel each other out at some given pivot point, so that the pivot will not be moving momentarily after the impulse.
| |
| The same point is called the '''center of oscillation''' for the object suspended from the pivot as a [[pendulum]].
| |
| | |
| Centers of percussion are often discussed in the context of a bat, [[racquet]], [[sword]] or other long thin objects. The center of percussion may or may not be the "[[sweet spot (sports)|sweet spot]]" depending on the pivot point chosen.
| |
| | |
| ==Further explanation== | |
| [[Image:Centre of percussion.svg|thumb|upright=1.4|Effects of a blow on a hanging beam]]
| |
| Imagine a beam is suspended from a wire by a [[U-bolt]] so that it can move freely along the wire. A blow to the beam below the center of gravity will cause the beam to rotate around the CoG (center of gravity) and also cause the CoG to move away from the blow. If the blow falls above the CP (center of percussion) the movement of the CoG will cause the U-bolt to move away from the blow since the effect of the translational acceleration will outweigh the effect of the rotational acceleration. If the blow falls below the CP the opposite will occur, rotational acceleration will outweigh translational acceleration and the U-bolt will move towards the blow. Only if the blow falls exactly on the CP will the two cancel out to produce no net movement of the U-bolt.
| |
| | |
| ==Calculating the center of percussion==
| |
| For a free, rigid beam, a force F applied at [[right angle]] at a distance b from the [[center of gravity]] (CoG) will result in the CoG moving at a velocity V according to the relation:<ref>{{cite journal |author=Rod Cross |year=2004 |title=Center of percussion of hand-held implements |journal=[[American Journal of Physics]] |volume=72 |issue=5 |pages=622–630 |url=http://www.physics.usyd.edu.au/~cross/PUBLICATIONS/26.%20COPHandHeld.PDF |format=[[Portable Document Format|PDF]] |doi=10.1119/1.1634965 |bibcode=2004AmJPh..72..622C}}</ref>
| |
| | |
| :<math>F=M\frac{dV}{dt},</math>
| |
| | |
| where M is the mass of the beam. Similarly the [[torque]] exerted will be as per the relation:
| |
| | |
| :<math>Fb=I\frac{d\omega}{dt},</math>
| |
| | |
| where I is the [[moment of inertia]] around the CoG and <math>\omega</math> is the [[angular velocity]].
| |
| | |
| For any point P on the opposite side of the CoG from the point of impact, the velocity of point P is
| |
| | |
| :<math>v = V - A\omega\, ,</math>
| |
| | |
| where A is the distance of P from the CoG. Hence:
| |
| | |
| :<math>\frac{dv}{dt}=\left(\frac{1}{M}-\frac{Ab}{I}\right)F.</math>
| |
| | |
| The velocity v is then given by:
| |
| | |
| :<math>v=\left(\frac{1}{M}-\frac{Ab}{I}\right)\int F dt.</math>
| |
| | |
| The axis of rotation is situated where <math>v = 0</math> and the corresponding center of percussion is at distance b from the CoG, with
| |
| | |
| :<math>b=\frac{I}{AM}.</math>
| |
| | |
| This is also the [[center of oscillation]] of a [[physical pendulum]] of the same mass M, hung at the pivot point. (The center of oscillation is the position of the mass of a simple pendulum that has the same period as the physical pendulum.)<ref>{{cite web |url=http://www.kettering.edu/~drussell/bats-new/cop.html |title=What is the COP and does it matter? |work=Physics and Acoustics of Baseball & Softball Bats |author=Daniel A. Russell |publisher=[[Pennsylvania State University]] |accessdate=May 24, 2012 |date=June 16, 2005}}</ref>
| |
| | |
| ==Center of percussion of a uniform beam==
| |
| | |
| For the special case of a free beam of uniform density of length L the moment of inertia around the CoG is:
| |
| | |
| :<math>I=\frac{ML^2}{12}</math> (see [[moment of inertia]] for proof)
| |
| | |
| Hence:
| |
| | |
| :<math>b=\frac{L^2}{12A}</math>
| |
| | |
| ==Relation to the sweet spot==
| |
| The [[sweet spot (sports)|sweet spot]] on a [[baseball]] bat is generally defined as the point at which the impact feels best to the batter (it is also occasionally defined as the point at which the maximum [[velocity]] is imparted to the ball, but this may not be the same point).
| |
| | |
| Although it has long been believed the center of percussion and the sweet spot are the same, recent practical observations have indicated that the point many batters feel is "sweetest" corresponds to a pivot point in the arm, beyond the handle of the bat. {{Fact|date=March 2007}}
| |
| | |
| ==Application to swordmaking==
| |
| The '''center of percussion''' of a [[sword]] is the point on the [[blade]] where cutting produces the least hand shock. It is also the division between the ''weak'' and ''middle'' sections of the blade.
| |
| | |
| Like the [[center of balance]] of a sword, the center of percussion can be moved by employing a heavier [[Hilt#Pommel|pommel]] or changing the mass distribution of the blade.<ref name="Turner">{{cite web |author=George Turner |url=http://www.thearma.org/spotlight/GTA/motions_and_impacts.htm |title=Sword Motions and Impacts: An Investigation and Analysis |publisher=Association for Renaissance Martial Arts |date=1999 |accessdate=May 24, 2012}}</ref>
| |
| | |
| One of the vibrational nodes of the second harmonic of a vibrating sword (the node closest to the tip) is also often (mistakenly) referred to as the center of percussion. The significance of the vibrations about this mode have been contested as having little relevance to sword physics.<ref name="Turner"/>
| |
| | |
| So-called “blade harmonics” are a commonly misunderstood concept. The common belief is that a sword must be “harmonically balanced” in order to cut properly, because the vibrations would otherwise interrupt the line and power of the cut. As explained above, this proposition is false: the vibrations caused by a sword cut are almost unnoticeable except as a mild stinging to the hands even in blades that lack this quality. It has also been demonstrated that the object the sword cuts through serves to further reduce the intensity of any vibration, making it even less noticeable.
| |
| | |
| Many experts speculate that harmonic balance is merely a byproduct of proper construction and balancing, rather than an intentional quality added to weapons. Unfortunately, some sword vendors advertise "secret techniques" of harmonic balancing in an attempt to "prove" the superiority of their products. This only serves to amplify the false impressions of the value of harmonic balance by seeming to lend them legitimacy.<ref name="Turner"/>
| |
| | |
| ==See also==
| |
| *[[Weight distribution]]
| |
| | |
| ==References==
| |
| <references/>
| |
| | |
| [[Category:Swords]]
| |
| [[Category:Mechanical vibrations]]
| |
| [[Category:Geometric centers|Percussion]]
| |
Myrtle Benny is how I'm known as and I feel comfy when people use std testing at home the home std at home std testing test full name. One of the very best issues in the globe for me is to do aerobics and I've been doing it for quite a while. Her husband and her reside in Puerto Rico but she std testing please click the next page at home will have to transfer 1 working day or an additional. Managing individuals is his profession.
Also visit my web blog; at home std test (mouse click the up coming website)