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本帖最后由 happydad 于 2014-5-11 16:22 编辑
英國氣槍雜誌登的一篇文章提供給大家做參考!
CD = COEFFICIENT OF DRAG / 風阻系數
BR = BALLISTIC RANGE / 彈道範圍
(原文)
The Ballistic coefficient (BC) of pellet is often used as indicator of its effectiveness the larger the value of the coefficient, the better. Whilst this is correct in principle, a high value of BC only indicate how effectively a pellet retains its velocity and kinetic energy on its journey from muzzle to target. When the pellet impacts the target, its kinetic energy is converted into work on the target material and the pellet itself. This energy conversion is manifested as combination of impact force, penetration depth and pellet deformation. In general, the lower is the value of BC, the higher will be the impact force and the shallower will be the penetration into the target material, in physics, things are sometimes not as straightforward as they seem and , ironically, this particular issue is actually complicated by using BC as parameter. In fact, I am of the view that it was a great pity that the idea of the Ballistic Coefficient was ever introduced at all. The whole issue of flight ballistics versus terminal ballistics is much easier to make sense of when discussed in terms of the Coefficient of Drag. rather than the Ballistic Coefficient, which, in reality, is not a coefficient at all, The core physical phenomenon which ties everything together is dynamic pressure.
DYNAMIC PRESSURE AND AIR DRAG
Any object in fluid flow experience a pressure caused by the movement of fluid molecules around the object(Figure 1) The higher the relative velocity between the object and the denser the fluid, the higher will be the pressure. This dynamic pressure, acts over the effective normal area of the pellet, giving rise to a decelerating force. which saps the pellet of velocity and kinetic energy. The effective surface area of the pellet is its actual projected cylindrical cross sectional area multiplied by the Coefficient of Drag(CD). So a pellet with a CD of 0.5 experiences only half the deceleration of a same diameter pellet with a CD of one. The rate of deceleration (or retardation) is given by the the square of the pellet velocity, 'V' divided by a constant which has the dimensions of length. As I have explained in previous articles, I call this constant the "Ballistic Range" or BR. It is expressed in feet or metres, depending on how the velocity is measured, if the velocity is in ft/sec, then BR is in feet, alternatively, if the velocity is in m/sec BR is expressed in metres, Typical value ranges for BR are 240 to 720 feet or 73 to 220 metres, where the higher values of BR indicate a better ballistic performance for the pellet, Knowledge of BR, which is easily calculated from the formula on Figure 1, allows the estimate of velocity loss and pellet drop at different ranges. We don't need the ballistic coefficient to be able to do this, we simply need the drag coefficient, the diameter and jass of the pellet and a figure for the density of air, So where does the ballistic coefficient come in and why do we need it?
BALLISTIC COEFFICIENTS : MUDDLED AND CONFUSION
If we look closely at the formula for BR, we can see that it can split into two components, The first component (8/....) depends on the density of the air but does not depend on the design of the pellet. Using the quoted density of air at standard temperature and pressure in imperial units(0.0023 slugs/cubic foot), we get BR=1093(the air constant) x m/d2x1/CD, The value of the mass divided by the square of the diameter is called the Sectional Density of the pellet and when this is divided by the coefficient
of drag, CD, we have, in essence, the definition of the ballistic coefficient, So is the ballistic coefficient simply the term in square brackerts(m/d2x1/CD)? unfortunately , not quite; this where the confusion arises. The classical imperial definition of the ballistic coefficient of a bullet is Consequently, not only is weight substituted for mass, but specific units are used and a reference coefficient of drag is introduced. (I won't go in to the reasons why here, but interested readers can look up an easy to understand explanation at http://www.precisionshooting.com). The reference drag factor normally used is that for the so-called G1 bullet and this averages out at about 0.2 for normal air gun velocities. Factoring in all thies aspects, we can find simple ratio of BR to BC:BR/BC=1093(air constant)x144(square feet to square inches)/32.17(acceleration due to gravity)/0.2(reference coefficient of drag)=24462, which I round off to 24000, ( I have spelt this out in detail because I have been asked many times where the number of 24000 come from) So to find BR in feet. we simply multiply BC by 24000, or by 8000, if we want the ballistic range in yards, This seems to be a handy simplification, but using the ballistic coefficient as catch all measure of what might be termed ballistic quality obscures a key fact. the ballistic coefficient does not indicate how good the aerodynamic design of a pellet is; it indicates combination of coefficient of drag and weight. A much better measure of the aerodynamic efficiency of the design is the drag coefficient, CD, on its own; it is just a number, a true coefficient which has the same value irrespective of the system of units used for any calculations, The BC on the other hand, mires our understanding by having units embedded in it, along with a quasi-arbitrary reference coefficient of drag: heavy pellets with a lousy drag coefficient can have a good ballistic coefficient and vice versa. The aerodynamic efficiency of an aircraft or motor car is measured in terms of CD, not BC, so why should we be different? it is largely an accident of history and tradition, but as far as I am aware, no professional ballistician actually uses ballistic coefficients these days, even though BC is the most commonly used comparator between different pellets. The question is then: do we actually need ballistic coefficients? The answer is " no we don't! But are we stuck with them? Unfortunately, yes!
TERMINAL BALLISTICS
Some time ago, in The Quest for the Perfct Pellet, I cam up with a rule of thumb: In terms of short range impact, switching from a round head pellet to a flat headedpellet is equivalent to going up one calibre. The photographs illustrate the principle and show the level of deformation for round head and flat head pellets impacting modelling clay a 6ft. lbs. energy. Note that the degree of deformation depends strongly on the coefficient of drag, not on BC, in fact in each case. the level of length contraction and diameter expansion is broadly proportional to the coefficient of drag of the pellet. So, does this imply that a high drag pellet is more effective on impact than a more aerodynamically efficient pellet? Yes it does, but only if the pellets impact the target with the same muzzle energy. At any given range, this will not be the case, because the pellet with the higher drag coefficient will lose more energy on its way to the target. there must, then be a cross over rage, within which the highdrag pellet has the greatest impact and beyond which the honors go to the low drag pellet. Figure 2 shows my computed graphs for a round head pellet and flat headed pellet with the same weight and fired at the same muzzle velocity the graphs show that the cross over range is about 33 yards suggesting that the flat head is the pellet of choice up to this range. In prctice I would limit the use such pellets to more like 25 yards, because of accuracy and wind susceptibility issues. Certainly, at anything over 30 yards. the low drag pellet would be my choice for use such as like round one.
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Pandamalone 於5月6日發表
给没时间详细读的朋友们大致总结一下
首先这里引入了风阻系数的概念取代了原本用的弹道系数，因为后者实际上是风阻系数和弹丸重量的结合，而且涉及到一些经验公式总结，而前者是一个无单位的完全可进行测量的参数。
其次基于风阻系数，说基本上对于对猎物的杀伤力而言，风阻系数越大的弹丸，截面积扩大和弹丸长度减小的效应越好，同样的到达动能下可以更好的的传达杀伤力。但反过来风阻系数更大的弹丸在飞行到目标期间的动能衰竭也更多，所以在接触目标时存留的动能小于风阻系数小的弹丸。所以这里有一个临界点,在这个距离内风阻系数更大的弹丸更有优势,超过这个距离,风阻系数小的弹丸有优势。具体到平头和蘑菇头弹丸的对比，作者的分析得出，临界距离大概在三十三码，保险起见他建议25码内用平头弹，更远则用蘑菇头。
所以我们要简单记住的结论就是,二十五码内用平头,以上用蘑菇头。
有一个问题是这里没有考虑空尖弹的情况,不知道它的的风阻系数如何。另外也不知道空尖弹的空尖设计会不会给它在命中猎物时带来额外的好处。 |
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发表于 2014-5-10 04:04
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发表于 2014-5-10 07:21
