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Rifles, Reloading, Optics, Equipment
Rifles, Bullets, Barrels & Ballistics
Improved Stability Formula for Plastic Tipped Bullets
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<blockquote data-quote="Michael Courtney" data-source="post: 738949" data-attributes="member: 28191"><p>Right, but only if everything else is held constant. But everything else is not held constant when comparing a plastic tipped bullet with an identically shaped bullet with constant density. In addition to moving the center of gravity slightly backwards, the effect of the plastic tip<strong> increases</strong> the axial moment of inertia and <strong>decreases</strong> the tumbling moment of inertia. Both of these effects on the moments of inertia tend to increase the gyroscopic stability and they more than compensate the change in the center of gravity. </p><p></p><p><img src="http://www.nennstiel-ruprecht.de/bullfly/gyrocond.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p><p></p><p>The fundamental equation for gyroscopic stability is shown above, taken from</p><p></p><p><a href="http://www.nennstiel-ruprecht.de/bullfly/gyrocond.htm" target="_blank">http://www.nennstiel-ruprecht.de/bullfly/gyrocond.htm</a></p><p></p><p>Ix is the axial moment of inertia; it appears twice in the numerator, so increasing Ix, increases stability strongly. Iy is the tumbling moment of inertia; it appears in the denominator, so decreasing Iy also increases stability. Moving the center of mass backward slightly increases C<span style="font-size: 9px">Ma</span>, the derivative of the overturning moment coefficient. </p><p></p><p>So the plastic tip changes three terms in the stability equation. The change in one term tends to decrease stability, but the changes in the other two terms tends to increase the stability, so the net change is an increase in stability.</p><p></p><p>If you don't believe the theoretical explanation, then believe the experiments reported in the Precision Shooting papers. We've also conducted additional experiments showing that the original twist formula is accurate for metal bullets, but it underestimates the stability for plastic tipped and open tipped bullets. The effect of a plastic tip or an empty space in the tip of a bullet is to increase stability relative to a constant density bullet of the same dimensions.</p></blockquote><p></p>
[QUOTE="Michael Courtney, post: 738949, member: 28191"] Right, but only if everything else is held constant. But everything else is not held constant when comparing a plastic tipped bullet with an identically shaped bullet with constant density. In addition to moving the center of gravity slightly backwards, the effect of the plastic tip[B] increases[/B] the axial moment of inertia and [B]decreases[/B] the tumbling moment of inertia. Both of these effects on the moments of inertia tend to increase the gyroscopic stability and they more than compensate the change in the center of gravity. [IMG]http://www.nennstiel-ruprecht.de/bullfly/gyrocond.gif[/IMG] The fundamental equation for gyroscopic stability is shown above, taken from [URL]http://www.nennstiel-ruprecht.de/bullfly/gyrocond.htm[/URL] Ix is the axial moment of inertia; it appears twice in the numerator, so increasing Ix, increases stability strongly. Iy is the tumbling moment of inertia; it appears in the denominator, so decreasing Iy also increases stability. Moving the center of mass backward slightly increases C[SIZE=1]Ma[/SIZE], the derivative of the overturning moment coefficient. So the plastic tip changes three terms in the stability equation. The change in one term tends to decrease stability, but the changes in the other two terms tends to increase the stability, so the net change is an increase in stability. If you don't believe the theoretical explanation, then believe the experiments reported in the Precision Shooting papers. We've also conducted additional experiments showing that the original twist formula is accurate for metal bullets, but it underestimates the stability for plastic tipped and open tipped bullets. The effect of a plastic tip or an empty space in the tip of a bullet is to increase stability relative to a constant density bullet of the same dimensions. [/QUOTE]
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Improved Stability Formula for Plastic Tipped Bullets
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