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Bullet Tractability

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Unread 12-23-2002, 04:29 PM
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Join Date: Sep 2001
Location: San Jose, CA
Posts: 66
Re: Bullet Tractability

No. Check out this equation. Note that for a projectile to be 'tractable' it must have a tractibility factor greater than 5.1 (according to Mr. Ruprecht) and that this factor is inversely proportional to the gyroscopic stability factor. So the higher the angular velocity of any given bullet, the lower the tractibility factor. At some point, according to this equation, the bullet simply becomes fixed in space as shown here. The way that I interpret this is that as long as the precessive forces don't overwhelm the pitching moments, but instead these forces are in dynamic balance, as the bullet slows and the pitching moment decreases, the bullet will close its angle of repose always with respect to its relative wind which means that as the bullet begins to decend, it will nose over in order to keep a proper angle of repose. Where the bullet is over-spun, the gyroscopic forces fix the bullet's attitude and no matter how great the pitching moment becomes, the bullet is unaffected.

Now, the foregoing may be wrong, but that is how I understand it.

I wish Warren would weigh in here. He always has something interesting to say.
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Unread 12-23-2002, 05:12 PM
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Re: Bullet Tractability

[ 07-12-2003: Message edited by: S1 ]
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Unread 12-23-2002, 05:43 PM
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Join Date: Jun 2001
Location: Palmer, Alaska
Posts: 2,539
Re: Bullet Tractability

Trust me, I'm straining to follow just half of the things you gents are discussing. I do remember the VV manual talking about a ultra high atack angle presents a bigger problem, as in slow MV or ultra long distance or both. It was very interesting but could not understand all the terms used in it as well, so some was not absorbed as a result. In time it will come together.
Brent Moffitt
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Unread 12-23-2002, 06:03 PM
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Join Date: Dec 2002
Location: Asuncion, Paraguay
Posts: 39
Re: Bullet Tractability

Hi Blaine, have you worked out with numbers Ruprecht's formula (I'm too lazy to do it [img]images/icons/smile.gif[/img])?
He says: "Over-stabilization is said to occur, if the angle enclosed between the bullet┤s axis of form and the tangent to the trajectory (the yaw of repose) exceeds a value of approximately 10░". Probably most bullets never approach this angle.
In Vaughn's book, Fig. 10-8, you can see this angle is always 2.5║-3.0║, depending on the match number, for the 7.62 NATO bullet (a 147gr. SBT FMJ bullet).
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Unread 12-23-2002, 07:29 PM
MAX MAX is offline
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Join Date: Sep 2001
Posts: 263
Re: Bullet Tractability

Another source is Robert A Rinker's articles in Varmint Hunter issues 39 & 40, "Projectile Stability-A Comprehensive Technical Study". Or his book UNDERSTANDING FIREARMS BALLISTICS. His explanations are understandable to me and that's sayin' a lot my friends.

He says the bullets nose over and that this was established in U.S. Army tests in 1880 using .45 Cal (45-70?) to ranges up to 3500 yards. Current technology(radar) verifies this. It may be possible to overstabilize to some degree, but he doesn't sign off on the idea of a bullet achieving this to the degree necessary to preclude tractability. It will increase the angle of repose.
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[ 12-23-2002: Message edited by: MAX ]
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Unread 12-23-2002, 08:06 PM
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Join Date: May 2001
Location: Arco, ID 83213
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Re: Bullet Tractability


Ruprecht gives the formula. Essentially tractability is inversely related to the gyroscopic stability factor to a point. As the SF exceeds 4.0 due to overspin (a more correct term than overstabilized) the nose of the bullet wants to pull high and to the right. There are countervailing forces. On bullets with long bearing surfaces the shank acts as a wind vein and will tend to hold the axis parallel to the direction of travel or directly into the oncoming air. This is true whether the bullet is yet to reach it's ordinate or after.

Tractability is not mysterious at all. I have many target imprints that are perfectly round and at ranges where the fall angles would by themselves cause keyhole imprints if the bullets were not turning over. Nontractability can be caused by overspinning. Specifically, because the forward drag is so much greater than the angular (rotational) drag that the SF increases with flight time to values of 9.0, 10.0 and even 12.0. It is improper design, but unfortunately it was quite common design 30 and 40 years ago. An example would be a 147 gr. FMJ shot in a .308 with a 10 twist barrel. Expect a SF of over 9.0 past 800 yds. at sea level. Also, expect severe precession, yaw, and instability.

So how do you avoid this? Balance the forward drag with the angular drag. The forward drag has to be quite low to even make this remotely achievable. Nothing with a BC of less than .600 has a chance. Then increase the angular drag. When you have figured out how to do this, then give the bullet a long shank. You can amplify this by using materials that are less dense. This also gives you more surface area (increasing angular drag). You are not faced with a static problem. It is possible to increase the angular drag to a point where the SF begins to decrease. This is bad. Bullets fly poorly and are definitely not tractable when they are swapping ends.

Those arguing that bullets cannot be tractable belong in the same room with the flat-earthers and those folks who say Apollo 11 landed somewhere in Nevada.
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Unread 12-23-2002, 08:23 PM
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Re: Bullet Tractability


You are right. The test was done in 1880 with .45 cal. military rifles and a 500 gr. bullet. The tests that at all ranges the bullets landed point first, even out at 3500 yds. where the bullet's angle of descent was 65 deg. (Page 104 for those interested.)

Thanks for that reference. Until I can find something more rigorous, I'll use this as evidence supporting bullet tractability.
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