Bullet Tractability

[Blaine Fields]

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.

 

[Guest]

[ 07-12-2003: Message edited by: S1 ]

 

[Brent]

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.

 

[TiroFijo]

Hi Blaine, have you worked out with numbers Ruprecht's formula (I'm too lazy to do it

)?
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 2.5º-3.0º, depending on the match number, for the 7.62 NATO bullet (a 147gr. SBT FMJ bullet).

 

[MAX]

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.
Buy your acquaintance a book for Christmas, and help kill another superstition.

And a MERRY CHRISTMAS to all!!!!!!!!!!!

[ 12-23-2002: Message edited by: MAX ]

 

[Warren Jensen]

Blaine,

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.

 

[Blaine Fields]

Max,

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.

 

[TiroFijo]

Warren, how good is bullet stabiliy through the transonic speed when you mantain a good "normal" gyroscopic stabily factor (1.3 - 1.5?) at this range? Is the bullet still accurate at subsonic speeds?

 

[Blaine Fields]

Warren, great to hear from you.

<BLOCKQUOTE><font size="1" face="Verdana, Helvetica, sans-serif">quote:</font><HR> 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. <HR></BLOCKQUOTE>

I had quite an argument with one of these flat-earthers that finally got me kicked off that board. Apparently, I didn't pay proper respect to the resident guru in challenging his wisdom. (Actually, you've had a rather vicious run-in with the same correspondent.) Although he wouldn't provide any reference material to support his position, he assured me that 1) bullets remain fixed in attitude from muzzle to target; and, 2) I was out of my depth in trying to discuss the matter with him. He also said that the Ruprecht website was wrong and showed numerous errors and misunderstandings, but failed to give any specifics.

I'm glad to hear that your experience supports a result that seems to be intuitive even without the 1880 Army study or Ruprecht's math. I think that I can put this particular matter to rest.

Have a good holiday.

 

[Blaine Fields]

S1,

I have Vaughn's book and have read through it but didn't find a specific reference to this issue. In his description of various trajectory topics, there is an assumption that the bullet noses over, but no specific discussion of the phenomena. In fact, one of things on my 2003 'to do' list is to track Vaughn down and engage him in conversation regarding this matter.

At any rate, thanks to all for the input. If anyone comes across any further information, either pro or con, please post it.

 

[Guest]

[ 07-12-2003: Message edited by: S1 ]

 

[Warren Jensen]

S1,

It is not only possible to cause instability due to overspinning it happens quite a bit. Not at the muzzle but many yards down range where the increase in SF causes a dramatic precession and yaw, which can lead to instability. At the muzzle there is insufficient different between bullet's angle of attack and flight path. Downrange, past the trajectory ordinate, there can be a significant difference.

I have radar data of bullets coming apart due to insufficient structural strength at high rotational velocities. I also have radar data of instability due to overspin down range. This is from the US Army's Yuma Proving Grounds last summer during a two day test which I ran. I spent many years working the formulas and talking theory and physics. Many of my questions were not convincingly answered. It is the test range with a good doppler radar that answered these questions. You can get meter by meter data and if set up right you can even see the spin of the bullet.

You can do it, too. A day's range time at Yuma only costs about $3500, and that includes the radar. It is the breakdown of the data that is expensive, because you have to do it yourself, and it takes time. The last shoot filled two CDs or about 1.2 gigabytes.

 

[Guest]

[ 07-12-2003: Message edited by: S1 ]

 

[Warren Jensen]

S1,

Simply put, your facts and theory are wrong. For one the GS, as you put it, continues to increase on the 147 gr. It is above 9.0 at 800 yds.

I have spent many years arguing the math and the theoretical with some very bright and experienced ballisticians, Bob McCoy being one. I recommend leaving the office and the computer programs and going to the range where a modern radar provides the solid answers.