rate-of-twist?

[Zonie]

John:
Perhaps your confusing me with someone else? :hmm:

I have consistently said over the years that people who dwell on twist rates and their usefulness in shooting roundballs are on the wrong track.
The depth of the rifling grooves is the important issue with deep grooves being "better" and shallow grooves being "worse".

For instance, I have always said the Thompson Center Hawken shoots patched roundballs very well despite its fairly shallow rifling (.005) if the ball is tightly patched.

 

[Ken Rummer]

Your chart is interesting because the twist listed gives a Greenhill number of 150 to 155 for roundballs.
It seems to me that ideal twist rate was initially calculated using the ball diameter and a Greenhill number of 150. [G= twist/RB dia]

A .490 RB in 1:70 gives Greenhill = 147
A .490 RB in 1:48 gives Greenhill = 98

I believe the closer you get to G=150 the better the gun will shoot and other issues will have a smaller effect, e.g. spin rate.

 

[paulvallandigham]

The Greenhill formula, as I understand it, was designed to determine the best ROT for Conicals, not round balls. For RBs, some use the multiplier-120- instead of -150- . Still other competent shooters, and even barrel makers believe that the best ROT for a round ball rifle is -100-- times caliber, so a .40 caliber rifle should have a 1:40 ROT!

I am not so sure any are wrong.

I do believe that the slower Rate of Twist is more foregiving of slight differences in powder charges, so that it makes sense to use this slower ROT in a gun intended for hunting, where you will be pouring powder from a powder horn, into a measure- adjustable or fixed-- and then into the gun barrel.

Why do I think both may be right?

Well, I read somewhere that the multiplier of -150- is useful in shooting cast bullets that generally are not traveling more than 1500 fps. And, if you are pushing a bullet faster than that, you should change the multiplier to -180- as you near that 1800 fps velocity range! So, even the Greenhill formula as used for conicals may need some "adjusting"!

I have a copy of a page from "Rifle " magazine on
"Theoretical Rates of Twist" using the Greenhill formula that came from an article written by Kenneth S. Hulmes, titles " Basics of Ballistics", in a 1986 issue of "Handloader" magazine. The tables list bullet diameter in inches, and bullet length in inches, using the Greenhill formula, to give the optimum ROT. Calibers range from .172-.458, so its not particularly useful for Determining RB ROTs, but it does give insight into the Greenhill formula.

For those not familiar with the Greenhill Formula it is:

Caliber times caliber( caliber squared) times 150, divided by the length of the bullet( total length, not just the portion that contacts the rifling)in inches, equals the optimum Rate of Twist for the rifliing to shoot that bullet accurately.

Or, Diameter squared, x 150, divided by bullet length = ROT.

To use the Greenhill formula with Round Balls, instead of conicals, the diameter of the ball and its length are the same. So, multiple caliber( diameter of the ball, in inches) x 150 = ROT.

Example: .490( .50 caliber) x 150 = 73.5( 1:73.5" ROT. That is one 360 degree turn, or revolution, in 73.5 inches.)

Those of us who shoot .50 caliber rifles with a 1:48 twist will immediately see that the formula used with our barrels is closer to caliber times 100, than it is to the Greenhill formula, and we know the guns shoot RBs accurately, too. The 1:48 ROT is often described as a " Compromise ROT" that will allow the shooting of both RB and Conicals, (as long as the conicals are not very long!)

If you are working on a cast bullet load for a rifle, use the Greenhill formula to determine the optimum ROT for that length of bullet. If you are working on a RB load, I would not worry a lot about the Greenhill formula. Its use does provide you with a ROT that is very forgiving of casual powder measuring techniques in the field, but its not NECESSARY to get good accuracy shooting a RB from your gun.

Since hunting seasons are often short, and bag limits are very small, many hunters today will go into the field with pre-measured powder charges carried in separate containers, rather than take their powder horns and measures, and risk damaging or losing either. With premeasured( or weighted) powder charges, the Rate of Twist in your barrel can be " faster" than the Greenhill formula suggests.

 

[Zonie]

As Paul says, the Greenhill formula was established for elongated bullets which need to spin at a minimum speed to maintain stability.

To understand this, think of a top. They are quite stable if they are spinning fast enough but at lower speeds they wobble badly.
Thinking of the same top, if it is short it can be stable at very low rotational speeds. If it is tall it must be turned much faster to maintain this same stability.

If an elongated bullet looses its stability in flight, or, if it never had it from the time it leaves the muzzle (due to low velocity or slow rates of twist) not only will it wobble but as it does it will change its trajectory because of the forces of the wind that is hitting it.
A bullet that is not stable can even start to rotate end over end. This leaves elongated holes in the target which shooters call "keyholing".

To enter the realm of "Armchair Theorists" (that roundball hates so passionately) let's consider the roundball.

A roundball is inherently stable and even if it "keyholed" who would be the wiser? It has no long axis to rotate about, only a "center of gravity".

If this is true, then why would a tightly patched roundball shot from a good smooth bore which imparts no rotation to it, start to deflect from its intended path while in flight?

Let's consider this roundball shot from a smooth bore a little more.

My answer to this uncontrolled deflection is "surface abnormalities" and wind working together, or, an off center "center of gravity" caused by some internal void in the casting. (Remember, we are talking about shooting it from a smooth bore.)

While in flight, the balls (or bullets) "center of gravity" will follow a straight line (side to side) towards the target and, as we all know, some sort of force must act on the ball/bullet to deflect it from this straight line.

If the "center of gravity" is offset from the balls center the wind pushing against it will start the ball rotating in an uncontrolled and unpredictable direction due to a higher pressure existing on the "large side" of the sphere (measured from the center of gravity).

Now, with the ball rotating in this uncontrolled direction the surface abnormalities of the ball and wind start to control the direction of the ball.

Surface abnormalities can consist of one area of the ball that is not perfectly round, or is rougher than an adjacent area. As the often "supersonic" blast of air hits these rough or mis-shaped areas it creates different pressures across the surface and these differences will deflect the ball from the straight line of sight we wished the ball to fly along.

The longer the ball is in flight, the longer these pressure forces will have to act on the balls direction which explains why a well patched roundball shot from a smooth bore will have little or no problem hitting the target at 15 or 25 yards but at 75 or 100 yards it may be very inaccurate.

Now, if the patched ball was shot out of a rifle and it is spinning in a controlled direction along an axis that is parallel with the desired line of flight and its center of gravity is offset, the center of the geometrical sphere will be spinning around the center of gravity.
Any differences in pressure that are being exerted against the sphere from its true center of gravity will constantly be changing about the axis of rotation so the ball will not be directed in some unforeseen direction off of the line of sight.

Also, by presenting the rapidly rotating surface to the high velocity air that is hitting it, any force created by a surface abnormality and the wind will constantly be directed into a different direction about the balls axis of spin, thus the force cannot act in any particular direction away from the line of sight.

With all of this in mind one can see that the rotational velocity of a patched roundball does not need to "stabilize" the ball at all.
It needs only to be fast enough to keep redirecting the forces produced by the wind in a controlled manor around the balls spinning axis.

That said, a patched roundball can fly straight with a comparatively slow rotation such as is produced by a 1:48, 1:60 or 1:70 twist gunbarrel.

(To the highly knowledgeable folks in the audience, yes, I'm aware of the deflections that are created by the spinning bullet/ball but at muzzleloading ranges I think they have very little effect. )

OK, OK! I'll get out of my armchair now. :grin:

 

[mykeal]

Wow.

Two words: rotational inertia. Oh, and don't forget the circulation effect Mr. Bernoulli opined on.