Yaw and shell flight.

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George Elder
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Yaw and shell flight.

Post by George Elder » Tue Mar 29, 2005 11:34 am

Hi Bill:

I am not at all sure how to begin a discussion on this subject, and I have contemplated a number of examples that may be useful. It strikes me that we ought to consider shells that have much in common, but that may differ in one or two details that could be tied to flight dynamics. Along this line, I contemplate Mr. S's observations regarding the US 16" 2,240 pound shell vs the 16" 2.700 pound shell. As you know, Mr. S maintains that the lighter shell performed better for long-range shoots, and I wonder how this could be the case. The heavier shell should be less effected by wind resistance, and I find myself wondering if their are physical differences in the shells that may cause one to be more subject to yaw effects than the other? So I suspect that we could begin by examining the shell's physical parameters. I think I can dig out my drawings, although I have no idea of how to post them on this board. Yet this would be a fool's errand if you don't think this approach to the subject matter will offer any insights. There are some problems here, not the least of which is the efficacy of the view that the 2,240 lb shell was indeed more accurate for very long range shoots. But here I must depend on the insights of those who actually worked with the guns.

George

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Flight differences

Post by Bill Jurens » Tue Mar 29, 2005 3:18 pm

I am sure that 'Mr. S' is correct in his observations. It is really not that uncommon to find that projectiles of closely related types and of apparently identical external geometries range somewhat differently both regarding range vs Q.E. per se, and regarding dispersion at the target. It is (or was) quite common for artillery types to deliberately manufacture shells with identical or nearly identical external geometries so as to attempt to avoid needing new range tables, etc. in the field. Sometimes it worked, sometimes it didn't.

With new projectiles, if the differences in ranging etc. are important and the budget sufficient, the causes of these differences can inevitably be 'hunted down' via the applications of new technologies. With older projectiles, this is rarely the case.

One will find, in general, that dispersion at the target at long range is primarily controlled by consistency of initial velocity and consistency in drag. It turns out, for any of a number of reasons, that some combinations of projectiles and propellant just result in a more consistent intitial velocity. In some cases, getting a small I.V. scatter is effortless, whilst in others, attaining this goal might prove nearly (or, in rare cases, actually) impossible. Getting this right remains somewhat of a 'black art', in which experience and intuition sometimes play a major part, albeit (usually) backed by a considerable background in theory and technology.

The sources of inconsistent flight dynamics, i.e. inconsistent or unpredictable in-flight drag, can be equally difficult to predict. Yaw is usually not an issue, as the variables that control yaw over the course of the trajectory are usually fairly stable over a relatively wide range of conditions, provided the mount itself is in good condition. My experience has been that in most cases, drag inconsistencies stem from some relatively small geometric issue that renders the transition point from laminar to turbulent flow a bit unstable, from irregularities in the configuration of the driving bands after ejection (e.g. 'fringing') from some instability of flow around the base, or from some often relatively small variation in geometry which affects the origin and initiation of the shock waves which eminate from various and sundry positions along the projectile during flight. Tracking all of this stuff down, especially in the '30s, was very difficult indeed.

Simple drag and/or initial velocity inconsistency usually simply results in a larger pattern. This is not necessarily bad, particularly if target location is relatively ambiguous. Quite often, if the instability is large and takes the form of an 'on-off' variation, the pattern not only becomes large but develops a 'hole' in the middle, which can be very frustrating accuracy-wise.

Often the effects of drag instability and/or initial velocity instability are intertwined, and it can -- or at least could, prior to ubiquitous radar velocimeters -- be very difficult to separate them. A lot can be done by careful analysis of the fall of shot patterns, as each pattern type contains, in effect, the 'fingerprint' of the problem(s) which created it. A bit like reading tea leaves or goat entrails sometimes...

Bill Jurens.

George Elder
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Interesting.

Post by George Elder » Tue Mar 29, 2005 5:04 pm

I well understand your point about teasing apart the other variables from possible yaw effects themselves, and that is one of the reasons I am so uncertain about the exercise. Indeed, it may be pointless, but let us test run it for a bit. The 16" shells in question have different physical characteristics, and these may be useful to examine. So let us consider the differences:

16" MK 5 Mods. 1-5

Overall length w/cap & WS: 64"
Without cap & WS: 43.387"
Distance base to band: 4.03"
Width of band: 5.32"
Diameter at base: 15.977"
Diameter of Bourrelet: 15.997"
Weight of filling: 34 lbs.
Weight of loaded projectile: 2,240 lbs.
Charge Weight ratio: 1.5%

16" MK 8 Mods. 1-6

Overall length w/cap & WS: 72"
Without cap & WS: 51.6"
Distance base to band: 4.03"
Width of band: 5.32"
Diameter at base: 15.977"
Diameter of Bourrelet: 15.997"
Weight of filling: 40.9 lbs.
Weight of loaded projectile: 2,700 lbs.
Charge Weight ratio: 1.5%

Perhaps the most obvious difference is in shell length, and here we see an 8" difference overall and 8.21" difference in the shell itself minus the cap and windshield. Despite the length and weight difference, the distance of the band from the base is the same, as is the band's width. Of course, this is probably more of a factor in internal ballistics. In terms of form, I sure wish I could pictures here.

The 16" Mk 5 has a more blunt head shape than the MK 8, and also has some differences in the shape of the cap. I cannot make out the CRH figures on these plans because of feeble eyes, but I am fairly certain the mass distribution is different in these two shells. It seems certain that most of the added length in the heavier shell is toward the front. So what we now need is a center of mass location for the two shells. Do you have this data?

George

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Shell stability

Post by Bill Jurens » Tue Mar 29, 2005 5:55 pm

I have all of the engineering drawings and data for these bullets here, but the amount of time I can put into doing extensive computations and analysis is limited.

The change in the longitudinal position of the center of gravity should not be a big issue.

If we are talking about the relative dispersions of various projectiles fired from the same gun at similar velocities, my first guess in this instance would be that this is a twist-related issue, i.e. that the twist of the rifling for the 16" gun in use for the tests was more suited to the shorter 2400 lb bullet than the longer 2700 lb bullet at high angles of departure. Given equal twist, it would be normal, all things considered, for the longer, heavier projectile to have a somewhat larger summital yaw at larger angles of departure -- i.e. when fired for very long range -- and the recovery from this condition is usually accompanied by some degradation of dispersion and range. If the range is great and the target relatively small, then the increase in hitting power resulting from the extra shell weight, will usually override the associated increase in dispersion.

In that regard, it should be noted that an increase in dispersion and a decrease in range in and of itself is not necessarily harmful unless our fire-control performance is perfect and the behaviour of the target is perfectly predictable. That's one reason why one hunts ducks with shotguns rather than deer rifles.

Selecting the appropriate twist for guns that operate over large ranges of angle of departure, e.g. 10 through 45 degrees, always involves some unavoidable compromises. In such cases, the designer must use his best judgement, usually within budgetary restraints, to select what he feels represents the best overall solution to the problems at hand.

Bill Jurens

George Elder
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Dr. C may be help us with the center of mass calculations

Post by George Elder » Tue Mar 29, 2005 8:22 pm

... although on occasion they can be found in the plans. No such luck here. The reason I bring this up is because the location of the center of mass relative to the center of air pressure resistance may be a factor here in the relative flight stability of the two shells -- and especially at the summatal levels in the trajectory. So the issue I am contemplating is not the relative change in each shell's center of mass (CM) so much as it is how the CM location in each shell relates to the relative center of air pressure resistance that is influencing each projectile. From this, we can deduce the center of pressure of the normal lift force and Magnus force, both of which are involved in stability calculations. However, these issues may be moot with regard to practical applications because the point you raise about twist is surely very important as it relates to the spin stabilization of the heavier projectile. To examine this issue in the abstract is possible, if we assume both the heavier and lighter projectile have rotational moments that cancel each other out. But is that a viable way to proceed? It will take us into a realm of theorey more than practical application.

George

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Yaw etc.

Post by Bill Jurens » Wed Mar 30, 2005 3:29 am

The center of gravity of the projectile is relatively easy to calculate. Many years ago -- c.1986 -- I did a study for Dahlgren regarding the probable effects of muzzle blast from adjacent guns. This revealed that perpendicular to the line of flight the c.g. and the c.p. for the long bullet were in near-correspondence. Of course they are in near correspondence when the yaw is zero as well.

Doing some rough calcs shows that the c.g. of the 2400 lb. bullet, less windscreen and filler but including a (generic) cap, would lie about 22.1" (c.1.38 cal) forward of the base. For the long 2700 lb bullet the corresponding figure is about 26.2" (1.64 cal). The movement of the c.g., as might be expected, is about 4" (0.25 calibers).

The longitudinal center of pressure for projectiles like these varies with Mach number, starting out quite near the nose and typically moving back -- sometimes quite unpredictably -- at the rate of about 1 caliber per M, i.e. 1 caliber per 1000 f/s. Assuming a yaw angle of 2 degrees and a reasonable average position for the c.p. this gives us an overturning couple of about 0.92" for the long bullet and 0.78" for the short bullet, i.e. a change of about 0.12". This is not much, and should be well controlled by spin.

A fair amount more work -- about half to three-quarters of a man-day -- might refine these values somewhat, but probably not by much.

What many people do not realize is that the variation in fall of shot for guns fired for dispersion, even under nearly identical conditions, is often very great; the manuals draw a nice straight (or, more commonly, somewhat curved) line for dispersion vs range, but this line is, in reality usually drawn through a very cloudy constellation of actual data points. In such situations, the effects of any one variable, such as the one being discussed, are inevitably swamped by other random processes. Predicting dispersion via theoretical analysis of yaw is a bit like attempting to predict gas mileage via an analysis of carburetter fuel jet tolerances on a carburettor assembly line. An awful lot more, in any individual case, depends upon the driver, wind, ambient temperature, altitude,vehicle load, tire pressure and you-name-it.

In that regard, I can't help wondering exactly why you are interested in pursuing this, i.e. exactly what you are trying to prove? Knowing that might help a lot in answering your questions.

Bill Jurens

George Elder
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Examining issues.... that is all.

Post by George Elder » Wed Mar 30, 2005 12:39 pm

Hi Bill:

I am examining just one of the variables involved in shell flight -- and am not out to prove anything. You mention the 2,400 pound projectile, but the example here is the 2,240 pound projectile vs the 2,700 pound projectile. The general concept is to examine the behavior of a shorter and lighter projectile vs that of a longer and heavier projectile of the same caliber. As you know, in general, longer penetrators are more subject to yaw-related flight effects than are those with shorter forms. Of course, here we find the extermes being used to make the point, and I wanted to examine the 2,240 vs 2,700 pound shell to see if even modest difference in length make much of a difference in flight dynamics. That is all. This all evolved out of Mr. S's observations regarding long range shoots. These were counter to the pervailing general view that heavier projectiles "are more accurate" than lighter ones when the ranges are very long. I think we now see that many other elements are in play here -- and the happy notion that heavier is better at long range needs to be examined. For example, you seem to be implying, if I understand you correctly with regard to rifling twist, that heavier projectiles may also require more initial stilization. Is this a fair conclusion?

George

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more stability stuff

Post by Bill Jurens » Wed Mar 30, 2005 3:28 pm

O.K. This gives me a better perspective.

Sorry about the error; I wrote 2400 lb instead of 2240 lb by accident.

In general, the longer the bullet, the heavier the bullet and the more rapidly it is spun, the less it will tend to follow a highly curved trajectory. When bullets get really long -- e.g. in the case of rockets -- or when the trajectory is very highly curve -- e.g. in the case of mortar fire -- then the designer must often resort to fins to move the center of pressure aft and keep it there. Even fins sometimes fail if velocity and/or air density is low.

Internet discussion groups -- which by their very nature allow virtually anyone with a computer to put forth an opinion regardless of experience and or knowledge -- have provided a lot of material about such things as heavier shells being more accurate and/or the supposed differences between lighter high-velocity shells vs heavy low-velocity shells and so forth. Much of this is essentially nonsense. There is, in particular, a good deal of effort put forth to somehow try to extrapolate the experience and observation of low angle small arms fire to large caliber high angle trajectories. In reality, little carries forward.

The relationship between the weight of a given bullet and the appropriate amount of stabilization is a tricky one. Weight and caliber per se don't have much to do with it, which is why the twist of rifling used in really tiny guns -- e.g. hunting rifles -- is usually nearly the same as that employed in really big rifles -- e.g. 16 inchers.

The appropriate level of stabilization is more closely related to the curvature of the trajectory, i.e. whether one wishes to stablize for long-range or short-range fire.

The equations for static and dynamic stability, often with worked examples, can be found in a variety of places on the internet. One must keep in mind, however, that the majority of these sites are small-arms related, and thus the rules of thumb etc. often quoted usually relate more to flat-fire trajectories than to long range fire situations where the bullet almost reaches the stratosphere. There, because air density is low, things are a little bit different.

Bill Jurens

George Elder
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Thank you.

Post by George Elder » Wed Mar 30, 2005 10:03 pm

Hi Bill:

This general conclusion is inescapable. I think it might be fun to crunch the numbers of the 2,240 pound shell vs the 2,700 pound shell with regard to stability indicies over various points in the mid-range and maximal range trajectory curves, and this might make a very interesting exercise for Dr. C's class. I'm not sure they will find anything dramatic, but perhaps (?). I will have an interesting document on some of these issues in a few days -- or at least I hope so. Exercises such as this are how I learn, and I am thankful.

George

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"running the numbers"

Post by Bill Jurens » Wed Mar 30, 2005 10:19 pm

It would be interesting to see what results come out of this. I doubt if there would be anything dramatic, but it is a better exercise than most insofar as it does actually adress a question of at least minor interest, as opposed to purely textbook exercises, which usually address no interest at all.

Bill Jurens

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Post by tommy303 » Wed May 11, 2005 4:30 am

Bill,

I have a question on topic, or at least an observation to put forth. If I recall correctly the 16in 50s and the 16in 45s were originally designed to fire the lighter shell were they not, and the adoption of the 2700-lb shell came after the guns themselves were already in production. That being the case, I am not too suprised that the guns performed best in terms of general accuracy, with the lighter shell, as that was the one around which the guns had been designed. It seems to me, that the rifling twist selected must have been optimised for the lighter shell and the velocity produced by the selected service charge. If so, perhaps the heavier projectile required a different rate of spin stabilization for optimum results with the different velocity and differing dynamics of the shell (meaning in this instance presumed different centre of gravity, drag producing surface area, etc). Is this a reasonable assumption, or have i wandered completely off the field.

thomas

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16" projectiles

Post by Bill Jurens » Wed May 11, 2005 4:05 pm

That IS a good question!

I haven't formally checked my sources, but I think you are correct in assuming that the 16"/45 was originally designed for the 2240 lb projectile. What exactly was going through the minds of the designer(s) at the time, is largely lost to history, but there is little evidence suggesting that the design of the 16"/45 and 50 was very significantly different from guns that had been designed before. Usually the designer would choose to design for the best performance at moderate ranges, letting the 'ends' of the range bands more or less take care of themselves. In any case, this sort of thing would represent a second-order refinement, not a primary concern.

The gyroscopic stability is directly proportional to the ratios of the transverse vs the longitudinal moments of inertia of the bullet, i.e. essentially proportional to the mass, with --as one might expect -- a heavier projectile being somewhat more stable than a lighter one. Making the projectile longer doesn't help if the trajectory is highly curved.

This would lead to increased yaw at high angles of fire where the heavier shell would have a tougher time following the trajectory.

All that being said, the practical effects on the accuracy at long range should be minimal, because although the yaw of a heavier projectile might be greater at the summit, it is CONSISTENTLY greater, and thus can easily be accounted for in the range tables. So long as the yaw is consistent from round to round, then all one gets is a (very) slight increase in drag, which can be taken into account by slightly adjusting the ballistic coefficient.

Generally during World War II, the navy found few if any practical differences between the various types of rounds fired at long range, as difficulties with variations due to propellant temperatures, gun wear, ramming variations, propellant lots and what-have-you more or less submerging any effects due to yaw well into the 'noise'.

In the '80s, some shell-to-shell differences in accuracy were noted, but things were more sophistocated then, and even then the differences -- though observable statistically -- were of little practical consequence.

Hope this helps...


Bill Jurens.

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Post by marty1 » Thu May 12, 2005 5:59 am

This is unrelated to 16” APC, but hopefully is germane to the discussion of projectile yaw and its influence upon firing table calculations. I was looking through Royal Navy: “Progress in Gunnery Material” 1920 and came across the following:

“Long "Range Proving Ground.—The range available at Shoeburyness is only 19,000 yards, and by the end of 1916, fighting ranges were about double this distance ; but is no use having a long practice range unless the wind and air density at high altitudes can be ascertained and allowed for. The question of doing this was, therefore, gone into first and satisfactorily settled early in 1917, as will be explained later. In July 1917, the necessity of constructing a longer range was put before the Ordnance Committee, and by November 1917, it had been decided that the Ministry of Munitions should undertake the construction of a range of 35,000 yards with the firing point at Grain Island opposite Shoeburyness. The range was primarily required for naval guns and was,the best arrangement under the circumstances to meet our immediate needs, though it was pointed out that it would be necessary at some future time to consider a longer naval range where firing could take place under full service conditions. Special proof mountings were ordered, and work was commenced in December 1917, and it was hoped to finish it in six months, In November 1918, the work had to be stopped by direction of the War Cabinet, and since then the project has passed through many vicissitudes. A range in this vicinity turned out to be a costly undertaking, but it is hoped that it will be completed this year. Until this is done, range tables have to based upon extrapolation beyond 16,000 yards, the variation in ballistic coefficient caused by yaw at the vertex being unknown. It is just possible that a particular projectile may become unstable, but from firings carried out by monitors at 30,000 to 40,000 yards, it does not appear probable that any service projectiles would behave in this way, and so far as could be judged from the firing, the 18-inch through 9.2-inch guns with 8 c.r.h. projectiles shot in good agreement with their calculated tables.”

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Summital Yaws

Post by Bill Jurens » Thu May 12, 2005 6:30 am

This is just about what one would expect in 1920 or so, as at that time very few ships had guns which would elevate above 20 degrees or so and ballistic theory really wasn't up to the task for much longer ranges. Semi-empirical methods certainly worked well enough, but most ballisticians considered these methods somewhat 'impure' theoretically. Also, commencing about that time there was some uncertainty regarding how to compute the drag of new projectiles, which were now becoming quite streamlined compared to the old 2CRH "Projectile Type 1". Further, Fowler hadn't written his paper on projectile stability yet. So they really were, at least by current standards, in a bit of a fog back then.

The French Army did a lot of work on this during World War I, and for a long time their ALVF tables were the only ones really capable of modelling long-range high-angle-of-departure tables. They used the Type 1 bullet as a model. Sadly, even they didn't work that well, and so the computation of long-range trajectories remained somewhat problematic. The British attempted a set of comprehensive tables after WWI using a 5/10 CRH bullet (the so-called "1940 Law") but these didn't really work very well either. The three volume set "Exterior Ballistic Tables Based on Numerical Integration" produced in the USA and springing from the French ALVF tables DID work, but the set was not completed until after the outbreak of WWII. Actually, EBTBONI Vol III was never really completed at all, the electronic computer 'caught up' with the problems before the hand-generated document could be finished, and it was abandoned about 3/4 done.

Bill Jurens

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Huh?

Post by marty1 » Thu May 12, 2005 2:43 pm

That's an interesting come-back. My interpretation of the Naval Gunnery Materials snippet was that range table calcs of the period seemed to agree fairly well with actual firing trials. Moreover it specifically states that while in-flight yaw was in theory a bit of a bogie-man, firing trials indicated that service projectiles were not experiencing any practical deviation from firing table predictions.

It is just possible that a particular projectile may become unstable, but from firings carried out by monitors at 30,000 to 40,000 yards, it does not appear probable that any service projectiles would behave in this way, and so far as could be judged from the firing, the 18-inch through 9.2-inch guns with 8 c.r.h. projectiles shot in good agreement with their calculated tables.”

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