1921 firing trials against Baden

 
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Some good basic Drag info...
Hi Marti:
Please contact me by email, and I will give you some very good information of drag that is from my teacher. Drop me a line at GHE101@aol.com
George Elder
Please contact me by email, and I will give you some very good information of drag that is from my teacher. Drop me a line at GHE101@aol.com
George Elder

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15" Range Table
As it turns out, I have a copy of O.U. 6090 (D), the official range table for the 15" gun and the 1920 lb projectile here.
The preamble states"
"Calculated to small arc accuracy with O.B. Ballistic Tables with values of Co varying from Co=12.493 (ks = 0.682) at 5 degrees elevation to Co = 11.529 (ks=0.739) at 45 degrees elevation".
This would have been done against Projectile Type 1. I cannot copy the Greek letters, and so have substituted s for a lower case sigma. The coefficient of steadyness, s, could not be (and normally was not) separated from the form factor as a whole...) Note that the calculators have made a small correction for caliber to the calculation; one must add 0.005 to the form factor to make this all come out exactly right; the 'official' correction for caliber from my tables is 0.01 for the 15", but obviously somebody fudged the figures or (more likely) simply used a different table.
The table is dated October 1927 and states that it is applicable to "all marks" of A.P.C. bullets. It is for the 1920 lb projectile, 4 c.r.h. and 2400 f.s. This very nearly (or exactly) matches the projectile sketches you posted earlier. This table superceded Table No. 4 (O.U. 6090 (D), but it appears that the changes were innocuous, and that the body of the main table at least was essentially unchanged.
Excerpts from this table are reproduced in Campbell's "Naval Weapons", and in fact the middle table on page 27 of "Naval Weapons" appears to be directly derived from it. So, so far as striking velocities are concerned, you can graph Campbell and 'take that to the bank'.
Be careful trying to simulate reduced charge firings this way, however...
Hope this helps...
Bill Jurens
The preamble states"
"Calculated to small arc accuracy with O.B. Ballistic Tables with values of Co varying from Co=12.493 (ks = 0.682) at 5 degrees elevation to Co = 11.529 (ks=0.739) at 45 degrees elevation".
This would have been done against Projectile Type 1. I cannot copy the Greek letters, and so have substituted s for a lower case sigma. The coefficient of steadyness, s, could not be (and normally was not) separated from the form factor as a whole...) Note that the calculators have made a small correction for caliber to the calculation; one must add 0.005 to the form factor to make this all come out exactly right; the 'official' correction for caliber from my tables is 0.01 for the 15", but obviously somebody fudged the figures or (more likely) simply used a different table.
The table is dated October 1927 and states that it is applicable to "all marks" of A.P.C. bullets. It is for the 1920 lb projectile, 4 c.r.h. and 2400 f.s. This very nearly (or exactly) matches the projectile sketches you posted earlier. This table superceded Table No. 4 (O.U. 6090 (D), but it appears that the changes were innocuous, and that the body of the main table at least was essentially unchanged.
Excerpts from this table are reproduced in Campbell's "Naval Weapons", and in fact the middle table on page 27 of "Naval Weapons" appears to be directly derived from it. So, so far as striking velocities are concerned, you can graph Campbell and 'take that to the bank'.
Be careful trying to simulate reduced charge firings this way, however...
Hope this helps...
Bill Jurens

 
 Posts: 168
 Joined: Mon Oct 18, 2004 4:23 pm
How can we place formulae on this board...
I have some excellent material that is on point and even factors procession, etc., into the drag effect  the socalled wobble factor. But I cannot do a cut&paste here to save my life. Jose, we need your help.
George
George

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Addition to previous.
I neglected to add the air density for this table, which was 534.22 grs per cubic foot.
Bill Jurens
Bill Jurens
Thanks Bill. I reckon I was satisfied with your previous comment regarding J.Campbell’s research work being very good. However it is always nice to have an independent confirmation.
Just so I am clear on this – you indicated that a line drawing was included in the material you were reviewing that matches one of the 15” projectile drawings posted earlier. To which of the three 15” APC drawings posted earlier do you refer?
Does your drawing look like the 15” New Type (MkV) drawing, or the 15” MkIa Old Type with New Type Cap (MkIa Converted)?
Lastly, the Jutland 15” APC (Old Type MkIa) appears to be a 3CRH projectile where as the O.U. 6090 (D) reference you have reviewed appears to be discussing a 4CRH projectile. In other words, unless I have misunderstood the information you just posted, it still appears that I need to estimate velocity vs. range for the Jutland 15” 1920lbs 3CRH APC projectile.
Regarding standard conditions, my copy of the British manual “Text Book of Gunnery” Vol1, dated 1914, indicates the British Standard Conditions for Range Tables during this period were:
Air Temperature = 62deg F
Barometric Pressure = 30” Hg
As I recall – and I will check this again tonight after work – nothing was indicated for Relative Humidity, so for the purposes of my previous 15” 3CRH calculations I assumed Relative Humidity at standard condition to be 78% (the ASM condition).
I think at some point – postWWI – British standard conditions were changed to 60deg F and 30” Hg. I don’t have the exact date on the switch over although the difference in velocity drop is not huge between 60F and 62F.
Just so I am clear on this – you indicated that a line drawing was included in the material you were reviewing that matches one of the 15” projectile drawings posted earlier. To which of the three 15” APC drawings posted earlier do you refer?
Does your drawing look like the 15” New Type (MkV) drawing, or the 15” MkIa Old Type with New Type Cap (MkIa Converted)?
Lastly, the Jutland 15” APC (Old Type MkIa) appears to be a 3CRH projectile where as the O.U. 6090 (D) reference you have reviewed appears to be discussing a 4CRH projectile. In other words, unless I have misunderstood the information you just posted, it still appears that I need to estimate velocity vs. range for the Jutland 15” 1920lbs 3CRH APC projectile.
Regarding standard conditions, my copy of the British manual “Text Book of Gunnery” Vol1, dated 1914, indicates the British Standard Conditions for Range Tables during this period were:
Air Temperature = 62deg F
Barometric Pressure = 30” Hg
As I recall – and I will check this again tonight after work – nothing was indicated for Relative Humidity, so for the purposes of my previous 15” 3CRH calculations I assumed Relative Humidity at standard condition to be 78% (the ASM condition).
I think at some point – postWWI – British standard conditions were changed to 60deg F and 30” Hg. I don’t have the exact date on the switch over although the difference in velocity drop is not huge between 60F and 62F.

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projectile shapes etc.
So far as line drawing were concerned, I was referring to the drawings that you posted earlier on this thread, and apparently the drawings you have just posted now, the difference being that posting 1 contained two drawings and posting 2 contains three. Those profiles, all nearly the same, are what I was basing my estimates on.
All three of the projectiles in the posting you just sent are essentially identical so far as exterior geometry is concerned, and so should range nearly identically. I have to admit that I am, I think, once again a bit confused here. The O.U. refers to a 4 CRH projectile because this is essentially what we have on your drawings; the shape of the windscreen (dimensioned as 4 CRH) defines the drag characterstics, not the shape of the head of the capless bullet (which is indeed 3 CRH). It is unlikely that the variations of cap shown in the drawings would have any measurable effect on flight characteristics at all.
If I read you correctly, it appears that it is your feeling that the British used a 3CRH windscreen shape at Jutland and that the 4 CRH drawings posted in this thread (and hence the associated range table) are for projectiles of later vintage. I'm at work now, so can't check my files, but photos of British projectiles of the period should show if this is true or not.
If that is the case, then either we will have to locate a Jutland vintage range table describing the trajectory of the 3 CRH bullet, or we will have to recompute a 3CRH range table from scratch. Fortunately, if all we are talking about is a change from the 2 CRH tangent ogive design of Projectile Type 1 to a (perhaps slightly longer) projectile with a 3 CRH tangent ogive, then this should represent, ballistically, a relatively simple problem.
Bill Jurens
All three of the projectiles in the posting you just sent are essentially identical so far as exterior geometry is concerned, and so should range nearly identically. I have to admit that I am, I think, once again a bit confused here. The O.U. refers to a 4 CRH projectile because this is essentially what we have on your drawings; the shape of the windscreen (dimensioned as 4 CRH) defines the drag characterstics, not the shape of the head of the capless bullet (which is indeed 3 CRH). It is unlikely that the variations of cap shown in the drawings would have any measurable effect on flight characteristics at all.
If I read you correctly, it appears that it is your feeling that the British used a 3CRH windscreen shape at Jutland and that the 4 CRH drawings posted in this thread (and hence the associated range table) are for projectiles of later vintage. I'm at work now, so can't check my files, but photos of British projectiles of the period should show if this is true or not.
If that is the case, then either we will have to locate a Jutland vintage range table describing the trajectory of the 3 CRH bullet, or we will have to recompute a 3CRH range table from scratch. Fortunately, if all we are talking about is a change from the 2 CRH tangent ogive design of Projectile Type 1 to a (perhaps slightly longer) projectile with a 3 CRH tangent ogive, then this should represent, ballistically, a relatively simple problem.
Bill Jurens
This interesting  as I have been talking about 3CRH for quite sometime now. I have been going off of the drawing of the 15" MkIa Old Projectile as the basis for determining CRH of the Jutland projectile. And I have relied upon my own constructions to back calc CRH.
You had posted earlier that the nose length was 1.5 calibers. I guess I had assumed that since you took the time to determine nose length, that you had also looked at CRH as well. The 1.5caliber nose length you determined matches up well with my own scaling  i.e. nose length looks to be about 22.5inches. However, the windscreen geometry lends itself better to a 3caliber radius circle than a 4caliber radius circle. Left click on the image to enlarge.
And I've already recalc'd velocity drop based upon 3CRH. Those were the graphs I posted on page 6 of this thread. (?)
You had posted earlier that the nose length was 1.5 calibers. I guess I had assumed that since you took the time to determine nose length, that you had also looked at CRH as well. The 1.5caliber nose length you determined matches up well with my own scaling  i.e. nose length looks to be about 22.5inches. However, the windscreen geometry lends itself better to a 3caliber radius circle than a 4caliber radius circle. Left click on the image to enlarge.
And I've already recalc'd velocity drop based upon 3CRH. Those were the graphs I posted on page 6 of this thread. (?)

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15" Ogive
No, it's a 4CRH ogive in my book. I think you've made an incorrect assumption, namely that the center of the ogive for the bullet body is in the same place longitudinally as the center of the ogive for the windscreen. It isn't; if you move the center of your 4CRH ogive towards the stern about 4.08 inches, you will see that the windscreen profile now matches a 4 CRH nearly perfectly. (My guess is that the actual figure was 4.00 and scaling errors account for the rest...)
The original draftsman actually drew it this way; if you extend the extension line for the "60.0 Rad (4 Cals)" dimension back to the origin, you will see that the center of this arc is aft of the 3 caliber nose radius.
This makes this, I guess, a sort of 'semisecant' design. To me, it's a 4 CRH with a fairly healthy nose radius (which would not really affect drag that much anyway...)
Bill Jurens
The original draftsman actually drew it this way; if you extend the extension line for the "60.0 Rad (4 Cals)" dimension back to the origin, you will see that the center of this arc is aft of the 3 caliber nose radius.
This makes this, I guess, a sort of 'semisecant' design. To me, it's a 4 CRH with a fairly healthy nose radius (which would not really affect drag that much anyway...)
Bill Jurens

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Head height
The head height or the nose height (or head length or nose length)  many nearsynonymous terms are used  is really only clearly defined in the case of a tangent or secant ogive with a perfectly pointed tip. As soon as one rounds off (or chops off) the nose, then the theoretical length no longer matches the actual length. Similarly, except in the case of a perfectly defined secant ogive, the exact point of tangency with the body is often somewhat illdefined as well. So, a lot depends upon how one measures it. There is nothing unusual with having a head height that does not match the CRH figure as derived by equation. The 5/10 CRH projectile later used by the British  I think as "Form A"  had a 10 CRH ogive with a head height equal to a 5 CRH tangent ogive. As I recall (again at work and do not have exact figures handy), the bullets in the British range table are defined as 3.12/4 CRH, which would usually mean that the head height  however they decided to measure it  was equal to that of a 3.02 CRH tangent ogive, but that the actual ogival radius was 4 calibers.
Sometimes, a projectile is described as a such and such C.R.H. design when the actual ogive is actually shaped completely differently. What they mean then is that the shell ranges like a Type 1 with a such and such CRH tangent ogive and a pointy tip.
I would measure the head height for the bullets you posted from the tip of the actual nose back to where it seemed the most reasonable place to assume that the nose contour actually intersected the cylindrical body. Different people using different rules might get slightly different answers, which could lead to misleading results if one then converted this nose height figure into a CRH value via the standard equations.
I'd stick with the first figures I quoted earlier on in this thread for the nose height, though the exact utility of those estimates, ballistically, is actually somewhat problematical.
Hope this helps...
Bill Jurens.
Sometimes, a projectile is described as a such and such C.R.H. design when the actual ogive is actually shaped completely differently. What they mean then is that the shell ranges like a Type 1 with a such and such CRH tangent ogive and a pointy tip.
I would measure the head height for the bullets you posted from the tip of the actual nose back to where it seemed the most reasonable place to assume that the nose contour actually intersected the cylindrical body. Different people using different rules might get slightly different answers, which could lead to misleading results if one then converted this nose height figure into a CRH value via the standard equations.
I'd stick with the first figures I quoted earlier on in this thread for the nose height, though the exact utility of those estimates, ballistically, is actually somewhat problematical.
Hope this helps...
Bill Jurens.

 
 Posts: 168
 Joined: Mon Oct 18, 2004 4:23 pm
Also confused...
Hi Bill:
I have been following this thread with some interest, and now find myself confused. If we are discussing drag here, then the windscreen is a central element. Yaw is also a huge factor here, and it must be determined before drag can be calculated. To do all this, we must consider...
air density
velocity (scalar)
velocity (vector)
projectile reference area
pitch angle
yaw angle
approximate total yaw
Dynamic Pressure
projectile diameter
projectile spin in radians/second
These are some of the main elements needed to calculate total yaw and drag. I have a Power Point Primer on this, but I cannot possibly post it here because of limitations in this board's ability to represent various terms. The Center of mass relative to the center of pressure is also a factor in flight dynamics. But part of the reason windscreens evolved with the improve aerodynamic form... and I am not sure how evolved they were at Jutland. But as of now, I'm not sure we are using the right tools to solve this problem. I will forward the material to Bill.
George
I have been following this thread with some interest, and now find myself confused. If we are discussing drag here, then the windscreen is a central element. Yaw is also a huge factor here, and it must be determined before drag can be calculated. To do all this, we must consider...
air density
velocity (scalar)
velocity (vector)
projectile reference area
pitch angle
yaw angle
approximate total yaw
Dynamic Pressure
projectile diameter
projectile spin in radians/second
These are some of the main elements needed to calculate total yaw and drag. I have a Power Point Primer on this, but I cannot possibly post it here because of limitations in this board's ability to represent various terms. The Center of mass relative to the center of pressure is also a factor in flight dynamics. But part of the reason windscreens evolved with the improve aerodynamic form... and I am not sure how evolved they were at Jutland. But as of now, I'm not sure we are using the right tools to solve this problem. I will forward the material to Bill.
George

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Projectile drag
Hello George:
Certainly the shape of the ogive is of great importance in determining the drag. The difficulty lies in selecting an appropriate drag function that reflects the shape one is interested in. For simple bullets, e.g. tangent ogives, and simple secant ogives, this is fairly straightforward. But particularly with older projectiles where spark range firings etc. were never done, it is often quite difficult to determine exactly what drag coefficients to assign to a given shape. A lot often depends on very subtle variations in geometry which affect the flow patterns, sometimes in unexpected and unpredictable ways. Projectiles with ogives of nearly identical shapes can range quite differently, and projectiles with markedly differently shaped ogives can range nearly the same. So getting the 'correct' or best drag function for some of these older projectiles remains somewhat of a black art. That's why we still do a heck of a lot of range firing.
I am sorry to report that in general the effects of yaw on the drag are relatively minor and are wellunderstood. Instabilities outside the muzzle, within the first couple of hundred calibers of travel are, in principle, calculable, but there is rarely (if ever) enough data on the old guns and projectiles to enable one to make more than a rough guess at the input variables needed for calculation. At any rate, such instabilities damp out relatively quickly and are  if not calculable, at least repeatable, and their effects on the trajectory overall are easily compensated for.
The inflight yaw of well designed relatively large caliber bullets, except at very high angles of departure is usually very well behaved. The added drag due to yaw is usually just added on to the zero yaw drag coefficient by means of a tiny form factor. Generally yaw is a second or third order effect, except as it relates to drift, and this is more properly a fire control problem than a problem in exterior ballistic prediction. Properly designed projectiles, in general, 'trail' very well, with residual damped yaws of only one or two degrees.
These problems can (again in principle) be almost completely solved by modern 6DOF computer models, and in fact I have two of these in my library. In general, for this type of work, the additional 'accuracy' provided by these models over a straight 2 DOF model properly used is minimal  even illusory. And they run ten to fifteen times slower. For most older projectiles many or most of the additional coefficients and variable values required to solve the problem in all degrees of freedom (e.g. the offset of the transverse center of gravity from the geometric center of the projectile) are simply unknown, and to a large extent, unknowable, with the result that the user and the program rapidly approach 'paralysis by analysis'. Knowing what the variables are in great detail is of little use unless one can predict their magnitudes. Fortunately, the net effects of such variables are small, and are, in practical terms, completely swamped by our inability to measure and predict the exact characteristics of the atmosphere  including wind  along the course of the trajectory.
In general, the good old drag equation which equates the drag force to
1/2 rho V^x A Cd works as well as anything, with all of these 2nd and 3rd order effects 'lumped' into the Cd term. These old bullets were, quite literally 'Model T' projectiles, and 'Model T' computational methods are usually more than enough to predict their flight characteristics to the accuracy required for practical gunnery. By current standards, crude. But by current standards the projectiles were pretty crude as well.
Bill Jurens.
Certainly the shape of the ogive is of great importance in determining the drag. The difficulty lies in selecting an appropriate drag function that reflects the shape one is interested in. For simple bullets, e.g. tangent ogives, and simple secant ogives, this is fairly straightforward. But particularly with older projectiles where spark range firings etc. were never done, it is often quite difficult to determine exactly what drag coefficients to assign to a given shape. A lot often depends on very subtle variations in geometry which affect the flow patterns, sometimes in unexpected and unpredictable ways. Projectiles with ogives of nearly identical shapes can range quite differently, and projectiles with markedly differently shaped ogives can range nearly the same. So getting the 'correct' or best drag function for some of these older projectiles remains somewhat of a black art. That's why we still do a heck of a lot of range firing.
I am sorry to report that in general the effects of yaw on the drag are relatively minor and are wellunderstood. Instabilities outside the muzzle, within the first couple of hundred calibers of travel are, in principle, calculable, but there is rarely (if ever) enough data on the old guns and projectiles to enable one to make more than a rough guess at the input variables needed for calculation. At any rate, such instabilities damp out relatively quickly and are  if not calculable, at least repeatable, and their effects on the trajectory overall are easily compensated for.
The inflight yaw of well designed relatively large caliber bullets, except at very high angles of departure is usually very well behaved. The added drag due to yaw is usually just added on to the zero yaw drag coefficient by means of a tiny form factor. Generally yaw is a second or third order effect, except as it relates to drift, and this is more properly a fire control problem than a problem in exterior ballistic prediction. Properly designed projectiles, in general, 'trail' very well, with residual damped yaws of only one or two degrees.
These problems can (again in principle) be almost completely solved by modern 6DOF computer models, and in fact I have two of these in my library. In general, for this type of work, the additional 'accuracy' provided by these models over a straight 2 DOF model properly used is minimal  even illusory. And they run ten to fifteen times slower. For most older projectiles many or most of the additional coefficients and variable values required to solve the problem in all degrees of freedom (e.g. the offset of the transverse center of gravity from the geometric center of the projectile) are simply unknown, and to a large extent, unknowable, with the result that the user and the program rapidly approach 'paralysis by analysis'. Knowing what the variables are in great detail is of little use unless one can predict their magnitudes. Fortunately, the net effects of such variables are small, and are, in practical terms, completely swamped by our inability to measure and predict the exact characteristics of the atmosphere  including wind  along the course of the trajectory.
In general, the good old drag equation which equates the drag force to
1/2 rho V^x A Cd works as well as anything, with all of these 2nd and 3rd order effects 'lumped' into the Cd term. These old bullets were, quite literally 'Model T' projectiles, and 'Model T' computational methods are usually more than enough to predict their flight characteristics to the accuracy required for practical gunnery. By current standards, crude. But by current standards the projectiles were pretty crude as well.
Bill Jurens.

 
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Well, Dr. DC seems to believe the...
... inherent yaw of a projectile is a considerable factor is determining its drag  as is indicated in the material I forwarded to you  which is for a 500level ballistics course. Incidently, Dr. C. uses both FH and cemented armor in some of his penetration problems. I'll proceed as he indicates...
George
George

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Computations
Well, please keep me posted on your results.
It's easy to bury your head so far in theory that you forget that the theory  at least theoretically  should lead to practical solutions as well. I suspect that you have somewhat overemphasised Dr. C's concern regarding yaw effects, or that he is speaking in the context of very long projectiles fired in high crosswind conditions rather than the rather mundane computation of 'stoneage' early Twentieth Century armorpiercing bullets fired from what would now be considered rather low velocity guns at low angles of departure. But that, admittedly, represents mere speculation on my part.
I notice that the material you sent was, at least in part, adapted from McCoy's text, which is used as one of the basic textbooks in the program.
So it might be fair to take two specific quotations right from McCoy's text...
"Modern numerical integration of the 6DOF differential equations of motion gives the most accurate solution possible, for the trajectory and flight dynamic behaviour of a trotationally symmetric, spinning or nonspinning projectile, PROVIDED THAT ALL THE AERODYNAMIC FORCES AND MOMENTS, AND THE INITIAL CONDITIONS, ARE KNOWN TO A HIGH DEGREE OF ACCURACY. Scientists and engineers who routinely use 6DOF methods are often heard to say, "GIGO" (Garbage InGarbage Out!). No computed trajectory or flight dynamic analysis can be any better than the quality of its input data." (Emphasis mine)
This is an almost perfect restatement of the point(s) I was trying to make in my previous post. I've done 6DOF with old range tables. It's GIGO!
Also:
"It was noted in the first chapter of this book that 6DOF trajectories are not required for routine work in exterior ballistics. If the total angle of attack is small everywhere along a projectile's flight path, a pointmass trajectory is often sufficiently accurate for all practical purposes."
Couldn't have said it better...
You will find that in practical purposes the yaw for virtually all of these big projectiles was very small throughout the normal flight path, and further that the effects of small angles of yaw on the drag of the projectile are typically quite minimal  and what's more important  quite easily predictable. In point of fact, for many of these old rangetables, etc., it's impossible NOT to automatically include the effects of yaw in the trajectory computations, simply because the ballistic test firings on which the original drag functions were based measured actual bullet motion and thus automatically included the effects of flight yaw in the observations. To get the more modern "zero yaw drag coefficient" one has to actually SUBTRACT the effects of yaw from range firing results, and  somewhat ironically  add it back in again when running actual trajectories because actual bullets almost never run with exactly zero yaw. (Close though, often...)
The effects of small angles of yaw on armor penetration have been understood for a long time now; at least eighty years. The conditions at the proving ground, which involved firing at odd velocities over short ranges had to be watched carefully to ensure that the projectile was not still experiencing some initial nutation/precession effects when it struck the plate. For this reason, yaw cards were routinely placed in front of the plate to ensure the yaw was within reasonable bounds just before impact. As a rule, the effects of residual yaws under about 35 degrees was considered entirely inconsequential, i.e. the differences due to yaw in such situations could not be separated from the effects of random variations in the plate, projectile, and striking velocity. If one wanted to be incredibly picky, a simple linearextrapolation formula was used to 'adjust' the measured penetration to the effective penetration that would have occurred if the yaw were zero, which was never the case anyway in real life when shells were fired long distances downrange in battle. It was relatively rarely used, and I can, offhand, recall no instances where the correction involved a difference of more than three or four feet per second. Actually about the only time this was done was when a plate or projectile was just on the line between acceptance and rejection, and the addition of that additional few feet per second would bring the whole plate series into the acceptance level.
So far as I know, highyaw impacts (i.e involving yaw angles exceeding 10 or so degrees) of large projectiles was never studied anywhere by anybody. It was simply too difficult to get the big projectiles to yaw significantly without damaging them before they hit the plate. These projectiles are BIG, and it's not easy to deflect them without breaking something.
Hope this helps. Again, please do keep me informed of your progress. Your attempt to clear the the rain forest of ballistics armed with a computational chain saw may reveal more (or may reveal more faster) than I could with my crude mathematical machete(s) , but I doubt it, as this particular piece of land has been cleared many times before and the map  for better or for worse  has already been drawn. At this stage, your chances of finding anything new or significant 'under the bushes' are small...
Good luck!
Bill Jurens
It's easy to bury your head so far in theory that you forget that the theory  at least theoretically  should lead to practical solutions as well. I suspect that you have somewhat overemphasised Dr. C's concern regarding yaw effects, or that he is speaking in the context of very long projectiles fired in high crosswind conditions rather than the rather mundane computation of 'stoneage' early Twentieth Century armorpiercing bullets fired from what would now be considered rather low velocity guns at low angles of departure. But that, admittedly, represents mere speculation on my part.
I notice that the material you sent was, at least in part, adapted from McCoy's text, which is used as one of the basic textbooks in the program.
So it might be fair to take two specific quotations right from McCoy's text...
"Modern numerical integration of the 6DOF differential equations of motion gives the most accurate solution possible, for the trajectory and flight dynamic behaviour of a trotationally symmetric, spinning or nonspinning projectile, PROVIDED THAT ALL THE AERODYNAMIC FORCES AND MOMENTS, AND THE INITIAL CONDITIONS, ARE KNOWN TO A HIGH DEGREE OF ACCURACY. Scientists and engineers who routinely use 6DOF methods are often heard to say, "GIGO" (Garbage InGarbage Out!). No computed trajectory or flight dynamic analysis can be any better than the quality of its input data." (Emphasis mine)
This is an almost perfect restatement of the point(s) I was trying to make in my previous post. I've done 6DOF with old range tables. It's GIGO!
Also:
"It was noted in the first chapter of this book that 6DOF trajectories are not required for routine work in exterior ballistics. If the total angle of attack is small everywhere along a projectile's flight path, a pointmass trajectory is often sufficiently accurate for all practical purposes."
Couldn't have said it better...
You will find that in practical purposes the yaw for virtually all of these big projectiles was very small throughout the normal flight path, and further that the effects of small angles of yaw on the drag of the projectile are typically quite minimal  and what's more important  quite easily predictable. In point of fact, for many of these old rangetables, etc., it's impossible NOT to automatically include the effects of yaw in the trajectory computations, simply because the ballistic test firings on which the original drag functions were based measured actual bullet motion and thus automatically included the effects of flight yaw in the observations. To get the more modern "zero yaw drag coefficient" one has to actually SUBTRACT the effects of yaw from range firing results, and  somewhat ironically  add it back in again when running actual trajectories because actual bullets almost never run with exactly zero yaw. (Close though, often...)
The effects of small angles of yaw on armor penetration have been understood for a long time now; at least eighty years. The conditions at the proving ground, which involved firing at odd velocities over short ranges had to be watched carefully to ensure that the projectile was not still experiencing some initial nutation/precession effects when it struck the plate. For this reason, yaw cards were routinely placed in front of the plate to ensure the yaw was within reasonable bounds just before impact. As a rule, the effects of residual yaws under about 35 degrees was considered entirely inconsequential, i.e. the differences due to yaw in such situations could not be separated from the effects of random variations in the plate, projectile, and striking velocity. If one wanted to be incredibly picky, a simple linearextrapolation formula was used to 'adjust' the measured penetration to the effective penetration that would have occurred if the yaw were zero, which was never the case anyway in real life when shells were fired long distances downrange in battle. It was relatively rarely used, and I can, offhand, recall no instances where the correction involved a difference of more than three or four feet per second. Actually about the only time this was done was when a plate or projectile was just on the line between acceptance and rejection, and the addition of that additional few feet per second would bring the whole plate series into the acceptance level.
So far as I know, highyaw impacts (i.e involving yaw angles exceeding 10 or so degrees) of large projectiles was never studied anywhere by anybody. It was simply too difficult to get the big projectiles to yaw significantly without damaging them before they hit the plate. These projectiles are BIG, and it's not easy to deflect them without breaking something.
Hope this helps. Again, please do keep me informed of your progress. Your attempt to clear the the rain forest of ballistics armed with a computational chain saw may reveal more (or may reveal more faster) than I could with my crude mathematical machete(s) , but I doubt it, as this particular piece of land has been cleared many times before and the map  for better or for worse  has already been drawn. At this stage, your chances of finding anything new or significant 'under the bushes' are small...
Good luck!
Bill Jurens

 
 Posts: 168
 Joined: Mon Oct 18, 2004 4:23 pm
Hmmmmm....
I take it that you are no big fan of experiments wherein small caliber projectiles are used to model effects. As you know, this technique has been in vogue for many decades, and most scientists in ballistics research are keen fans of the notion. I do note that your view on yaw effects, especially as they relate to the last third of the trajectory are not congruent with what the modern literature tells me. And I am not talking about longrod penetrators here. Be that as it may, I am more intertested in how you interpret the formulae I sent you. When using them, the importance of yaw on flight dynamics quickly reveals itself. So what specific problems with these formulae do you have?
George
George