"Trajectories" Topic

Dear JC :

You mentioned Magnus in your prior post, it was the only instance in your prior post that was responsive to my initial question : how exactly could spin imparted by carooming cause enough lift opposed to gravity to raise a cannonball above its line of fire . It is the Magnus effect, where spin causes lift, that would be the mechanism for causing a cannon ball to rise above its line of fire.

From the website you referenced :
"Though windage had its justifications, it further impaired accuracy since the loose fit of a round shot made it tend to "carom" from side to side as it went down the bore of a gun and emerge from the muzzle with an inherent "wobble" in its flight which increased with range."
Nothing here about spin. Actually, this is the "yaw" efffect that I wrote of in my prior post, as far as I can tell.

Dr. Guilmartin is an historian.
JOHN F. GUILMARTIN, JR., LTC USAF (Ret), is an Associate Professor of
History at Ohio State University, Columbus, Ohio, where he teaches
military history, maritime history and early modern European history. He
holds a B.S. in aerospace engineering from the USAF Academy and an M.A.
and Ph.D. in history from Princeton University. He served two tours in
Southeast Asia in long range combat aircrew recovery helicopters during
1965-66 and 1975. He was a Senior Secretary of the Navy Research Fellow
at the U.S. Naval War College during 1986-87, and served as Leader of
Task Force II, Weapons, Tactics and Training, for the Secretary of the
Air Force/Gulf War Air Power Survey.

From the referenced article :
"Smoothbore cannon firing a spherical projectile were inherently inaccurate; the loosely fitting cannonball "balloted," or bounced, unpredictably down the barrel, acquiring "spin" in a random and uncontrollable fashion. As a result of this spin, the cannonball might slice or hook like a golf hall, or "float" erratically like a baseball pitcher's knuckleball."
He asserts that the spin imparted by carooming may cause a cannonball to "float" – but without either sources or calculations. The article really doesnt address ballistics in any detail- the quoted comment is really all I found there directly pertinent ot this question. It was interesting otherwise, for which my thanks.

The other sources you mentioned are too early to have ever performed any kind of instrumented test.

Cannon wear-out does not need to come from balls clanking their way down the bore. The repreated pressure of the decomposition of the charge would be the greater force, would be applied in the same place each time with only minor variation and would cause long-term fatigue failures. If you have detailed, modern empiracal analysis on this topic of cannon wear out, and the exact failure modes invloved, I would be very interested.

I am sorry you cannot provide any calculations or sources to suport your contention about spin imparted lift, other than Dr. Guilmartin's making of a similar assertion – and that you "don't understand the mathematics."

Please allow me to try the calc ?

For a cannon ball to rise above its line of fire, let us first look at the lift required :

The magnus force results from the asymmetric distortion of the boundary layer displacement thickness caused by the combined spinning and flow past the spherer. In the case of a sphere(or cylinder), the so-called whirlpool, or more accurately the circulation, does not consist of air set into rotation by friction with a spinning object. Actually an object such as a sphere or a cylinder can impart a spinning motion to only a very thin layer next to the surface. The motion imparted to this layer affects the manner in which the flow separates from the surface in the rear. Boundary layer separation is delayed on the side of the spinning object that is moving in the same direction as the free stream flow, while the separation occurs prematurely on the side moving against the free stream flow. The wake then shifts toward the side moving against the free stream flow. As a result, flow past the object is deflected, and the resulting change in momentum flux causes a force in the opposite direction.

See : link

The lift, L, imparted by the Magnus effect , properly the Robins effect for a sphere, can be given by :

L = C times p times D cubed times f times V
where
p is is the density of the fluid = 1.2 kg/m3 for air
V is velocity = 450 m/s muzzle velocity (see abbove in the thread)
f is rotations per second
D is the radius of the sphere = .11 m for a 12 lber
C is a constant , approximately equal to .5 for middle Reynolds numbers examples such as a cannonball (see below and the referenced source)

For the lift to raise the cannon ball, it must be greater than its weight (mass times acceleration due to gravity), or :
m times g = 54 N
where
m is the mass of the cannon ball = 5.5 kg for a 12 lber.
g is the gravity = 9.8 m per sec. per sec.

So …..

.5 x 1.2 x .11 x .11 x .11 x f x 450 > 54
f > 150 revolutions/sec
or, f > approx 1000 radians/sec

This simple model is based on the Bernoulli effect. The Magnus phenomenon is influenced by the conditions in the thin layer next to the body, known as the boundary layer, and there may arise certain anomalies in the force if the spin of the body introduces anomalies in the layer, such as making the flow turbulent on one side and not the other. One such is the reverse Magnus effect which may occur for smooth spheres. Rough balls such as cricket balls, baseballs, golf balls and tennis balls, do not show this anomalous effect.

We have made quite a "low limit estimate" for f :
> it is the estimate of just enough lift to counteract gravity at the instant the round leaves the bore, not to actually raise the cannonball above the line of firing or hold it there long enough to be observed
> it assumes the initial muzzle velocity is not reduced by air resistance
> it assume that the rate of spinning is constant, not diminishing.
> it is assuminng that the ball is sufficiently dimpled /worn /rough textured /etc. to have an appropraite Reynolds number
Thus, empiracally one might expect to see values for f in the range up to 1500 revolutions/sec required to actually see the cannon ball float (or about 10,000 radians/sec).

Looking at the " low limit " ….
The moment of inertia, I, for our 12 lb cannon ball , 2/5 times mass times radius squared, is about .0067 kg meters x meters. The kinetic energy required to generate the spin = 1/2 times I times f times f = 3350 J
At the high limit estimate for f, the kinetic energy required to generate the spin = 1/2 times I times f times f = 335,000 J

The greatest amount of energy that could be applied to create the spin would be from the following scenario :
The ball, resting at the bottom of the bore is bounced once to the top of the bore at the middle of the length of the tube and then carooms at the mouth of the gun at the bottom of the bore. Let us assume our 12lber has 3% windage and 18 caliber's bore. The angle of the ball's impact at each caroom is simply calculated to be about 0.058 radians or about 3.3 degrees.

Noting that the original kinetic energy of the round is given by 1/2 times m times V times V, or about 557,000 J, we can decompose the 3.3 degree angle of arrival into a horizontal component and a vertical one, the vertical one notionally capable of imparting spin and the horizontal one sending the cannon ball down range toward its target.
The vertical component would be sine of .058 radian times the total 557,000 J or about 32,000 J which would be dissapated in the impact at the middle of the bore (lets assume no spin is put on the ball this time, since we would have to counter-act any such spin to get our lift-off at the second carrom).
Some 525,000 J remain as we head to the second caroom , where (by the same calculation) we lose another 30,000 J. Some of these 30,000 J will be lost in impact as heat and some may impart spin to the cannon ball.

The round has slowed from the two impacts to 300 m/sec. At 300 m/sec, our new lower limit estimate for f is now about 1500 rad/sec. and the kenetic energy required to spin the ball fast enough to generate lift is thus some 7500 J

So, if all the planets are aligned and everything clicks just right, and we assume that the round does in fact bounce down the tube , as opposed to riding in a torus of compressed air, then it is arithmetically possible that the round will rise above the line of fire. If any of the factors and assumptions listed above are other than perfectly favorable to the imparting of spin in the desired direction, then there is arithmetically not possible to generate enough lift to see a "floater".

Whether this perfect conjunction of conditions occurs and endures long enough for anyone to notice it seems doubtful to me. If so, it would be "once in a blue moon".

I still think the "floaters" are from atmospheric wind conditions.

You will also note that the scenario of clanking down the barrel carooming loses quite a bit of kinetic energy (and/or velocity) at each clank. The amount lost per clank, if the number of clanks were greater than two, would increase because the angle of incidence at each clank would be greater. I dont think they would like the result , in terms of range, of a or 4 or 5 clank shot. By 8 clanks or so, I am not sure the round is still moving, but I didnt do the calc. In any case, I feel this consideration supports the notion of the round riding on compressed air down the bore.

Please do not hesitate to correct my calculations, if you think it appropriate.

g

Dear donlowry :

Yes, I think I agree with you that a good part of the pressure would begin to dissapate by the time the round reached the muzzle. I think this would be especially true of black powder, vs. nitrocellulose, and is a reason for the 18 caliber's bore length design rule.

But no, I dont think the pressure wave would over-reach the ball, since
> it would be riding in front of the advancing wave acting upon its center of mass
> it would not , if my compressed torus of air concept is correct, have overmuch friction with the air around it (some though, since that would be hot compressed air)

If you start looking at the energy loss sources, as I did in my prior post, either the muzzle velocity (sic – looks like initial velocity in truth, at the base of the bore) are low (which I doubt looking at the decomposition chemistry) or the ball departs without too much hindrance.

Otherwise, I dont think it would go very far !

But, as always, I eagerly await correction.

g

And the quote is on p40 under the title 'Bore'. You are not, I hope, disputing that caroming took place.

JC

Dear just-g,

I am surprised that you dismiss Muller and Roberts. The observations of professional artillerists of the smoothbore
period, whether they had done any "instrumented tests" or not, seems to me me to be valuable evidence of a lot of
things to do with the arm and are certainly going to be more valuable than the theoretical musing of anybody involved in this thread. I am not sure why evidence of caroming needs to be instrumented at all, to be honest. They would have been perfectly capable of inspecting the interior of their weapons. I am surprised you question the existence of caroming because it is quite clear that it did. Whether it imparted spin or not is another question but the evidence of period gunners that caroming did indeed take place, and that it was a significant cause of wear, is sufficient for me to doubt, very much, your notion that round shot was ejected "riding on compressed air down the bore" from which I infer you think it did not touch the sides.

As for Guilmartin, I am similarly surprised that you dismiss him as "an historian", from which I infer you do not consider him to be a subject matter expert. He has written at least two books on the subject of 15th and 16th Century maritime ordnance and I concede that writing a book does not make somebody an authority. That notwithstanding, I would have thought a man with a degree in aerospace engineering was rather more than just "an historian" in this particular context. That, however, is your prerogative but I doubt you are right in your assessment of his competence.

Returning to Gustav Magnus, as I am not a physicist so your calculations could be anything. I also think your invitation to correct them is a little potronising. But, you are correct that "It is the Magnus effect, where spin causes lift, that would be the mechanism for causing a cannon ball to rise above its line of fire."

Magnus conducted his experiments with cannon in 1852 and by employing pieces with deformed barrels found that the shot could be made to curve predictably in the opposite direction. He attributed this to the interaction between bore and shot and concluded that it imparted spin – in other words the Magnus Effect caused by caroming. I believe his experiments were documented in his "On the deviation of projectiles; and on a remarkable phenomenon of rotating bodies" which was published in the same year.

Your are also right to mention Robins. His experiments, as I understand it, also demonstrated that a projectile spinning about its axis experiences lift – no I can't quote them chapter and verse so don't ask. Existence of such a lift was verified by Magnus a hundred years later.

My object is not to persuade you that external forces described by such as Magnus affected the flight of round shot, and I suspect that would be fruitless. I am more interested in effect than cause anyway. All I would conclude by saying is that Magnus experimented with cannon and something is clearly going on which is explained by the Magnus Effect, to my satisfaction anyway. I accept that atmospherics have an effect on range but I remain unconvinced by your side-wind theory, at least not in isolation.

JC

Dear JC :

This discussion was stsrted by your assertion that carooming imparted spin sufficient to lift a cannonball above its line of fire.

I asked for source or calculations behind this assertion. You provided none. While I dont discount Muller and Roberts. I do not know where in there works calculations suchas I requested concerning spin imparted lift could be found. Certaining not on the pages or works you referenced.

As to Dr. Guilmartin, the articel you referenced was simlarly mute , except for a bold assertion (without source or calculation) similar to your own. Nothing in the authors's biography struck me as qualifying him to make such an assertion without at least adducing some evidence.

The is nothing in the cannonball-specific experiments of Magnus or Robins that demonstrates your proposition. At least not that I have found. But perhaps I have missed something more pertinent, as I am no expert (which led me to my initial request for your calculations or sources !)

Similarly, I regret that you feel patronized, even if only a little. As I said, i am no expert, and am just trying to study this material and see if the effects that you aserted to exist actually could happen. I would , quite sincerely, appreciate better information, or correction.

As to carooming in general, I am not convinced of its amount or the conditions which prompted it nor its effect on long-term wear-out. There seems to be some sort of long-standing conventional wisdom that this was quite common, but – as I wrote previously – I have some doubt and would think that only an instrumented test would really answer the question. i do not assert that it did not exist, but only have the doubts previusly described, and based on the considerations mentioned in my prior posts.

When you write : "My object is not to persuade you that external forces described by such as Magnus affected the flight of round shot", I am confused, since it was your own assertion on this heading that prompted my questions. If the quote is correct, one could only think that your initial assertions were not ones that you sought to persuade others to agree with. Which strikes me as odd, since I assume your prior assertion was made in good faith and reflected your considered view of the question. Equally in good faith, i could be very easily convinced of anything on this topic where evidence or calculation could be adduced in support of someone's ideas.

If your prior assertion was merely a re-tellling of conventional wisdom, or a topic of which you had no interest in analyzing in greater detail, I would have found it polite if you had just so stated in response to my request for details.

I also apologize if my tone or wording is not agreeable to you — as English expression is not at all an area of special skill for me , I can easily make mistakes in tone, idiom or syntax.

I should think that we might suspend our discussion at this point ? i certainly did not wish that my interventions on this forum should cause any ill-will, and am suitably chagrined.

g

g,

You didn't do anything incorrect or improper. I have enjoyed your postings and the detail in which you have illustrated your points.

The problem is that Mr. Cook has been saying the same thing on this subject for quite some time and cannot back it up. The bottom line is that the round does not rise from the line of firing and there is no evidence of this in any of the artillery texts that I have seen. I have quite a few, including Muller, and none of them state that the round rises above the line of firing after leaving the gun tube.

The Muller quotation from page 40 is:

The windage, or difference between the diameters of the shot and the bore, is not thesame in England as abroad. Suppose the diameter of a shot divided into 20 equal parts, then the diameter of the bore is 21 of these parts; the French suppose the diameter of the shot divided into 26 parts, and the diameter of the bore to be 27; what the proportion is in Holland and the other parts of Germany I do not know; but it is evident, that the less windage there is, the truer the shot will go; and having less room to bounce from one side to the another, the gun will not be spoiled so soon; for which reason I suppose, in the following constructions, the diameter of the shot to be divided into 24 equal parts, and make the bore 25, which is a medium betwenn the English and French method. This we do not so much in order to differ from others, as on account of the convenient scale it affords, to construct not only guns thereby, but also their carriages, as will be seen hereafter.'

While the 'process' of carooming is described, the word isn't used at all, which somewhat surprised me when I read the passage as I though it would be in there and that it would be the main thrust of the passage, which it is not-windage and its reduction allowing a 'truer' shot is.

Therefore, this discussion would be enhanced if Mr. Cook would just admit one of two things: one, that he is incorrect, or, if he cannot bring himself to do that, admit that he cannot find or produce any evidence that the round once fired does not rise from the line of firing.

Sincerely,
Kevin

Dear just-g,

It's not a problem

JC

Dear Kevin,

You should pay more attention I think, or stop being selective in you interpretation of material to suit your purposes.

"While the 'process' of carooming is described, the word isn't used at all, which somewhat surprised me when I read the passage as I thought it would be in there and that it would be the main thrust of the passage, which it is not-windage and its reduction allowing a 'truer' shot is."

So what?

The question was whether caroming existed at at all. This passage shows that it did. You are being particularly gratuitous if your only objection to the passage is that Muller uses the term 'bounce' not 'carom'.

You must also learn that people will not always agree with you and getting indignant when they don't is really rather peurile.

JC

There wasn't any question as to whether carooming existed. That was a given. The issue was whether or not rounds rose from the line of fire. They don't, and you have always maintained that they have.

You might want to make a reevaluation who is being 'puerile.'

You have repeatedly erred on artillery subjects and have displayed little or no knowledge or understanding of the subject. Further, you haven't supported your position on rounds in flight with any evidence whatsoever. You have also self-servingly chose to ignore primary source evidence that proves you wrong. You have great dexterity with the English language when denigrating others or sources with which you don't agree. It is too bad that most of your efforts usually involve obfuscation of some type when you are proven wrong.

Sincerely,
Kevin

Looking into the following artillery manuals:

-The Artillerist's Companion by T. Fortune (1778)
-Treatise of Artillery by LeBlond (1746)
-DeScheel's Treatise on Artillery (US edition 1800)
-The Artillerist's Manual by Gibbon (1863)
-Ordnance and Gunnery by Benton (1864)

there is no reference, statement, or allusion to an artillery round rising after it leaves the gun tube.

The last two discuss the round bouncing or ricocheting down the bore because of the difference in windage between bore and round, but the term, interestingly, carooming (or caroming) isn't used. Both Gibbon and Benton refer to and discuss Magnus, his experiment, and its results on projectiles, but there still is no reference to a round rising above the line of fire because of the effect of the air or any other external force.

What is discussed is drift (from the French term 'deriviation') which is the round going to the left or right of the line of fire because of spin. The two manuals are quite definitive stating that every round will spin as it leaves the gun tube, but even if it is an 'upward' spin, as opposed to a 'downward' spin, it doesn't cause the round to rise. Perhaps references to an upward spin of the round confused some people.

Robins experiments were also discussed somewhat. What Robins did find out about rounds was there was drift to the right and left, and nothing about rounds 'rising' from the line of fire.

There is a reference of a round 'rising' immediately upon leaving the tube, but that is due to how it strikes the side of the gun tube due to ricocheting down the tube upon firing. Again, there is no upward deviation from the line of fire after the round leaves the gun tube, Bernoulli, et al, notwithstanding.

Sincerely,
Kevin

What about oblong cannonballs?

link

Yes, Kevin, there was a "question as to whether carooming existed". You must stop twisting things to suit your particular script.

See just-g's post of 30 November above: "It is not clear to me that the process of decomposition of the gunpowder would cause the cannonball to bounce its way down the bore. Rather, since air compresses so much better than iron, it occurs to me that the pressure exerted in the windage might be sufficent to keep the ball roughly "centered" and not banging its way down the tube."

My answer was in response to that as, I suspect, you know perfectly well.

JC

Dear just-g,

I found the article by the research group I alluded to earlier, written by Robert D Smith of the Royal Armouries, this described a test conducted using a modern replica of a small bronze medieval cannon of 36mm calibre, whose carriage is a trestle-type with four legs – not quite a Napoleonic smoothbore I am happy to concede but a
smoothbore black powder cannon none the less.

Although their purpose was principally to measure the efficiency of various different kinds of powder, and
notwithstanding that Smith notes that results might be different with large pieces, their tests using radar to determine range, velocity and trajectory are interesting. The target was a 2m square set at 200 paces from the gun. The shot was lead and specially made to reduce windage to a minimum.

Their target shooting tests used the same powder 'recipe' and were to determine accuracy. At 2.2 degrees with
velocity of 216mps the range was 285 metres and the shot elevated such that it went over the target at a height of 4-5 metres. At 1.7 degrees with a velocity of 209mps the range was 240 metres and the shot elevated approximately 3
metres and veered to the right. At 1.6 degrees with a velocity of 238mps and a range of 435 metres and the shot
elevated approximately 5 metres. At 1.4 degrees the radar could not record the flight. At 1.1 degrees with a velocity
of 240mps and a range of 240 metres the shot elevated approximately 1 metre.

Smith noted that "it was clear that the trajectory of the ball was erratic as would be expected by the Magnus Effect. It should be noted that setting the elevation of the gun was difficult even using a modern clinometer." It is not hard to understand why setting elevation was difficult when the primitive four-leg carriage is seen.

If Smith is right that this is the Magnus Effect at work, and one assumes he is is a subject matter expert, it follows that the ball must be spinning. If it isn't, then something else must be at work to produce consistent random elevations of the ball.

Smith concludes that the gun is not very accurate! He summarises that "This must be due to inherent inaccuracies of the bore of the gun, in its aiming and elevation as well as the Magnus Effect which randomly affects the trjectory of spherical objects".

I merely offer this for interest's sake.

JC