problems with range charts

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sineatimorar
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problems with range charts

Post by sineatimorar »

Have ever noticed how western cannon shell GAIN velocity at longer ranges. When I queried this phenomenon with key websites I got an answer that evolved round lower air resistance at high altitude. While this explains the increased range, it goes nowhere near explaining the extra boost in final velocity. Can any shed light on this question?

This is an extract from my website showing an example and further explanation of the problem.

The weird part of working the above chart was, although using a 'known' caliber thru the ballistic program ( to proof test the program) I was able to get the exact flight time for the given elevation except the 'calculated' striking velocity was reduced by, approx., one quarter of the recorded 'historical' value at the 'SAME' range. I do not see how two shells fired at exactly the same elevation,same muzzle velocity, same weight , have the same flight time and strike within meters of each other and have completely different striking velocities.I am first to admit I am no scientist, but this result defies what I remember about conservation of energy etc.

Interestingly the plotted range chart seem show a flight path seems to be as expected.

Comparison range chart between officially published values [o p v ]and ballistic computer results.
range chart USA 40.6/50 mk 7 canon with 2,700 lbs. (1,224.5 kg) AP Mark 8 muzzle velocity of 2,500 fps
Range-------------Angle of Fall /o p v--------Striking Velocity----------Time of flight------elevation
10,000 yards-------------5.23 / 5.7-----------2012 / 2,074 fps----------13.3/13.2---------4.66
15,000 yards-------------9.46 / 9.8------------1789 / 1,892 fps----------21.2/np-----------7.82
20,000 yards------------14.99/ 14.9-----------1581 / 1,740 fps----------30.2/29.6--------11.4 /17,650yds@10degs
25,000 yards------------21.99 / 21.1----------1388 / 1,632 fps----------40.3/np------------5.72 / 23,900ys@15degs
30,000 yards------------30.15/ 28.25----------1210 / 1,567 fps----------51.8 /50.3--------20.6 / 29,000yds@20degs (most accurate of comparison)
35,000 yards------------40.22/ 36.0------------1043 / 1,556 fps---------65.8/np------------26.46 / 33,300yds@25degs
40,000 yards------------50.18 / 45.47-----------962 / 1,607 fps(1)------80.8/80.0---------32.66
42,345 yards------------53.92 / 53.25-----------931 / 1,686 fps (1)-----88.2/np-----------35.65 / 39,500yds@35degs

Except for a noticeable strike velocity difference most values are within acceptable tolerances.

(1) Now while the explanation as to why at certain barrel elevation above 30 degrees will travel further down range than otherwise indicated in a vacuum(45 deg is max range in vacuum) is logically acceptable. The reason being the reduced air pressure at altitude reduces the drag experienced while at that altitude which reduces the rate of reduction in velocity for that time period only. The shell still has to experience the same amount of drag on decent at any given altitude. Even in a vacuum the shell would still experience the effects of gravity (hence the curved flight path) any increase in velocity would be limited by the terminal velocity particular of that shell which is the same for any given altitude and if the shell does increase its momentum [ something I do not believe possible; Conserve maybe, but not increase] there would be an increased in both parasitic, aerodynamic drag as the thicker atmosphere is encountered and that would counter any increases so I refuse to believe that there such an increase in final velocity. This is confirmed if the reader takes the time to plug some different height values into the free fall equations found online at .http://hyperphysics.phy-astr.gsu.edu/hb ... lq.html#c1 which confirms there is no increase in velocity due to any increase in height that would effect any vertical component of the shell's momentum.Therefore the above range chart not only figures obtained using the computer program will be used due to the more realistic answer in my mind. Flight time and range are the same or very close as is clearly shown.
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Re: problems with range charts

Post by Guest »

A slight increase in striking velocity at long range is common and to be expected; it's just a function of the physics involved and the relative effects of drag vs gravitational acceleration.

I am not sure how to deal with your other questions or comments, except to ask 'What software are you using?' There is a fair amount of fairly unreliable stuff out there, and it's often not used properly.

Bill Jurens.
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RNfanDan
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Re: problems with range charts

Post by RNfanDan »

@ sineatimorar;

I do not understand your use of the term "western". If you mean a shell fired in a westerly direction, i.e., from a gun on the ground that is AIMED to the west, then you will see that shell return to Earth beyond its target, unless range correction is applied. This is because the Earth rotation is from west to east, and the target moves with the Earth (fixed targets assumed and all other things equal).

While the shell is in the air, the target at which it is aimed will be moving toward the shell, in other words---but this is not a gain in "velocity", at least in terms of relative "air speed" of the projectile through the atmosphere. The shell travels the same speed relevant to the atmosphere in either direction--again, assuming all other factors equal. The opposite is true for that same projectile fired at a target lying 20 miles EAST of it. The target will continue to move with the Earth's rotation, in an easterly direction; thus, while the shell is in flight, the aiming point has increased in distance and the projectile will fall short.

With respect to the target, itself, the projectile's velocity WOULD be slightly greater, in the westerly example, if compensation were applied---but this is simply because the shell travels a shorter distance and has less time to be affected by wind resistance, etc. The projectile simply lands sooner. This might be confused with "gaining velocity", but it is merely a difference of rates of decay in speed over distance, since no propulsion of the shell takes place beyond the gases driving it from the muzzle of the gun from which it was fired (discounting gravity). It doesn't gain speed, it just loses less. How much this affects the impact velocity is FAR beyond my ability to describe--it may not be significant at 20 miles, either way.

All of this is very oversimplified of course, because ballistics involves dozens of factors---wind speed, humidity, air density, air temperature, rotational speed, shell shape and size, and more.

But I hope this is helpful, nonetheless.

Dan
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sineatimorar
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Re: problems with range charts

Post by sineatimorar »

Ar Dan droll very droll ha ha. Just love a happy chappy.
My choices of example should be answer enough.
To the other responder care to quote what 'simple physics' you refer to please?
The effect of terminal velocity limits any acceleration due to gravity.
I assume you did the simple physics experiment in senior school of rolling two identical steel balls; one off the the edge of a table and the other off a curved ramp which launched that ball of in a horizontal direction yes? The trick been that both balls leave the ramp and edge at the same instance?
Result been sort after is they hit the ground at same instances. Cool yeah?
That experiment is part of the proof behind my conundrum and is the start of the 'physics' mechanism behind external ballistics. See if I can put it any simpler. The shell requires a certain height to descend from to reach terminal velocity, the value of which said velocity is governed by the shell's weight and cross sectional value .Once the shell reaches terminal velocity it will not change for any given altitude as long as that altitude allows for terminal velocity to be obtained. That takes care of gravity.
The final velocity is governed by terminal velocity, initial velocity ( muzzle velocity ) and is inversely effect by drag and the length of time in flight ( this means more time in air more drag SLOWER the shell ( I not going to fast am I? ). Other effects been rate of rotation of shell. If you care to see two range charts I have posted on the internet go to my website sineatimorar.com you will see the expected flight path graphics, correct flight times, similar elevation for given range and similar angle of strike that is historically recorded except strike velocity. Yes you would be correct that simulation could be queried, which I diligently did and yes the program is meant for rifle use , and the authors of the program believes that it should not return valid results. My problem with that is I am on the money as it were on all requirements of accuracy and flight profile except strike velocity. To obtain this extra momentum there has to be provided some external source and gravitational force effect is limited by the terminal velocity. Give me some flesh to your theory. I am happy to be corrected if I have forgotten some part of the Laws of Motions
vague unsupported statements is all I have got so far.
sineatimorar
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Re: problems with range charts

Post by sineatimorar »

sineatimorar wrote:Ar Dan droll very droll ha ha. Just love a happy chappy.
My choices of example should be answer enough.
To the other responder care to quote what 'simple physics' you refer to please?
The effect of terminal velocity limits any acceleration due to gravity.
I assume you did the simple physics experiment in senior school of rolling two identical steel balls; one off the the edge of a table and the other off a curved ramp which launched that ball of in a horizontal direction yes? The trick been that both balls leave the ramp and edge at the same instance?
Result been sort after is they hit the ground at same instances. Cool yeah?
That experiment is part of the proof behind my conundrum and is the start of the 'physics' mechanism behind external ballistics. See if I can put it any simpler. The shell requires a certain height to descend from to reach terminal velocity, the value of which said velocity is governed by the shell's weight and cross sectional value .Once the shell reaches terminal velocity it will not change for any given altitude as long as that altitude allows for terminal velocity to be obtained. That takes care of gravity.
The final velocity is governed by terminal velocity, initial velocity ( muzzle velocity ) and is inversely effect by drag and the length of time in flight ( this means more time in air more drag SLOWER the shell ( I not going to fast am I? ). Other effects been rate of rotation of shell. If you care to see two range charts I have posted on the internet go to my website sineatimorar.com you will see the expected flight path graphics, correct flight times, similar elevation for given range and similar angle of strike that is historically recorded except strike velocity. Yes you would be correct that simulation could be queried, which I diligently did and yes the program is meant for rifle use , and the authors of the program believes that it should not return valid results. My problem with that is I am on the money as it were on all requirements of accuracy and flight profile except strike velocity. To obtain this extra momentum there has to be provided some external source and gravitational force effect is limited by the terminal velocity. Give me some flesh to your theory. I am happy to be corrected if I have forgotten some part of the Laws of Motions
vague unsupported statements is all I have got so far.
If it looks like a duck, walks like duck and quacks like a duck, then it must be a duck.
Byron Angel
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Re: problems with range charts

Post by Byron Angel »

Herrmann's "Exterior Ballistics 1935" [US Naval Academy textbook] addresses the issue. It is a function of the effect of gravity.

B
sineatimorar
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Re: problems with range charts

Post by sineatimorar »

Thank you I will enjoy reading that book now. I will get back to you all soon
sineatimorar
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Re: problems with range charts

Post by sineatimorar »

As per previous post. Suggest that anyone who holds to the theory that a increase in strike velocity at or near max range, make themselves familiar with plate iv pg 105 of suggested manuscript. That chart and text proceeding it, show no mathematical support or proof of increase in strike velocity greater than lesser ranges. The program obliviously uses the accepted method of intergration mentioned in that text. There for if you cannot come up with an exact references to what mathematical formulation supports this premise then I will continue to consider it not proven and a fictitious record of fact until proven otherwise.
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Re: problems with range charts

Post by Guest »

I think you are misreading the figure in Exterior Ballistics 1935, which actually has the values for velocity listed in inverse order. In other words, the smaller values are at the top of the page and increase downward. Read this way, you can see that the lowest striking velocity, just over 1400 ft/sec occurs at an angle of departure of about 25 degrees, and that the striking velocity begins to increase again thereafter until reaching about 1560 ft/sec at a 45 degree angle of departure, i.e. at maximum range. This confirms what I said earlier. Each gun varies a bit, but for a 'typical' 16" gun, the minimum velocity usually occurs at about 3/4 of the maximum 45 degree angle-of-departure range. The velocity at that range is about 7/8 the final striking velocity and about 50-55% of the initial velocity.

I glanced quickly at the diagrams you posted on your website, and the shape of the trajectories, especially at high angles of departure just does not look quite right to me. My suspicion -- but it's only that -- is that if you are using a small-arms type program, that the atmospheric density does not vary with altitude, i.e. that the program allows you to change the density for each trajectory, but thereafter assumes the density (of whatever value might be chosen) remains constant with altitude thereafter.

It's certainly true that a program designed for small arms ballistics, e.g. rifle fire, is usually not adequate to deal with long range large caliber artillery fire. The exterior ballistic theory used to handle long range artillery fire is much more complicated than that typically used in small-arms studies.

Bill Jurens.
Byron Angel
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Re: problems with range charts

Post by Byron Angel »

..... Well, apparently every exterior ballistician on planet Earth has apparently had this wrong. Who knew?!?!

Actually, I think you might want to review your assumptions about projectile "terminal velocity" in relation to the classic falling object case and how it relates or doesn't necessarily relate to calculation of a curve of ballistic trajectory, and also re-consider how the gravity vector acts upon a projectile at various points along its ballistic path when angle of fall passes beyond 45deg.

Have a nice day.

B
sineatimorar
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Re: problems with range charts

Post by sineatimorar »

I am not saying that .All I am saying is I personally do not 'see' the mechanism behind it. People keep given me hint just like your last that suggests titles of ballistic theory with no 'flesh' as it were to explain what they mean. Look at the chart indicated and explain were it supports the phenomenon.It should be obvious that I am missing a key understanding which I am happy to admit I might be lacking. But so far the response I have got is based on assumption that goes along a line of ' This what was always believed, so it has to be correct, so believe it and do not ask why ' It like I have asked the wrong question in Sunday school. Here another way to ask the question; Why is this phenomenon not present in some other charts with similar ballistic performance? This is what I first noticed . Now it is being suggested to me I need to talk to Bill Juren .can anyone direct me to his email or contact point please.
Byron Angel
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Re: problems with range charts

Post by Byron Angel »

sineatimorar wrote:I am not saying that .All I am saying is I personally do not 'see' the mechanism behind it. People keep given me hint just like your last that suggests titles of ballistic theory with no 'flesh' as it were to explain what they mean. Look at the chart indicated and explain were it supports the phenomenon.It should be obvious that I am missing a key understanding which I am happy to admit I might be lacking. But so far the response I have got is based on assumption that goes along a line of ' This what was always believed, so it has to be correct, so believe it and do not ask why ' It like I have asked the wrong question in Sunday school. Here another way to ask the question; Why is this phenomenon not present in some other charts with similar ballistic performance? This is what I first noticed . Now it is being suggested to me I need to talk to Bill Juren .can anyone direct me to his email or contact point please.

..... Re Herrmann's book "Exterior Ballistics", I think you are misreading the chart on page 105. In the case of the gun in question, striking velocity falls dramatically as gun angle of elevation progresses from 0deg to 15deg, falls very slowly between 15deg and 25deg until, at elevation angles beyond 25deg, striking velocity slowly increases. The multi-functional nature of the graph can be confusing, but note that the striking velocity curve is argued versus angle of departure across the bottom of the graph, and it values are read from the striking velocity values shown vertically on the right side of the graph.

Another way to visualize this issue is to fire a theoretical projectile vertically into the air. On the upward path, both retardation and gravity act to diminish projectile velocity until it reaches zero at trajectory apogee. On the downward path, the increase in velocity is strictly a function of gravity while retardation continues to act against velocity. The same logic holds true, albeit to a lesser degree, when angle of elevation is reduced. The trick here [IMO] is that the force of retardation varies dramatically versus projectile velocity. At high velocity, retardation has a powerful effect, but, since retardation effect reduces by something like a factor of [Vx/Vo]^2, it can reach a point as projectile velocity falls sufficiently where the deceleration caused by retardation is < the acceleration vector imparted by gravity - in which case, projectile velocity increases.

Hope this helps.

And Bill Jurens' ("Guest") point about reduced atmospheric density at high altitudes must be given serious attention as well.

B
sineatimorar
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Re: problems with range charts

Post by sineatimorar »

Yes Byron it does.this and Bills private correspondence helped .l am happy to admit to "barking up the wrong tree" here and get on with other more useful endeavours. I needed someone to flesh things out for my understanding and Bill has. Your point about acceleration verses retardation via drag is the last peace of the puzzle.
Sorry if I irritated anyone over my b.s. above.
Byron Angel
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Re: problems with range charts

Post by Byron Angel »

sineatimorar wrote:Yes Byron it does.this and Bills private correspondence helped .l am happy to admit to "barking up the wrong tree" here and get on with other more useful endeavours. I needed someone to flesh things out for my understanding and Bill has. Your point about acceleration verses retardation via drag is the last peace of the puzzle.
Sorry if I irritated anyone over my b.s. above.

..... No worries. Bill J is a good man.

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sineatimorar
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Re: problems with range charts

Post by sineatimorar »

Just thought I would mention why I got it so wrong. Hopefully I have got my explanation correct.
Simply put the acceleration seen and proven with the radar equipped proofing ranges and modern ship based radar systems, is due to the fact that they ,the shells in flight, are operating at velocities far above the terminal velocity accorded to them from their respective weights and dimensions therefore the principle does not apply under stated conditions. As stated previously I was missing the fact,either through ignorance or faulty memory.
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