To get back to your question. As far as I know: The whole point CEP is to give an estimate of the Standard Deviation that is reasonably easy to obtain. Fire a lot of shells at a target with nobody around, measure the distance from the center (marked with X) to all the holes in the ground, take the least accurate of the 1/2 that is nearest to "X" - you get your CEP. Let the math freaks tabulate, from that estimate the distance (10%, 20%, 30% and so on) shells are within. Decide your level of safety: Then take that distance and add it to the lethal distance (assuming it is a hard figure) of the shell, correct for conditions (standing up, lying down or in cover), then you have your "safe" distance.

Yes, but I am looking for an actual figure for the standard deviation. Basically, I want to be able to calculate that if the CEP is X meters (say 50) than maximum deviance of shells is Y meters (say 200). Maximum deviance meaning that 100% of the shells fall within this distance of the target.

Events have a distribution, if it's a 'standard distribution' (or 'bell curve') then statisticians slice it into 'standard deviations' such that almost 100% of events will fall within 3 standard deviations either side of the mean. However, artillery doesn't use standard deviations it uses 'probable errors'. With PE all events will fall within 4 PEs either side of the mean. The reason for slicing the standard distribution this way is that 50% of events will fall within 1 PE either side of the mean, hence 2 PE is called the '50% zone', which is more convenient for artillery purposes. PEs appear throughout the artillery system. For example the round to round error in laying, the accuracy of the ballistic calculations, the target location error, the accuracy of the mean point of impact in relation to the aimpoint, and many other events are all normally distributed and therefore have a PE. It should also be pointed out that there may also be events that are not normally distributed and be skewed or have some other distribution. The PE that attracts lots of attention and is probably what underlies the question is the one given in firing tables, actually there's 2 if not 3 of them: the PE in range, the PE in line and the PE in HOB for airburst fuzes. CEP applies to missiles, for guns the PEr it always much bigger than the PEl. You can combine PEr and PEl using root mean square (RMS) but frankly the resulting number doesn't mean a whole lot and is actually dangerous. If the line of fire is overhead, the ammo HE groundburst, and the angle of descent fairly low then 4 PEr is a fair measure of safe distance because very few fragments travel backwards in these circumstances. If the line of fire is across the 'line' of own troops then PEl is a factor but slight, more important are the 'wings' of fragments that come laterally from the shell burst, these depend on the size of shell. Since these fragments also come forward then the length zone is also a consideration. High angles of descent, such as mortars, send their fragments all around. Airburst will also send some fragments a bit backwards and the possibility of early bursts is also a consideration, such bursts might be caused by fuze errors but trees can also be a factor. Of course the distance that fragments travel is also normally distributed (in the statistical sense). Lots of other things influence the safe distance, the slope of the ground affects where shells fall, the posture of the troops 'at risk' (dug-in who cares about fragments going overhead, standing up - beware), the 'brokenness' of the ground obviously affects its protective properties for troops that are prone but not dug-in. There's some explanation on this site http://members.tripod.com/~nigelef/index.htm on the 'Errors & Mistakes' and 'Weight of Fire' pages.

Neutralizer, thanks for the explanation and a special thanks for the link! The link you provided is simply amazing!

Its not so much the CEP, but the RDE. A cannon (15mm+), by its nature has a longer range dispersion than its deflection dispersion, this is more pronounced from a gun than a howitzer. Our standard rule was danger close at 600 meters for artillery and mortars, 750 for NGF 5inch or less, 1000 over that, but all this doesn't mean missions won't be called in closer. There are many variables to be considered. In Korea we routinely fired within 600 meters of our OP with 105s and 4.2 & 81mm mortars.

Safe distance is a somewhat arbitrary concept. Some (most?) armies have a concept of 'safe planning distances', typically a distance for each type of gun, etc. NATO procedures include one for 'Danger Close' engagements (which usually use the 'safe planning distance'). In SVN theatre SOPs required that opening rounds were never aimed closer to known troop locations than 1000 metres. Realistically how close you bring shells to yourself depends on your appetite for risk. Fired overhead, where there are no trees in the way to cause an early burst, and if you are prone then twice the range PE is OK, and you can get away with less, plenty of people have. You take the choice, be killed by the enemy or take a bit more risk with your own guns. It also depends on whether the opening rounds are aimed close or the fire is adjusted to close, adjusting takes out the errors in target location and accuracy. The main elements are: A Target Location Error, how close the aimpoint is to target centre. The CEP in this is highly dependent on how the target location was determined. Accuracy, the difference between the aimpoint and the mean point of impact, basically a function of the gun to target range but can change with circumstances. Dispersion, tabulated in the Firing Table but can be reduced if you can predict the MV of the next round. How far the fragments go with 'lethal' mass and velocity. Basically the bigger the gun the further, but the further from the burst the less the density of fragments to the less the chance of a hit. Also depends on the angles of descent of the shell, steep and fragments go all around, flat and they are limited to 'wings' at right angles to the line of fire. Of course vulnerability is also important, standing up is a lot more risky than being in a hole. You can reduce all these to CEPs for a particular situation and combine them. Of course the issue is how you define such things as 'lethal area'. This dosn't really give you a safe distance, it merely tells you the chance of it being dangerous, ie if you can say what chance of casualties is the threshold between safe and unsafe then you can calculate the distance that this represents in a particular set of circumstances.

Well,, Mostly the deviation is (along the flight path) 0.3% sideways and 1% lengthvice. So the CEP is not round but it is an oval, and from infantry point of wiev depends on the direction arty is firing from. As to safe distances: FDF has following rules. for heavy artillery(155-152mm) safe is 300m, (ie you can get that close to impacts and be safe.) medium (130-105mm)it is 200m, heavy mortars (120mm) 100m and light mortars (82mm)50m. But FDF has about the worlds best artillery arm, so the safe distances and what you are allowed to do are much more broad (or shall we say more dangerous) than NATO armies.

haven't a clue who 'FDF' is, but am most impressed to hear that they are the 'worlds best artillery arm'. No doubt they are legends in their own lunchtime. 'Mostly the deviation is (along the flight path) 0.3% sideways and 1% lengthvice.' - I love meaningless data, competant artillery arms work in Probable Errors because dispersion is statistical and arty finds standard deviations an inconvenient way of handling the problem. A fairly normal practice is to express 1 PE as a % of range. I'd guess 1% isn't one PE because if it was then a complete replacement of the gun and ammo fleet is about 100 years overdue. "As to safe distances: FDF has following rules. for heavy artillery(155-152mm) safe is 300m, (ie you can get that close to impacts and be safe.) medium (130-105mm)it is 200m, heavy mortars (120mm) 100m and light mortars (82mm)50m." In the terminolgy used by some western and other armies 152/155mm is not heavy it is medium. Furthermore if these distances are 'regulations' with everything that that implies then 'FDF' is well behind the game. Effective armies don't dictate such things, they are guides - the old saying 'rules are for the obedience of fools and the guidance of wise men', is very applicable to artillery.

Do you ever get frustrated explaining the same things to people over and over again :-). Think FDF might be French Defence Forces...maybe.

That was my first thought, but I'm now tending to Finnish!