understanding drift and probability

[Harry's Lad]

Wow!

If you’re consistently hitting a ¾” pole @ 80 m then Dr. Mann must have been right all along … but then his august work was never really in doubt, was it?

An interesting use of the ‘Mil’ as a measurement of angle (you’re not an artillery gunner are you?). Please excuse my ignorance in these matters but do folk generally use Mils (or milliradians) for measuring displacements?
If so, would it be of some benefit if the next ChairGun version had milliradians as an alternative to MoA, clicks and Mil-Dots?
Say now or forever hold your … whatever.

The probability part of you title is much more, er, problematical.

With anything up to ~3% variation in BC for pellets of similar weight from the same batch, ~1% variation in MV from a well regulated PCP, the practically un-measurable variations in the wind vector and the implicit accuracy of the rifle/shooter combination, actual deflection is always going to be something of a guess. Mann’s expression can be used to calculate the limits of the deviation (using MV, the magnitude of the wind-vector and using the BC value to calculate the flight-time) and to that you need to add your estimate of implicit accuracy. Having calculated/guessed at the possible range of the deviations you could then assume that the deviation follows the normal distribution (a valid enough assumption in the circumstances) and then use that to estimate the statistical probabilities involved. i.e., if we assume that the difference between the maximum and minimum deviations equates to 6 standard deviations (SD) then 94% of the possibilities lie within +/- 2 SD of the mean position, 68% within +/- 1 SD, 38% within +/- 0.5 SD, and so on.

You might want to look at the WindCalc application that I uploaded to the www.chairgun.com site a while ago (Software page, towards the bottom).

I particularly like the idea of the ‘wind-clock’ – I’ve not seen the like before. Hmmm, I think I feel a new ChairGun3 applet coming on …

ATB
Dave

[flims]

ok so let me start with the first part. Mils, mil dots milliradians Mrads, they are the SAME thing mate just different way of writing it, so Chairgun already gives you this info under the Mildot column. i'm not an artillery gunner no but mils are easy to work with and using a mildot reticle makes sense to use a mildot Turret.
displacement is measured in anything you want,
MOA easier to work in Inches and Mrad to work with cm and meters. many europeans army guys use Mils to measure displacement since they use metric and the US ever since they adopted the S&B scope they use Mrads too.

about BC, now i don't really base everything on BC, all my data was shot in the field, measured error for Elevation, inputed this in chairgun till the numbers onchairgun came close to my real world conditions and i managed this through out. i played with the BC abit later after inputting conditions etc.

there are variances in pellets like there are in bullets but don't worry so much about it, after you test your pellets for drop consistancy don't worry too much about wind. there is really not much difference in wind even when changing the velocity by 20-30ft/s. that is :
if you measure the drift of a pellet at 924ft/s muzzle velocity at 100m and 944ft/s it is not incredibly different for our purposes. remember that any wind call you do is always dependant on the grouping capabilities of your rifle so if your average group at distance X is 2" then your best wind call will be withing 2" of your point of aim.
the difference arises in Elevation mainly so once your real world data is like that shown on airgun you can print out a wind drift chart for a 10mile.hour wind. this however is correlated to Yards not to meters as Distance so in my case i had to convert the values to meters since i wanted to use this as a gauge for measurement.

i know the limitations of my setup and with regard to gauging the wind, it will ALWAYS be a guess, but rather than a guestimation in can be a very well informed windcall, so well that i might only have to compensate 0.4mils at 120m, better than the majority that will hit 3feet away or not even pick up the hit because itwas outside their Field of view. my stringing at 120m is between 2-3" for vertical elevation. if you look at the groups i have posted on other threades you will see that most of the time the difference arises in the VERTICAL component not in the horizontal one dependant on wind.

you have to shoot like this everytime you shoot to be able to pick up a feel for the wind by looking through a spotting scope or rifle scope, you should be looking at the grass between you and target or debree, or in the case of home, mirage was always very heavy. Chairgun if used correctly with real world Data can be really accurate but that data has to be gathered at longer ranges not at 50m otherwise you cannot point out the error.

with regard to the pole mate, there are 80m conditions are there are 40m conditions. if wind is 3mph full value constant that is an 80m condition.
if wind is 3mph switchin to 6 from full value to half value, then that will be a good guess situation that might have you dial a condition and hold off over your dial or hold less than your dial but its not technically speaking at 80m condition. the more you shoot in 7mph winds at 100+ ranges, those closer shots seem relatively easy.
i wrote more info here on using the wind clock, will only take you about an hour to make one and it allows you to take the info in the field in a layout that is usable without much confusion. More over when explaining to new comers it is not intimidating like a chart full of numbers. it gives you what you need to see only. Remember all values are for a full Value wind(3-9, or 9-3 oclock)
http://www.airgunbbs.com/forums/show...ght=wind+clock
btw What about Dr.Mann?

[Harry's Lad]

ok so let me start with the first part. Mils, mil dots milliradians Mrads, they are the SAME thing mate just different way of writing it, so Chairgun already gives you this info under the Mildot column.

1 Mil = 360/6400 = 0.05625 degree = 3.375 MoA
1 milliradian = 360/(2 x Pi x 1000) = ~0.057296 degree = ~3.4377 MoA
--- close but not the same ---
1 Mil-dot = 1 milliradian only @ 10x magnification.
I’ve never heard of a ‘Mrad’ but it sounds like an abbreviation of ‘Milliradian’ to me.
ChairGun would only equate milliradians to Mil-dots if the magnification were set at 10x.

about BC, now i don't really base everything on BC, all my data was shot in the field, measured error for Elevation, inputed this in chairgun till the numbers onchairgun came close to my real world conditions and i managed this through out. i played with the BC abit later after inputting conditions etc.

I mentioned BC only because it is fundamental in calculating the projectile flight time – lower BC means that velocity diminishes at a greater rate … so the projectile takes longer to get to the target … so the wind-drift is increased.

there are variances in pellets like there are in bullets but don't worry so much about it, after you test your pellets for drop consistancy don't worry too much about wind. there is really not much difference in wind even when changing the velocity by 20-30ft/s. that is :
if you measure the drift of a pellet at 924ft/s muzzle velocity at 100m and 944ft/s it is not incredibly different for our purposes. remember that any wind call you do is always dependant on the grouping capabilities of your rifle so if your average group at distance X is 2" then your best wind call will be withing 2" of your point of aim.
the difference arises in Elevation mainly so once your real world data is like that shown on airgun you can print out a wind drift chart for a 10mile.hour wind. this however is correlated to Yards not to meters as Distance so in my case i had to convert the values to meters since i wanted to use this as a gauge for measurement.

Variations in the Ballistic Coefficient of pellets are – generally – more pronounced than are to be found in bullets. This is particularly acute because the BC value is – generally – much lower (~90% lower) to begin with. A ~3% BC variation is a fairly nominal variation for good quality pellets in the same batch. Differences between batches, of course, may be much worse.
This variation will be seen as ‘stringing’ in windless conditions or as increased group size at longer ranges.

i know the limitations of my setup and with regard to gauging the wind, it will ALWAYS be a guess, but rather than a guestimation in can be a very well informed windcall, so well that i might only have to compensate 0.4mils at 120m, better than the majority that will hit 3feet away or not even pick up the hit because itwas outside their Field of view. my stringing at 120m is between 2-3" for vertical elevation. if you look at the groups i have posted on other threades you will see that most of the time the difference arises in the VERTICAL component not in the horizontal one dependant on wind.

Have a look at WindCalc (mentioned above).

with regard to the pole mate, there are 80m conditions are there are 40m conditions. if wind is 3mph full value constant that is an 80m condition.
if wind is 3mph switchin to 6 from full value to half value, then that will be a good guess situation that might have you dial a condition and hold off over your dial or hold less than your dial but its not technically speaking at 80m condition. the more you shoot in 7mph winds at 100+ ranges, those closer shots seem relatively easy.
i wrote more info here on using the wind clock, will only take you about an hour to make one and it allows you to take the info in the field in a layout that is usable without much confusion. More over when explaining to new comers it is not intimidating like a chart full of numbers. it gives you what you need to see only. Remember all values are for a full Value wind(3-9, or 9-3 oclock)
http://www.airgunbbs.com/forums/show...ght=wind+clock

Thanks for that. I was just joking (well, half joking anyway) that I could write a ChairGun3 application to generate a wind-clock - like the one you’ve described – having all of the data pre-printed onto it.

btw What about Dr.Mann?

Mann, F. W., a leading American ballistician of the 1930’s derived the expression for wind-drift (Mann’s Expression as it’s known) first published in his ‘The Bullet's Flight From Powder to Target-- Ballistics of Small Arms’ sometime in the early 1940’s - although, apparently, it had been used by the military for some years earlier. I used to have a much later re-print but I must have lent it to someone.

Anyway, we’ve been through all of this before but …

D = 12 * W * Sin(A) * (T - (3 * R / V )) …. (Inch)

where:
D = Wind Deflection (Inch)
W = Wind Velocity (Ft/s)
A = Angle between the Wind Velocity Vector and the trajectory
T = Transit time between muzzle and target (sec)
V = Muzzle Velocity (Ft/s)
R = Distance between muzzle and target (Yard)

We also know that the transit time (T above) can be found from:

T = 24000 * BC * (Exp(R / (8000 * BC)) - 1) / V …. (second)

where:
BC = Ballistic Coefficient

So, substituting T in the first equation:

D = 12 * W * Sin(A) * (24000 * BC * (Exp(R / (8000 * BC)) - 1) / V - (3 * R / V )) …. (Inch)

… simple as that.

HTH
Dave

[flims]

Dave i always leave it on TRUE Mil calibration so i know that the MIL is always equal to the proper value, i dont like to mess with that and on my menace its at 10x.

Mrad you can find it on some S&B scopes too written as 1click = 0.1Mrad and also on army field manuals.
you dont have to convert to MOA if you are using a Mil retile and Mil turrets like me then no conversions need, if you hit 4Mils low you dial in 4Mils on the turret its a very common and efficient system. if i hit 1.5Mils left, i will simply Dial 1.5Mils of Windage, no conversions whatso ever thats the whole point about this. you're the first one i heard saying that they are not the same, if you look at the S&B manual it will explain how to use reticle and turret combo and each 1Mil on the reticle is divided into 10 increments on the turret for each 10 clicks represent 1Mil. 1Mil =10cm at 100m and thats what i use. the only time i use Imperial is for wind reading. i had MOA and Mildot reticle and even though it works, its old technology and when you have the facility of Mil/Mil just keep it that way. If you want MOA get a night force with MOA reticle.

my scope is calibrated at 10x so people should check at what mag is theirs calibrated, something which many in my experience have no clue about. on the S&B i use on the 338 its First focal plain so any mag would do. i would actually include a note so that people check their mil-dot calibration, i often here many say i'm 1Mil left or 4Mils low and the shooter isn't even aware that his scope is not properly calibrated so his 1Mil correction is nothing in the real world.

i don't know about the other pellets but the 31grain barracuda i have been buying are an excellent lot and i've been using the same data for as long as i have been buying them the last 3 years and no real variation.

here is a photo of the Mrad turret. each number on that turret represents a Mildot on the reticle so if you turn it to 4 then its like if you hold off 4Mils, the only difference is that you aim dead on.
http://accurateshooter.net/GOTW/zakscopex300.jpg

[Harry's Lad]

Dave i always leave it on TRUE Mil calibration so i know that the MIL is always equal to the proper value, i dont like to mess with that and on my menace its at 10x. Mrad you can find it on some S&B scopes too written as 1click = 0.1Mrad and also on army field manuals. you dont have to convert to MOA if you are using a Mil retile and Mil turrets like me then no conversions need, if you hit 4Mils low you dial in 4Mils on the turret its a very common and efficient system. if i hit 1.5Mils left, i will simply Dial 1.5Mils of Windage, no conversions whatso ever thats the whole point about this. you're the first one i heard saying that they are not the same, if you look at the S&B manual it will explain how to use reticle and turret combo and each 1Mil on the reticle is divided into 10 increments on the turret for each 10 clicks represent 1Mil. 1Mil =10cm at 100m and thats what i use. the only time i use Imperial is for wind reading. i had MOA and Mildot reticle and even though it works, its old technology and when you have the facility of Mil/Mil just keep it that way. If you want MOA get a night force with MOA reticle.

So it looks like Mrad is simply an abbreviation of milliradians then. The Mil would seem to be an easily-calculated approximation to the milliradians (360/6400 instead of 360/6283.185; strange when 360/6300 would have been closer …). As far as I understand, the Mil was used for calculating artillery elevations in the days when such things were calculated on a slide-rule and with the use of tables. I simply converted Mils and milliradians to MoA to illustrate that, although they’re close in value, they’re not identical.

my scope is calibrated at 10x so people should check at what mag is theirs calibrated, something which many in my experience have no clue about. on the S&B i use on the 338 its First focal plain so any mag would do. i would actually include a note so that people check their mil-dot calibration, i often here many say i'm 1Mil left or 4Mils low and the shooter isn't even aware that his scope is not properly calibrated so his 1Mil correction is nothing in the real world.

I can see that the milliradians system has a lot going for it (compared to the more commonplace click/MoA systems). However, as you suggest, it becomes very important that the scope is correctly calibrated to the True Mil-Dot magnification – otherwise it all fails.

i don't know about the other pellets but the 31grain barracuda i have been buying are an excellent lot and i've been using the same data for as long as i have been buying them the last 3 years and no real variation.

Just shoot a couple of dozen through a pair of chronos, calculate the BC values, observe the variation and see if you still believe that!

here is a photo of the Mrad turret. each number on that turret represents a Mildot on the reticle so if you turn it to 4 then its like if you hold off 4Mils, the only difference is that you aim dead on.
http://accurateshooter.net/GOTW/zakscopex300.jpg

Looks like a nice piece of kit – just remember to keep it on calibration.

ATB
Dave

[flims]

Dave, with the S&B, you don't have to remember to keep it on calibration, its a First Focal plain reticle mate and the reticle 'grows' as you turn the Magnification and thus at any magnification, it is true Mil so no worries.


The Mil system is not unlike any other system in that if the reticle is not on calibration then you are out of business. Even an MOA reticle would need to be on true MOA to provide proper information.

With the old system of Mil reticle and MOA turret, you still had to be on True Mil so that you could convert what you see on reticle to what you dial.

with the Falcon Menace calibrated on 10x i dont usually touch the magnification, i have learnt to shoot on 10x and if i need to have a closer look i just use the spotting scope. You are right Mils were common in directing artiller fire. Optics are moving Towards Mil with the likes of Nightforce adopting Mil/Mil combos and also in FIRST FOCAL PLAIN reticle, i've just seen a post on another forum were someone just played with one.

Dave with regard to the BC issue, again it might be true in theory but in the real world i would rather practice alot of windcalls then play and fiddle with the BC's especially when the field results im getting are not suffering from such consequences. if i can keep groups under 3" at 120m with an air rifle im happy.
ATB