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Gary laPook wrote:
I spent more than 10 years in the field artillery launching 200.0
pound projectiles (yes, they weigh exactly 200.0 lb..) from 8 inch
howitzers at targets up to 22,600 meters away.  And yes, we
compensated for as many errors as we could by allowing for meteorlogic
conditions (wind speed and air density for several different levels
from the surface up to maximum ordinate which could be 30,000 feet of
altitude) temperature of the propellant powder (this affects the burn
rate, the resulting pressure and ultimately the muzzle velocity), wear
of the bore (which is measured with a pull over gauge, a worn bore
results in lower muzzle velocity) and even the rotation of the earth
since the earth turns a significant amount while the projectile is in
the air for 90 seconds. We also had surveyors determine the exact
positions of the guns. So I am aware of  the desirability of
eliminating as many of the errors as you can.

But after doing that, we also had to allow for all kinds of random
errors, include range probable error, deflection probable error,
height of burst probable error, time fuze probable error and CEP. We
accomplished this by use of the Firing Tables which contained data on
the the sigmas of these errors as determined by experimentally firing
thousands of rounds at  Aberdeen Proving Grounds and at Fort Sill. So
we knew what our sigmas were and could apply them in planning fire
missions to determine the number of rounds that needed to be fired to
accomplish, at a specified level of confidence (probability), the
destruction of the target while also taking into account the size of
the target.

In the celestial field, you are right that you can't determine your
sigma from one fix. However, if you take a number of sights from a
known position and do the number crunching to determine the sigma then
you can use this to get a good estimate of the possible error in the
fix. You should take a series of sights in both good conditions and
bad and derive two different sigmas to use based on existing
conditions.


On Mar 16, 1:05 pm, "P F"  wrote:
> DW: "An attemp to summarize and establish consensus."
>
> > 1. The most likely location is the center of the cocked hat.
> > 2. The probability of being within the cocked hat is 25%.
>
> DW; one statement contradicts the other! The thing about the centre is not
> that it is the most likely location, it is this:
> It is the ONLY fix position that can be calculated.
>
> Let's say that you are terribly worried that your shape might not enclose
> the position (why, I'm not sure, although this assumption underlies this
> subject). So you decide to enlarge the shape by an equal amount applied to
> each position line, equal to one standard deviation. Now you have a larger
> triangle, and are assured that it contains the position by an increase of
> about 70%.
>
> Let's say you're still worried (oh yes, you're a determined worrier). So you
> increase the size of your shape by another same amount. Now you have an even
> bigger shape, and the assurance that, on average, 90% of the time this much
> larger shape contains the position.
>
> Phew! That's a relief. Now you can relax.
>
> Having relaxed, you then need to put all this work to some useful purpose.
> Oh yes, that's right, while all this worrying was going on the boat was
> proceeding on its merry way. You now need to run that (increasingly) old fix
> forward to establish what you REALLY want to know: where you are! and
> establish a DR that you can use for your next round of sights.
>
> And where is that fix?
>
> Why, its at the centre of all three of these increasingly large shapes that
> you have constructed, of increasingly larger dimensions! It has remained in
> exactly the same place!
>
> At this point you may (or may not) wonder why you went to the effort, since
> it has changed nothing in terms of your practical navigation.


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