dunmunro wrote: ↑Mon Jan 24, 2022 4:31 pm
wmh829386 wrote: ↑Mon Jan 24, 2022 5:53 am
dunmunro wrote: ↑Sun Jan 23, 2022 7:53 pm
If the target's predicted vs actual course causes a range error of 5% (range actual vs range predicted), then we have to add that (ToF x 5%) to the fuze timing error.
No, no, no. We are dealing with
two seperate events. The fuse time error I was taking there is the inherent uncertainty of the MT fuse. What you are referring to is the error in the FC solution. Adding them directly doesn't make sense.
BV = shell velocity in fps at instant of burst.
Yes, I get that the MT fuze has an inherent error of .15sec which creates an uncertainty in the burst location of .15sec x BV. If the predicted ToF = 4 secs then the fuze timing error is all we need to consider. However, a 5% ranging error due to target manoeuvre will cause the MT fuze time to be set for a incorrect ToF so if actual target range is equal to a ToF of 4 secs (3k yds) but the MT fuze is set to a ToF of 3.75->4.25 secs (2.85 to 3.15k yds) then the burst location is somewhere between to -.33 secs to +.33sec away (1/2 fuze timing error plus 1/2 range timing error) from the target's actual location, or .33sec x BV (~1900fps) = (80/630ft)/2 = ~16 x lower than the VT TTB probability. Pout:
CASE 4: VELOCITY TRIGGER (VT) SHELL FUZING
At this point in the story of the improvement of AA gunnery it is
necessary to return to shell fuze-setting, which, after radar had greatly
reduced range errors, partly offset the gains and reduced the kill rate in
Cases 2 and 3. It caused rms errors of 310-yds at a future range of 6-kyds,
rising to 350-yds at a future range of 4-kyds, and 420-yds at a future range
of 3-kyds.
Although the ship's radar played no part in the improvement of shell
performance, by 1944 another radar-like device had become available for
insertion in AA shells . This was capable of improving AA gunnery
performance by a factor greater than that achieved by all the techniques
so far described. This small and extremely robust unit not only
eliminated shell fuze-setting, but also eliminated the effects of futurerange
prediction errors, leaving the lateral and vertical aiming errors
dominant in the determination of kill probability. Even these errors were
reduced, since future prediction no longer included the dead-time
component in the prediction time allowed for fuze-setting, that is, 6-secs
in all cases so far discussed in this analysis. Thus prediction-times of 16sees,
12-secs and 10-secs became respectively 10-secs, 6-secs and 4-secs,
and future-position line errors were reduced by factors of 0.625 at Rf = 6kyds;
0.5 at Rf = 4-kyds; and 0.4 at Rf = 3-kyds. Thus vertical and lateral
errors in line were reduced to 125-yds rms, and 110-yds rms at a future
range of 6-kyds, compared with Case 2 and Case 3 with 200-yds rms and
175-yds rms, respectively.
Sorry, I misread your ToF and dead time. i don't have the range tables with me.
Let me go through the problems with your estimate again.
1. You introduce 15 degree course change. For an approaching target (per the drone test), the deflection error that alone
238sin(15) =55.6 ft per second
The 4s ToF cause more than 200ft of deflection error. So no TTB anyway.
That makes the whole calculation moot anyway. But still your calculation have more problems.
2. We are doing probability calculation. You cannot assume all the FC solution to have the exact same error value. You are calculating the probability modifier for
the case when FC have 5% range error stacked on the fuse time error while what you should be calculating is
the case when FC have error range of +5% to -5% while the fuse time error range from +0.15s to -0.15s.
*I am not sure whether 0.15s error is +-0.15s or +-0.75s. You can check the source.
3. The idea of dealing with this kind of probability is to consider the combination of errors that will led the burst in the effective range. Stacking all the errors then magically pull a uniform distribution is a big no no and will make your math teacher angry/sad.
An illustration of why pulling a uniform distribution is bad. Even if we started with (well, you insist), three uniform distribution.
Let's compare the value of the probability density of burst with zero range error vs maximum range error.
For maximum range error, that means maximum value for all independent errors. (max FT error, max DT error, max FC error)
For zero range error, that means
a. No errors for from all three events.
b. Error cancellation between either two variables with one with out error.
c. Error cancellation between all three variables.
Note that both a. and all max error both approach zero.
So the probability density for zero range error is much higher than maximum range error (which approach zero)
Honestly, I am getting worried about you interpretation of Pout's work.