British 4.5"/45 (11.4 cm) vs American 5"/38 (12.7 cm) Mark 12

[dunmunro]

That's not the case for a closely packed TF with screen placed around 1500 yards from CV. There will be far more weapons firing at the target inside the screen rather than outside the screen. If you consider the 40 mm Borfors, its effective range overlaps quite a lot with 5" too.

No. The screen, by definition, is designed so that each ship is outside the effective range of non SD (SD= self destruct) 20mm auto cannon ammo and the SD range of 40mm autocannon.

????
When did USN use SD Bofors round and their Mk51 director has maximum range setting of 4000 yds.

The USN always used SD ammo in the Bofors 40mm.

Some info from Navweaps:

1D) USA produced HE-SD ammunition was set to detonate at 4,000 - 5,000 yards (3,700 - 4,570 m) so as to minimize problems due to "friendly fire." HE and AP rounds that did not self-destruct were also manufactured.

3A) The many Mods of USN ammunition were primarily bookkeeping designations used to indicate the manufacturer. USN AP had a windscreen. USN HE ammunition was issued in HE-T/SD, HE/SD, HE-I-T/SD and HE-I/SD forms. Plugged forms for training purposes were also manufactured. There was also a Mark 3 HE round that did not contain a tracer, but this was used only for a brief time during World War II and was replaced in 1945 by Dark (non-luminous tracer) and Dark Ignition (delayed ignition tracer) ammunition. Dark Tracer was issued only in HE/SD and HE-I-T/SD forms. Dark Ignition ammunition was issued only in HE-I-T-SD form.
4a) USN tracer burned out at 5,000 yards (4,570 m) horizontal, 15,000 feet (2,740 m) vertical.

[dunmunro]

That's not the case for a closely packed TF with screen placed around 1500 yards from CV. There will be far more weapons firing at the target inside the screen rather than outside the screen. If you consider the 40 mm Borfors, its effective range overlaps quite a lot with 5" too.

No. The screen, by definition, is designed so that each ship is outside the effective range of non SD (SD= self destruct) 20mm auto cannon ammo and the SD range of 40mm autocannon.

Untrue -
40mm self-destruct was about 4-5,000 yards. Complaints/comments about damage from fire directed by nearby friendly ships against intervening low flyers were commonplace in AA after-action reports all the way through to the end of the war.

"By March 1943 the Americans had concluded that the ideal was two carriers per task force, with the task forces concentrating for strikes and separating by at least 25 miles when air attack seemed imminent. The ideal screen was 20 to 24 destroyers and either six heavy cruisers, or two battleships and four antiaircraft cruisers. The destroyers were stationed in a circle at a radius of 1500 to 2500 yards from the center of the task force, with the heavier warships stationed closer to the carriers. In practice, there were simply not enough screening vessels for such extravagant protection, and most task groups consisted of three or four heavy or light carriers protected by fewer heavy warships and much fewer destroyers than the ideal. For example, Task Group 50.1 at Tarawa had two fleet and one light carrier screened by five heavy cruisers, one antiaircraft cruiser, and just eight destroyers.

The rapid growth of the U.S. Navy led to the adoption of additional levels of organization within a task force. These were the task group, which was often as large as the task forces of the early months of the war, and the task unit, which could be a single ship or a small group of ships within a task group.

References
Evans and Peattie (1997)
Friedman (2006)
The Pacific War Online Encyclopedia © 2013 by Kent G. Budge. Index

Here's the USN TF screens for 19 June 1944:

June19.jpg

(183.68 KiB) Not downloaded yet

So, some ships are within 40mm SD range, but the screen is designed to minimize the number of ships within the danger zone. Additionally, low altitude targets will not be deliberately engaged with 40mm fire, if the resulting trajectory would hit a screening ship.

[dunmunro]

Please read the premise of the calculation. It is to produce a scaling factor for the post war drone test. All the shells that we considered it this exercise have been brought near the drone and burst. All that matters is how MT introduce range error compare to VT. Hence, there is no need to consider the entire 3D problem except for introducing a reasonable range cut off.

[ A burst of 80ft off in range + 80ft off in deflection = 113ft from target by Pythagoras. I talk advantage that 96.5% of the VT burst is within 80ft anyway but TTB is counted to 100ft.]

I also don't need to consider the target motion because, again, all the shells we are considering have been brought close to the drone.

Note that I have converted all errors from time to range. The whole exercise is based on the information from the drone test report, meaning there's no information about individual target path anyway.

The fuze timing order is based upon DT and ToF of the shell and therefore MK37 fuze timing is calculated by the FCS about 8 secs prior to firing the gun, at a future range of 3k yds. OTOH, target position data is updated continuously, and is based only upon ToF, or about 4 secs prior to firing at a future range of 3K yds.

If the target drone was flying a straightline course, then your assumptions would be valid, but it is actually flying a maneuvering course and the fuze timing is predicated upon the course that it was flying at the time of fuze prediction. Therefore fuze timing errors are likely to be considerably higher than simply the mechanical errors in the timing mechanism or load timing errors, because a maneuvering target is not likely to be at the predicted fuze timing range.

If you really understand what I was calculating, you can introduce your own estimate of the range error (in this case, similar to dead time, is a function of range rate) can be introduced as a third error.

However, I find that unlikely to contribute much as if a manuver is not radical enough to throw off deflection during ToF and the lag in the Mk1 solution, I doubt it can throw off the range by much.

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.

[wmh829386]

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.

Where does that 5% come from? Any justification?
Anyway 5% of 3000 yards is 150 yards. Perhaps you can show me how a plane can produce 150 yards of range error in 12s while not throwing the FC deflection such that the shell is with 80 ft to trigger the VT fuse.

If this is the motion analysis you were talking about. By all means go ahead.

Btw, don't add the error due to FC solution directly on to the error due to MT fuse when calculating probability.

[wmh829386]

No. The screen, by definition, is designed so that each ship is outside the effective range of non SD (SD= self destruct) 20mm auto cannon ammo and the SD range of 40mm autocannon.

Untrue -
40mm self-destruct was about 4-5,000 yards. Complaints/comments about damage from fire directed by nearby friendly ships against intervening low flyers were commonplace in AA after-action reports all the way through to the end of the war.

"By March 1943 the Americans had concluded that the ideal was two carriers per task force, with the task forces concentrating for strikes and separating by at least 25 miles when air attack seemed imminent. The ideal screen was 20 to 24 destroyers and either six heavy cruisers, or two battleships and four antiaircraft cruisers. The destroyers were stationed in a circle at a radius of 1500 to 2500 yards from the center of the task force, with the heavier warships stationed closer to the carriers. In practice, there were simply not enough screening vessels for such extravagant protection, and most task groups consisted of three or four heavy or light carriers protected by fewer heavy warships and much fewer destroyers than the ideal. For example, Task Group 50.1 at Tarawa had two fleet and one light carrier screened by five heavy cruisers, one antiaircraft cruiser, and just eight destroyers.

The rapid growth of the U.S. Navy led to the adoption of additional levels of organization within a task force. These were the task group, which was often as large as the task forces of the early months of the war, and the task unit, which could be a single ship or a small group of ships within a task group.

References
Evans and Peattie (1997)
Friedman (2006)
The Pacific War Online Encyclopedia © 2013 by Kent G. Budge. Index

Here's the USN TF screens for 19 June 1944:
June19.jpg

So, some ships are within 40mm SD range, but the screen is designed to minimize the number of ships within the danger zone. Additionally, low altitude targets will not be deliberately engaged with 40mm fire, if the resulting trajectory would hit a screening ship.

Are you really suggesting a kamikaze will be under more ships' fire outside the screen compared to inside the screen?

[dunmunro]

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.

Where does that 5% come from? Any justification?
Anyway 5% of 3000 yards is 150 yards. Perhaps you can show me how a plane can produce 150 yards of range error in 12s while not throwing the FC deflection such that the shell is with 80 ft to trigger the VT fuse.

If this is the motion analysis you were talking about. By all means go ahead.

Btw, don't add the error due to FC solution directly on to the error due to MT fuse when calculating probability.

VT TTBs were, by definition, short of the target, where they were most effective. An MT shell that bursts long will have greatly reduced efficacy, thus errors that cause the shell to burst long effectively reduce the probability to damage from that shell to near zero.

Not all shells were within 80ft, but a combination of course change (or initial estimate course error) and altitude change can readily cause a ~5% range error (and the radar itself was only accurate to about ~.8%). A ~15deg course change and a ~100ft change in altitude will cause about a 5% range error.

also:
5in/38 shell velocity
2K yds = 2,141 fps (abridged range table)

3K Yds = ~1900 fps

4K yds = 1,725 fps (abridged range table)

[dunmunro]

Untrue -
40mm self-destruct was about 4-5,000 yards. Complaints/comments about damage from fire directed by nearby friendly ships against intervening low flyers were commonplace in AA after-action reports all the way through to the end of the war.

"By March 1943 the Americans had concluded that the ideal was two carriers per task force, with the task forces concentrating for strikes and separating by at least 25 miles when air attack seemed imminent. The ideal screen was 20 to 24 destroyers and either six heavy cruisers, or two battleships and four antiaircraft cruisers. The destroyers were stationed in a circle at a radius of 1500 to 2500 yards from the center of the task force, with the heavier warships stationed closer to the carriers. In practice, there were simply not enough screening vessels for such extravagant protection, and most task groups consisted of three or four heavy or light carriers protected by fewer heavy warships and much fewer destroyers than the ideal. For example, Task Group 50.1 at Tarawa had two fleet and one light carrier screened by five heavy cruisers, one antiaircraft cruiser, and just eight destroyers.

The rapid growth of the U.S. Navy led to the adoption of additional levels of organization within a task force. These were the task group, which was often as large as the task forces of the early months of the war, and the task unit, which could be a single ship or a small group of ships within a task group.

References
Evans and Peattie (1997)
Friedman (2006)
The Pacific War Online Encyclopedia © 2013 by Kent G. Budge. Index

Here's the USN TF screens for 19 June 1944:
June19.jpg

So, some ships are within 40mm SD range, but the screen is designed to minimize the number of ships within the danger zone. Additionally, low altitude targets will not be deliberately engaged with 40mm fire, if the resulting trajectory would hit a screening ship.

Are you really suggesting a kamikaze will be under more ships' fire outside the screen compared to inside the screen?

Take the example screens that I provided. Assume a target aircraft is located and fire is opened at ~12k Yds at 5K ft altitude. At ~4k yds from the screen, every ship in the formation will have opened fire on the same target.

[wmh829386]

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.

Where does that 5% come from? Any justification?
Anyway 5% of 3000 yards is 150 yards. Perhaps you can show me how a plane can produce 150 yards of range error in 12s while not throwing the FC deflection such that the shell is with 80 ft to trigger the VT fuse.

If this is the motion analysis you were talking about. By all means go ahead.

Btw, don't add the error due to FC solution directly on to the error due to MT fuse when calculating probability.

VT TTBs were, by definition, short of the target, where they were most effective. An MT shell that bursts long will have greatly reduced efficacy, thus errors that cause the shell to burst long effectively reduce the probability to damage from that shell to near zero.

Not all shells were within 80ft, but a combination of course change (or initial estimate course error) and altitude change can readily cause a ~5% range error (and the radar itself was only accurate to about ~.8%). A ~15deg course change and a ~100ft change in altitude will cause about a 5% range error.

also:
5in/38 shell velocity
2K yds = 2,141 fps (abridged range table)

3K Yds = ~1900 fps

4K yds = 1,725 fps (abridged range table)

A FC that produce fuse time can bias towards shorts inherently or by the operator. I am surprised if nobody did that. However, it is possible that the fuse time error makes such effort irrelevant.

Yes, that's my mistake for the projectile velocity.
So the scaling factor is 80/(1900*0.15)=0.28
If we ignore any long burst, the factor will be halved again=0.14
Note that with the criteria of effective shot being 80ft Infront of target, the fuse time error will be even more dominant over the dead time error.

How much deflection error does 15 degree of course change at 140kt produce?
140kt~238 ft per second
238sin(15) =55.6 ft per second
In 8s ToF, that's over 400ft off in deflection, so no TTB anyway.

[wmh829386]

The fuze timing order is based upon DT and ToF of the shell and therefore MK37 fuze timing is calculated by the FCS about 8 secs prior to firing the gun, at a future range of 3k yds. OTOH, target position data is updated continuously, and is based only upon ToF, or about 4 secs prior to firing at a future range of 3K yds.

If the target drone was flying a straightline course, then your assumptions would be valid, but it is actually flying a maneuvering course and the fuze timing is predicated upon the course that it was flying at the time of fuze prediction. Therefore fuze timing errors are likely to be considerably higher than simply the mechanical errors in the timing mechanism or load timing errors, because a maneuvering target is not likely to be at the predicted fuze timing range.

If you really understand what I was calculating, you can introduce your own estimate of the range error (in this case, similar to dead time, is a function of range rate) can be introduced as a third error.

However, I find that unlikely to contribute much as if a manuver is not radical enough to throw off deflection during ToF and the lag in the Mk1 solution, I doubt it can throw off the range by much.

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.

[dunmunro]

If you really understand what I was calculating, you can introduce your own estimate of the range error (in this case, similar to dead time, is a function of range rate) can be introduced as a third error.

However, I find that unlikely to contribute much as if a manuver is not radical enough to throw off deflection during ToF and the lag in the Mk1 solution, I doubt it can throw off the range by much.

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.

[Byron Angel]

Here's the USN TF screens for 19 June 1944:
June19.jpg

So, some ships are within 40mm SD range, but the screen is designed to minimize the number of ships within the danger zone. Additionally, low altitude targets will not be deliberately engaged with 40mm fire, if the resulting trajectory would hit a screening ship.

Per your Jpeg -
The screen for TF 58.7 was deployed on a 6,000yd radius. There were NO CVs in this this TF. The only ship in the center of the formation was BB USS Indiana.

The other TF screen formations involved had multiple CVs deployed about a 2,000yd radius, with the outer screen deployed around them all at a 4,000yd radius from TF center point. In other words, the distance between the CVs and the ships of the outer screen was .....

4,000 minus 2,000 = 2,000 yards.


B

[wmh829386]

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.

[dunmunro]

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.

I am a bit worried about your interpretation as well. I tried to introduce future range errors as per the quote from Pout and you seem to ignore them.

[wmh829386]

I think I have laid out clearly how you can introduce additional errors properly. I have pointed out your mistake in probability calculation and if you choose to ignore them, it's your choice and I have nothing more for you.