"BARR & STROUD Range-finders - FQ2 (9ft) versus FT24 (15ft)" Topic

Excerpted this for a discussion on another forum and thought it might be of interest here.

C.B. 269 – HANDBOOK FOR BARR & STROUD NAVAL RANGE-FINDERS AND MOUNTINGS – 1916

Page 156
TABLES OF APPROXIMATE UNCERTAINTY OF OBSERVATION WITH RANGE-FINDERS OF VARIOUS BASE-LENGTHS AND MAGNIFICATIONS, UNDER FAVOURABLE CONDITIONS OF OBSERVATION

"The Tables of Approximate Uncertainty of Observation are based upon the fact that, on the system adopted in the range-finders, and under favourable circumstances of observation, it is possible to detect a want of alignment between the images when they subtend at the eye and angle of about 12 seconds, or, say, 0.0000582 in circular measure. The expression –

dR = [0.0000582] x [R(sq)] / [MB]

gives the error in range or the uncertainty of observation due to the visual limitations above mentioned, when R is the Range, M the Magnification, and B the Base Length, R and B being, of course, expressed in the same units of measurement.

From the above expression it will be seen that the errors within which any one range-finder can work at various ranges are proportional to the squares of the ranges and that the comparative accuracies of the range-finders are proportional to the products of their respective base-lengths and magnifications."

APPROXIMATE UNCERTAINTY OF OBSERVATION VALUES -

FQ2 – 9-ft Base Length;
By 1916, being produced with dual 20x/28x magnification.
Range >> 5,000 yds --- 10,000 yds --- 15,000 yds --- 18,000 yds (max listed)
28x ------ 17 yds ------- 69 yds --------- 156 yds ------- 224 yds
20x ------ 24 yds ------- 97 yds --------- 218 yds ------- No value given

FT24 – 15-ft Base Length;
By 1916, being produced with dual 20x/28x magnification.
Range >> 5,000 yds --- 10,000 yds --- 15,000 yds --- 19,000 yds --- 20,000 yds
28x ------ 10 yds ------- 42 yds --------- 94 yds ---------------------------166 yds
20x ------ 15 yds ------- 58 yds --------- 131 yds ------- 210 yds ------ No value given

Scrutiny of the above values will show the convincing technical superiority of the 15-ft range-finder, especially at long ranges.

Double Post – please delete.

B

Blutarski,
Good post.

I've read this over and some other technical publications to model my gunnery system. When you look at the idea factors you can expect excellent results. Where it gets interesting is when in combat with vibrations, poor lighting, surface dazzle, poor or non-existent salvo spotting, fatigue, near miss splashes, etc.

Then you have the German device that averages multiple readings and throws out ones that don't seem to fit.

My estimates were that they could estimate the range with a +/- 1 to 5 degree error depending on different factors.

Wolfhag

It is unclear to me what "By 1916, being produced" means, since the table values are just the formula values rounded to integers.

Posted at the request of Blutarski:

1 – Re "in production from 1916", I was referring to the dual-magnification versions which came out post-Jutland. Prior to that time, AIUI, both were being built with single-magnification.

2 – Re NCC's comment about B&S's average observational data values, it's pretty clear to me that they were presenting best possible case (the giveaway being their "favorable conditions of observation" stipulation. My opinion, based on what I've read, is that the FQ2 limit of effective ranging performance … under actual battle conditions … was about 12-13,000 yds and for the FT24 about 19-20,000 yds. (Referring to the single-magnification versions in use at Jutland.

Blutarski

Thanks Blutarski and Wolfhag,

Apologies for not making my question clear. The OP gives a formula for uncertainty, and tables of uncertainty values. At first glance, I thought the formula was derived from theory and the table data was experimental, especially since the tables had "No value given" entries. Doing the spreadsheet showed that the table values match the formula so closely (within a yard) that they seem unlikely to be independent. If the tables were generated from the formula, why were FT24 values given at 19,000 yards for 20x but at 20,000 yards for 28x, and why no FQ2 20x 18,000 yard value? Perhaps they thought (and as you suggest for battle conditions) that the optics were not useful beyond those ranges/magnifications.

Additional comment: The handbook says that the formula is ‘based on the fact' of detecting a 12 seconds of arc want of alignment. It would be interesting to know how that was determined. I agree that it is likely to be ‘best possible case'.