Trigonometry Formulas

[JMV]

Thank you Redwine. Will have a look at that. JMV

[ronnybengt]

HEllo Red..thats a fantastic manual..you dont ahappen to have it in pdf...

cheers
R

[Redwine]

Originally Posted by ronnybengt

HEllo Red..thats a fantastic manual..you dont ahappen to have it in pdf...

cheers
R

No skills to made it on .pdf... but you can download it to browse on your HD, using HTTrack free web downloader... it is a great and easy to use free web downloader.

P.D: sorry the bad english used on the tutorial... was the best i was able to do...

[GoldenRivet]

OLC ubermod... takes all the guess work out of any mathematics and you will be workign with equipment available to U-boat commanders at the time.

It takes me about 10 -15 seconds to set up each shot.

its a snap.

[ronnybengt]

no wories..m8.....we are all in thea sme...same...uboat:rotfl: :rotfl:

R

[Pisces]

I suppose the most frequently used/needed trig-formula would be the sin-rule (not to be confused with "sine law": sin(angle)= opposite side/hypotenuse). It's needed for finding intercept-lead or for calculating torpedo-lead.

Using an arbitrarily shaped triangle:

side A/sin(angle opposite side A)=side B/sin(angle opposite side B)=side C/sin(angle opposite side C)

For the above mentioned situations, where the triangle sides represent speeds it would become:

speed_target/sin (intercept or lead_angle)= speed_uboot_or_torpedo/sin(AOB)

after unfolding that a bit you get:

sin (intercept or lead_angle)= sin(AOB)* speed_target / speed_uboot_or_torpedo

And then ofcourse you need to do the inverted sine (or arcsin) operation on the result to get the actual 'lead' angle. There are some situations where the result is impossible: sin(intercept_leadangle)>1 this then is because; 1: the target is too fast, or 2: you/torpedo are/is too slow, or 3: the AOB is too big meaning you are in the wrong position to make it.

The third part (C-side) of the sin-rule is redundant for that equation. But from the same triangle using that 3rd C-angle (relative course or course difference) it could provide closure speed along a bearing line, and hence time to intercept as you can measure the range from the map (and do a time=distance/speed, taking good care of km/naut. mile conversion):

closure_speed_along_bearingline= speed_uboot_or_torpedo * sin(AOB+lead_angle) / sin(AOB)

That 3rd C-angle I mentioned is hidden in the sin(AOB+lead_angle) part because of a simplification. It does not imply that AOB+lead_angle=rel. course.

Other than that, and your basic speed=distance/time (but that's not 'trig'), I see or know of no formula that needs to be done and can be used easily. You could use the cosine-rule to get target_distance_moved (and thus speed if you know time) from 2 periscope ranges with a bearing change, but it is not a "quick 'n easy" keypress-formula (imho). And you'd still only get relative distance_moved(speed) which you would need to correct for based on your own speed/course with another (sin-rule based) formula. And so I never even tried it in practise. I preffer getting target course and speed with the graphical approach: plot positions as you move and measure in between. Much easier.

Then again, maybe I haven't studied the Attackdisk manual enough. Might be some inspiration in there for me.

Originally Posted by Pisces

I suppose the most frequently used/needed trig-formula would be the sin-rule (not to be confused with "sine law": sin(angle)= opposite side/hypotenuse). It's needed for finding intercept-lead or for calculating torpedo-lead.

Using an arbitrarily (*2D) shaped triangle:

side A/sin(angle opposite side A)=side B/sin(angle opposite side B)=side C/sin(angle opposite side C)

note: * : 3d or spherical triangles are a different 'ball'-game. (pun intended nevermind)

For the above mentioned situations, where the triangle sides represent speeds it would become:

speed_target/sin (intercept or lead_angle)= speed_uboot_or_torpedo/sin(AOB)

after unfolding that a bit you get:

sin (intercept or lead_angle)= sin(AOB)* speed_target / speed_uboot_or_torpedo

And then ofcourse you need to do the inverted sine (or arcsin) operation on the result to get the actual 'lead' angle. There are some situations where the result is impossible: sin(intercept_leadangle)>1 this then is because; 1: the target is too fast, or 2: you/torpedo are/is too slow, or 3: the AOB is too big meaning you are in the wrong position to make it.

The third part (C-side) of the sin-rule is redundant for that equation. But from the same triangle using that 3rd C-angle (relative course or course difference) it could provide closure speed along a bearing line, and hence time to intercept as you can measure the range from the map (and do a time=distance/speed, taking good care of km/naut. mile conversion):

closure_speed_along_bearingline= speed_uboot_or_torpedo * sin(AOB+lead_angle) / sin(AOB)

That 3rd C-angle I mentioned is hidden in the sin(AOB+lead_angle) part because of a simplification. It does not imply that AOB+lead_angle=rel. course.

Other than that, and your basic speed=distance/time (but that's not 'trig'), I see or know of no formula that needs to be done and can be used easily. You could use the cosine-rule to get target_distance_moved (and thus speed if you know time) from 2 periscope ranges with a bearing change, but it is not a "quick 'n easy" keypress-formula (imho). And you'd still only get relative distance_moved(speed) which you would need to correct for based on your own speed/course with another (sin-rule based) formula. And so I never even tried it in practise. I preffer getting target course and speed with the graphical approach: plot positions as you move and measure in between. Much easier.

Then again, maybe I haven't studied the Attackdisk manual enough. Might be some inspiration in there for me.

Well said!

[XLjedi]

Originally Posted by Redwine

No skills to made it on .pdf... but you can download it to browse on your HD, using HTTrack free web downloader... it is a great and easy to use free web downloader.

P.D: sorry the bad english used on the tutorial... was the best i was able to do...

CutePDF Writer is a good free PDF print utility/driver. You just print your doc to it like any other printer.