Trigonometry Formulas

[JMV]

Gruss Gott alle Kaleun,

I'm not very good at Maths, and even though I have made my 3 Wizz wheels I'm still not too proficient with it. I'd rather use my Scientific calculator. -
So planning to take one more step toward more realism and Manual Targetting ( I'm at 74% ), I wonder if a good soul ( and a good Math brain too) could make a resume of all ( or as many as possible ) trigo formulas that this game involve. I think it would be usefull for the all community. All that could be classified in various sections, like : Target Speed, Range, AOB etc... But that's only a suggestion.
Thanks in advance, if it ever takes shape. JMV

[Redwine]

Look at my signature, there is a complete procedure to manually shoot... i made long time a go for a SH II Mod... but it is valid for any subsim, maths are the same.

[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.

[von Zelda]

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!

[Pisces]

Thanks, good thing I didn't respond to it right away but went to sleep first. At 5 am.

Also, I figured that closure_speed formula out while writing the response. Never knew before it was so simple.

[klh]

Redwine's tutorial and the other replies are spot on, so you probably have all you need. In case you want a little more information on how to use the whiz wheels (along with explaining the math), you can also download my user's guide by my signature.

[JMV]

Sorry Pisces,
I must be a very dumm one, I don't get a damn thing on your before last thread...
Thanks for trying however. JMV

[Pisces]

Originally Posted by JMV

Sorry Pisces,
I must be a very dumm one, I don't get a damn thing on your before last thread...
Thanks for trying however. JMV

That's too bad. Wasn't sure how much background info/ formula derivation you were after. No, no, I don't want to hear that!. Dummies go sit in a car that is about to get crashed on purpous. I may not be the best in explaining complicated stuff. (besides, what's a math discussion worth thesedays without a drawing to make it clear) Don't give up yet. ... But why don't you come up to the chalkboard, .... here's a piece of chalk, ... and show where you get lost.

You wanted formulas for use with a scientific calculator. I supposed you knew how to translate those formulas into keypresses for your own specific brand of calculator. As each brand has it's own way of organising math functions with certain buttons, and how to acces them. I could help with a Casio probably (I have a "fx-82SX Fraction", pretty ancient by now) but some calculators are different in their use. Is that the problem?


p.s. my thread? You must mean my 'post' or my message. You are the one that started this 'thread' with your original message. Sorry, I'm a semantic nitpicker aswel sometimes. And wanted to make sure you didn't mean someplace else.

[aaronblood]

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.

[JMV]

Hello Pisces,

Thank you for helping. There is an old saying : "when the student is ready, the master appears " in french, if you can understand, " Quand l'eleve est pret, le Maitre apparait " Ok, obviously the time is not there yet for me.... You showed up but it doesn' seem I'm ready...But let's leave it there with phylosophy and mysticism.
I have a Casio fx-83ES. The problem is not with using the Calculator, and after all I've got the manuals, so this is another topic ( How to use your calc machine ) this is not the real issue.
The real issue for me is to get all "navigation" ( only ) trig formulas applied for Sh3. With down to earth concrete examples.
What I probably miss, if I have a formula under my eyes, is a down to earth example for such things as SPEED, DISTANCE, AOB calculation. Basically I can't choose what formula applies to what situation.
For example you write :
side A/sin(angle opposite side A)=side B/sin(angle opposite side B)=side C/sin(angle opposite side C). I mean, what gives ? To what particular situation does it apply?
And what does it apply to ? Are we searching for an angle or for the length of one of the sides ??
So from what I understand :
If you look for the length of the adjacent side of a triangle, knowing the value of the angle which has this side as adjacent, and knowing the length af the opposite side of that angle, you can know the length of the other side, with :
Tan (A) = Length of opp. side
--------------------
Length of adj. side
If you look for the value of an angle, having the length of the opposite side of that angle, and the adjacent angle,
Sin (A) = Length of opp. side applies
-------------------
Length of hypotenuse
Now, Cos (A) = Length of adj. side What do you get ? the length of one of
------------------- the other sides or the value of an
Length of hypotenuse angle, and if yes, which one ?

You can see now that I'm very thick on those trig things, but I suppose, from what I've seen, that I'm not the only one... And I'm not the only one that would like to get very basic applied trig solutions for SAH3, whithout daring ask or look too stupid. So I making the sacrifice.Or may be I sould take some private trig 50 Euro/hour courses...

Thanks for any help, and to you Pisces, please be patient and methodical to me
poor numb on that subject. Don't ever surrender trying. Thanks to you all .
Thanks for your help, if you have the patience.
- JMV