Trigonometry Formulas

[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!

[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.