The problem with angular size formulas

[Ugarik]

Those are the current angular size formulas we use:

Angle: 2*atan(tan(70/2)*(object height/panel height))

Distance: object size*panel height/[object height*2tan(70/2)]

Size: 2tan(70/2)*distance*object height/panel height

These formulas are correct HOWEVER "tan(70/2)" means tangent of 35 degrees or ~~0.700 .

But if we input any of the folowing formulas in google it will calculate tangent of 35 radia or ~~0.474

If you're using google as a calculator you should input those formulas in the following form:

Angle: 2*atan(tan(70/2 deg)*(object height/panel height)) and so on

Now we need to recalc several hundreds feats...

 

[Ugarik]

For those of you know don't understand how these formulae even work.

Horivontal viewing angle is assumed to be 70 degress. Next we calculate the angle of the particular object based on how much of the field of view it obstructs

https://en.wikipedia.org/wiki/Angle_of_view

70 rad angle of view obviously doesn't make any scence

 

[Andytrenom]

I remember "investigating" this on my own a while back. Although I may have to stress my brain a little bit to remember what exactly I found.

 

[Ugarik]

I remember "investigating" this on my own a while back. Although I may have to stress my brain a little bit to remember what exactly I found.

The current formulas are perfectly fine but we are using rad insted of dergees

 

[Spinosaurus75DinosaurFan]

Seems to make sense.

 

[Therefir]

This is similar to that rant on reddit about our angular size formulas.

I agree with the change.

 

[Andytrenom]

One thing I do remember is deducing that the formula is based on the field of view (or whatever the correct term is) of a human eye. Maybe this is problematic maybe it isn't, since field of view being the same as a human eye isn't a guarantee.

Also yeah, the formula seemed to work properly while only using degrees.

 

[Mephistus]

This basically means that the values would be undersold for all the angsize feats that didn't adjust the formula for google to interpret accordingly if you used it as a calculator? Meaning larger distances, sizes etc?

after checking wolfram alpha, it seems to do the same error google calculator does actually unless you put the deg for degrees.

 

[Ugarik]

Technically this is not even a mistake. Just wherever a scientific calc sees a trigonometric function it assumes all the values are in radians unless you state otherwise.

 

[Therefir]

@Mephistus I'm getting shorter distances using degrees instead of radians.

 

[Andytrenom]

So I managed to remember the maths I did




In the above very rough diagram, H is panel height (BC), h is object height (EF). The angle BAO will be half of a human eye's range of view (The range is 70 degree I believe).

In triangle BAO,

-Tan 70/2=(H/2)/Base

In triangle EAO

-Tan(x/2)=(h/2)/Base

If we divide the two equations

-h/H=Tan(x/2)/Tan(70/2)

Bringing tan70/2 to the left side

-Tan(70/2)*(h/H)=tan(x/2)

Using inverse

-Tan-1{Tan(70/2)*(h/H)}=x/2

-Or 2Tan-1{Tan(70/2)*(h/H)}=x

x is the angle you are supposed to find

 

[Andytrenom]

This is how I made sense of the formula, and if what I did is correct which is impossible the conversion to radian shouldn't be a thing.

 

[Ugarik]

So I managed to remember the maths I did



In the above very rough diagram, H is panel height (BC), h is object height (EF). The angle BAO will be half of a human eye's range of view (The range is 70 degree I believe).

In triangle BAO,

-Tan 70/2=(H/2)/Base

In triangle EAO

-Tan(x/2)=(h/2)/Base

If we divide the two equations

-h/H=Tan(x/2)/Tan(70/2)

Bringing tan70/2 to the left side

-Tan(70/2)*(h/H)=tan(x/2)

Using inverse

-Tan-1{Tan(70/2)*(h/H)}=x/2

-Or 2Tan-1{Tan(70/2)*(h/H)}=x

x is the angle you are supposed to find

This IS correct. Exactly the formula we are using. 70 rad or 4010,7 deg view angle is obviously impossible. This is what I was talking about

 

[LephyrTheRevanchist]

Oh damn, this is huge. This should get a highlight.

Edit: Heck, huge is an understatement.

 

[Andytrenom]

So many highlights

This does need a lot of attention, I agree.

 

[The_Causality]

IIIUC the problem is just the fact that we use (70/2 rad) instead of (70/2 deg) ?

 

[Ugarik]

yes

 

[Andytrenom]

@Cause Using 70/2 for every occasion itself might be flawed, but I don't think that's what the OP is trying to discuss.

 

[LephyrTheRevanchist]

Many hightlights indeed. Busy couple of months, eh? ovo

 

[Mephistus]

downgrade time ayooo

 

[Ugarik]

downgrade time ayooo

Actually Vaccine Ma is going to be upgraded. Though he is probably the only character who will recieve an upgrade from this

 

[Ugarik]

Another fan fact is User blog:Ryukama/Suiryu Cloud Part Redone is probably the only calc with the correct angsizing. Even though Lina Shields thinks he did it wrong

 

[Andytrenom]

Kris has a angsizing based speed calc which I guess I'll have to scrap completely and just rate him as Relativistic via scaling.

 

[TheRustyOne]

Actually, the Esdeath calc appears to have correct angsizing as well.

 

[The_Causality]

Well, since there is many thread about wiki changes, i suggest to create a thread for organize what we do firstly, we can't handle The Universal Stuff, plus the AP alongside the Angsize problem at the same time.

 

[Captain_Torch]

Damn, good find Ugarik. Came as a shock to me at first, but after a little experimenting realized that the calculator does indeed use radian for tan(70/2).

Maybe it's better to use "0.70020753821" as a pre-set value instead of tan(70/2)? Because the "tan(70/2 deg)" doesn't work for all calculators (e.g. Web 2.0 scientific calculator), and could cause confusion for some calcers.

 

[Ugarik]

Maybe it's better to use "0.70020753821" as a pre-set value instead of tan(70/2)?

I used different value in this calc (see commects) because I thought it would be more consistent. So we should probably leave it as it is for such specific cases

 

[DontTalkDT]

Just went through some of my calcs and it seems I used degree everywhere. Good for me not having the revise my stuff ^^

Anyways, we might want to specifiy that in the Calculation Guide.

 

[Andytrenom]

So should we change

Calculate the value as Radians, then convert the Radians into Degrees. The formula for doing so is the following: Radians * 180┬░/¤Ç.

to

The value will be found in degrees

?

 

[Captain_Torch]

I used different value in this calc (see commects) because I thought it would be more consistent. So we should probably leave it as it is for such specific cases

Hmm, fair enough.

 

[DMUA]

Oh boy

Luckily I only have..

... 1... 2.... 3... 4... 5 calcs that use this

wow

 

[Ugarik]

Actually, the Esdeath calc appears to have correct angsizing as well.

Isn't not. Yes it uses degrees but the parentheses are missplaced

 

[TheRustyOne]

Oh that's embarrassing, should've looked closer.

 

[ShrekAlmighty]

Seems simple enough, just a question, would the already accepted calcs that get affected by the change need to be re-evaluated?

 

[DemonGodMitchAubin]

Thank God, Deus Sema's Calc was adjusted a while back for this very reason

 

[ByAsura]

Does this mean we have revise any angular size calcs? Fortunately, I only have one that's actually linked to a profile.

 

[Antvasima]

We obviously need to strive for accuracy, but I do not know how we are realistically going to first find all of the calculations that use the wrong method, then redo and evaluate them, and finally revise all of the connected profiles.

It would turn into a massive wiki project involving as much of the staff as possible, and I would much prefer to prioritise improving the accuracy of our lower Attack Potency chart borders first.

You should ask for input from the rest of the calc group in any case.

 

[Antvasima]

Just went through some of my calcs and it seems I used degree everywhere. Good for me not having the revise my stuff ^^

Anyways, we might want to specifiy that in the Calculation Guide.

Feel free to do so if you wish.

 

[Spinosaurus75DinosaurFan]

We should probably update the relevant pages to prevent further mistakes regarding the formula first. I am uncertain how to deal with previous wrongly calculated calculations as well.

 

[Antvasima]

Which instruction pages need to be updated?