# Use of trig in lighting design

#### nrcafootball68

##### Member
Hi, I'm Brandon. I've been on here before, but never really stuck around much. I have a project for school that requires me to find practical applications for trigonometry, and i know it is used in lighting design, but am not sure exactly how. (I mainly do sound.) Any help would be appreciated. Thanks

-Brandon

#### gafftaper

##### Senior Team
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I'm not much of a math guy. But I would say look at photometrics and how you calculate the size of the pool of light at a given distance from a light. Also calculating the actual throw distance. Probably some trig involved in designing lenses as well.

#### derekleffew

##### Resident Curmudgeon
Senior Team
See this thread. Beam angles require trig. Google for "Angle of Incidence=Angle of Reflection." Also reflection and refraction.

Reflector design requires geometry. Calculating the Effective Focal Length of a lens train comprised of two or more lenses requires algebra.

Ever wonder why in 3Ø power the voltage from any hot to neutral is 120V, but between any two hots it's only 208V? Shouldn't it be 240? Where did 208 come from? Hint: How far apart are the hot legs?

#### gafftaper

##### Senior Team
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Ever wonder why in 3Ø power the voltage from any hot to neutral is 120V, but between any two hots it's only 208V? Shouldn't it be 240? Where did 208 come from? Hint: How far apart are the hot legs?
DUH... yes Electricity... lot's of trig there.

#### phil000

##### Active Member
See this
Ever wonder why in 3Ø power the voltage from any hot to neutral is 120V, but between any two hots it's only 208V? Shouldn't it be 240? Where did 208 come from? Hint: How far apart are the hot legs?
Two words: Elven Magic. That's what that silly sign next to the three indicates, the presence of elves.

#### avare

##### Active Member
You are a sound guy and don't know applications of trig in real life? Read "Sound Systems Engineering" by Davis. Or cheaper, because it free, the "sound systems design manual" from JBL. On their website.

How do you determine coverage of speaker arrays? Answer: trig.

#### Goph704

##### Active Member
This might be a little weird but I'm going to suggest doing the math on a cyber light. Try sketching out a dance peice in your head and then follow your dancer around the stage. Figure the throw distace, the luman out put, and the beam and feild angles for each new position you find your dancers in and then show the math as they change from one position to another. For example with 1000w lamp 25 feet from throw distance you lumin out put is going to be X. You change your distace the lumin out put will either increase or decrease. It can be as simple or as complex as you need it to be.I had to do something similar awhile ago for school and it's a pain, but stuff like that really pays off.
Good luck and let us know how it goes.

#### Timmyp

##### Member
I think most things I can think of have been covered.

As soon as I started doing Lighting Designs for school and am-dram shows I went and apologised to my Maths teacher; I'd basically sat through the lessons saying how useless trigonometry was, and that I'd never use it in my life. Oh how wrong I was! Fortunately I hadn't just ignored the lessons, and I had actually learnt how to do it all!

Tim

#### Footer

##### Senior Team
Senior Team
If you are in audio, do it for audio. Get a hold of a good acoustics book and go nuts!

#### nrcafootball68

##### Member
You are a sound guy and don't know applications of trig in real life? Read "Sound Systems Engineering" by Davis. Or cheaper, because it free, the "sound systems design manual" from JBL. On their website.
How do you determine coverage of speaker arrays? Answer: trig.
I knew how it was used in sound, but instead of just repeating something I already knew, I wanted to actually learn something new, such as its uses in lighting...

Thanks for all the replies. You guys have been immensely helpful.

#### nrcafootball68

##### Member
Ever wonder why in 3Ø power the voltage from any hot to neutral is 120V, but between any two hots it's only 208V? Shouldn't it be 240? Where did 208 come from? Hint: How far apart are the hot legs?
Is it because the hots aren't 180 degrees out of phase?

#### phil000

##### Active Member
Is it because the hots aren't 180 degrees out of phase?
you mean...90? 360 degrees (or multiples of 360) means that they are in the same phase, 180 degrees means that they are opposite (2 phase, if it exists (not sure)), means that when one peaks +, one can peak -, while the middle remains @ 0.

This is all if I recall correctly, as I just learned this...

Phil

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#### nrcafootball68

##### Member
you mean...90? 360 degrees (or multiples of 360) means that they are in the same phase, 180 degrees means that they are opposite (2 phase, if it exists (not sure)), means that when one peaks +, one can peak -, while the middle remains @ 0.
thats what I meant, if they were 180 degrees apart, there would be 240 volts between legs 1 and 2 instead of 208... correct?

#### phil000

##### Active Member
thats what I meant, if they were 180 degrees apart, there would be 240 volts between legs 1 and 2 instead of 208... correct?
my bad, the pictures look like 120 degrees too...hm, how did i get 90?

#### derekleffew

##### Resident Curmudgeon
Senior Team
Still haven't said where the number 208 comes from.

Another hint: what kind of wave is AC voltage?

#### icewolf08

##### CBMod
CB Mods
Single Phase power is 180 degrees out of phase, 3 Phase power is 120 degrees out of phase, two phase power (obsolete) is 90 degrees out of phase.
There are many things about that statement that are just wrong.

1) "Single Phase power is 180 degrees out of phase..." Let's think about this. There is only one phase in a single phase system, so it can't be out of phase, there is nothing for it to be out of phase with.

2) "3 Phase power is 120 degrees out of phase..." This is somehwat true, but I think you need to qualify this by saying that each hot leg of a 3ø system is 120˚ out of phase with each of the other hot legs.

3) "two phase power (obsolete) is 90 degrees out of phase..." In the US, two phase power is still in use (in a form). Most homes are wired with a type of two phase power. The transformer on the street has two hot legs from a 220v 3 phase system come in, the transformer has a center tapped secondary winding, creating a neutral. The center tapped neutral provides 120v between either hot leg and ground. The hot legs in this system are still 120˚ out of phase with eachother.

I'll let someone else answer Derek's question, as I know the answer.

#### derekleffew

##### Resident Curmudgeon
Senior Team
ac voltage is a sine wave... the distance between 2 legs 120 degrees out of phase would be 208, correct?
Yes, but why? You still haven't stated which trigonometric function you used and where to plug in the constants to determine the variables.

I.e., "The formula for determining the potential difference between any two hot legs of a '60Hz, 120/208VAC, Wye-Connected, 4wire+ground, xxx Amps/Leg' is... "

Another hint, and sort-of side-track: Ever wonder why industrial light fixtures (fluorescents and discharge) use 277V? What's the relationship of 277 to 480?

Thank you, Icewolf08, (and others), for not helping.

#### nrcafootball68

##### Member
Yes, but why? You still haven't stated which trigonometric function you used and where to plug in the constants to determine the variables.
I.e., "The formula for determining the potential difference between any two hot legs of a '60Hz, 120/208VAC, Wye-Connected, 4wire+ground, xxx Amps/Leg' is... "

Another hint, and sort-of side-track: Ever wonder why industrial light fixtures (fluorescents and discharge) use 277V? What's the relationship of 277 to 480?
Thank you, Icewolf08, (and others), for not helping.
I honestly have no clue, I just kind of reasoned it out, and I don't have a graphing calc with me to try to figure it out right now...