# Algebra and Trigonometry for Lighting Designers

Discussion in 'Lighting and Electrics' started by derekleffew, Nov 21, 2007.

1. ### derekleffewResident CurmudgeonSenior TeamPremium Member

Messages:
4,552
2,982
Location:
Las Vegas, NV, USA
So I've been thinking about my future book titled Algebra and Trigonometry for Lighting Designers. Filled with, you know, fun stuff like this:

Deriving a lighting fixture's multiplication factor from its beam angle using trigonometry:
[Excel format] Multiplying Factor(MF) =2*TAN((x/2)*PI()/180),
where x is the beam angle in degrees.

Note: the "*PI()/180" portion of the equation is just to force Excel to express the answer in degrees rather than radians, and therefore isn't needed if calculating by hand.

I've realized I need collaborators. Other than "W=VA" and "P=IE in your E=IR," what are some other formulas/calculations you use regularly? This may end up just being a pamphlet rather than a book, and will in inevitably become a wiki entry, so any/all help is appreciated.

2. ### phil000Active Member

Messages:
109
3
Location:
Austin, Tx

You'll notice it is all password protected...The password is controlbooth2007, I trust you guys to rearrange as you want it, as I'm going to put this in my portfolio for upcoming stuff, I'd appreciate it if you just left my name on it.
Enjoy. Distribute.
Hopefully this is a good first post.

Last edited: Nov 25, 2007
3. ### derekleffewResident CurmudgeonSenior TeamPremium Member

Messages:
4,552
2,982
Location:
Las Vegas, NV, USA
Hey, Phil000, an excellent first post. Be sure to start a new thread in the New Member Board. Tell us all about yourself, we're kinda nosy. People will ask you all sorts of strange questions, just ignore them.

I like your spreadsheet, I have to investigate it some more. I never thought about using charts, that's cool. Here's the one I use.

4. ### SerraAvaActive Member

Messages:
361
11
Location:
Southern New Jersey
Sometimes use the Pythagorean Theorem to find the throw distance of the light. Measure straight down from the light to stage level if its your target, then to where your focusing from that point. a^2 + b^2 = c^2 or (a^2 + b^2)^1/2 = c where a is your height, b is your length, and c is your throw distance. You can then multiply c by your MF to determine beam size.

5. ### gafftaperSenior TeamSenior TeamFight Leukemia

Messages:
12,813
2,894
Occupation:
Theater Manager & T.D.
Location:
Seattle, Washington
Nice Spreadsheet Phil and welcome to the booth.

This is the modification I would like to see in a photometric spreadsheet. I want to be able to manually enter:
Instrument Height, Height above deck of target (for example 6' for head height), Horizontal distance to target, and the downward angle of the instrument. Both your sheet and Derek's automatically calculate Throw distance and beam angle. But I want to accurately know what's going on 6' above the deck. Simply changing the height in your sheets, changes the angle and results inaccurate information. So it would be great if all four of those factors were independent.

6. ### phil000Active Member

Messages:
109
3
Location:
Austin, Tx
I can make them independent, should have it done by the end of the day...

the only problem is that the angle function in Excel in on some serious crack. It can prove consistency, but if you try and create a 30 60 90 triangle, it'll say like 54 degrees for the 60 degree angle...
Just for you buddy :
Phil

Last edited: Nov 25, 2007
7. ### derekleffewResident CurmudgeonSenior TeamPremium Member

Messages:
4,552
2,982
Location:
Las Vegas, NV, USA
You want to manually enter the downward angle of the instrument? You'd need a level and a protractor to physically measure that, and we're generally more concerned with the angle of elevation (at least McCandless was) so you'd need to take the complement, not that I'm complimenting you. Maybe Phil understands your desires better than I do.

Check out this for a real-time web-based tool. Does it do what you want?

8. ### icewolf08CBModCB Mods

Messages:
4,079
690
Occupation:
Controls Technician - TAIT Towers
Location:
Lititz, PA
Or, if you already own LightWright, you can use BeamWright, which does all the photometrics work for you, and will let you place an instrument anywhere relative to a subject. It also has a huge library of fixtures built in. John McKernon rocks!

9. ### derekleffewResident CurmudgeonSenior TeamPremium Member

Messages:
4,552
2,982
Location:
Las Vegas, NV, USA
Oh, Alex, you take all the fun out of it with your practicality. I recently bought LW4, after not having used it since the late '80s when it was ALDpro, and have yet to explore BeamWright. Totally agree that John McKernon rocks!, and he's a big Mac-Head too.

Anyone remember Great American Products' "Chart-A-Beam"? I could never afford it, and made do with homemade cardboard triangles, as I was a starving college student.

10. ### phil000Active Member

Messages:
109
3
Location:
Austin, Tx
I really put the time into this sheet to have it be something sendable to everyone with a PC, and most likely excel. I've seen lightwright, and that's nice, but I like being able to see ALL of my instruments at once...

I developed this for my college. Since then, it's been used:
to grade all of lighting I's projects for 2 yrs now

Used to do most of the lights for Diviners
All of the lights for Urinetown
A good amount of the lights for Lysistrata, and keeps adding on more...

...And I'll add those other things gafftaper wanted...see first post...working on the angle idea (Some people are never satisfied...)

Phil

Last edited: Feb 14, 2008
11. ### gafftaperSenior TeamSenior TeamFight Leukemia

Messages:
12,813
2,894
Occupation:
Theater Manager & T.D.
Location:
Seattle, Washington
No one understands my desires like you do Derek.

I really like your sheet Derek. But I want a sheet that tells me whats going on at a given height above the deck. In your sheet I can change the height of the instrument but not the height of the target. So the end result is a change in calculated angle and then all the numbers change. At least I think that's what's going on Right? Actually the more I think about it the more I think I need something else. I'm NOT a math wiz. Am I just misunderstanding how these two sheets work?

The ETC website tool is really cool until you use it and realize it's only programed for 10' intervals. Want to know what instrument to use at 22' vs 28', sorry you only get 20' and 30'. It won't calculate anything in between.

As for using VW or LW, while that works for me, I was looking for a simple spreadsheet to use for teaching beginning students.

Messages:
4,552