# 6x9 or degree



## mixmaster (Aug 12, 2008)

I'm a sound guy by trade most of the time, although I do enjoy lighting work too. I'm standing in for my boss who's on an extended vacation and had a question come up that I need help answering. A show coming in is looking at our FOH lighting inventory, all of which is indicated in degrees of beam width (19 and 24 degree Source 4), it's silk screened right on the end of the barrel. That's fine I understand that. The LD for the show is looking for more ellipsoidals, but is referring to them dimensionally, as 6x9s or 6x12s. I understand those terms also but am having trouble making the conversion between dimensionals and degrees. I've worked in venues that use one term or the other but never had to mix them. Is there a conversion chart that someone could post, something like a 6x9 is an xx degree instrument?
Thanks in advance
Matt


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## waynehoskins (Aug 12, 2008)

4.5x6 = 50
6x9 = 36 or 40
6x12 = 26 or 30
6x16 = 19 or 20
6x22 = 10

Altman and CT like to use even-ten-degrees notation, ETC and Strand like to use the other numbers, which are in my experience more commonly quoted.

You can tell what era somebody learned lighting in by what they call fixtures.


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## Charc (Aug 12, 2008)

waynehoskins said:


> 4.5x6 = 50
> 6x9 = 36 or 40
> 6x12 = 26 or 30
> 6x16 = 19 or 20
> ...



I'm curious, so someone correct me if I'm wrong, but here is my hypothesis:

19, 26, and 36 are what the x9-x16 actually breakdown into as real angles. I hypothesized that ETC went with these angles, so that the beam spreads would be familiar to LDs, and thus facilitate the transition to the S4. Whereas, it looks like other manufacturers who went with 20, 30, 40, were trying to have "nicer" numbers, akin to the metric system in its logic.

Was I close?


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## waynehoskins (Aug 12, 2008)

charcoaldabs said:


> I'm curious, so someone correct me if I'm wrong, but here is my hypothesis:
> 
> 19, 26, and 36 are what the x9-x16 actually breakdown into as real angles. I hypothesized that ETC went with these angles, so that the beam spreads would be familiar to LDs, and thus facilitate the transition to the S4. Whereas, it looks like other manufacturers who went with 20, 30, 40, were trying to have "nicer" numbers, akin to the metric system in its logic.
> 
> Was I close?



That's been my thought on it. Alt's and CT's (and maybe others; I forget) numbers were picked because they're nicer (and that seems to have been the trend in the '80s: see 1KL). After all, why use such an archaic description as the descriptions of the lens geometry to express the size of a unit when you could just use a beamwidth in degrees? Especially when your fixture may not even have a pair of 6" optics (see S4).

I learned the lens geometry notation first, and then the ETC/Strand-style notation. When I have to use Alt or CT fixtures, I end up converting that to geometry in my mind: "okay, a 30 is a kluge of a 6x12..." 

By the way, I left something off earlier:
6x22 = 10 *= stupid front-heavy*
*5 degree = why?*


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## cdub260 (Aug 12, 2008)

As I understand it in the 6xwhatever notation, a 6x9 was an elipsoidal reflector spotlight with 6 inch lenses that had the focal point of the beam 9 inches out from the front of the light. A 6x12 would have it's focal point 12 inches from the end of the light, etc. 

As an experiment, you might try putting on a thick pair of gloves and holding your hand 16 inches from the front of a 6x16 or 19 degree. I did this, probably 15 or so years ago, and smoked a ratty old pair of gloves. Just don't try putting your bare hand in the beam.


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## Charc (Aug 12, 2008)

cdub260 said:


> As I understand it in the 6xwhatever notation, a 6x9 was an elipsoidal reflector spotlight with 6 inch lenses that had the focal point of the beam 9 inches out from the front of the light. A 6x12 would have it's focal point 12 inches from the end of the light, etc.
> 
> As an experiment, you might try putting on a thick pair of gloves and holding your hand 16 inches from the front of a 6x16 or 19 degree. I did this, probably 15 or so years ago, and smoked a ratty old pair of gloves. Just don't try putting your bare hand in the beam.



I don't think it's from the front of the light, but rather the center of the lamp. Think of the two focal points of an ellipse.


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## Charc (Aug 12, 2008)

waynehoskins said:


> By the way, I left something off earlier:
> 6x22 = 10 *= stupid front-heavy*
> *5 degree = why?*



I think isn't the 6x22 something like 11º or 12º? The fact that it's a "torpedo" is a PITA, and it's obnoxious and front heavy, but still it's alright.

5º, clearly there was a need for this unit. I can think of some applications, and most have to do with really long throws, or really tight shows, or possibly the homebrew followspot?


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## cdub260 (Aug 12, 2008)

waynehoskins said:


> That's been my thought on it. Alt's and CT's (and maybe others; I forget) numbers were picked because they're nicer (and that seems to have been the trend in the '80s: see 1KL). After all, why use such an archaic description as the descriptions of the lens geometry to express the size of a unit when you could just use a beamwidth in degrees? Especially when your fixture may not even have a pair of 6" optics (see S4).
> 
> I learned the lens geometry notation first, and then the ETC/Strand-style notation. When I have to use Alt or CT fixtures, I end up converting that to geometry in my mind: "okay, a 30 is a kluge of a 6x12..."
> 
> ...



Why use a 5 degree?

My venue is a 2600 seat ampetheatre. From my rear of house trusses, the only lights that are affective are 5 degrees, 10 degrees, and 19 degrees.

As for the issue of front heavy lights, while is true of my old Colortran 5 degrees and 10 degrees, which I haven't used in the last 5 years, are all around heavy lights, my ETC Source 4, 5 degrees and 10 degrees have 1/4 inch thick plastic fresnel type lenses, making them only slightly heavier than a standard Source 4. Focusing them can be a challenge, due to the long barrel, but once you learn to compensate for that issue, they're actually fairly easy to use.


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## Charc (Aug 12, 2008)

cdub260 said:


> Why use a 5 degree?
> 
> My venue is a 2600 seat ampetheatre. From my rear of house trusses, the only lights that are affective are 5 degrees, 10 degrees, and 19 degrees.
> 
> As for the issue of front heavy lights, while is true of my old Colortran 5 degrees and 10 degrees, which I haven't used in the last 5 years, are all around heavy lights, my ETC Source 4, 5 degrees and 10 degrees have 1/4 inch thick plastic fresnel type lenses, making them only slightly heavier than a standard Source 4. Focusing them can be a challenge, due to the long barrel, but once you learn to compensate for that issue, they're actually fairly easy to use.



I take it you don't have any 14º units?


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## LightStud (Aug 13, 2008)

cdub260 said:


> As I understand it in the 6xwhatever notation, a 6x9 was an elipsoidal reflector spotlight with 6 inch lenses that had the focal point of the beam 9 inches out from the front of the light. A 6x12 would have it's focal point 12 inches from the end of the light, etc.


 Hogwash. You DO know that 6x9 and 6x12 have TWO lenses, don't you? So much for your understanding. Do an search for "effective focal length" of a lens system for the formulas.

As to others, Berkey Colortran may have bben the first to do the 30,40,50 degree with the horrible, but great for it's time and better than the Altman 3 1/2x6,8,10,12; MiniEllipse--still a good concept becuase to change degrees you just opened the lens tube and put the same lenses in different slots. Through the 80s/90s Strand and Colortran continued with 5, 10, 15, 20, 30, 40, 50 degree units, until ETC took a huge step backwards by saddling us with 19, 26, 36 units. Had they had any confidence in the success of the sourceFour, they wouldn't have had to use the "it's the same size beam as the 360Q" sales pitch. Maybe it was just that they could obtain lenses in the focal lengths to achieve those degrees, which were close enough to the Altman units. Hell, it took them until 2005 to produce a fixture with a 6 inch lens. Bigger lens=more light through it. ALL UNITS SPACE ON 18" CENTERS, so why the need for a fixture smaller than a 6"Leko? Think what the Source4 could be if the had used six inch diameter lenses? Maybe wouldn't have need a 750 version, and I'm still waiting for a 1000watt, but it will probably be a 975watt lamp. Sorry to rant.


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## derekleffew (Aug 13, 2008)

charcoaldabs said:


> I don't think it's from the front of the light, but rather the center of the lamp. Think of the two focal points of an ellipse.


 The fact that one can interchange lens tubes, as well as the fact that all ERS fixtures in a family have the exact same reflector, would indicate flawed logic.

I don't think it was explicitly stated above, in the FEL-based units, the 10° was an 8x13, and the 5° a 10x23, single plano-convex lens.


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## Charc (Aug 13, 2008)

derekleffew said:


> The fact that one can interchange lens tubes, as well as the fact that all ERS fixtures in a family have the exact same reflector, would indicate flawed logic.
> 
> I don't think it was explicitly stated above, in the FEL-based units, the 10° was an 8x13, and the 5° a 10x23, single plano-convex lens.



Your statement makes absolutely no sense.

That's the whole point. One point is constant, the lamp, inside the reflector. However, the second focal point will change, based on the lense.

How about a diagram?


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## cdub260 (Aug 13, 2008)

LightStud said:


> Hogwash. You DO know that 6x9 and 6x12 have TWO lenses, don't you? So much for your understanding. Do an search for "effective focal length" of a lens system for the formulas.
> 
> As to others, Berkey Colortran may have bben the first to do the 30,40,50 degree with the horrible, but great for it's time and better than the Altman 3 1/2x6,8,10,12; MiniEllipse--still a good concept becuase to change degrees you just opened the lens tube and put the same lenses in different slots. Through the 80s/90s Strand and Colortran continued with 5, 10, 15, 20, 30, 40, 50 degree units, until ETC took a huge step backwards by saddling us with 19, 26, 36 units. Had they had any confidence in the success of the sourceFour, they wouldn't have had to use the "it's the same size beam as the 360Q" sales pitch. Maybe it was just that they could obtain lenses in the focal lengths to achieve those degrees, which were close enough to the Altman units. Hell, it took them until 2005 to produce a fixture with a 6 inch lens. Bigger lens=more light through it. ALL UNITS SPACE ON 18" CENTERS, so why the need for a fixture smaller than a 6"Leko? Think what the Source4 could be if the had used six inch diameter lenses? Maybe wouldn't have need a 750 version, and I'm still waiting for a 1000watt, but it will probably be a 975watt lamp. Sorry to rant.



As a matter of fact I do know that they have two lenses, having first worked with Altman 6xwhatevers 19 years ago.

As for Colortran Mini's, I have 40 of them in my inventory. While I agree that they are a good concept (The ability to quickly change from one beamspread to another is always a good thing.), they do have their drawbacks. Foremost among those drawbacks is that even a well maintained Colortran Mini doesn't have a lot of punch. This is in large part because it can be a little tricky locking down the lamp alignment, not impossible, mind you, just tricky. Also, on the subject of the lamp, why did Colortran pick a lamp with a mini screw base? Have you ever tried to change one of these things? Unless I wear gloves, I have a hard time not leaving fingerprints all over the lamp. Another issue, though a relatively minor one, is the non-standard gel frames and gobo holders. Of course, the same thing could have been said about the Source 4 before it became the standard.


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## Sean (Aug 13, 2008)

cdub260 said:


> Another issue, though a relatively minor one, is the non-standard gel frames and gobo holders. Of course, the same thing could have been said about the Source 4 before it became the standard.



Umm.... except 6.25" WAS used in fixtures before the S4.....check out Altman's Mini-zoom.

--Sean


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## mixmaster (Aug 13, 2008)

Thanks to everyone for their timely replies. I knew the answer was out there. This is what I get for taking over the whole department for a month.
Matt


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## Darthrob13 (Aug 13, 2008)

Sean said:


> Umm.... except 6.25" WAS used in fixtures before the S4.....check out Altman's Mini-zoom.
> 
> --Sean



Don't forget the 1KL......(shutter at the box of light)


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## cdub260 (Aug 13, 2008)

Sean said:


> Umm.... except 6.25" WAS used in fixtures before the S4.....check out Altman's Mini-zoom.
> 
> --Sean



Thanks for the correction. I've never worked with that fixture.


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## gafftapegreenia (Aug 13, 2008)

Darthrob13 said:


> Don't forget the 1KL......(shutter at the box of light)



Did someone say 1KL?


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## derekleffew (Aug 13, 2008)

charcoaldabs said:


> Your statement makes absolutely no sense.
> 
> That's the whole point. One point is constant, the lamp, inside the reflector. However, the second focal point will change, based on the lense.
> 
> How about a diagram?


 Could you elaborate further? I'm more than a little confused as to how the Primary Focal Point (filament) remains constant, and yet the Secondary Focal Point ("lense," says you? Is that your final answer?) will change, without some alteration of the size or shape of the reflector. Does a 490 have a different distance between its reflector's focal points than a 405? I thought a 6x22 used the exact same reflector as a 4.5x6.5? Do Variable Focal Length ERSs (Zooms) vary their reflector somehow when moving the Lens knobs?

How ABOUT a diagram, this time depicting a longitudinal section of an Ellipsoidal Reflector Spotlight, with a few representational paths of its light rays. If I'm not mistaken, there's one in _A Method of Lighting the Stage_. Stanley McCandless. Theatre Arts Books. First publication, 1932. (There might even be one in that shaver guy's book, on page 54.)


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## Charc (Aug 13, 2008)

derekleffew said:


> Could you elaborate further? I'm more than a little confused as to how the Primary Focal Point (filament) remains constant, and yet the Secondary Focal Point ("lense," says you? Is that your final answer?) will change, without some alteration of the size or shape of the reflector. Does a 490 have a different distance between its reflector's focal points than a 405? I thought a 6x22 used the exact same reflector as a 4.5x6.5? Do Variable Focal Length ERSs (Zooms) vary their reflector somehow when moving the Lens knobs?
> 
> How ABOUT a diagram, this time depicting a longitudinal section of an Ellipsoidal Reflector Spotlight, with a few representational paths of its light rays. If I'm not mistaken, there's one in _A Method of Lighting the Stage_. Stanley McCandless. Theatre Arts Books. First publication, 1932. (There might even be one in that shaver guy's book, on page 54.)



I'm essentially disregarding what you're writing, and attempting to explain my perceived understanding of ERSs, but am open to correction.

Looking back at the previous diagram, the Primary Focal Point is the Filament, and that point is static for the 405 through 490, simply because all of those units use the *same lamp*, *same housing*, and *same reflector*. That makes their relationship to each other constant. If you were to remove the barrel from both your hypothetical 405, and 490, then the output of light from both bodies should be the same, no?

No when you put in the barrel, you're also putting in the lens, or lenses, whatever the case may be for whichever barrel you're using, you introduce a new factor into the path of the light. These optics direct the light to the Secondary Focal Point, but are not themselves the Secondary Focal Point.

The Primary focal point has to be the lamp (filament), because that's what the source is. The secondary focal point is where the light, once again, (theoretically) comes back to one point, before spreading out again. The focal length would be the distance between the foci, right?

Here is another diagram:


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## gafftapegreenia (Aug 13, 2008)

Alright, I was trying to stay out of this one, but, well, here goes.

As a base, let me establish that I am talking about the 360Q and all of its copies/brothers/relatives in the world.

As we all know, an ellipsoidal reflector has two focal points. The first focal point, as we will call it, is located inside of the reflector. It is at this focal point that the filament of the lamp of the ellipsoidal is ideally located, so that the filament is best positioned for the reflector to most efficiently and evenly capture the light. Ideally, this would be a point source, but because there is no such thing as ideal point source in theatrical lighting, an ellipsoidal reflector is slightly modified to account for the linear filament. This modification that allows better performance does not change the principal of how an ERS works. 

The reflector never changes. In the 360Q series, all reflectors are of the same shape and focal length. 

The second focal point is located outside of the reflector. In an ellipsoidal, this focal point will be just past the shutters/gobo holder. If the focal point were infact at the shutters, there would be little to actually shutter cut and the shutters would essentially be useless. Same goes for the gobo. If the focal point was actually on the gobo, little of the image would be captured. By having the focal point just past the shutters/gobo, the majority of light coming through the opening is essentially the same diameter as the opening itself, thus it can be effectively chopped and gobo'd. (I made a word) Note I say majority. In a perfect world with a point source, all the light would be focused. However, because of the imperfect filament, there is stray light that is captured. This is the same stray light that makes gobos fuzzy, even in a perfectly centered, hard focused ERS. 

Now, if you ever take apart various degree 360Q's, you will notice that the lens trains are in fact all the same length. This is one part made for all the models. The differences are that the lenses put into this lens train by Altman are of difference focal lengths, and the longer body of a higher 6-x-whatever places the lens train farther from the second focal point of the ellipsoidal reflector. Take, for example, a 6x9. It has a 6" diameter lens with a focal length of 9". When in hard focus, the first lens in the lens train will have its focal point, which is 9" away, at the second focal point of the ellipsoidal reflector. Since the focal point of these two items is in the same location, all the light that strikes the first lens in the train will leave that lens as parallel rays. The second lens is then positioned to take those parallel rays and focus them back down. The focal point of the second lens is 9" in front of the fixture. The rays of light converge hear, and then spread as they make their way to the stage. As you move on to 6x12's, 16's and 22's, the fixture becomes longer because, since the lenses used have longer focal lengths, they must be farther away from the focal point of the ellipsoidal reflector in order to focus correctly. 

The relationship of the two plano-convex lenses is a constant. It is the relationship of the focal point of the first plano convex lens to the focal point of the ellipsoidal reflector that is user selectable. 


Now, what ETC did, and what was the genius part, is that they decided they wanted to use the same body length for all their fixtures. So, using math and engineering brilliance, they departed from the double plano convex system. Each degree of Source 4 uses a specially designed set of lenses. Some have one lens, others have two, some use biconvex lenses, which are rounded on both sides. All of this allows different lens combinations to produce difference beam spreads, while keeping all instruments of uniform length. By changing the lenses themselves, ETC was able top make lens trains interchangeable, thereby revolutionizing the industry. 

So, that is my understanding.

Charc, you second graphic is showing an ERS that is not in hard focus. The lens train on that ERS would be all the way in, thus spreading the rays as they leave the first plano convex lens, and giving a soft beam/image.


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## Serendipity (Aug 14, 2008)

gafftapegreenia said:


> The second focal point is located outside of the reflector. In an ellipsoidal, this focal point will be just past the shutters/gobo holder. If the focal point were infact at the shutters, there would be little to actually shutter cut and the shutters would essentially be useless. Same goes for the gobo. If the focal point was actually on the gobo, little of the image would be captured. By having the focal point just past the shutters/gobo, the majority of light coming through the opening is essentially the same diameter as the opening itself, thus it can be effectively chopped and gobo'd. (I made a word) Note I say majority. In a perfect world with a point source, all the light would be focused. However, because of the imperfect filament, there is stray light that is captured. This is the same stray light that makes gobos fuzzy, even in a perfectly centered, hard focused ERS.
> 
> Now, if you ever take apart various degree 360Q's, you will notice that the lens trains are in fact all the same length. This is one part made for all the models. The differences are that the lenses put into this lens train by Altman are of difference focal lengths, and the longer body of a higher 6-x-whatever places the lens train farther from the second focal point of the ellipsoidal reflector. Take, for example, a 6x9. It has a 6" diameter lens with a focal length of 9". When in hard focus, the first lens in the lens train will have its focal point, which is 9" away, at the second focal point of the ellipsoidal reflector. Since the focal point of these two items is in the same location, all the light that strikes the first lens in the train will leave that lens as parallel rays. The second lens is then positioned to take those parallel rays and focus them back down. The focal point of the second lens is 9" in front of the fixture. The rays of light converge hear, and then spread as they make their way to the stage. As you move on to 6x12's, 16's and 22's, the fixture becomes longer because, since the lenses used have longer focal lengths, they must be farther away from the focal point of the ellipsoidal reflector in order to focus correctly.



1. Thanks for the amazing post, Greenia.
2. Because the second focal point is further away in smaller beam spread fixtures, would it have an affect on the less-than-perfect filament's extraneous light, making it more difficult to create sharper-edged patterns? Because in S4s the location of the shutters/gobo does not change, even if using the behemoth 5°s..? Or am I creating some sort of fallacy in my head? 

Thanks!


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## cdub260 (Aug 15, 2008)

charcoaldabs said:


> I'm essentially disregarding what you're writing, and attempting to explain my perceived understanding of ERSs, but am open to correction.
> 
> Looking back at the previous diagram, the Primary Focal Point is the Filament, and that point is static for the 405 through 490, simply because all of those units use the *same lamp*, *same housing*, and *same reflector*. That makes their relationship to each other constant. If you were to remove the barrel from both your hypothetical 405, and 490, then the output of light from both bodies should be the same, no?
> 
> ...




cdub260 said:


> As I understand it in the 6xwhatever notation, a 6x9 was an elipsoidal reflector spotlight with 6 inch lenses that had the focal point of the beam 9 inches out from the front of the light. A 6x12 would have it's focal point 12 inches from the end of the light, etc.
> 
> As an experiment, you might try putting on a thick pair of gloves and holding your hand 16 inches from the front of a 6x16 or 19 degree. I did this, probably 15 or so years ago, and smoked a ratty old pair of gloves. Just don't try putting your bare hand in the beam.



Thanks charcoaldabs for this wonderful diagram.

In my original post I screwed up my terminology. Bear in mind its been 18 years since I had my lesson on how lekos work, and haven't thought about it much since. What I was referring to as being "16 inches from the front of a 16 degree" was the point where the beam crosses itself.

Feel free to correct me if I'm wrong here.


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## LightStud (Aug 18, 2008)

cdub260 said:


> Thanks charcoaldabs for this wonderful diagram. ...


Wonderful? Perhaps. Inaccurate? Absolutely. 

_N.B.,_ Speaking mathematically, ellipsoidal shapes do not have focal points. Focal points are a component of a lens', or lens system's, definition. Conical sections have one *focus* or, in the case of an ellipse, two *foci*. 

In the diagram, only the two outer light rays are shown leaving the secondary focus of the reflector. One assumes the others have been omitted for clarity, a marginally acceptable practice. Had some others been included, the following error might have been avoided. 
Can *anyone* explain how a lens system can possibly take a *single* light ray and bend it *two* different places, one veering off away from the longitudinal axis and the other bending toward it?


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## SteveB (Aug 18, 2008)

gafftapegreenia said:


> By changing the lenses themselves, ETC was able top make lens trains interchangeable, thereby revolutionizing the industry.



Excellant post, BTW.

And FWIW, Century Lighting had interchangable lens tubes on their LekoLite series in the 60's ?, or whenever the old grey radial ellipsoidals were introduced. The 4.5x6, 6x9 and 6x12 lens tubes were interchangable between bodies. Colortran, Kliegl, ADB/CCT among others had this feature before the S4 ellipsoidal was introduced in the early 90's. For whatever reason - cost ?, not wanting a different standard ?, the biggie rental shops stuck with the 360 and 360Q until the S4. 

So this part wasn't really revolutionary, even though I agree with the rest. 

Steve B.


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## church (Aug 19, 2008)

Actually the mathematical definition of an ellipse is:

an ellipse is the path traced out by a point whose distance from a fixed point, called the focus, maintains a constant ratio less than one with its distance from a straight line not passing through the focus put anothr way: an ellipse is a locus of points in a plane such that the sum of the distances to two fixed points is a constant. The two fixed points are called foci (singular- focus). An easy way to draw an ellipse to illustrate this is to make a loop of string hammer two nails into a piece of wood. Loop the string around the nails - hint this only works if the loop of string is bigger than the distance between the nails. Then place a pencil inside the loop and move the pencil until the loop is tight. then move the pencil always keeping it tight to the string as if you are trying to draw a circle - you will end up with an ellipse. the two nails are your focal point.

In an ellipsoidal you want the filament of the lamp to be as close to a spot as possible located at one locus. Because light travels in straight lines (at least in the wave nature of light - lets forget photonic behaviour in this instance) the light waves incident on the reflector are reflected at the same angle angle as they are incident to the reflector. This means if the lamp filament was a perfect spot source at the first locus or focus of the ellipse then all the light would also pass through the second focus and into the optics.

You could build an ideal spotlight if you could get perfect bits.

This is why lower voltage fixtures tend to be more efficient because you can make the filament smaller so it becomes closer to the ideal condition. This is why 240v lamps are not as efficient as 120V lamps and why 24V lamps are better still. So if you can improve the reflection coefficient of the reflector you will also maximise the light coming out. 

Because you can't make a perfect lamp, reflector or lens we end up with less than perfect fixtures and the debate on which is best and with what combination of lamps. Note dust changes the reflection coefficient of the lenses and reflectors - this is why dirty fixtures give poor light output.


Because you can't get perfect bits to build a fixture the goal is to design one that allows for the imperfections in the design and maximises the performance hence the HPL lamp optimised to the reflector. This can be done with the analysis and simulation tools available to today's engineers but was beyond the reach of engineers in the 80s.



Other applications of ellipses inlude planet orbits, gears etc.


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