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#### lovingdvd

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I wonder if someone can help me with some basic geometry (I knew I should have paid more attention in 8th grade!).

In order to calculate the effective gain of the DaLite HighPower screen, I need to know what my off-axis angle is. I'm not sure exactly what off-axis refers to, but I guess the idea is that with the screen serving as a center point, I need to know what angle exists between my mounted projector lens running to the center of the screen. off the screen, and down to my eyes across the seating position.

Can someone tell me what the formula is for calculating this angle?

For one particular set of numbers, the projector lens will be 89" high off the floor, with a run of 15.5 feet to the center of the screen. The center of the screen is 61.5" off the floor. Then my seating distance is also 15.5 feet from the screen. With my eyes at 34" off the floor when seated.

Based on these numbers can someone please tell me a) what is the off-axis angle, and b) what is the formula you used to determine this. By having A it will enable me to calculate the screens gain at my seating position (I have a chart for this). By having B I can run various sitting/throw scenarios to see how I can minimize the angle.

Please note that in this case the projector throw and seating distance are identical at 15.5 feet so I guess this forms an isosceles triangle. However please do not count on this in your formula, as I want to try some scenarios where my throw distance and seating distance will not be the same.

Thank you very much in advance!

#### Brandon B

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You have a screen axis perpendicular to the screen. This forms a right triangle with the line from lens to screen center. If the angle theta between these two lines is your question, it is found using

sine theta = length of opp side/length of hypotenuse

or

theta = inverse sine( (89-61.5)/15.5x12) = inverse sine( 26.5/186)

Don't have a trigonometirc calculator or sine table handy, so you do it.

For the angle between your line of sight and the perp. to screen axis, same thing but substitute 61.5-34 for the opp. side value.

Add those 2 angles together for your total off axis angle.

BB

#### lovingdvd

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Thanks this was very helpful but I am still a bit confused.

I am using Excel's ASIN function who's definition is: "Returns the arcsine, or inverse sine, of a number. The arcsine is the angle whose sine is number. The returned angle is given in radians in the range -pi/2 to pi/2." I assume this is the correct function.

Ok, first I started with (89-61.5) / 186 which comes out to 0.14296. But ASIN(0.14296) returns 0.14296. Am I doing something wrong or is it ok to get the same number back from ASIN that I passed in?

Next point of confusion is for the angle between my eyes and the screen. If I understand your instructions correctly, I am supposed to substitute 61.5-34, or 27.5 for the 61.5 number used in the first equation. So that would be (89-27.5) / 186 = .330645 = ASIN(.330645) = 0.336997.

So then I add .330645 + 0.14296 which equals 0.479947. So does this mean that the angle between my eyes and the projector lens, using the screen's veritcle center as a middle point is a 48 degree angle? Am I doing this correctly. Thank you!

#### JimmyR

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You guy's are so far over my head your making me dizzy.

Lovingdvd, I forgot what size screen you want. If it's 120" diag. and electric please contact me (pm). I don't have one for sale but will make you an offer so you can see one in your home

--cheap shot of the day--

Pipe smokers never get anything done

#### jamin

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lovingdvd,

.479947 * 180 / Pi = 27.4989 degrees

the asin function returns angles in radians - the 180 / PI() converts to degrees.

in Excel the Pi function is PI()

#### Brandon B

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Sorry. I thought you'd be using a calculator that would calculate in degrees, or at least let you choose between degrees and radians.

As Jamin says, just convert. 360 degrees = 2(Pi) radians. So call it 27 and and a half.

BB

#### lovingdvd

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Thanks to all. This is very helpful.

So a) it is normal for the ASIN function to sometimes return the same value (per the question in my previous post), b) it is ok to add the ASIN results together and then convert to degrees, and c) everyone is in agreement then that based on the parameters I listed in my first post I have about a 27.5 degree angle.

Too bad, based on this it looks like I'd only get about .7 gain out of the HighPower. In any event this formula will come in handy, and I'm sure others searching for this info in the future will find it handy too.

#### jamin

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lovingdvd,

a. asin() of number is angle (in radians) within 1 percent until number is greater than about .25

b. yep

c. ?

EDIT: for stupids

#### blitzkreig

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Quote:
 Originally posted by JimmyR You guy's are so far over my head your making me dizzy. Buy the damn screen already !!
I couldn't agree more. The only angle that really counts is the Johnson angle,... and the Hi-Power is the Viagra of screens

#### JJay

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Let me clear this up for you:

The angle you are looking for is the angle from your eye to your screen plus the angle from the screen to the pj.

eye angle is:

inverse tangent(distance from eye level to screen/distance from screen to seating area)

pj angle is:

inverse tangent(distance from pj level to screen/distance from screen to pj)

remember to convert to all feet or inches for your measurements.

eye angle=inverse tan((61.5-34)/186)=8.41 degrees

pj angle=inv tan((89-61.5)/186)=8.41 deg.

your total angle=8.41+8.41=16.82 degrees

I don't know if that is what is meant by off-axis angle but that is the anlgle from your asking for .

I would say the easiest way to lower this angle is to sit 'higher' (meaning closer to screen center) and/or moving the pj/seating area back. Not knowing your set-up, I'm not sure what is the most feasable to do.

Note: It is correct to use sine only if you are actually measuring the hypotenuse, which is actual distance from the center line of screen to where your eyes are when sitting (or pj lense is)--which seems tough and cumbersome to do . I am assuming that you are measuring a straight line perpendicular to the screen to the spot where you sit (or where pj is).

Also, you can use the calc that comes with windows to do the math

#### jamin

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lovingdvd,

I agree with Brandon B concerning the Pj angle calculation, however:

you say:
Quote:
 Then my seating distance is also 15.5 feet from the screen. With my eyes at 34" off the floor when seated.
which is a bit different than 15.5 feet from the center of the screen.

As a result - the second calculation should, I believe, be

ARCTAN ( opp / adj )

in each case the opp = 27.5 and the hyp ( adj ) = 186 and lets just let

R = ratio of opp / hyp

So ans = 180 / Pi * (atan(R) + asin (R)) = ?

Your version of excel seems to differ markedly from mine in that

some of your posted calcs come up differnt on my version.

None the less, I get ? = 16.9 Degrees, How about you.

How did you get the measurement of your

screen center to lens center?

EDIT: Changed hyp to adj where appropriate -

in other words - edit for stupids

#### Douglas_B

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I agree that the angle is 16.82 degrees (2 X 8.41). Interesting that the vertical center of the screen is halfway between your eyes and the pj. Was this intentional?

Doug

#### jamin

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JJay,

Long story short - we cross posted.

#### Brandon B

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"the projector lens will be 89" high off the floor, with a run of 15.5 feet to the center of the screen. The center of the screen is 61.5" off the floor. Then my seating distance is also 15.5 feet from the screen. "

I was assuming 15.5' WAS the hypotenuse, since he said from the lens to the CENTER of the screen. Guess not, so JJay's number is closer.

BB

#### lovingdvd

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Hi all - thanks for all the updated information.

Yes JJay - your assumption is correct. I had measured a straightline of sight from the lens to the screen, and not to the center of the screen as I had written incorrectly - same goes for the eye distance. Thanks for picking up on that. I'm glad to hear your calculations take this into account, as its much easier to measure this way!

To help me play with various scenarios, and to help others that find this thread down the road, I created a spreadsheet that takes the various params as inputs and shows the angles.

Could someone please verify this is correct? Using the inputs for my situation does indeed yield an angle of 16.82 degrees.

Please feel free to make any changes or enhancements that you think others may find useful and repost it back here.

It is very interesting - I would have never guessed that my angle was only 16 degrees - I would have thought for sure that it is at least double that. But that's the beauty of raw math - if I have my measurements correct (which I'm quite sure I do) I can count on the answer being accurate.

The spreadsheet is attached. Thanks again!

Quote:
 Originally posted by JJay Let me clear this up for you: The angle you are looking for is the angle from your eye to your screen plus the angle from the screen to the pj. eye angle is: inverse tangent(distance from eye level to screen/distance from screen to seating area) pj angle is: inverse tangent(distance from pj level to screen/distance from screen to pj) remember to convert to all feet or inches for your measurements. in your example: eye angle=inverse tan((61.5-34)/186)=8.41 degrees pj angle=inv tan((89-61.5)/186)=8.41 deg. your total angle=8.41+8.41=16.82 degrees I don't know if that is what is meant by off-axis angle but that is the anlgle from your asking for . I would say the easiest way to lower this angle is to sit 'higher' (meaning closer to screen center) and/or moving the pj/seating area back. Not knowing your set-up, I'm not sure what is the most feasable to do. Note: It is correct to use sine only if you are actually measuring the hypotenuse, which is actual distance from the center line of screen to where your eyes are when sitting (or pj lense is)--which seems tough and cumbersome to do . I am assuming that you are measuring a straight line perpendicular to the screen to the spot where you sit (or where pj is). Also, you can use the calc that comes with windows to do the math

viewing angle calc.zip 2.36328125k . file

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#### lovingdvd

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Quote:
 Originally posted by Douglas_B I agree that the angle is 16.82 degrees (2 X 8.41). Interesting that the vertical center of the screen is halfway between your eyes and the pj. Was this intentional? Doug
No - it wasn't intentional at all. In fact I keep thinking I may be doing something wrong with my measurements, etc, but I think my measurements are all correct so it may just be a coincidence.

I think the reasons it is working out this is mainly because I'm sitting under the pj so the distance to the screen is the same and the distance in height between the vertical center of the screen and the pj is the same as the distance from vertical center to my eye.

#### Brandon B

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Oh, by the way, this is the same PJ to screen distance as my hipower (120" diagonal). But my PJ is at about 65", screen center is at about 74" and eye height is about 36" at 12 feet.

So my angle is less than yours will be on my couch. When I sit at my kitchen table, bringing my eye height to 47" or so (but at a range of about 18-20 feet), I get a LOT more punch from the screen. You will be losing some of the benefit of the hipower in my opinion. Its retroreflectivity is working against you here. You really want the PJ closer to the axis of or on the lower half of the screen if possible. Can you raise your screen or lower the PJ at all? Do you have tall ceilings?

I presently have my PJ on a tall rack I made, but it is proving cumbersome to have it located there, and I am about to make some sort of ceiling mount which will swing/telescope/somehow pivot up out of the way when not in use. This might work for you too, if you are seated when under it and it could not be walked into by anyone if mounted lower.

BB

#### lovingdvd

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Quote:
 Originally posted by Brandon B Oh, by the way, this is the same PJ to screen distance as my hipower (120" diagonal). But my PJ is at about 65", screen center is at about 74" and eye height is about 36" at 12 feet. So my angle is less than yours will be on my couch. When I sit at my kitchen table, bringing my eye height to 47" or so (but at a range of about 18-20 feet), I get a LOT more punch from the screen. You will be losing some of the benefit of the hipower in my opinion. Its retroreflectivity is working against you here. You really want the PJ closer to the axis of or on the lower half of the screen if possible. Can you raise your screen or lower the PJ at all? Do you have tall ceilings? I presently have my PJ on a tall rack I made, but it is proving cumbersome to have it located there, and I am about to make some sort of ceiling mount which will swing/telescope/somehow pivot up out of the way when not in use. This might work for you too, if you are seated when under it and it could not be walked into by anyone if mounted lower. BB
Hi Brandon,

Yes, I'm aware of the drawback due to my angle. In fact it is this very issue that sent me in search of the fomulas to calculate my angle. At 17 degress my gain supposedly drops to 0.7, thus making it a show stopper.

Unfortunately it is not possible to mount the pj lower, nor sit higher, nor sit further back, nor lower the screen.

You bring up an interesting question though... How would lowering the screen help me here? No matter how much I lower the screen, won't my angle remain fixed at 17 degrees provided the height/length of the pj and seating position to the screen do not change?

#### Brandon B

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You want to RAISE the screen or lower the PJ. Since the angle between your eyes and the PJ (assuming you raise the screen) is with respect to the center of the screen, raising this center point decreases this angle.

Take a piece of string and try it on a table or desk.

So can you raise your screen?

BB

#### lovingdvd

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Hi Brandon. Can't low the pj because of its fixed offset and no lens shift. Could raise the screen a few inches, but its already a good foot+ higher than I'd like. Any higher and I may get a crink in my neck watching it.

But this does raise an interesting question. How is it that raising the screen could help me here? Yes, by raising it the center point comes up higher so the angle decreases from the lens to the center of the screen. But then doesn't the angle from my eyes to the center point of the screen increase by the same amount? Wouldn't the overall angle be the same? Thanks.

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