CC stand height/angle--geom and trig experts needed! (1 Viewer)

[Ari]

I'm moving to FP and will need to mount my current center channel on a stand which I will have custom-made. The speaker stand guy needs to know how much angle back to front I need in the stand -- basically how much higher the front will be than the rear.
I've tried using my limited recollection of high school geometry and trig but have come up with nothing -- and I'm hoping that one of you guys can help....here are the pertinent figures:
-CC is 8.5" deep and will be 25.5" from the front wall. The tweeter is 3.5" from the bottom of the CC
-bottom of screen is 32" from the floor, and the speaker is around 6" high so I figure the stand should be around 24"-26" high
-there will be two seating areas: first one is 157.5" from the front wall and ear height will be 47", second one is 217.5" from the front wall and ear height will be 55.25".
I basically want the tweeter aimed at ear height of both listening areas....so I will need to know both the height of the stand and how much higher the front of the stand should be.......
Engineers and math wizzes.....your help is needed!!
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[nolesrule]

In order to calculate the listening angle, you need to caculate the angle over horizontal between the 2 rows of ears first, and that is 7.829 degrees.
x = 217.5 - 157.5 = 60
y = 55.25 - 47 = 8.25
tan(a) = y/x
a = 7.829 degrees
Now that you know the angle, you need to figure out the height above the floor of the tweeter.
The tweeter will reside 0.475 inches behind the base of the speaker (on the horizontal plane) due to the inclination.
x = distance from tweeter to ears (horizontal) = 157.5 (wall to listener) - 25.5 (wall to front of speaker)- 0.475 = 131.525
tan(a) = y/x
y = distance vertical from tweeter to ear = xtan(a) = 131.525tan(a) = 18.08
So, the height of the tweeter should be 47 - 18.08 = 28.92 above the ground, at a distance of 25.5 from the wall.
So, the front of the stand should be 25.92 inches high (28.92 - 3 for tweeter height).
The speaker is 8.5 deep (h) and sin(a) = y/h
So, y = hsin(a) = 1.16.
Stand depth = hcos(a) = 8.42
Therefore, the back should be 1.16 inches below the front
Front of speaker stand height = 25.92 inches
Back of speaker stand height = 24.76 inches
Depth of stand = 8.42 inches
Remember, this takes into account that the center of the tweeter will be almost 0.5 inches behind the bottom front edge of the speaker (25.5 inches from wall). Make sure the bottom edge is at the 25.5 mark. DO NOT center the tweeter on that mark.
Anyone want to verify my numbers?

 

[Bill Catherall]

I drew it up in AutoCAD.

) or you can lift the screen or the viewer. It shouldn't be a problem though.
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Bill

 

[nolesrule]

I'm glad to know I'm not too rusty at this trig and geometry stuff. I wish I had access to AutoCAD to give me an assist. I wouldn't have had to do all the calculations by hand. But at least now I know I'll be able to do the math when it comes time to build my own home theater (I lurk in this category compiling ideas...I'm probably at least 5-7 years away from starting my own project).
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My DVD Collection

 

[Ari]

Thanks for the quick trig refresher......never thought I'd ever use if after high school!!
After remeasuring the HT, I think I've come up with the ideal CC height and tilt. My question now is how much latitude do I have playing around with CC height before things sound different. I haven't mounted my FP screen yet and I fear that the ideal height for the stand might get in the way of the screen. BTW, I'll be using the Energy eXL:C as my center channel......