Speaker Set Up...Math/Geometry Experts Please Help

Hey guys, I need your help. I am helping a friend of mine set up his speakers and can't figure something out.

His speakers need to be tilted back to time align the drivers. According to the graph supplied from the manufacturer, we need a rake (tilt) of a 1/2 inch. This is measured using a plumb bob hanging from the back of the speaker, (which is perfectly flat). You measure the distance from the string to the back bottom of the speaker. The problem we are having is that even if we let the plumb bob settle, as soon as we try to measure the distance, the string moves just from the air disturbance around the string. We are having trouble getting an exact reading.

My question is: Can you convert the 1/2 inch distance to a degree? I have a really nice digital level that we can put on top of the speaker, start with it perfectly level and zero out the level. My level only reads in degrees, so I need to know how many degrees correspond to 1/2 inch tilt.

I've actually done this a few times in the past and always used the plumb bob method, but with current technology, was hoping to get it perfect.

Maybe this can't be converted? I've tried looking it up online, but Geometry was always my weak subject.

Thanks guys!
Sorry, I should also add that we can't measure the distance
from the top and bottom of the speaker to the front wall,
(the wall behind the speaker) because he has a bunch of stuff
that sits back there and none of it has even edges.

I thought that maybe a laser tape measure would work, but
there are no even/flat surfaces that are the same from the
top of the speaker to the bottom of the speaker that we could
bounce the laser off of.
Hi Mofi,

First, let me make sure I understand how the 1/2 inch tilt is being defined. I think what you are saying is that the speaker should end up tilted back such that if the level is rested against the top front edge of the speaker, and the level is placed perfectly horizontally, the top back edge of the speaker would be 1/2 inch below the point where that level passes above it.

If so, the required angle would be arcsin(0.5/the depth of the top of the speaker in inches). "Arcsin" = "the angle whose sine is," also known as "inverse sine."

If my interpretation of the requirement is correct, and you let me know the depth of the top of the speaker, in inches, I have a scientific calculator which can easily compute the answer. Or you can use the calculator that is built into Windows, under "Accessories." You would set the calculator to scientific mode under its "view" menu. You would then press the "inv" button to cause the inverse sine button to appear.

-- Al
Al...thank you for responding. I was hoping you would know the answer.

I think what you stated above is correct. The digital level would be placed on the top of the speaker, but facing from front to back not side to side?

The depth of the top is 10 inches. I tried to use the calculator you suggested, but again, not my forte. I think I got an answer of 2.3 degrees. If you could check that, that would be great.

Thanks again sir!
Yes, I was envisioning that the level would be oriented front to back, not side to side.

I get 2.866 degrees, based on the inverse sine of (0.5/10).

-- Al
Al...thanks! I knew I wasn't using that damn thing right. I did finally get the same answer.

This will make it way easier to set up.

Happy Halloween!!!
"According to the graph supplied from the manufacturer, we need a rake (tilt) of a 1/2 inch. This is measured using a plumb bob hanging from the back of the speaker, (which is perfectly flat). You measure the distance from the string to the back bottom of the speaker."

Actually, the above quote indicates that the measurement is made from a plumb line extending down from the back of the top edge of the speaker, so the 1/2" is measured at the very bottom of the back.

This would change the angle considerably from what Al has calculated. For instance, if the speaker is 36" tall, the calculation would be arcsin(0.5/36) = 0.796 degrees or 0 degrees, 47 minutes, 45 seconds (a little over 3/4 of a degree).
Mink...thanks for your response. What you said is correct.
You measure the 1/2 inch from the very bottom back of the
speaker to the string on the plumb bob.

Sorry, I tried to be very specific on how the 1/2 inch was
measured, but it's hard to say. Easy to see or draw, if we
could post pictures on here.

The speaker is 38 inches tall. I get .7539 degrees.
Thanks, Minkwelder. Based on your interpretation, which Mofi confirms, and based on the 38 inch height, 0.7539 degrees is correct. That would be the angle between the rear surface of the speaker and vertical, which I'm pretty certain is numerically equal to the angle between the top surface of the speaker and horizontal (assuming that the top and rear surfaces of the speaker form a 90 degree angle with each other).

-- Al
Yes, 0.7539 degrees. I remember having a pair of Vandersteen 1C's and the manual had setup directions like that which used a plumb line in back and a dimension to the bottom which was based on the distance to the listening position and ear height. I ended up using a plumbed carpenters level resting on the floor and touching the back of the speaker. It was a whole lot easier than measuring from that swinging plumb bob line (and I'm a surveyor!).
After you get them set up per manufacturer's specs be sure to tune them by ear. I set up a pair of Vandersteen 2CEs per Vandersteen manual a few years ago and for days I was unhappy with the sound. I performed the stand up sit down test and made some major adjustments in the tilt angle. Ah, there was that three dimensional sound I was expecting.
Thanks everyone for all your help! You guys are the best...
I am very impressed with the math-related gymnastics being performed by the student body, but is this hobby really supposed to be this anal?
Lindisfarne - you've been around here a long time and you ask THAT question!? :-)
Even after you tilt the speaker cabinet back, the resulting time-alignment is good for only one listening height, is it not? Does anyone sit exactly the same height the whole time they are listening to music?!
We got these set up over this weekend and they sound really good. It does indeed help being a little anal and following the manufacturer's procedure.

Bdp24...not sure how you listen, but my ears are pretty much the same height when I listen. I might turn my head from side to side at times, but it would look kinda funny if you bob your head up and down :-)

Thanks again guys for all the help.
Go to Cardas.com and look at speaker placement
use a laser