Dumb math question

[midhvac]

:confused:

How would you mathematically calculate this for the following problem?

You cut a 1” horizontal slot in a very thin piece of sheet metal.

The piece of sheet metal is standing upright. So you can fit a 1” thick piece of wood through the slot at a completely horizontal angle.

But then you start to tilt the top of the piece of tin farther toward you. So the thickness of the piece of wood you want to place horizontally through the slot must be thinner as the angle of the piece of tin becomes closer to horizontal.

What math function would you use to calculate the maximum allowable thickness of wood that will fit straight horizontally through the slot when the slot is at x angle?

Would this be the sine of the angle?

[timebuilder]

You can figure this using a grid square diagram, as if you were going to graph a function.

Use the length of the y-axis as the original one inch slot value, with 20 or thirty grid squares to represent that inch, and then draw the angle you want using a line the same length as the inch value.

The end of the line will be a certain number of grid squares above the x-axis, and and that height will show you how thick your wood stick can be at your desired angle.

[Tool-Slinger]

thickness x .9 = angle?

[Carnak]

I would go with your hunch, the slot thickness times the sine of the angle.

[Tool-Slinger]

It seems to work in my math formula, 1 inch being 100. A=100 x .9

50=1/2 inch, ectcetera.

[Andy Schoen]

Despite partaking of excess libations today, my trig recommends the following: board thickness divided by cosine of board angle. There will be a point when angle gets near 90 degrees where you need to know the length of the board as it is a limit to this function, i.e., at 90 degrees, the slot will be the length of the board. I'm unable to incorporate it into this equation tonite. :p

[Andy Schoen]

BTW, the above assumes we define the board perpendicular to the ductwork as 0 degrees, not 90 degrees, and 0 degrees is the length of the slot equal to board length.

I'm thinking sideways at the moment. :p

[Carnak]

I think mid meant the board is horizontal and the sheet of metal is varying from zero to 90 degrees from the horizontal. Sine should give the 'vertical component' of the opening. Board would have to be marginally thinner to pass through.

[ryan_the_furnace_guy]

I would just start with the 1" thick piece of wood, then get out my wood files...:):p

[flyrfan]

Take the sine of the angle of the piece of tin relative to horizontal. The angle is the vertical edge relative to horizontal.

So if it is standing straight up, the tin is 90' to horizontal & sine 90'=1". When the tin is parallel to horizontal the angle is 0' & sine 0'=0".

[Shophound]

I would just start with the 1" thick piece of wood, then get out my wood files...:):p

A jointer would work better.... :D

[toddfather]

If I understand your question properly, the formula would be: The original opening (1") times the cosine of the angle you tilted at. Keep in mind that the opening size would be changed as you indicated however, the slot would also be lower than it was in it's original position. There is a formula for that also.

Hope that was helpful!

Toddfather

[timebuilder]

If I understand your question properly, the formula would be: The original opening (1") times the cosine of the angle you tilted at. Keep in mind that the opening size would be changed as you indicated however, the slot would also be lower than it was in it's original position. There is a formula for that also.

Hope that was helpful!

Toddfather

Good point. My method assumed that he would fit the plate to the needed position, rather than have it hinge orf flex from a fixed position.

[mattm]

All this math to stick a piece of wood through a piece of sheet metal ?

[Shophound]

A) Determine desired angle of sheet metal.

B) Move sheet metal to that angle and lock it into place

C) Measure width of slot where wood is to be fitted

D) Go to table saw and set fence on saw at this width

E) Rip wood to width

F) Fit wood into slot

G) Done

:D

[smokin68]

persuade metal with hammer to fit the wood


since it's a right angle, I'd use a(sq)+b(sq)=c(sq) to determine wood thickness

[hvaccolo]

If you're going to go through all the trouble of calculating the trig functions, be sure to take into account the thickness of the sheet metal. If you assume that the metal is theoretically infinitely thin, then there is no affect. However, as the thickness increases, it's affect becomes more drastic on the fit of the wood board. For example, if your using a 1" thick piece of metal, the opening in the metal would reach zero long before a 26 gauge piece of tin. I have no idea how to calculate this or if it even matters to your question.