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Braincurdler - calculating length of arc

Trying to work this out for a design project, but I can't wrap my head around the solution. Note - the arc does not meet the orange line on the right at a 90 degree angle; it is slightly acute

Screenshot 2019-03-21 at 15.51.00.png

(edited 5 years ago)

Reply 1

RDKGames

Study Forum Helper

Original post by XMaramena

Trying to work this out for a design project, but I can't wrap my head around the solution:

You can model the arc as an upside down parabola, and the hypotenuse as its horizontal axis.

Then once you have the eqn. of this parabola, use the formula for the arc length.

Reply 2

the bear

is it supposed to be an arc of a circle ?

:holmes:

Reply 3

the bear

if it is a circle then you can find the radius using a bit of algebra.

Reply 4

XMaramena

Original post by the bear

is it supposed to be an arc of a circle ?

:holmes:

It is an even arc, but will actually be a curved roof beam, not part of a full circle. I have an estimate of 3700, but not an exact measurement. After some googling, it appears I have a half chord and a sagitta, and need to somehow find the formula to calculate the length of the minor arc.

This is far too heavy for my feeble brain.

(edited 5 years ago)

Reply 5

the bear

Original post by XMaramena

It is an even arc, but will actually be a curved roof beam, not part of a full circle. I have an estimate of 3700, but not an exact measurement.

i worked it out as the arc of a circle and got 3667 units

Reply 6

XMaramena

Original post by the bear

i worked it out as the arc of a circle and got 3667 units

Would the angle between the black bottom line, and where the arc meets it on the left, possibly have come up in that wizardry? Something around 30*?

Reply 7

RDKGames

Study Forum Helper

Just do it on a program... takes seconds:

ArcApprox is the approximate length of it, accurate to 5 d.p

(edited 5 years ago)

Reply 8

XMaramena

Not sure what that program is you've used, but what happens if you reduce the length of the black horizontal line down to 3500?

Reply 9

RDKGames

Study Forum Helper

Original post by XMaramena

Not sure what that program is you've used, but what happens if you reduce the length of the black horizontal line down to 3500?

It's Maple.

Reply 10

XMaramena

Original post by RDKGames

It's Maple.

I must look into that, looks super useful. By mapping it in sketchup in my plans and working backwards from the volume of the component, I've come up with a length of 3694, which probably accounts for the overlap of the beam's angle to the edges of the frame:

Screenshot 2019-03-21 at 16.24.19.jpg

Reply 11

the bear

Original post by XMaramena

Would the angle between the black bottom line, and where the arc meets it on the left, possibly have come up in that wizardry? Something around 30*?

i found the length of the blue line using pythagoras: this then becomes a chord on the circle sector
.

then you can work with a right angled triangle whose sides are r, r-100, and half of the chord length. r is the radius of the circle.