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aathithiya · Dec 20, 2009, 12:21 AM

I want to know the chord length of helix. The item is a cast iron wear shoe with 1/8 of helix 1675 outside diameter and with a pitch 0f 1220, kindly tell me how to calculate the chord length for 1/8 of helix i.e. 45 degree.
My name is nava.

galactus · Dec 20, 2009, 05:20 AM

What is a wear shoe? This problem is poorly described. Please explain what pitch 1220 means?
We can find the length of a helix by knowing some pertinent information, but this one I do not get. What is a chord length of a helix?

aathithiya · Dec 20, 2009, 07:37 AM

Wear shoe is a white castiron helical segment used in screw conveyors.

I want to know how to find the chord length of a helical segment. The helical segment have diameter of 1675mm. Pitch of the helical segment is 152mm. This helical segment is made of 1/8 of a helix with 1220mm pitch of one full turn of helix.

galactus · Dec 20, 2009, 08:50 AM

Originally Posted by aathithiya

wear shoe is a white castiron helical segment used in screw conveyors.

I want to know how to find the chord length of a helical segment. The helical segment have diameter of 1675mm. Pitch of the helical segment is 152mm. This helical segment is made out of 1/8 of a helix with 1220mm pitch of one full turn of helix.

I am not totally sure what you mean. Therefore, I will give you an example of how to find the arc length of a helix and maybe you can use it as a templete for your problem.

Let's say we have some tubing with a diameter of 1/2 inch wrapped around a cylinder that has diameter 12 inches.

What length of tubing will make one complete turn around the cylinder in a distance of 20 inches measured along the axis of the cylinder?.

A helix can be represented parametrically by $x=a\cdot cos(t), \;\ y=a\cdot sin(t), \;\ z=c\cdot t$

Where $a=\text{radius of cylinder plus radius of tubing}=6.25 \;\ inches$ and $c=\frac{20}{2\pi}=\frac{10}{\pi}$ ,

so that the radius of the helix is the distance from the axis of the cylinder to the center of the tubing, and the helix makes one turn in a distance of 20 inches( $t=2\pi$ ).

The length of the helix is $2{\pi}\sqrt{6.25^{2}+(\frac{10}{\pi})^{2}}\approx 44 \;\ inches$

To find the arc length of a helix, we use calculus. Specifically, the arc length integration formula.

aathithiya · Dec 21, 2009, 06:46 AM

That was really needful to me sir. Thanks for that reply mail. You have explained me how to find the arc length of helix with one complete turn, but tell me sir, how to find the true chord length of a helix segment, that is when a helix with one complete turn is cut into 12 equal segments. I want to know how to calculate the chord length(not the arc length) of that 30 degree segment.

InfoJunkie4Life · Dec 21, 2009, 06:52 AM

aathithiya is defining pitch like you would on a roof. You don't give it in degrees, but rather in ratios. I think what is going on here is that the standard whole helix being worked with has a diameter of 1675mm and after one full turn of the helix, would measure 1220mm long (Cylindrical Height). If you were to transform this into a triangle, the height would be 1220mm the base would be the circumference and the hypotenuse would be the length of the helix chord.

$C = \pi{D}$

$C = \pi{1675}$

$C= 5262.16$

The hypotenuse is found via:

$a^2 + b^2 = c^2$

$\sqrt{1220^2 + 5262^2} = c$

$5401.58 = c$

That is a full helix.

The helix presented is actually only 152mm long.

Thus we get a similar triangle with smaller measurements.

$\frac{152}{1220} = 0.1246$

$0.1245 * 5401.58 = 673.04$

Thus our new triangle has a height of 152 and a hypotenuse of 673.04

Law of similar triangles.

aathithiya · Dec 21, 2009, 08:30 PM

Hi InfoJunkie4Life,
Thank you very much for the reply. I have attached a drawing with this reply regarding the helix segment. The answer you gave is for the 45 degree segment, tell me precisely what will be the chord length for the helix segment with 3mm gap on either side as per drawing.

Alty · Dec 21, 2009, 08:35 PM

If this is a homework assignment then we need to see your work first. We won't do your homework for you, it's against the rules of this site.

So, what equation have you come up with?

What work have you done?

Show us and then we can help you further.

aathithiya · Dec 21, 2009, 08:49 PM

Hi Altenweg,
This is not a home work. I am a manufacture of ferrous and non ferrous castings. I got a helix segment to manufacture, I am trying to find the chord length for that. Kindly please help me in this regards.

Alty · Dec 21, 2009, 09:45 PM

Can you get a close up picture? I really can't see the writing.

Unknown008 · Dec 21, 2009, 10:42 PM

Ok, my take of this:

Circumference (when helix is squished into a full circle) = 1675 pi

Length of chord (chord of flat circle) = $\frac{1675 \pi}{360} \times 30 = 438.5$

Now, taking along vertical:
Height = 1220 mm
Height of chord = $\frac{1220}{360} \times 30 = 101.67$

Having horizontal and vertical dimensions of chord, use of Pythagoras Theorem to approximate the length of chord:

Chord (actual) = $\sqrt{438.5^2 + 101.67^2} = 450.1\ mm$

Is that what you are asking for?

aathithiya · Dec 29, 2009, 01:40 AM

29/12/2009

Unknown008,
You calculated length of chord for flat circle (that is helix squished to flat circle) = 1675pi x30 divided by 360, but what you calculated is arc length of the flat circle. We have to calculate chord length of the circular segment which is going to be our adjacent side of the right angled triangled.
chord length of the 30 degree segment = 2 x sin(15)x hypotenuse(which is our radius)

= 2 x sin15 x 837.5
Chord length of 30 degree segment = 433.52mm

therefore actual chord of helix = square root of(433.52x433.52) + (101.67x101.67)

Chord length of 30 degree helix segment =445.28mm.

Unknown008 · Dec 29, 2009, 01:48 AM

Sorry, I forgot about it:o

I needed to find the flat chord length, then apply the height.

Flat chord then is 433.52, then use pythagoras.

My mistake is easily seen :o

aathithiya · Dec 29, 2009, 03:23 AM

Anyway unknown008 it is because of your previous work I was able to sort things successfully, Thank you very much.

aathithiya · Jan 21, 2010, 07:41 AM

how much of length is needed to roll a plate of 50mm thick to form a cylinder of outside diameter 500mm, height of cylinder is 250mm. I know that the circumference= 2 X Pi X radius of cylinder, from this we can calculate the length of plate for thin wall sheets or plates but when the thickness is increased how to calculate the length for rolling a cylinder?

Unknown008 · Jan 21, 2010, 07:50 AM

Is it a hollow cylinder? If yes, find the circumference of the circle making the base of the cylinder and the width is given by the height of the cylinder. The thickness is already given.

aathithiya · Jan 21, 2010, 08:38 AM

Yes, it is a hollow cylinder. You are right and the answer will be correct for thin walled cylinder, but when the thickness is more say like 50mm or 100mm then what will be the answer for the length?

Unknown008 · Jan 21, 2010, 08:54 AM

Well, it's obvious that if you want a 'perfect' cylinder, you'll have to have a prism with a trapezoid cross section.