How can I calculate a helical “arc length”, “radius” and “height”?

Question

Known given:
Helical climbing angle: constant 20 degrees
Radius r of the helical coil: 270 mm
Revolutions: 0.5

The main problem is the 20 degree climbing angle. So far I haven’t found a formula that relates the “constant climbing angle” with the above.

Answer 1

sumzrfun hits the basic principle. The distance around the 'cylinder' is r (theta), where r is the radius and theta is the angle.

There's 2 PI radians in a circle, so half a revolution is PI radians. That gives you r * PI for horizontal distance around the 'cylinder'. (The 2 PI radians is why the formula for circumference of a circle is 2 PI r).

If you remember your trigonometry, the distance of the side adjacent to your angle is c * cos(phi) where c is the hypotenuse and phi is the angle of incline (just two keep from confusing the two different angles). You know the adjacent side and want the hyptenuse. Therefore, divide your result by the cosine of 20 degrees to get the distance along the helix.

You should get about 904 mm.

Answer 2

Imagine a circle with radius r, the circumfrence is 2*pi*r.
Now imagine a right triangle. If one side has an angle A with hypotenuse and the length of the side is l then the length of the hypotenuse is l divided by cosine of A, that's the key idea. In the helix the same thing happens that is the arc length is 2*pi*r * number of revolutions / cosine of climbing angle. In the case here it becomes :
2*pi*270*0.5/cos(20) = 902.7 mm

Answer 3

Imagine the helix on the surace of a cylindrical sheet of paper. Cut the cylinder parallel to the axis and fold it out flat.
You now have a sheet of paper with lots of straight lines sloping up at 20° - and your paper's width is the circumference of the original coil. It is not difficult to work out the rest - you only want half the width of one of the slopes, so a little Pythag and some basic trig will be fine.

Hope this will be enough ! Cheers.

Answer 4

nicely, as quickly as around is 2pi*r. If there are N turns interior the coil, then the excellent length is N * 2pi*r. so which you're able to be able to desire to verify what N is. least complicated thank you to estimate it extremely is count form the style of turns in a million cm by potential of conserving it up against a ruler, then multiplying by potential of 5 to get the style in 5 cm. i'm puzzled by potential of your description although. you're saying the cord basically is going around 360 ranges. it somewhat is one circle. you're asserting that your spring is a single circle, not a coil? The circumference of a circle is in simple terms 2pi*r. regardless of whilst you're taking that circle and stretch it out, if the cord basically is going around as quickly as this is 2pi*r.