Crooked Church Spire

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

A crooked (or twisted) spire is a pyramidal tower with a twist relative to its base. This can be by design or as a result of changes over time caused by weathering [1].

[more]

This Demonstration simulates the twisting process of a pyramidal tower of fixed height caused by an expansion of its lateral edges due to faulty materials (undried wood), temperature, or humidity.

A classic example of a crooked church tower is the one in Chesterfield, Derbyshire, England [2].

[less]

Contributed by: Erik Mahieu (June 2015)
Open content licensed under CC BY-NC-SA

Details

The twisted lateral edges of a right pyramid have the parametric equation of a conical spiral:

.

The base of the pyramid is a -sided regular polygon (and is also is the number of lateral faces of the pyramid), is the height of the apex, and (equal to in this Demonstration) is the radius of the circle through the vertices of the base.

Using the built-in Mathematica function ArcLength, the length of the lateral edges can be calculated using the formula:

.

From this, one can calculate a numerical approximation of the number of twists over as a function of the arc length . Using regression analysis, one finds this fitted model:

.

The twist angle is taken to be or the angle by which the pyramid is twisted relative to its base.

References

[1] Friends of Chesterfield Parish Church. "Notes on the Church." (Jun 9, 2015) www.friendsofthecrookedspirechesterfield.co.uk/notesonthechurch.php.

[2] Wikipedia. "Church of St Mary and All Saints, Chesterfield." (Jun 9, 2015) en.wikipedia.org/wiki/Church_of_St _Mary _and _All _Saints,_Chesterfield.

Permanent Citation

Erik Mahieu

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send