John Renbourn; 1944 – 2015

John Renbourn

John Renbourn, who has died aged 70, was one half of the powerful guitar duo of Pentangle, the innovative jazz-folk band of the 1960s and 70s. While his fellow guitarist, Bert Jansch, brought great emotion and inventiveness to his playing, it was Renbourn who provided a high level of technical accomplishment. They revelled in one another’s virtuosity.

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Re-sizing Array Functions

The recent updates to the ConBeamU spreadsheet contained two new functions for entering and re-sizing array functions, and since they will be useful on any spreadsheet containing array functions (which here means almost all of them) I thought they deserved a blog post of their own.

I have added the new functions to the CSplineA spreadsheet, which can be downloaded from:

The code for the new functions was taken from: Technicana .  The only changes I have made are:

  1. If the original function failed for any reason the array function being re-sized was deleted.  I have added a couple of lines so it will be re-written back to the spreadsheet.
  2. I have changed the shot-cut codes as detailed below.

To use the functions start by entering any function that returns an array in the top-left corner of the desired output range:


To expand the function to display the full extent of the array, press Ctrl-Shift-S:


To re-size the array select the required range and press Ctrl-Shift-R:


To move the array to a range overlapping with the original range (with the new range to the right and/or below the original), select the top left cell of the new range then press Ctrl-Shift-S (for the full array), or select the output range required and press Ctrl-Shift-R:


If the destination range is either to the left of, or entirely outside, the original range then the array function must first be copied to the top-left cell of the destination range, then proceed as above.

A word of warning: the functions clear the undo stack, and will write over any data in the output range without warning, so if there is any danger of the output range writing over any data you need, save your work before proceeding.

Posted in Arrays, Excel, UDFs, VBA | Tagged , , , , , , | 2 Comments

ConbeamU Update Update

Following some comments from 4Step on the last ConbeamU update, and a thorough check of results against Strand7 results, I have posted a new version that fixes a number of issues with the previous one.  The new version number is 4.01, and it may be downloaded from:

The file is a free download, and includes full open-source code.

The download zip file also contains a summary of the check runs performed with the Strand7 finite element software. In Strand7 I have set up a model with 15 separate continuous beams, with the same loading but different support conditions, ranging from a single cantilever to a 3 span beam with cantilevers at both ends. These beams have been analysed in Strand7 and ConbeamU with different restraints applied at each support, and the results are compared in the Check Conbeam spreadsheet included in the zip file. The results show near exact agreement in all cases.

Continuous beams model in Strand7


Strand7 Results


Strand7 and ConbeamU results compared in Check Conbeam.xlsb


Posted in Beam Bending, Excel, Frame Analysis, Newton, Strand7, UDFs, VBA | Tagged , , , , , | 3 Comments

ConbeamU Update; defined support deflections

As promised in a recent post, I have updated the ConBeamU spreadsheet to allow defined deflections to be specified at any support.

The new spreadsheet (including full open-source code), can be downloaded from

In addition to the support deflections the new spreadsheet has the following changes:

  • In addition to providing a list of output point positions it is now possible to specify the number of points required for each span.
  • At support positions output is now provided for the shear and moment on either side of the support.
  • VBA routines are now provided to simplify the entry or re-sizing of array functions.
  • Behind the scenes, the VBA code has been re-arranged to allow many of the functions to be used in the frame analysis spreadsheets, reducing duplication of code.

Defined support displacements and the new input of output points is shown below:

The output from this data is similar to the previous version, except that output X values are included in the output:


The output points may also be defined from a list as in the previous version:


Note that where the same output point is defined twice, at a support or point load position, the output now returns the shear force and moments immediately to the left of the point, followed by the values immediately to the right.

The array entry routines are illustrated below.  Any of the functions may be entered in a single cell:


Then press Ctrl-Shift-S, and the full array will be returned automatically:


The array range may also automatically be reduced in size.  Select the required output range and press Ctrl-Shift-R:


More details of the array entry routines are provided on the spreadsheet:


Posted in Arrays, Beam Bending, Excel, Frame Analysis, Newton, UDFs, VBA | Tagged , , , , , , , , , | 12 Comments

Falling Faster

A recent paper by  Alexander Klotz of McGill University, Montreal, has stirred a bit of interest in the pop-science press.  The paper looks at the old question of the time taken to fall through a hole passing through the centre of the Earth, and back up to the surface at the opposite point on the Earth’s surface.  This calculation makes the usual assumptions of a perfect vacuum, and zero friction, but instead of the usual simplification of assuming the Earth to be of constant density, it allows for the actual estimated varying density along the length of the hole, and finds that the transit time would be reduced from 44 minutes to just over 38 minutes.

There is a good article on the paper at How long would it take you to fall through Earth?, and a rather more excitable one at How Long Would It Take To Fall Through The Center Of The Earth?

The latter article suggests that “Klotz went where no physicist has gone before”.  I suppose that is possible, but I know that at least one engineer has looked at the question before, I have on this very blog:

The hole through the middle of the Earth – revised transit time

I came up with a time of 38 minutes and 57 seconds, compared with 38 minutes and 11 seconds found by Klotz.

Another surprising finding was that if a constant acceleration of 9.81 m/s2 is assumed all the way to the centre, then -9.81 m/s2 all the way back up to the surface, the transit time is only reduced to 38 minutes.  The graph below shows what is happening; the effect of increasing density is that the acceleration does remain close to constant over much of the journey, and it is only in the final stages that the velocity assuming constant acceleration becomes significantly faster than the velocity based on the actual (estimated) density.


More links on the topic of holes through the middle of the Earth:

The hole through the middle of the Earth – moved to the Equator

The hole through the middle of the Earth – filled with air

Elegant solutions, Column buckling, and the hole through the middle of the Earth

Posted in Excel, Maths, Newton | Tagged , , | 4 Comments