trevtheshed wrote:Well, John, I think you're there, or very, very nearly. Well done! Sorry about that last bit. Not sure why that didn't get into the book!

It was probably not required for those less mathematically challenged. I'm sure there's whole bunch of people out there that have already got it up and running without having to hassle you like us thick heads.

trevtheshed wrote:
Some of the residual differences may be computing "differences". For example, my computer (Toshiba Tecra running XP) gives:

αat (alpha at) = 2512.222087

αab = 2336.950779

αbt = 15972.83733

...which for a simple multiplication are some quite big differences from your numbers. (I used your values in my model, BTW, and it made very little difference, but if this sort of thing is happening on every operation, you can imagine what would result).

Interesting...

I just hand calculated the alpha products based on your input parameters and got:

alpha at = 2515.72187

alpha ab = 2340.20639

alpha bt = 15972.8378

in the spreadsheet I calculated the area and mass values of the air plug and the value for k and had

alpha at = 2506.61132

alpha ab = 2331.73146

alpha bt = 15792.83733

by removing the calculation and changing the parameters to the values in the book I got the same as the hand calculations. If you used Excel to do the calculations then I suspect you are right and it's all to do with rounding as I know that regardless of how the cell is formatted Excel keeps the full value to n significant digits in memory and uses that value in further calculations. It probably doesn't fully explain the plot shape but it certainly wouldn't help as I am wondering about how this problem could be compounded by the IM functions given that there is probably a lot of rectangular to polar conversions and vice versa going on in the background

I've copied all the intermediate values to the front sheet of the spreadsheet and attach it to give you an idea where I'm at.

trevtheshed wrote:
I tried a few quick changes, but no simple change would come up with anything that gave a closer approximation to your curve. It seems it would have to be changes across a number of areas that are required, hinting that the issue may be in the calculations/rounding etc. I guess you could have a go at doing the same and see if anything points to one of us making a coding error.

I think any coding error will be mine. I've passed my spreadsheet to Dom and asked him to go through it and see if fresh eyes can see anything. It's easy overlooking the obvious when reviewing your own work.

trevtheshed wrote:
When I was putting this stuff together, one of the early things I did was to code up and replicate Christensen's Fig 3 results from his 1984 paper (full ref. in the book). I matched his curves pretty well exactly, so I felt reasonably confident that the way I approached that was OK and approached the 4-DOF model calcs the same way. Maybe that's something you could try, which might check out the computers a bit.

I'll look it up and get onto it.

trevtheshed wrote:
Anyway, a good effort, mate. I'm off to get some shut-eye.

Thanks, it's a lot of fun in some sort of masochistic way. A bit of a way to go yet but very much appreciate your kind assistance.

Os.