Each material has it's own shrink,iron, brass or aluminum, so therefore each has it's own shrink numbers. When calculating a dimension you have to add shrink, draft and finish and to be safe you have to add a little more. Better to have a touch more than to start over.
I threw together a quick spreadsheet which will allow you to calculate the thermal expansion for different materials. You can select the material from a drop-down list, enter a length and starting/ending temperatures, and get the results in inches or mm.
I'm not sure if I got the access permissions right on this, so if someone can try it out and let me know if it works for you I would appreciate it. Any other suggestions for improvement would be appreciated.
This is a google spreadsheet so if you access the link below you should be able to use it online.
Paul - thanks for the feedback. After much experimentation and web research I have concluded that Google spreadsheet will not enable the required sharing mode. Consequently, I have created a downloadable spreadsheet (in both LibreOffice and Excel formats); I also made some additional improvements to the spreadsheet.
You can find the spreadsheets here (scroll down to Thermal Expansion):
By the way, in answer to the original posting, for cast iron a cube at 2200 deg. F with dimensions of 1.123" will shrink down to 1" at room temperature. Other materials will give other answers, of course (which you can now determine with my spreadsheet!).
In closing, I will note that I had planned to do something like this spreadsheet anyway, as I am planning to do some experiments with shrink-fitting. This spreadsheet will help me estimate some initial parameters.
Edited to add this: If anyone downloads this spreadsheet and tries it out, I would appreciate some feedback.
Chiptosser - thanks for the feedback. I found an error in my spreadsheet (missing 0 resulted in factor of 10 error); I have corrected the spreadsheet.
Correction: for cast iron (not just iron as previously) a cube at 2200 deg. F with dimensions of 1.0106" will shrink down to 1" at room temperature, equivalent to 0.127"/foot. Other materials will give other answers, of course (which you can now determine with my spreadsheet!).
Chiptosser, this is closer to your answer, which I assume is based on the rule of thumb of 1/8" per foot. Thanks again for catching my error.