Occasional athlete,
The consensus among the scientific community on the 3min test is that it is not reliable test for CP. Andrew Coggan himself told me this test needs to go into the waste heap of history.
Secondly, CP and FTP are not really interchangeable. CP, in terms of wattage, is tad bit higher, It is the boundary between heavy and severe intensity and thus is the maximum metabolic limit beyond which instability occurs.
Please use a combination of 4 and 20 min tests in a regression model to estimate your FTP. If you want a simpler no brainer test, it would be a 40K TT. The other method , which is most popular, is the 20min FTP test. If you’re going to do the 20min FTP test, you need to include the 5 min all out effort, so ideally you would follow the original protocol set in the book ‘Training and Racing with a Power Meter’. To derive the FTP, that is the contentious point among various practitioners. I’d use a range between 90-95% of the 20min average power and see what correlates best with your 40K effort.
Regards,
Ron