Detection risk at what range

[Yskonyn]

I have a few questions regarding detection. In almost all articles you read that a speed of 1/3 keeps you from being detected by warships, but if you're intercepting a convoy you have to come inbound at a much higher speed.
Are there any references regarding running the risk of being detected versus range to convoy (or target) and inbound speed?

Especially if the convoy is steaming along a trade route, intercepting takes a fair bit of speed to get into a good firing position.
Are there any known 'danger areas' as far as distance to warships are concerned for being likely to be detected?

I find that my strategy is often hampered by my fear to be detected, leaving me either at too great a distance or not even able to keep up with/intercept the targets.

Of course lone merchants have no detection capabilities, but it's the escorted convoys that pose the problem.

Any help is greatly appreciated!