But if you match the effort equally, then I reckon the 1:4 theory is about right.
Hmm, I like this idea. You could (in theory) get a meaningful comparison by matching effort levels i.e. by HR. So for example, I would probably run a marathon (42k) at HR=135*.(Complete guess says 5hr pace. Ish. So 8kph).
Now, I know I can ride 320miles (probably more) in around 24H at that heart-rate.(On a nearly flat course.) That's 13mph-ish.
So 1 question might be:
at what point would things start to ache/break to the same extent as on my 5hr marathon?
It's got to be over 600k, possibly 800? That's around
17:1 distance (using 700k/438m) or
7:1 time (using 34h)
But then I've never trained much in running, so there will be huge bias there.(And there's probably some errors from all my mixed units).
So of course the answer you get depends on what variables you keep constant! I've assumed running the marathon at a conservative HR - others might run it much harder. And note the flattish course assumption. (On a velodrome it would be even higher)
*HR is moreoften round 150 when I'm running, but if I'm really disciplined I can keep it round 135.