Human energy depends on oxygen

Here are some things to consider in response to your questions:

- Is there a generally accepted protocol for investigating running economy with measuring oxygen consumption during sub-maximal running (with controlling speed, i.e. on a treadmill)?

Answer: Not really. What you exactly want to investigate will determine the exact protocol (e.g. duration, speed, condition).

- Specifically, how long would you have runners run in each condition (assuming you want to compare 3 to 4 different conditions) in order to prevent possible fatigue effects?

A steady-state oxygen consumption is usually reached after 2-3 minutes, so if you collect data during 1 minute you could use 4-minute conditions. 3-4 minutes is therefore also the minimum period required per condition. The number and order of conditions and rest between conditions can be manipulated to minimize fatigue.

- Given they know their 10k race performance (e.g. 40 minutes), how fast would you ask them to run?

Also this depends on what you want to know. Runners are most economical at the speed where they run most at. But if you want to have a valid comparison of their technique then you should match the speed. Usually, studies use a speed of up to 12 km/h because this is a speed where most recreational runners also have a RER

Human energy depends on oxygen

Four different sub-maximal running speeds, four minutes each, last minute as reference, five-minute rests+heart rate down to rest value or at least