I suspect these are related:

1. Please characterize the effort that a helicopter expends to hover in place. Work is force dotted with distance, but distance here is 0, so it seems the usual physics quantification of work yields 0, which I find highly unsatisfactory. Perhaps impulse is relevant, but we don't typically use impulse to characterize effort and it has strangeness of it's own. Please explain.

2. Characterize the effort that a cyclist expends to climb a hill with constant gradient theta at two constant speeds, s1 and s2 where s2 > s1, assuming there is no energy lost to friction or air resistance. The force required at the two speeds is equal (only need to overcome another constant force, gravity, in both cases), so the total impulse over some time period t is equal. Yet at speed s2 the cyclist has clearly accomplished more than at speed s1. But work doesn't seem a fair measure either -- the impulse applied was the same!