A while ago I was thinking about how river current slows down the racers in the CGT Kayaks and Paddleboards race series on the Imperial River. It's obvious that the current slows you down when you're paddling against it, and speeds you up when you're paddling with it. It's the same principle as walking the right way on an airport moving sidewalk vs. the walking the wrong way on an airport moving sidewalk; going with the flow gets you to your destination faster, going against the flow gets you there slower. What's less obvious is how the flow affects the time of a round-trip journey, where you go with the flow one way but have to go against the flow the other way. Does the time saved going with the flow make up for the extra time it takes when going against the flow?
It turns out the answer is, "No." You always lose more time going against the flow than you save going with the flow. There's not much difference if the current is very slow relative to the speed of the paddler, but the stronger the current is, and the slower the paddler is, the more the paddler's overall time is reduced relative to her time on a course with equal distance but no current. If it's hard to wrap you mind around that, maybe the math will convince you.
The formula for the total time it takes to complete a round-trip course up and down a flowing river is: t = d/(v+c) +d/(v-c)
d = 1 way distance of course
v = racer speed relative to the water
c = river current speed
t = time to complete course
If you don't want to do the math yourself, here's a pre-made spreadsheet you can use to see how much your speeds and trip times are affected by a river current. If you don't know what the river current is, the spreadsheet can figure it out for you from the difference between your upriver and downriver speeds.
There are some simplifying assumptions made in these calculations. One assumption is that the current is uniform in the river- it doesn't increase or decrease as you go upriver or downriver, or shift from one side of the river to another. Of course we know that's not true. In fact, we may be able to cheat the river current time penalty (at least to some extent) by picking the swiftest part of the river when paddling downstream, and picking the slowest part of the river when paddling upstream. I'll certainly be trying to do that in the CGT Kayaks and Paddleboards race tomorrow morning.