# "Mathy" pace calculation question

I'm using this year to begin my OWS as the goal transition.....

away from triathlons (my body said, "ENOUGH" with the running).

Anyway....this year's goal is to swim in as many different conditions as possible, and start to work out feeding/nutrition and all that.

I've done one formal event, current assisted, and had a blast.

The rest of my swims have been in the lake -- launching from a friend's house.

When looking at all of my training swims, I am generally holding a 34-35 minute mile (including time spent feeding). The lake is dam controlled, so there is sometimes current if we're in the river channel.... or wind.

For my current assisted swim, though, I held a 26-ish minute mile. The said that there was 13k cps being released from the dam that day. From what I can gather, that's about a half-mile per hour flow rate.

1) Is that approximate flow rate correct?

2) How do I calibrate my pace while also taking in to account the flow rate? Is the flow rate subtractive in some way? In other words, is there a way to estimate what my pace might have been over the same distance if there'd been no flow -- having only the information of flow rate and actual pace?

Unfortunately (or maybe fortunately), I'd forgotten my watch at home that day, so don't even have stroke rate data to examine for the down-stream event. But, it was a glorious "naked" swim..... I only almost ran into one channel marker buoy. (Dark green channel markers are really hard to see from water level!)

## Comments

Interesting topic!

Estimating the speed of a river based on flow rate (CFS) is complicated, and depends on factors like the width and depth of the river, and also where you are located within the river (in the middle? on the edges?).

Further reading here: https://www.pitt.edu/~jdnorton/sail/Speed/index.html

If you are fairly confident in your swim speed (calibrated in other swims in "flat" water), you can derive a rough estimate of the net benefit you gained from currents. If I can swim 10 miles in 4 hours (2.5 mph), and I covered 10 river miles in 3 hours (3.33 mph), then the river was probably moving about 0.83 mph on average.

@KarlKingery is our resident expert on this, and may have additional thoughts.

So basically, across similar distances, the aid that a current gives you is roughly subtractive from your “flat water” pace.

So, if I have an average flat water pace gathered over time across a variety of distances, I could use that as a rough estimate as the basis for determining benefit of current. Unless I’m misunderstanding something.

@Sara_Wolf , Yes, you have the general "drift" of it (Pun intended). Like @evmo said, the velocity of the water depends on the flow rate and the cross-sectional area of the water. The equation is Q=VA. (Q-flow rate; V-Velocity;A-Area). This equation is valid at any single location, but can easily be misused if it is being looked at over a range of locations. So, if you are moving (i.e. swimming) you need to be careful about where it is used because you may get a result that either says there is little to no current over much of the swim, when in fact there may be a significant current over a short distance or vice versa.

"Q" is usually a derived calculation based off of area and velocity at a known and stable location. It us usually published by the USGS (in the US) at different gauges.

Also, if you are in a current, the location you are in the channel/river/strait/etc. significantly effects the speed at which you go. Simply put, "V" changes over a cross-section. If you go out to a river, you will usually see faster moving water on the outside half of the bend (maybe 2/3 across the channel) and you may see very still water on the inside bend. "V" is also generally (not always) higher in the deepest part of the channel. If you want a direct measurement, you need a flow meter such as a pygmy flow meter and an idea of how fast you are actually moving.

Also, the "A" (area) is sometimes hard to find. You need to have good measurements of the depth to back into a good estimate of the current.

If you are in a current, the fastest water will be just below the surface in the center of the direction of momentum, so a swimmer will catch more flow than a stick, but only barely. (This is the same reason that oranges float down a river faster than ping-pong balls). For all intents and purposes, your "floating vector" can be assumed to be in the direction of the current at the same magnitude of the current. Your "swimming vector" will be in the direction you are swimming with a magnitude of the speed in which you swim. Your final end speed is the addition of these two vectors.

SO-if you are swimming directly up-current, then you can subtract the current speed from your speed and get a good idea of the average velocity. Similar, for swimming downstream, you can add it.

If, however, you zig zag (like me) then the current may have been moving faster than you were when you were swimming.

Wind also has a big impact on the surface velocity of the water, but that is a whole other topic.

Hope that this answers your question.

@Karl_Kingery

Awesome....thanks.

I’m definitely not looking for hard data..... ore along the line of a “gist”.....if only that was actually a unit of measure!

This particular event had some local swimmers in it who said that the fastest “line for that particular stretch of the river was actually about 30 yds off shore along the path of the course. We hugged on side of the river ... stayed outside of the channel markers ... so had some in and out curves that we swam, but not too badly.

I likely zig zagged, but had forgotten my garmin at home so don’t have actual track data to be certain. It was a nice “ naked” swim, then.

So while I had my total time, and what the course was supposed to be in terms of length, I likely swam more than the 4.5 miles started for the route.

Still....... knowing a general ideal of the benefit will help me have a better idea of how much I’m either progressing (or not).

Sounds like my answer was perhaps too far on the "mathy" side and I may have missed the boat with my response. If you need to back into your pace, you need to make some assumptions about the average speed of the water over the course of your swim.

Assuming you don't know river depths and cross-sectional areas, one approach would be to do the "stick test" if you are not too far away from the place where you swam and if conditions are similar to the day you swam it on. This is a method where you throw a stick (or something else floatable) into the river and count how many seconds it takes to go a known distance (10yds or something). if you divide the distance by the time it takes for the stick to go the distance, you will get a rough idea of the approximate velocity at one spot in feet per second (FPS). Do this at a few spots on the river along your swim route (top, bottom, middle) and convert it to mph. (or just estimate the velocity in fps if you can eyeball it)

Then multiply that water velocity by the time you took to swim the course to calculate your "float distance" and subtract it from the total distance to get a "Swum distance". Use the answer and divide it by the time you took to swim the distance and you will get a very rough average pace. Depending on your measurements and assumptions, you should theoretically be in the ballpark.

I spent an entire commute one day after Swim the Suck trying to figure this out (since there's literally no way I could have held that pace without a current assist). I don't remember what I did but I ended up deciding that it was about equivalent to 8 miles w/out the current assist for me (2017).

As bad as commuting is..... there is the added benefit to being able to do mathy things without worrying about rear ending someone!