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HomeNL-2018-03 Estimating Speed

River Math
Estimating River Speed

March 2018
by John Rich

While paddling on a river, have you ever wondered how fast the water is flowing?  Well, in this article I intend to give you a way to estimate that, because that can be useful information for a paddling journey.

To accomplish this feat, carry out the following steps.

Bring your boat to a stop somewhere in the river that represents the flow rate in which you are paddling.  Someplace like a beach with the water flowing past, holding steady in an eddy behind a big rock,or holding on to a snag sticking out of the surface. You can do it at the put-in, during a rest break, during lunch, or anywhere you might want to calculate your river speed. 

Be aware that the speed at your point of measurement may not be the same as the speed elsewhere on the river. On a straight stretch, the flow in the center will probably be faster than on the sides.  On a curve, the flow on the outside of the bend will be faster than on the inside of the bend. You also can't do this while moving with the water, as then you would only be measuring the difference between your canoe speed and the water speed - your boat must be stationary.

Next, what is your boat length?  An 18-foot tripper, or a 12-foot sit-on-top?  It doesn't matter, as long as you know the length. That's a number you should already know, and if not, measure it and find out.

Now, all you have to do is count the number of seconds it takes for something to float past the length of your stationary boat  A leaf, a blob of foam, a bug, whatever.



Make sure you know how to count accurate seconds in your head.  "One-Mississippi, Two-Mississippi", or "One one-thousand, Two one-thousand".  Practice it while watching a clock with a second hand and get your cadence correct. Or if you have a wristwatch with a second hand, check it to time the passing of the leaf.

Now you have the two pieces of data you need to calculate speed in miles per hour: time and distance.

If you can remember this, it'll make it easy: miles per hour (mph) equals almost exactly two-thirds of the number for feet per second (fps). So, for example, 6 fps = 4 mph. Mathematically, you would divide 6 fps by 3 to get the number for one-third of 6, or 6 ÷ 3 = 2.  And then, since you want two-thirds of the fps speed, you multiple that one-third number by 2.  So, 2 x 2 = 4 mph. 

Putting in all together into a formula: MPH = FPS / 3 x 2.  

Another way of getting two-thirds of a number, is to start with the whole fps number, and subtract one-third from it: FPS - (FPS / 3), 6 - (6 / 3), 6 - 2 = 4 mph. 

Or just do it intuitively.  If the fps is 6, you automagically know that one-third of six is 2, and subtract that from the 6: 6 - 2 = 4 mph.  

That's the math.  You don't really need to remember the darned formulas.  Just remember that if you add one-third to the fps you get mph.  That's the simple way.

Okay, now let's exit the classroom and try this with a real-world example out on the water.

Let's say it takes 3 seconds for a leaf to float past the length of your 18-foot long canoe.  If the leaf travels 18 feet in 3 seconds, then that is a speed of 6 feet per second.  18 ft / 3 secs = 6 feet per sec.  Converting to miles per hour, one-third of 6 is 2, so two-thirds of 6 is 4.  And there you have it!  The river speed is 4 mph. 

How about a little more complicated example where the numbers don't divide nice and evenly.  Let's say the leaf floats past your 15-foot boat in 3 seconds.  That's 5 feet per second.  One-third of 5 is about 1.7, and 1.7 x 2 = 3.4 mph.


That's how fast the river will be pushing you along if you're just sitting doing nothing with your paddle.

To get your total speed, you have to add your paddle speed to the river speed for total miles per hour. Paddle speed is usually 2 to 3 mph for most people on average over time, on a leisurely non-racing trip.  So, river speed of 3 mph + paddle speed of 2 mph = 5 mph total.

How do you calculate your paddle speed?  The same way you did it for river speed: time and distance.  On flat, un-moving water, count the number of seconds it takes you to move your boat past a fixed object from bow to stern.  Do the math.

Or, you can just jump directly to calculating your total speed the same way.  While paddling, on the moving water, count the seconds it takes to move past a fixed object.  Now you've got the combined river and paddling speed together.

How is this information useful?


It can be useful in estimating the time it will take to reach the take-out or planned campsite.  Will you make it comfortably before sunset?  On expedition trips, you can plan your daily mileage goals.  Knowing how long the planned segment is going to take, can help make decisions - do you need to start early in the morning, or can you have a lazy breakfast and take your time breaking camp?

Let's say you're paddling an 11 mile stretch of the Brazos River. At the put-in you position your 15-foot boat lengthwise on the shore, and count 10 seconds as a leaf floats by the length of the boat. The first thing you do is exclaim; "Woah, that river is barely moving!" Then do the math. 15 feet in 10 seconds is 1.5 feet per second, which gives a river speed of 1 mph. Add 2 mph paddling speed to that, and you'll be traveling downstream at 3 mph. 

So, if you go non-stop, 11 miles divided by 3 mph, means you'll be done in just under 4 hours. A couple of 20-minute rest stops and a 30-minute lunch break will add just over an hour to the trip. So your total trip time would be about 5 hours. If you start at 10 am, you should be done by 3 pm. Plenty of time to spare before sunset to add in some sand-bar-walking to hunt for fossils!  And of course, add some cushion time for the unexpected when conditions might be difficult, such as rescuing overturned boats in rapids.


Oh, if you have one of those newfangled modern high-tech GPS devices, it will calculate this speed for you. But it's much more fun to use your brain, instead of just being a piece of driftwood. Try it in your head, and then compare it to the GPS, and see how close were in your estimate.



The author, John Rich (middle)