How to Use Physics to Paddle Board Like a Pro
Question: How do you make a stand up paddle board go straight if you only paddle on one side? Of course, I’m not an expert paddler so my usual propulsion method means I paddle on one side then switch the paddle to the other side. Alternating left-right sides of the paddle board would mean I would mostly go straight. But it looks uncool to continually switch hands on the paddle. If there’s one thing I want to do on a stand up paddle board is to look cool—why else would I do it?
Every time I have to explain torque, I have trouble starting. Honestly, the concept isn’t so simple. But let’s try, OK? Think about forces and torque. You can exert a force on an object just by pushing it with your finger. But what does a force actually do? If you take all of the forces on an object and add them together (as vectors) then this net force changes the velocity of that object.
Now, what about torque? Let me start with an example. Take a small object and place it on a table surface. If you push towards the center of this block it will increase in speed and start to move. But now push on the block such that you are not pushing towards the center, like this:
If you push off-center, the block will both increase in speed and increase in rotation. This is a torque—or as I like to call it, a “rotational force.” The torque still depends on the force, but it also depends on the location of the force. One simple way to calculate torque (this just gives the magnitude of the torque) would be:
In this expression, these variables represent:
- τ—this is the torque. Physicists use a Greek letter because it looks cooler.
- F—the applied force.
- r—the distance from some point of rotation to the location where the force is applied. Normally we can pick the center of mass for the point of rotation but it doesn’t absolutely have to be this location.
- θ—this is the angle between the applied force and the vector from the rotation point to the force (r).
That’s torque. If you want a paddle board to go straight, you need to have zero torque.
Actual Paddle Boards
Like I said, I only think I’m an expert paddler. With that in mind, here is my first paddling demonstration. What happens if you just paddle on one side of the board?
Yes, you should be able to notice that the paddle board isn’t going straight. Why does it turn? Here is a diagram showing the board and paddle and three different locations during a typical stroke. Notice that I am showing the force on the board and not the force the paddle pushes on the water.
In all three of these positions there is both a force pushing the board forward and also a torque that will turn the boat to the left (as seen from above). You would have to eventually paddle on the other side of the board to get it to go straight. OK—yes, the board does have a rudder (fin) on the bottom at the back. This rudder can then exert a counter torque on the board once it’s moving through the water. However, if your rudder is too effective the board will never turn (sometimes turning is a good thing).
OK, and now for a different paddle stroke to make the board go straight (or at least straighter). Notice that I have a small PVC pipe on the paddle handle. This means that you can easily tell the direction that the blade is pushing on the water.
Really, the only difference in this stroke vs. the straight one is at the beginning. If you look carefully, you will see that the paddle blade is angled towards the left side of the board at the first part of the motion. Here is a diagram showing the forces at the same three locations as before.
In paddle position 1 the force is angled in such a way that it would causes a right turning torque on the board. But in the next two strokes the torque would be left turning. If you practice enough you can get the net torque effect to keep the board paddling straight—which is probably what you want. Oh, but you can still turn if you need to (such as in the case of a large alligator or Niagara Falls).
But of course this really isn’t a new thing. If you know what you are doing, you can paddle on just one side in a canoe. Perhaps the most common canoe stroke is the J-stroke (there is even a Wikipedia page on canoe strokes). The J-stroke is very similar to the above paddling on the board, but the counter torque is applied at the end of the paddle stroke. In a canoe, you can usually sit near the rear of the boat such that the J-stroke is more feasible compared to a stand up paddle board when you are standing in the middle.