# Boat Hull Drag in Shallow Water

I paddle several different types of small craft in the ocean and bays near my home. One phenomenon I've observed is beyond my understanding of drag on a narrow displacement hull. When paddling in water less than maybe 6 feet in depth, there is a very noticeable increase in drag, which increases as the depth decreases. This is true for all the types of boats I paddle, from a large 6-person Hawaiian outrigger canoe (L=40', width=2', draft=0.67') to a one-person racing kayak (L=20', width=1.5', draft=0.33'). I should add that hull speeds are generally in the 6-8 mph range. I've read that rowing shells also encounter this same drag and they are longer, narrower, but with drafts in more or less the same range.

I've read one explanation that the boundary layer on the hull makes contact with the bottom and the bottom increases the drag on the outer part of the boundary layer which in turn is transmitted to the hull. This seems highly unlikely to me, especially when the water is more than a maybe a foot deep. I don't believe the boundary layer from a 20 foot kayak extends that deep. As I said, this is noticable at water depths up to 6 feet or more.

I've also heard that pressure waves from the hull bounce off the bottom and reflect back up to the hull and cause drag but as an engineer that doesn't really sound very rigorous to me.

It seems to me there might be some interaction between the bow wave of a boat and the bottom, since I know that the dynamics of surface waves do extend approximately as deep as their wavelenth, and at these speeds the wavelength of a bow wave is certainly on par with the water depth. Can anyone give me a properly defensible answer to this?

• Here are a couple of data points: Aircraft start to feel a "ground effect" as they approach the ground. This results in increased lift and decreased drag, starting at an altitude of roughly ten chord lengths above the ground. Also, it is possible to detect and track (moving) submarines at hundreds of feet depth by looking for the wake-bulge on the surface. So the pressure wave of a body moving through water goes out a long way. – David Rose Apr 24 '15 at 2:15

Your experience with more resistance in water of depth of ~ 6ft is probably due to increased resistance of the boat against the bow wave which itself is beginning to "feel bottom".

There is an excellent post on the Earth Science Stack that explains what it means to "feel bottom" here.

If you can estimate the size of the bow wave (wavelength) then possibly you can use the mathematical relationships posted there to determine if the bow wave is considered a deep water wave, shallow water wave or otherwise in the region of transition. If the calculated regime is either shallow water or transition, that could explain your observation.

• I read the post you suggested and I agree that's probably the mechanism I've experienced. The theoretical hull speeds of the boats I paddle would put the bow wave wavelength at around 20 feet and therefore the critical shallow water depth at around 10 feet. Pretty close to my guess, especially since the effect would become more noticeable at shallower depths. – PJNoes Apr 24 '15 at 17:15

As I am not allowed to comment on the above answer I need to add a new one: You do not need to estimate the wavelength of your vessel, you can calculate it:

$\lambda = 2 \cdot \pi \cdot Fn^2 \cdot L_{pp}$

where Fn is the Froude number and Lpp is the length of your canoe.

$Fn = \frac{v}{\sqrt{g \cdot L_{pp}}}$

where v is the forward speed and g is the Earth's gravitational acceleration.

• You might want to rethink this. Expand Fn^2 and you get a term of Lpp in the denominator which cancels the product term. This gives a result which is independent of length, and depends only on the square of velocity and 1/g. You sure about that? – WhatRoughBeast Aug 25 '15 at 12:33
• The (secondary) wave system depends on velocity squared. But the above formulation is more frequently used in naval arcitecture as velocities are often expressed in terms of Froude numbers. – Simon Aug 25 '15 at 15:50

When waves roll in from deeper seas to a shallow shelving shore, they become steeper, pile up and eventually break as the amplitude of the wave increases. This may be caused by a shallow bottom interfering with the circular motion of water molecules as they are displaced by the passing wave energy.

If the bow wave of your boat builds higher than it would in deeper water, that creates a greater volume of displaced water that must be handled by the stern of your boat. This means more drag and less velocity. One way for you to reduce this effect is to design a shallow water rowing boat with a long overhanging stern which the displaced bow wave can roll under.

Incidentally, if you row so fast in shallow water that the bow wave becomes significantly more than the stern of your boat can handle, the boat may nose down into the bow wave and try to become a submarine. Obviously, this would have a detrimental effect on velocity over the surface of the water, as you would be rowing partially in the direction of a downward sloping vector.

When rowing a coracle style boat in shallow water along the shore a significant displacement of water is most noted on the shore side. My guess is horizontal water displacement is more restrictive to movement. The boat's shore side rises further out of the water, perhaps negating the drag as I couldn't note directional change.