How Kayak Displacement Affects Drag

[leong]

In an earlier post “Are Lighter Kayaks Really Faster” I used some rule of thumb formulas from a Physics of Sailing article to show that this is true. That is, an increase in displacement increases the total drag force on the kayak.

Here I quantified the results more accurately for myself using the high fidelity Kayak Drag Prediction program KAPER, developed by John Winters.

But first note that there are three ways that an increase in displacement (more weight) increases the work necessary to propel a kayak.

1. The beginning work to accelerate the kayak up to speed (that’s an inertial force, not drag).
2. The steady state drag on the hull due to the sum of friction and wave drag.
3. The work to accelerate the kayak at the start of each stroke (that’s an inertial force, not drag). Note a fraction of this work is returned because a heavier mass decelerates less between strokes.

The KAPER model only considers the drag case (number 2 above).

I considered the drag on my Epic 18X kayak. I compared the drag with three different displacements: 185lbs., 200lbs. and 215 lbs. (note displacement is the weight of kayak + weight of paddler + weight of cargo).

Here are the results:

Speed in knots % Drag increase going from 185 lbs. to 200 lbs.
3.5 1.7
4.0 1.8
4.5 2.0
5.0 2.3
5.5 2.6
6.0 2.7
6.5 3.0
7.0 3.1


Speed in knots % Drag increase going from 185 lbs. to 215 lbs.
3.5 3.4
4.0 3.6
4.5 4.0
5.0 4.7
5.5 5.3
6.0 5.7
6.5 6.0
7.0 6.2

For example, at 4 knots, going from a displacement of 185 pounds to 200 pounds increases the drag force by 1.8%. Or at 5 knots, going from a displacement of 185 pounds to 215 pounds increases the drag force by 4.7%.

Not counted is the increased inertial work when increasing displacement. That’s too hard to quantify (too many ergonomic variables to consider).

Note results would be similar for varying the displacement on any kayak model. For long distance paddling at, say, only 3.5 knots, adding 30 pounds of baggage might increase the drag by over 3%. Even that small increase in drag can affect your endurance. Also note that the increase in drag increases as speed increases.

No, I didn't write this to promote DR.Oz's 2-Week Rapid Weight Loss Program

-Leon

[josko]

Here is a related article: http://roguepaddler.com/weight2.htm

Edited September 29, 2014 by josko

[lhunt]

Here is a related article: http://roguepaddler.com/weight2.htm

Yes, I've seen that one before. There are two counter arguments. One is that a good quality rudder or skeg gives you good tracking with much less drag than extra weight gives you. The other is that the longer glide from extra weight is only one side of a 2-edged sword - more than offset by the harder acceleration at each stroke.

[leong]

Here is a related article: http://roguepaddler.com/weight2.htm

Josco,

Funny that you linked to that Rogue Paddler article. I read it about 4 years ago while I was thinking about the advantages and disadvantages of lightweight kayaks. In fact, my attachment here is based on several erroneous notions in the article.

Consider the article’s topic “Tracking penalty of just a single degree”. I think the author makes some unreasonable assumptions in this section: 1) He assumes that lightweight kayaks don’t track well, and 2) in his example he assumes that the tracking error will be constant.

The first assumption is not right in general. Lisa mentioned that in her post talking about skegs and rudders. Furthermore, a correctly sized lightweight kayak will probably track just as well as a correctly sized heavy kayak and better that an incorrectly sized heavy kayak. Consider a100-pound person paddling a 62-pound Cetus HV. The design weight of that Cetus is 143 pounds or more. I think that a 100-pound paddler will be able to track much better paddling a 35-pound KayakPro Nemo than that 62-pound Cetus.

So, obviously, I don’t agree with the author that lightweight kayaks don’t track well. But let that be. Consider the following.

The author says “Let's consider how a tracking penalty of just a single degree would affect a hypothetical paddler who paddles non-stop, at a constant rate of speed, for 8 hours (480 minutes)”. Based on this hypothetical he computes the tracking penalty (how much longer the trip would take relative to a direct beeline to the waypoint). But consider this: If you were paddling towards a waypoint with a constant heading error you would eventually notice the error and head back to the correct beeline. But in the author’s example, the tracking error isn’t noticed until the very end whereupon the kayak turns directly towards the waypoint. Also, a poorly tracking kayak would probably have a randomly changing heading error; i.e. it would tend to wonder back and forth around the correct heading angle (sometimes to the left and sometimes to the right).

Nevertheless, for the unreasonable example he gave, the author approximates an 8-minute time penalty for an 8-hour trip. He did the math slightly wrong but the error in his result is insignificant. Contrary to his example, I decided to calculate the penalty that would occur with the following more reasonable example. If, instead of making one correction at the end, the paddler would head a distance h with a one degree heading error and then head at the negative of that heading error for another distance h. He could repeat this correction over and over and over again until he got to the target. For this zigzag path the penalty is smaller and, in fact, the extra time relative to the beeline (the time penalty) is independent of the number of such zigzags. This is easier to visualize in the diagram of my attachment (don’t worry about the mathematics). The actual penalty for the 8-hour trip using this zigzag path is negligible (only about 4 seconds, not over 8 minutes as in the author’s example). Even accepting the erroneous tracking error argument, it’s most likely the longer zigzag trip with the lightweight kayak would be faster than the direct path of the heavier kayak; even the author accepts that the lightweight kayak moves faster along it’s route.

Finally note that the author said, “A lighter load in your pack, your bike, or your canoe can dramatically increase your comfort by reducing fatigue and improving performance. … That's right, I said modern ultralight thinking does not directly apply to a kayak”. Wow, he even mentioned canoes. There’s no small irony in his claim that lightweight canoes are good but lightweight kayaks are bad.

-Leon

PS

Of course a heavier kayak takes more work to accelerate during the power stroke. But, as Lisa said, and I said in the original post, you get a fraction of this back due to the momentum of the coast. It’s not easy to quantify how much you get back because it depends on numerous variables.

Mathcad - Heading Error Penalty.pdf

Edited September 30, 2014 by leong