Recently, Silbs asks,

Meanwhile, I have been driving myself nuts while mulling over an issue around boat size and speed. For starters, we all agree that a longer boat (all else being equal) can go faster than a shorter one. So far so good. In addition, we know that that longer boat will need more horsepower (muscle) to hit those higher speeds. Correct? Here’s where the waters get muddy.

Say a paddler is capable of putting out, oh say, 5 units of power. If we put this paddler into a long boat that needs 6 units of power to hit top speed, he will fall short. Okay? Now, let’s put him in a slightly shorter boat that tops out with only 5 units of applied power. Hurray, the paddler hits hull speed in that boat.

The question is, in which boat can he go the fastest?

This question is pretty common in paddlesports and comes from the use of a few generalities used in marketing copy and sales floor speak. The generality is: In general, a longer canoe or kayak is faster than a shorter one. The generality developed from the use of a calculation discovered about 100 years ago by William Froude called Hull Speed. John Winters in The Shape of the Canoe writes about this calculation:

As the hull plows a furrow through the water, two wave patterns are formed. The first, the divergent waves, fan out from the bow and stern and their significance is minor. The second, the transverse waves, also form at the bow and stern but their crests lie at right angles to the direction of travel. These waves are the visible evidence of energy lost pushing water out of the way at the bow and suction at the stern pulling it back to its original level. The length of these waves (crest to crest) is equal to the natural length of a wave traveling at the same speed as the hull. About 100 years ago, William Froude determined that the speed of waves in knots was equal to 1.34 x L1/2 in feet. At low speeds there will be a large number of waves along the hull but as speed increases the number of waves decreases until the hull lies cradled between wave crests at the bow and stern. At this point, the so called “hull” speed has been reached. For heavy displacement craft, this marks the maximum practical speed attainable and higher speed is possible only with extraordinary power increases.

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You calculate Hull Speed by entering the length of your kayak or canoe into a simple formula: Hull Speed = 1.34 * (LWL)^{1/2}

So, for a 14′ boat, the Hull Speed equals 5.01 knots. For a 15′ boat, the Hull Speed equals 5.19 knots. For a 16′ boat, the Hull Speed equals 5.36 knots. For a 17′ boat, the Hull Speed equals 5.52 knots. For an 18′ boat, the Hull Speed equals 5.69 knots. Simply looking at the calculations, it’s easy to see why it looks like a longer boat is faster than a shorter boat. Simple subtraction tells us that the Hull Speed of an 18′ boat vs. a 15′ boat is 0.5 knots faster.

**Example 1**: Now imagine three displacement hulls all 15′ long: a bass boat, a canoe, and a kayak. All three of these boats have a Hull Speed of 5.19 knots. Stick your average all-else-being-equal paddler into each of these boats and answer this question: Which boat is faster? Or better yet, let’s mix up the boats. Our bass boat becomes 18′ with a Hull Speed of 5.69 knots. The canoe and kayaks stay at 15′ long with a slower Hull Speed. According to the Hull Speed calculation, the bass boat has the fastest Hull Speed, but if you’ve ever had to paddle a bass boat with engine problems back to shore, you know it isn’t as fast as paddling a canoe or kayak back to shore.

**Example 2**: Another displacement hull example to look at is surf skis. In places on the Internet, people report average speeds of 6.5 knots or greater during races on 18′ skis that should have Hull Speeds of 5.69 knots. (Tangent: Check out what Björn Thomasson has to say about speed and stability.) According to the calculation, these surf skis are traveling faster than their Hull Speed.

I hope that these two simple examples show that the Hull Speed calculation doesn’t necessarily predict which boat will be faster to paddle, and we see that in some cases paddlecraft are exceeding their Hull Speeds. I hope after thinking through the above examples, you’ll agree that we can put the Hull Speed generality to rest, but if not, then check out the resistance info below.

A second generality emerging in the sea kayaking world is that a shorter boat is probably faster for a paddler that can’t drive his kayak to the Hull Speed. I imagine that at some point we’ll see an new generality emerge, which will state something like: in general, a short boat will be faster for paddlers that can’t produce much power. Below, I’ll use some computer generated resistance numbers to show that this generality isn’t true.

### How Fast Will This Kayak Go?

If we can’t use Hull Speed to determine if a boat is faster for a paddler, the question then becomes how do you determine if a boat will be faster for a paddler that can only output x amount of power? I posit, other than using controlled tests in each boat, the best way, assuming the paddler comfortably outputs the same amount of thrust in each boat, is by looking at resistance. (Comfortably outputs is making assumptions about boat stability, ergonomics, sea state, etc. being all-else-equal.) To show this, I’m going to show the resistance for three 40 pound boats paddled by a 160 pound paddler. I’m using Brian Schulz’s F1 (14’2″) design, my cedar strip Siskiwit Bay (17′) design, and Necky’s Chatham 16 (16′).

Speed | Resistance* | ||

Knots | F1 | Siskiwit Bay | Chatham 16 |

0.5 | 0.06 | 0.06 | 0.06 |

1 | 0.21 | 0.20 | 0.21 |

1.5 | 0.45 | 0.43 | 0.45 |

2 | 0.76 | 0.74 | 0.76 |

2.5 | 1.14 | 1.11 | 1.14 |

3 | 1.58 | 1.54 | 1.59 |

3.5 | 2.20 | 2.08 | 2.19 |

4 | 3.12 | 2.85 | 3.13 |

4.5 | 4.65 | 4.16 | 4.77 |

5 | 7.09 | 6.13 | 7.28 |

*smaller number is better.

Sea Kayaker Magazine claims that a fit paddler can maintain speed against 3 pounds of drag. So, if we assume that our paddler can cruise all day against 3 pounds of drag, we actually see that the longest kayak is faster for this paddler. He’ll be able to cruise along in the Siskiwit Bay a bit faster than 4 knots. We see that at speeds of 3 knots and lower all three boats are very similar in the pounds of resistance. At higher speeds, the shorter F1 is more efficient and thus faster at the same thrust than the longer Chatham 16. So, if our paddler can work against 4.65 pounds of resistance, then the F1 will cruise slightly faster than the Chatham 16, but the Siskiwit Bay beats them both. When comparing the boats and thinking about one of the generalities used by Silbs, “we know that that longer boat will need more horsepower (muscle) to hit those higher speeds. Correct?” we find an exception to the generality. In the case of these three boats, the longest boat actually requires less horsepower to hit the higher speeds. That doesn’t hold for all longer boats.

If we add more weight in cargo to these boats, the numbers may tell a different story. For example if we add cargo and run the numbers for 250 pounds of paddler, cargo, and boat, these are the numbers we get:

Speed | Resistance | ||

Knots | F1 | Siskiwit Bay | Chatham 16 |

3.5 | 2.44 | 2.26 | 2.39 |

4 | 3.45 | 3.09 | 3.35 |

Now, the Chatham 16 becomes easier to paddle than the shorter F1 at 3.5 and 4 knots, but the Siskiwit Bay still beats both. And this will vary differently for each hull design. Looking at these two charts, we can cast doubt on another generality: in general, a kayak will paddle fastest when loaded at its design displacement. You can see that there is more resistance for all the kayaks at every speed with more weight in the boat. For a paddler only able to produce three pounds of thrust, these boats loaded heavier, all else being equal, will paddle slower, than if they were loaded lighter.

### Conclusion

There really is no easy answer to Silbs’s question, “The question is, in which boat can he go the fastest?” The computer can give us suggestions. Sometimes it’s the shorter boat, sometimes it’s the longer boat. The only way to really know is design a set of on-the-water tests and put each kayak through the them.

I’m curious how you think about this. Any thoughts?

Great article Brian!

So many factors as you say.

Now FatPaddler would probably add….colour makes a difference also, as red kayaks are faster. :)

Too bad there isn’t a factor as for different paddle styles also to be figured in.

And I’d say using a GP might make a difference in whether that 160 lb paddler could paddle longer & faster. (you know I had to add that LOL)

Loved the article!

Jill

Glad you like it Jill. Paddles will definately make a difference. John Winters has an interesting article on paddles in The Shape of the Canoe. For this, I just factored that into the all-else-being-equal zone.

Nicely done Bryan. My favorite is always the horsepower/drag visual, reality sets in fast.

–

I would have used a calculator –

http://www.midwestik.com/midwestik/midwestik.nsf/dx/speed.htm

@Willi – That calculator seems extremely flawed. It just told me 6+ knots for my Explorer. The amount of power needed to get an Explorer to 6+ knots isn’t something I can do. I guess my point was that calculations like Hull Speed or the Midwestik.com calculator are a flawed way of comparing the speeds of boats and lead to wrong generalities.

I still have a headache since writing that blog. Problem is that there is no good data on waterline lengths for various kayaks, even though sail boats manage to come up with a working number. More over, in kayaks the beam turns out to be a huge factor as it adds tremendous resistance as it increases. Nice piece.

Thanks for chiming in, Silbs. A better number for guessimating might be surface area instead of waterline length and beam. Because it’s easy to roughly calculate frictional resistance once you know the surface area: Rf=.97C

_{f}SWv^{2}Another factor just to throw into the mix is how scratched up the hull is. Winters claims that a year worth of scratches can increase frictional resistance by 10% to 20%.

Still, we’re ignoring the “comfortably outputs” factor, which brings me back to my point that the only way to really know is to design some tests and run them in each kayak.

Very good article since I am a Naval Architect. Ultimately the answer lies in the total resistance of the craft at it’s operating displacement. No more, no less. Hull form plays just as much importance as length, beam, etc… What was your methodology for determining resistance data?

Thanks, William! I agree with you. An additional factor for paddle craft is the “comfortably outputs” factor. If the paddler isn’t comfortable in a kayak, he probably isn’t going to output the same horsepower in it as in one he is comfortable in.

I used KAPER as implemented in DelftShip Pro. I used KAPER, because that’s what Sea Kayaker Magazine uses.

I cannot disagree on that one since both comfort and ergonomics play heavily into human powered vehicles. Plus a 5 knot headwind is a 5 knot headwind whether it is self generated or not. I downloaded the spreadsheet version of KAPER and will have to take a look at DelftShip.

Math exercises… as long as you are comparing similar boats, the one that will go faster may be the one that works best in waves or chop, or the one that catches the least wind, or the one that provides just the right amount of stability for the paddlers ability… speed is a nice thing to consider in a vessel, but usually not the most important characteristic.

Hey, Scott, I agree with you. For this exercise, the point was to try to dispel some common generalities used when trying to figure out which boat would be faster. To take into account all the factors that you state, I used the “comfortably outputs” clause.

I am not a mathematician, however the article and discussion are interesting and I look forward to more comments. My conclusion so far is that little people need little boats and big people need big boats and they must find the boat comfortable – but I suspect deep down we already knew that.

Hey Rob, thanks for the comment. I don’t necessarily believe that people need boats corresponding to their sizes, unless you’re suggesting just for fit. Then I’d agree with you.

It is mainly fit I was thinking of, clearly one needs a boat that is suitable for the job, i.e. a big boat is needed for an unsupported 3 month trip no matter what your physical size.

Absolutely.

Goodmorning, love the research, I recently built an F1 at a school Brian ran hear in Australia , that was in Jan, and haven’t paddled anything else since. Great kayak . I personally don’t think that drag coefficients , hull speeds, and water lines can really successfully be used on small paddle craft, I don’t think the formulas were designed for these type of craft, they where designed for ships with a broader beam, etc… and as a consequence don’t translate to our small craft well. I’m starting to think wetted surface area is more the issue for kayaks/canoes my F1has less wetted area, is all waterline and cruises with less effort next to 16 & 17ft kayaks also look at the weight factor too, my F1 with a sail rig and safety gear is only 14.5 KG I’m not pushing as much through the water and that equates to speed and arriving at the other end in better condition. I really hope Skin on frame takes off here in Australia.

Thanks for the comment Mick. The KAPER drag formula was specifically designed for use with canoes and kayaks. I used KAPER for the drag numbers used in this post. While they may not be 100% accurate when applied to real world (although it was tested against tank tests), they are internally consistent and thus the numbers provide a good way to compare boats. Frictional resistance is a major part of the total resistance for canoes and kayaks, and because surface area is big part of frictional resistance, it makes sense that it becomes an issue when looking at the total drag numbers. For example, with the Siskiwit Bay at 4.5 knots 3/4 of the total resistance is frictional.

As for the weight comment, I agree.

I dident realise the KAPER formular was designd for kayaks. Is it also taking weted surface arear into the equasion ? another thing to look at is our paddeling tecneque, a good stroke combined with a good boat shold also be part of the equasion and if we have a boat with good alround figers we need the ability to “power ” the boat to perform at theas figers is that a sustanabel thing? and at the end of the trip are we going to be in good shape after trying to perform at a hightend level .

As a resent small boat convert, I put the question , are we paddling Kayaks that are to long?

PS, Im new to this site, and the hole site has made me re avaluate how Im doing things, and geting back to how I once traveld , I realy love All the articals, not one is out of place or uninformative or not Factual Regards Mick M

Yes, KAPER takes wetted surface into account. John Winter’s The Shape of the Canoe describes the formula in detail.

For this exercise, paddling technique is one of those all-else-being-equal things.

As for the question, “Are we paddling kayaks that are too long?” I think kayak length is a function of what you need to do with the boat. Sometimes a shorter boat will be better and sometime the longer.

Should I go outside and scrape all the barnacles off the bottom of my kayak then :-) I think it doesn’t actually matter too much what the theoretical hull speed is. At the moment my wife paddles a P&H sirius. She likes it cos it goes in a straight line when its windy and she can wield her paddle easily cos its narrow and she’s got short arms. I paddle a p&h quest lv cos its big enough for a weeks camping and i like its cruisy sort of straight line but actually quite manouverable handling. And it’s the first kayak i ever sat in that didn’t make my right leg go to sleep. Mind you , I haven’t built an f1 yet and they do look a lot of fun…

The difference in cruising speed between the 2 boats is obvious on a long crossing but would be less important to me than tracking, manouverability and comfort if i were choosing again.

thanks for letting me get that off my chest.

One problem I see with some of the data in the speed/Resistance chart is that you have given the F1 a weight of 40 lbs. They weigh about 28 lbs unloaded. Adding that 12 lbs (that in reality are not there) will increase the wetted surface thereby increasing the friction and giving a resistance number higher than what it would really be. So, in effect, the numbers have been “cooked” in a bias against the F1. The hull form (fish form/swede form/symmetrical) displacement, and wetted surface, as well as the overall flexibility (or rigidity) of the form and the skin (urethane coated nylon, coated wood, plastic, fiberglass) and it’s ability to resist or conform to the water pushing against it all play into the equation.

Based on my own experience paddling an F1 and many other rigid (plastic and composite) sea kayaks, while the F1 will not beat a longer boat in a flat out sprint over a short distance (all other things besides length being equal), it is, over the long haul, much easier to hold at speed for a longer amount of time due to it’s lower wetted surface, and lack of area for the wind to catch, as well as it’s flexibility, so that it does not get “slammed” by waves that give resistance to a rigid boat and make it harder to paddle for long distances (meaning it is less fatiguing to paddle a skin over frame boat for a long distance in choppy or rough water).

Overall, while this article is good at pointing out that length alone is not a determining factor in boat speed, it was also filled with enough errors in the speed resistance chart to be suspect. I would like to see some realtime numbers on the three boats mentioned (via a “tank test” with full sized boats). I think the F1 would look much better than it did based solely on the math, and even the math was wrong because it gave the F1 a 12 pound handicap.

You’re overlooking the “all things being equal” clause. For these kinds of comparisons to work the displacement must be equal, because if one was less it would give that hull shape an advantage in the comparison. Hull form, displacement, and wetted surface are addressed within the KAPER formula. The resistance numbers don’t account for material, sea state, stability, comfort, etc… Nor does it account for subjective opinions.

The numbers for a 28 pound F1 and a 160 pound paddler:

Knots – Resistance

1 – 0.2

2 – 0.74

3 – 1.54

3.5 – 2.14

4 – 3.03

4.5 – 4.53

5 – 6.95

Using Sea Kayaker Magazine’s stipulations:

1 – 0.24

2 – 0.87

3 – 1.82

4 – 3.68

4.5 – 5.31

5 – 8.05

I don’t buy your conclusion. The speed resistance chart is only suspect if you remove the “all things being equal” clause. All these hull shapes can be built in any material. Even a 17 foot cedar strip kayak built with 1/8″ strips and multiple layers 3.2 oz tight weave can weigh in at around 30 pounds while remaining plenty stiff.

If you’re willing to fund the tank test rental time, I’m game.

[…] kayaks go faster than those that are shorter and wider. Ok, this is a generality. It's discussed here, how weight, paddler ability and other resistances can affect a kayak's speed as well. However, […]