I am working with a physics teacher in developing curriculum for a high school problem-solving and design course. I would love to incorporate some paddling-related problem-solving challenges into the course and am looking for ideas.

Hull design would be a natural – but working with composites and building full size hulls would be beyond the scope of our course. Any suggestions for materials that would make this possible. (We’ve done cardboard boats before – but this material is pretty limiting.) Other ideas?

Another way to go might be in paddle size and shape. Again, are there any materials we might use that would be both easy to work with and economical?

Other problem-solving ideas related to kayaking?

Thanks in advance.

Tow Line!

How about doing a tow-line, maximum load, shock load problem.

You could do one experiment to measure the modulus of the line.

Use results from above to calculate the max load when a full size paddler at full speed yanks the towed kayak up to speed.

Assume towing paddler is much, much larger than the towed paddler (i.e. don’t conserve momentum).

Now assume paddlers are of equal mass (conserve momentum and energy).

Now consider towing paddler can maintain F forward force and is at steady state ( F = D )

Now consider thrust is actually cyclic ( T = F / (duty cycle) )

Now do experiments with a simple tension scale in the line.

Consider the effect of using a shorter tow line (is half the length twice the force?)

Weather cocking

Model the kayak as a symmetric NACA foil, use an online Java calculator to find the lift force and center of effort at various angles of attack.

Build experiment to identify the pivot point (think side slip, hanging draw) at various speeds. Does this agree with NACA estimate?

Cargo weight vs Drag

Considering that most of the drag on the boat is viscous (skin, friction, wall shear, parasitic, whatever), model the hull however it is easy, then calculate the drag force vs load weight.

Ultralights

A hull built using the geodesic ultralight method might be feasible within the confines of a classroom. Cheap, light, goes together pretty quickly, and could be a good vehicle for experimental designs. If full size is a problem, perhaps you could build 1/4 or 1/5 size models.

See: http://www.gaboats.com/

trusty concrete boat

Ryan L.

Thanks for the ideas!

Good ideas. I will check them out and discuss them with the physics teacher who is co-teaching the course.

Any other suggestions are still welcome!

skin on frame

Building skin on frame boats is the quickest and cheapest way to test and tweak hull designs:

http://www.post-gazette.com/pg/09182/980869-140.stm

and a variety of common materials can be employed to do so:

http://www.yostwerks.com

(look at the “gallery” for examples)

Boat heading

There is the classic problem in relative velocity - if you are ferrying across a current of say 2 knots, and you are capable of driving the boat at 3 knots with respect to the moving water, what bearing angle (usually Beta) do you choose to get the boat to travel directly from point A to B?

This is fairly straightforward if A and B are directly across the stream from each other, as the desired path is perpendicular to the current. The situation is more challenging if B is up- or downstream from A. The most revealing way to solve the problem is to use a vector velocity diagram. There’s a lot of fundamental physics that goes into learning how to solve this problem.

A more advanced application might be this - if I steered my boat at angle Beta and paddled at 3.5 knots to get from known points A to B, what was the magnitude of the current? This is something you could test in the field in a kayak with a GPS unit.

As an aside, a nice way to measure a current is to toss puffed rice cakes (you know, the 4" diameter ones) onto the surface of a stream and time them over a known distance. This can be done conveniently from a bridge of known width with two people spotting the cake as it moves under the bridge. This assumes the surface flow is the same velocity as that at depth, which is not so bad for something like a kayak that moves within the top few inches.

Good idea

Yost designs are a great idea. You can knock together SOF hulls quickly using drywall screws, 1x1 pine and plywood frames, cover with cheap canvas, paint and be done in a day or two, especially if you don’t bother with a proper coaming. It won’t last too long, although if you take some care and maybe use stainless screws, they might last a while.

yeah, the old concrete canoe…

It is a tester, but always makes for a heck of a portage…over terrain.

Velocity profile

With careful placement of 50 or 60 rice cakes, one could get a cool velocity profile of the stream. Very interesting around corners.

Do Asian carp prefer rice cakes?

D

Perhaps useful info

Hopefully you find this worthwhile

References :

http://www.guillemot-kayaks.com/guillemot/information/kayak_design/kayak_stability

http://www.atlantickayaktours.com/pages/ExpertCenter/Rolling/Rolling4.shtml

http://www.seakayakermag.com/PDFs/Kayak_Reviews_Info.pdf

http://www.sksa-ltd.com/resource/BoatStab1.pdf

http://www.engineeringtoolbox.com/centre-gravity-buoyancy-d_1286.html

http://www.topkayaker.net/Articles/Instruction/HullDesign.htm

material choices

Do spend some time looking at the “gallery” shots on the Yostwerks site. Many builders cover their frames with clear plastic so the “guts” are visible. Some of these installations are tough and semi-permanent but it is also common practice for frame kayak builders to wrap the finished frame in heavy duty saran wrap or plastic tarp material for test paddles to test the design before committing to the final skin installation. This can be easily removed and adjustments made to the frame design to change the performance. Sounds like that would be very practical for your school project.

Actually, if this was more of a design functionality (rather than physics) project, we were talking the other day about how cool it would be to have a metal frame collapsible kayak with components that could be reassembled into some sort of bicycle. YOu could paddle downstream on a long river and then turn the boat into a bike to pedal back to your car. We even fantasized about having the bike wheels turn into some sort of pedal powered stern wheel paddle arrangement.

really loaded asignment

Problems

- hydro anything is beyond scope of HS math

- ditto physics

- ditto structural mechanics

Asking HS student to do something way beyond their grasp will only teach internet research, not in a good way.

Then there is a danger of monkey see - monkey do approach, or “research” were students do what teacher suggests, needless to say doesn’t teach any useful skills.

Not knowing HS physics curriculum makes recommendation difficult, but white water Z-drag and pinning should be quite simple to grasp from both mathematical and engineering side

Can’t agree

I’m not clear on your point - are you saying physics is beyond the scope of HS math, or that hydro-anything is beyond the scope of HS physics? In either case, large portions of physics, fluid mechanics, solid mechanics, etc can be taught graphically, with essentially zero math. I’m sure, because I do it all the time.

On top of that, most of the math that actually gets used is rudimentary in practice. There’s a big difference between deriving Bernoulli’s equation (a graduate-level exercise), using it to calculate something (an undergrad task) and understanding what the terms mean (HS students can do this, it just needs to be taught clearly). Placing the bar too low for HS students doesn’t help anything, and sends them to me in college with no willingness to challenge themselves to learn.

Agreed

I just finished a week long class with a group of (high-achieving, talented, motivated) inner-city HS students.

We had 30 pressure taps along an airfoil and we studied lift and C_L as a function of angle of attack in a little open-loop wind tunnel.

Necessary math:

P + 0.5*rho*v^2 = C

P = rho*g*h

basic trig (sine, cosine)

unit conversions

F = m*a

P = F/A

Questions addressed included:

How does a manometer work?

What is the difference between absolute and relative pressure?

What is the relationship between pressure and force?

What does angle of attack do?

What is “conservation of energy”?

Why does anyone still use Imperial units?

Can an airplane really fly?

The kids were awesome - I’m exhausted.

I might mention that I never mentioned Bernoulli. Too often Bernoulli is over-simplified and misapplied.

D

Drag vs Speed

Granted - viscous drag in turbulent boundary layers is still pretty much unknown. However, you could plot the data and get a nice curve fit.

Designing the DAQ system would be a good challenge.

Hah?

How can Bernoulli be “over-simplified and misapplied” ?

It is so simple to start with, way simpler than the master equation, the Navier-Stokes; this one can certainly be over-simplified and misapplied.

Bernoulli equation

From teaching fluid mechanics many times, I'll confirm that the Bernoulli equation is routinely misapplied and otherwise abused.

You probably know already, but the Bernoulli equation is only valid for steady, incompressible, inviscid flow along a streamline.

Steady = no change of the flow in time, so it won't work in a dynamic flow situation, e.g. flapping flight, accelerating flows, etc.

Incompressible = constant density, usually a good assumption unless Mach number > 0.3

Inviscid = zero viscosity, i.e. no fluid friction!

Streamline = parallel to the flow velocity = the path of a fluid particle in steady flow

These conditions are routinely not satisfied in most flows that are of interest, so the Bernoulli equation is technically not valid. It does give reasonable results in many cases, luckily. The most common misapplication is computing a Bernoulli constant and applying it across streamlines, a fundamental no-no.

PS, it is interesting to note that Bernoulli's equation can be generated in two ways. From the ground up, by applying Newton's law to a moving fluid parcel to generate Euler's equation, which is then integrated with the assumptions above to get Bernoulli's equation. The second, top down version is to apply the various assumptions to the Navier-Stokes equation, which are then rearranged to give Bernoulli's equation. In either case, it's worth remembering that the process of simplification is made possible by making those assumptions, yielding an equation that, although manageable due to its simplicity, has a restricted range of use.