Mass-spring-damper problem for kayaking waterfalls

[WW Kayaker]

Working on installing shocks in my kayak seat to protect my back when landing flat off of tall waterfalls (necessary when there isn't a deep pool). I can't figure out if it will actually help. I guess you would call this a spring and damper in series problem (the damper being the water). Here's the problem I'm having:

Background: When landing flat on aerated water, it is generally assumed the kayak will sink 6 inches into the water reducing the G's and shock of impact. This is usually adequate to protect the back from injury when landing flat off waterfalls up to 20 ft tall (when sitting vertical in the kayak). So, I'm assuming 40 G is the max safe limit for landing with a vertical spine. The same can be done safely from 30 ft if one is tucked as far forward as possible but it will be a very hard landing (60 G?). My goal is to widen the margin of safety by adding shocks to the seat.

Problem to solve: If I install springs or shock absorbers with a 2 inch stroke on the seat of my kayak, how do I figure out whether or not that will decrease the G's of landing?

For example: If I currently have 6 inches of travel after impact and increase it to 8 inches by adding 2 inch shocks, that would presumably decrease the G's if the rate of deceleration was constant over the entire 8 inches. But I'm guessing it isn't since the springs or shocks will behave differently from the dampening effect of the water. I have no idea how they would work in conjunction. I'm assuming the deceleration from travel in the water is almost constant; but the curvature of the boat means more surface area hits the water as the boat sinks deeper into it, so rate of deceleration should increase somewhat after initial impact. But in general I'm assuming the boat is a blunt projectile and stops as soon as it has displaced a mass of water equal to the combined mass of boat and paddler. What I can't understand is how springs/shocks in my seat would affect the overall rate of deceleration on my upper body from the beginning of impact until I have come to a stop. How could I calculate that? Also, how do I calculate what spring rate to use (or other value if I use a damper) if my goal was to limit my upper body to a certain number of G's? Sorry I'm not a physics person and have limited grasp of mathematics above Algebra II but I'll try to follow if anyone has any ideas.

 

[scottdave]

The boat will initially go in further than the mass of displacement. The moving kayak (and you) has energy which must be absorbed/dissipated by the water. Drop a cork in a bucket of water and it will sink down then return (after maybe bobbing a few times) to the equilibrium position. So is your information of sinking in 6 inches a known fact, or is this the displacement of the water (in equilibrium)?
The same thing could be asked about the springs. Does it compress 2 inches when you sit on it or is this from jumping up and down.
I don't know the answers, but hopefully I have given you some things to think about and test out.

 

[berkeman]

Working on installing shocks in my kayak seat to protect my back when landing flat off of tall waterfalls (necessary when there isn't a deep pool). I can't figure out if it will actually help. I guess you would call this a spring and damper in series problem (the damper being the water). Here's the problem I'm having:

Background: When landing flat on aerated water, it is generally assumed the kayak will sink 6 inches into the water reducing the G's and shock of impact. This is usually adequate to protect the back from injury when landing flat off waterfalls up to 20 ft tall (when sitting vertical in the kayak). So, I'm assuming 40 G is the max safe limit for landing with a vertical spine. The same can be done safely from 30 ft if one is tucked as far forward as possible but it will be a very hard landing (60 G?). My goal is to widen the margin of safety by adding shocks to the seat.

Problem to solve: If I install springs or shock absorbers with a 2 inch stroke on the seat of my kayak, how do I figure out whether or not that will decrease the G's of landing?

For example: If I currently have 6 inches of travel after impact and increase it to 8 inches by adding 2 inch shocks, that would presumably decrease the G's if the rate of deceleration was constant over the entire 8 inches. But I'm guessing it isn't since the springs or shocks will behave differently from the dampening effect of the water. I have no idea how they would work in conjunction. I'm assuming the deceleration from travel in the water is almost constant; but the curvature of the boat means more surface area hits the water as the boat sinks deeper into it, so rate of deceleration should increase somewhat after initial impact. But in general I'm assuming the boat is a blunt projectile and stops as soon as it has displaced a mass of water equal to the combined mass of boat and paddler. What I can't understand is how springs/shocks in my seat would affect the overall rate of deceleration on my upper body from the beginning of impact until I have come to a stop. How could I calculate that? Also, how do I calculate what spring rate to use (or other value if I use a damper) if my goal was to limit my upper body to a certain number of G's? Sorry I'm not a physics person and have limited grasp of mathematics above Algebra II but I'll try to follow if anyone has any ideas.

Welcome to the PF.

Are you familiar with the concept of "impulse" and the math behind it?

 

[WW Kayaker]

scottdave, Good questions. The 6 inches figure is the number I have seen given by Pat Keller, the most prominent figure when it comes to kayaking waterfalls. Obviously, the amount of aeration in the water makes a huge difference but in my experience the depth of impact off of 20 ft drops has been 4-6 inches with the smaller number being the impact in less aerated water. From watching the impacts on video it doesn't seem like the boat goes much more than the depth it sits at equilibrium but I don't have any measured data on that.
On spring compression, I would like it to have a high spring rate so it does not compress when I am just sitting on it but only when my weight is increased by the G's of landing (maybe my terminology isn't correct).

berkeman, Thanks for the words of welcome. I recall seeing the term "impulse" in reading but it has been a while so I don't recall; I don't think I quite understood when I read about it either. The general idea I got (perhaps totally incorrect) was that there are two things in an impact which can cause damage: 1) the pressure to the spine from the increased weight from the high G's 2) the shock waves traveling through the body/spine. Is this second thing what is meant by impulse? Am I even on the right planet ;) ?
EDIT: So impulse is change in momentum over time. Increasing the time of impact decreases the impulse force. Is this basically the same concept as trying to decrease G's by increasing the distance traveled after impact, thereby increasing the time of the impact? Does adding shocks to the kayak seat actually increase the distance/time of the impact or is this effect canceled out by the way it works in conjunction with the dampening effect of the water?

 

[WW Kayaker]

Here's a short clip of an almost perfectly flat landing off of a twenty foot waterfall. I hit pretty hard on this one but tucked forward so it was ok. I don't have the view from the outside handy at the moment but you can sort of see the impact from the helmet cam.

 

[Ketch22]

My initial thoughts are that your numbers need a little more research. I do not white water Kayak much but I do a lot of ocean. I also do a lot of white water raft and rock climbing. My knowledge is that there are some good creditable studies that show that human bones start to break at close to 12 KiloNewtons of force. There is a fair amount of leeway depending on body attitude at the moment of impact. This is from the Rock climbing world and is based on British military studies.
Also I know that significantly aerated water has a very low buoyant force. I am usually in what is commonly called a 5000lb raft meaning that it has 5000 lbs of reserve buoyancy. These are approximately 14 foot in length and about 6 1/2 ft wide. The same ones you may have seen on many guided trips if you frequent such rivers. I have been over a 20 foot waterfall which had an active aerated impact pool and submerged the entire raft (with 4 occupants) under water. When we reached the lower end of the pool the raft folds and we come back out. This does not however compare favorably with your data. It would be good to confirm empirically what is correct.

 

[WW Kayaker]

My initial thoughts are that your numbers need a little more research...
Also I know that significantly aerated water has a very low buoyant force. I am usually in what is commonly called a 5000lb raft meaning that it has 5000 lbs of reserve buoyancy...I have been over a 20 foot waterfall which had an active aerated impact pool and submerged the entire raft...

If the kayak enters the water at an angle it will go deeper but if the landing is flat it does stay on the surface. I can't quite picture what you're referring to with the raft but would assume it entered with angle? I've had one flat landing from about twenty feet into very aerated water and it was so soft it was hardly noticeable as an impact, but most are not so aerated. See the landing in the video above. Here is the same waterfall but this time I landed on edge causing the boat to half sink into the water reducing the impact better than a flat landing:

In any case, I'd like to figure out whether shocks on the seat will help cushion the falls or whether the combined action of the shocks and the water will end up the same like putting two identical springs one on top of the other.

 

[WW Kayaker]

Here's another impact from 22 ft in slow motion. The boat didn't go much into the water so it was a hard hit. Start at 26 seconds into the video:

 

[JBA]

I had some extra time today, so I developed the attached Excel calculation that I believe will help you with your kayak seat damper and spring issue. There are several steps shown in this program that could be combined; but, I entered them step-by-step so you can see the process.

Edit: Technically this calculation is based upon a straightforward energy translation and absorption basis.
(I originally misspoke and used the term "creation of energy" which is a term that sadly misused far to many times.)

If you have any questions just post them.

 

[WW Kayaker]

I had some extra time today, so I developed the attached Excel calculation that I believe will help you with your kayak seat damper and spring issue.

EDIT: I'm not sure the calcs below are correct because of units used. Is the following formula from your spreadsheet correct?
"Es = Energy Absorbed by Spring (lb-ft) = 1/2 x k x dD^2 =_________"
It seems like since the spring rate (k) is in lb/in and the distance the spring travels is also in inches, the resulting KE would be in lb-in rather than lb-ft. That would be significantly less energy absorption. What am I missing?

JBA, Thanks for the spreadsheet! That's a huge help. Nicely broken down into steps I can understand. I think I can figure out the necessary spring rate using those calcs. I put a sample calc below; if you have a chance to review it that would be much appreciated. One question I have is this: since the energy absorbing capacity of a spring is progressively higher, how would this affect my overall G's of impact, especially as it would be working in conjunction with the water. I could make the spring rate such that the average G's is 40 but it would really go from 0 to something like 68 G's when the spring is fully compressed. I could eliminate most of that fluctuation by using a highly preloaded spring or by using a slightly preloaded spring with a high spring rate connected to a lever (such as in my sample calc below).

Sample:
KE of 175 lb Rider at impact after falling 20 ft = 3500 lb-ft
Total travel after impact = 6 inches (boat travels 4 inches into the water + 2 inches of seat movement with shocks)
Therefore, impact in G's = 40 G [3500 lb-ft / (6in./12in.)ft.]/175 lb
To maintain a steady impact of 40 G throughout the entire 6 inches of impact, the spring must absorb 1/3 of the KE of impact (2inches of the 6 inches).
Therefore, the KE absorbed by the spring = 1167 lb-ft.
We connect the kayak seat to a lever so that the seat can travel 2 inches but it only compresses the spring 0.25 inches. So we need a spring that can absorb 1167 lb-ft KE in 0.25 inches with relatively constant force.
If I've calculated correctly, a 1000 lb/in spring preloaded to 4543 lb (pre-compressed 4.543 inches) will absorb 1167 lb-ft of KE in the next 0.25 inches of travel. Since that's a large distance to compress the spring I could have 2 or 4 springs in combination with smaller preloads each. Are these calculations correct to maintain 40 G throughout the impact?

One thing I can't understand is this: A 100 lb/in spring compressed 1 inch will absorb 50 lb-ft of KE (correct units?). That's an impact force of 300 lb (KE/(2in./12in.). Yet the actual force on the spring when compressed 1 inch is only 100 lb. Why is one number 300 lb and the other 100 lb? Aren't they both force? I must be missing something.

 

[Baluncore]

Working on installing shocks in my kayak seat to protect my back when landing flat off of tall waterfalls (necessary when there isn't a deep pool). I can't figure out if it will actually help.

The deceleration in G can be approximated by dividing the time falling by the time it takes to stop. Anything that lengthens the stopping time will increase the depth of water needed.

When I was young and foolish I paddled slalom kayaks down wild rivers and in big surf. For several reasons I would not expect shock absorbers in the seat to be any advantage. Indeed they may be dangerous.
1. There is no free space for vertical movement of the seat. You should be seated low in the boat, if not, get a smaller boat to reduce the impact.
2. The hull will flex and rise to hit the seat faster than the seat will move on shock absorbers. If you look at the bottom of a kayak you will usually see damage to the hull caused where it is contacted by the seat when the bottom flexes in due to rocks in the river. Maybe glue a 12mm closed cell foam sheet between the hull and seat to reduce the point contact and hull damage.
3. A kayak is built from flexible sheet materials so there is no solid part that contacts a flexible part. That reduces damage by flexing and so prevents energy being focussed onto the junctions with more solid elements. The cockpit surround and seat suspension are probably the most rigid parts.
4. It is very important that you provide a solid foot rest to prevent the lower body moving into the front of the kayak when landing nose first. At the same time the seat should be uncomplicated so that you can get out when you need to, without getting caught. OK, so you can roll, but as your boat breaks up around you in a massive stopper wave, you will reach the point where you need to abandon ship safely, you will have to take the remains of the boat off.
KISS.

 

[WW Kayaker]

Thanks, Baluncore. Space under the seat is indeed limited. However, I've come up with a couple different lever sort of arrangements that allow the springs to be somewhere other than under the seat and also direct the force of the springs to opposite ends of an aluminum frame, thus keeping it from pushing on the plastic of the boat. It won't add anything in the cockpit area to impede bailing out of the boat. The frame will hopefully also keep the bottom of the hull from caving in on impact. I do have a bulkhead as it is a modern WW boat. The one thing I'm not sure of is whether the seat currently has two inches of space under it if I remove the stock plastic supports. There is at least an inch or inch and a half.

 

[Baluncore]

I think you are kidding yourself.
That 2” clearance only gives you 2” to stop at most, after the 20' drop. Landing flat with the 2” shock absorber, will take about 1 second to fall the 20', then decelerate from 16 ft per second in only 2”, which will take less than 21 msec. That does suggest a deceleration of about 50 G. In fact, the flexing of the hull and movement of water will be reducing the deceleration by a much greater proportion than any possible seat mounted shock absorber.
Orientation when landing will have much more effect. Landing on one side, or say 15° bow down, so as to extend the time that the kayak is breaking through the water surface, will reduce the deceleration by significantly more than any 2” shock absorber could.

 

[JBA]

Apart from your questions, which I will address directly later, counting on a spring (or springs) alone for a shock absorber is a really bad idea. Springs do not absorb energy, they store it, which means that as soon as they are compressed and impact action is over they will immediately "kick back" and return the total energy they have stored back to the rider and kayak. A true shock absorber (which dissipates energy) should be used to reduce the total "G"s with the spring only being used to return the shock absorber to it normal pre-shock extended height.

 

[WW Kayaker]

Baluncore, the spring is not intended to absorb the entire impact of the fall but only to add to the absorption capability which the water already had as noted in the OP. Indeed, if the whole impact of a 20 ft fall was absorbed in two inches that would be 120 G (neglecting any energy absorbed by the compression of the spine). But that's not the case as the boat goes 4-6 inches into the water. A 45 degree or steeper entry angle would indeed be much more advantageous but that is not always possible based on the shape of the lip of the falls and the approach, and sometimes the landing is too shallow. The purpose of this is to add to the margin of safety by increasing the total shock absorbing capacity. I think having two more inches does that better than not having springs at all, correct?

 

[WW Kayaker]

JBA, thanks. I realize they return the energy but wouldn't the purpose of reducing the force of impact still be accomplished? The energy would be returned after the impact is over so it wouldn't add to the impact, correct? I had considered dampers but I would need one that is conventional, i.e. it operates at a constant rate despite the decrease in velocity as the impact progresses. Normal dampers they would dampen at a much higher rate at initial velocity of impact. "Conventional" dampers exist but are considerably more costly than a simple spring shock from what I've seen. I also considered making shocks out of memory foam as it would absorb the energy and only return it at a much slower rate. Could be a problem for double waterfalls though with two impacts in close succession.

 

[Baluncore]

I think having two more inches does that better than not having springs at all, correct?

No. Because you would need to pre-adjust the suspension for the paddler weight, drop height, water density and orientation of the landing. Failure to get the adjustment right would significantly reduce the effectiveness of the minor 2” advantage.

I did not suggest a 45° entry angle because, although it would be easier to arrange, it would plunge the hull deeper. I would suggest a minimum 15° initial contact angle. It comes down to the difference between group velocity and phase velocity. Phase velocity of the contact can be infinite if you smack the surface by landing flat. I am suggesting the point of contact between the water surface and the hull can be arranged to travel from one end of the hull to the other in a progressive wave that follows the curve of the hull. That greatly reduces both the impact G and the entry depth. Keeping the phase velocity of the advancing contact below the speed of sound in both water and the hull material will significantly reduce damage to the hull and paddler. It will turn a smack into an osculation, and I know which I would prefer.

A skilled paddler will naturally 'land' in a way that minimises impact. They will do that without thinking because their feet, knees and seat sense and control hull orientation. Adding a 2” suspension to the seat will detach their body from direct contact with the hull and upset their ability to instantly 'know' and control the orientation of the hull. Don't underestimate the effect of the paddlers body being 'at one' with the hull, as opposed to a 'rider' sitting independently on a boat.

 

[WW Kayaker]

That sounds very interesting about phase velocity. I'm not familiar with the concept and didn't quite get it, but it definitely makes sense that a perfectly flat slap is going to be a harder landing (I've experienced it too from 20 ft in not very aerated water). About the adjusting the springs, I know it would be different for each height of the waterfall but my weight will remain the same I hope :) . The springs would be preloaded to such an extent that they don't even move except at higher impact forces, so I could at least not waste them by setting them for 10 ft drops. If I set them to function only on 20 ft or higher drops then they should do something, and 20 ft is what most of the drops I run are. There are some higher in the 30-40 ft range but those aren't flatlanded preferably. Also, since it will take a high force to move the spring at all that means it won't affect the normal boat-and-body-as-one contact. However, good boat contact and skill will not always ensure entering at just the right angle. Aiming for a 15 degree angle may end up being a flat landing if one little thing goes wrong. Some of the best skilled paddlers in the world have broken their backs that way. That's why I'm trying to work into the equation just a little bigger margin of safety by having shocks.

 

[Baluncore]

However, good boat contact and skill will not always ensure entering at just the right angle. Aiming for a 15 degree angle may end up being a flat landing if one little thing goes wrong. Some of the best skilled paddlers in the world have broken their backs that way. That's why I'm trying to work into the equation just a little bigger margin of safety by having shocks.

Vertical shock absorbers would only have an effect during a flat landing when the hull smacks the surface. A flexible closed cell foam under the seat would be a far better investment. While a kayak hull is not floating level you can control orientation with one simple paddle stroke or position. Reaching out and down with the paddle to the surface will spin the hull on it's long axis as you land.

If you cannot control the boat, you should not be taking the risk. Old kayak paddlers with white hair instinctively survive massive white water without thinking about it, or by portaging. As expected, young foolish male paddlers get to meet plenty of young women. For the paraplegics in wheelchairs, it is their nurses during toilet training.

 

[JBA]

Now that I am back online I will try to address your earlier question on the issue of the force vs energy transfer to the spring. First, the force during the spring compression shock reaction is not constant throughout the stroke. It essentially only the riders weight at the start of travel and then increases linearly as the spring compresses to reach the maximum 600 lbs at the end of of the compression stroke. At the same time, energy is being converted throughout the entire 2" of the spring travel and therefore cannot be directly related to just the maximum force alone.

Beyond that, I will continue to address strictly the design elements of your shock absorber design within my area(s) of knowledge and will leave the discussions about all elements of the problem to others with apparently more experience or/and apparent knowledge of kayaking. (My total time in a kayak consists of a few hours of training on very smooth pond).

In that respect , with regard to a spring as an "absorbing" device, spring operate reasonably well in that respect only when either: the level of G's and spring compression force is relatively low; or, where the action of the spring is strictly controlled by a shock absorber acting in parallel that controls both the compression and return actions of the spring, as on automobile suspensions.amount of seat cushioning could be adjusted just as that of an air mattress or pool float by removing a plug and blowing into an attached tube; and the

An absorbing medium that tends to both have it own inherent internal damping and, at the same time, spreads the load over an area of contact with the kayak bottom would seem to be a better approach than a spring mounted mechanism alone.

One alternative, that might have some possibility would be a tightly confined inflated air seat cushion. I have started a preliminary calculation on what the limits of something like this might be for a 12" x 15" seat size and with a 175 lb rider. I will let you know what I find when my calculations are completed.

Edit: Partial calculation with force error deleted.

(On a British Morgan sports car I once owned the suspension was so stiff that it was more like having the axles welded directly to the frame and seat supports were flat board panels. In this case, the car manufacturer's solution to giving a comfortable ride to the occupants, which worked very well, was a small bit of padding and the equivalent of about 10 ft of air filled bicycle tire tube coiled within each seat cushion. The seat cushion's inflated height was controlled by the diameter of the tubing and the expansion of the tubing by the cushion cover.)

 

[JBA]

I did not address your calculation in my above post so here is my response on that issue.

After spending time reviewing your loading calculations, I finally realized that regardless of any other factors one very basic problem with your plan for a 2 ft lever with a 2" end travel and a .25" spring travel is that the distance from the spring to the lever pivot can only be .02", so, in addition to that not allowing any room for a spring, it also means that a 275 lb rider sitting on the seat would result in a: 275 lb x 24 / .02 = 308,400 lb on the spring and on the lever pivot mounting.

At the same time I have to admit I made an error in my spread sheet of not correctly converting the inches to ft in my spring energy absorption calculation and as a result the amount of the 3500 lb-ft energy that will be absorbed by a 200 lb/in spring with a 2" stroke is only 33 lb-ft, not 400 lb-ft as is now indicated which reveals how really bad they are as shock absorbing devices.
The correct formula for example is: E absorbed =1/2 x 200 lb/in x 12 x ( 2 in. / 12)^2 = 33.33 lb-ft

 

[Baluncore]

The seat in a kayak is usually hung from the cockpit coaming. There is nothing else solid enough to spread the forces over a large enough area of hull. Any shock absorber system with long arms would need anchor points on a reinforced area of the hull with sufficient tapered perimeter to spread the load. That would increase the rigidity of parts of the hull, increase the boat weight and increase the chance of hull damage. I see no way to engineer a suspension system that would have a net benefit.

 

[jack action]

I've been following this conversation and I wanted to chime in as I didn't see anyone looking at this problem the same way I do (but I may be wrong).

The kayak entering the water can be modeled as a spring. The upward force is the mass of water displaced by the kayak against gravity which is $F = \rho V g$. If we assume the kayak is of constant area $A$ then $F = \rho Agx$ which has the form $F=Kx$ where $K$ is the stiffness of a spring.

The energy absorbed by a spring is $\frac{1}{2}K x^2$. So if the kayak sinks $6"$ due to potential energy of $3500\ lb.ft$, then $K_w = 2333\ lb/in$ . The maximum force absorbed by the spring is when it is compressed $6"$, thus $14\ 000\ lb$. Note that it is twice as much as the values calculated in earlier posts, because those values are averages and not maximum values.

If we add a spring below the seat, we then have 2 springs in series to absorb the shock. The question is: «What is the spring constant $K_s$ necessary to accommodate a $2"$ travel under the total energy absorbed?»

The spring constant of the two combined springs $K_c$ is:
$$\frac{1}{K_c} = \frac{1}{K_w} + \frac{1}{K_s}$$
We know that $K_s x_s = K_c x_c$ and that $E = \frac{1}{2}K_c x_c^2$ and therefore:
$$\frac{2E}{K_s^2 x_s^2} = \frac{1}{K_w} + \frac{1}{K_s}$$
Or:
$$K_s = \frac{1}{\frac{x_s^2}{4E}+\sqrt{\left(\frac{x_s^2}{4E}\right)^2 +\frac{x_s^2}{2EK_w}}}$$
For $x_s = 2"$, then $K_s = 5930\ lb/in$ and $K_c = 1674\ lb/in$.

We can verify that $x_c = \sqrt{\frac{2E}{K_c}} = 7"$ and the maximum force is $K_c x_c = 11\ 860\ lb$. Knowing this force $F$ goes through both springs, then $x_s = \frac{F}{K_s} = 2"$ and $x_w = \frac{F}{K_w} = 5"$ which agrees with $x_c = x_s + x_w$.

So the maximum force goes down from $14\ 000\ lb$ to $11\ 860\ lb$ (about 15% less) and the kayak sinks $5"$ instead of $6"$. This tends to agree with the posts that say that a spring wouldn't do much difference.

And a spring constant of $5930\ lb/in$ is extremely stiff and I'm not sure of the design of such a spring. Of course, you can use a softer spring, but it will necessarily bottom out while absorbing less energy and the model will go back to a single spring model (the water) which will absorb the rest of the energy. Thus the kayak will sink somewhere between $5"$ and $6"$ depending on how soft the spring is.

 

[JBA]

Thank you jack action for joining in. I have been wrestling with this and my solutions and really wishing someone would join the discussion so we could get new eyes on all of it and either confirm my approach or present a better calculation approach.

 

[JBA]

Yesterday I did the spring rate calculation for the kayak alone based upon the fact that it alone without any added effects is stated to submerge 4" on impact; but, then I began to question whether the kayak acts in the manner of a spring or more like a fluid displacement damper. The difference being that the resisting force would be higher upon the initiation of the impact and constant (or at least more so) during the submersion travel stroke. If so, then the kayak would absorb the impact energy at a lower maximum resisting force for the same 4" travel. Any thoughts on this issue?

 

[jack action]

I began to question whether the kayak acts in the manner of a spring or more like a fluid displacement damper.

A pure spring is pretty rare; there is always some damping effect, somehow. With a pure spring scenario, the water would push back the kayak 20 ft in air. If it «settles» at water level, then it must have some energy dissipation somehow. I say «settles» because even though the water doesn't throw the kayak 20 ft, throwing an object (that floats) into water will be thrown higher than water level for some distance while on its way up.

By studying the harmonic oscillation and observing a frequency $\omega_0$ and damping ratio $\zeta$ caused by a mass $m$, one could deduce a damping coefficient $C$ and a spring constant $K$ this way:
$$K = \frac{m \omega_0^2}{1-\zeta^2}$$
$$C = \frac{2m \omega_0 \zeta}{\sqrt{1-\zeta^2}}$$

 

[JBA]

WW Kayaker,

I would like to know more about the current seat mounting in your kayak. First, obviously that arrangement will withstand the forces you have experienced without damage; so, that indicates that there is a connection point(s) that could withstand the forces of a damper assembly.

Second, if the seat is hung from the upper section of the kayak, as suggested above, then it would seem that there might be some flexing of the kayak upper panel and/or hangers that are currently taking some of the energy of the impact. Have you observed or felt anything that would confirm that? (While you were busy just trying to control the kayak)

 

[JBA]

jack action, I think your comment somewhat confirms that there is a significant energy dissipation occurring during submersion because essentially any object dropped into open water from any height fails to ever rise much above its ambient buoyancy level on recovery unless it occurs in a confined pool where the outgoing waves quickly strike restraining walls and reflect back to elevate both the object its closely surrounding water level above the ambient water level. Experiencing or performing a water ski jump or the launching of a lifeboat from a barge or ship are examples of opportunities to observe this.

 

[WW Kayaker]

Sorry, for some reason my email stopped sending notifications of replies to this thread so I just now saw the most recent comments. Thanks for all the helpful information. I'll try to address all the recent points below. If any question is unanswered let me know and I'll do so.

Baluncore: "While a kayak hull is not floating level you can control orientation with one simple paddle stroke or position. Reaching out and down with the paddle to the surface will spin the hull on it's long axis as you land."
Not sure what you're describing here (but interested to know). I'm pretty familiar with all different techniques for landing waterfalls. I'm not aware of any technique that attempts to adjust the angle of landing using the paddle while impacting the landing zone (but I may have misunderstood you). The paddle is used to while coming off the lip, of course. Once airborne all adjustments are done by body movements (equal and opposite reaction...) but I don't know of any adjustment made while contacting the water on landing.
"If you cannot control the boat, you should not be taking the risk." The purpose of the shocks is not to compensate for lack of skill. I'm very careful to stay within my limits. Utilizing devices to make a sport safer does not mean one is being reckless to begin with. We all wear helmets; I could argue that if one is good enough one should not need a helmet (or a PFD for that matter) but what is intelligent about refusing to use a safety device because I think I'm skilled enough not to use it? It's like tightrope walking without safety...just stupid unnecessary risk taking in my opinion no matter how skilled one is. If shocks would make waterfall kayaking safer then I'm all for it, but I would never consider them a replacement for proper skill.

JBA and Jack Action: Many good points and questions. Hope I can answer them all without jumping around too haphazardly.
1) Seat design: the seat does hang from both sides of the cockpit rim as Baluncore said, but it isn't free-hanging. Rather, the bucket type (or U-shaped) plastic seat is attached on both sides of the rim by two bolts on each side and also the bottom rests on the plastic I-beam which runs longitudinally along the bottom of the hull for support. My plan was to replace this bottom support by a frame that fits in the cockpit and allows clearance for the seat to move downward on impact.
2) Does the seat absorb impact already by flexing the cockpit rim? I'm sure it does to some extent but the I-beam under the seat would allow very little travel. The hull must have some absorption capacity since if I land on bedrock from 5 feet (as I've done) it is a hard hit but doesn't hurt (if tucked fully forward on the bow), whereas if I just landed on my bottom from 5 feet outside the boat I'm sure it would hurt! However, maybe that is more a question of spreading out the energy over more surface area through the seat thus preventing high pressure points from point contact impacts on the tailbone if I land on rock outside the boat.
3) in-lb to ft-lb conversion: I made the same conversion by dividing by 12 and realized how small a percentage of the total energy would be absorbed by a 2 inch spring unless it had a very high spring rate and was preloaded. Also, as you mention, using a lever would put great pressure on the framework of the system even at rest (if preloaded).
4) This brings me to a conundrum: To absorb the necessary amount of energy, the springs would have to be preloaded to such a high force that it seems impossible for the body to withstand it. Yet, clearly all this energy is already being absorbed even without shocks in the seat. If we take 6 inches for impact depth in average aerated water and 4 inches for impact depth in water that is only slighly aerated (a low flow waterfall), then the average G's experienced by the body must be 40 G and 60 G respectively. That's a huge force on the body (7000 lb and 10,500 lb for a 175 lb paddler)...but I can't get around it. There's no way the average G's can be less than that unless the distance of travel after impact is greater (which experience shows it's not). This is all assuming a flat landing, not at a slight angle. These forces are also not necessarily the peak forces as you noted, unless the rate of slowing the fall is constant throughout the entire time of impact.
5) Part of this conundrum is explained by assuming the actual weight on the seat (and spine) is not 175 lbs but only a fraction of that. It makes a huge difference whether the paddler is tucked. If we assume a good tuck over the bow takes most of the weight off the lower back (the usual place paddlers break their backs when not tucked forward), maybe there are only 50 lb left over the lower spine. So, 50 lb at 40 G is a 2000 lb force on the lower back. That is above the 6kN (1349 lb) maximum spinal force allowed for fall-arresting harnesses for roof workers but still below what the military tests suggest as the "maximum tolerance" for forces on the spine from parachute canopy opening (which is 12kN or 2698 lb). These maximum allowances are from the following fascinating study which I just came across this week: http://www.hse.gov.uk/research/hsl_pdf/2003/hsl03-09.pdf This force (2000 lb) is also well within the limits that bones are said to be able to handle. They can supposedly take about 19,000 lb of force per cubic inch of bone before fracture, but obviously there are many other factors.
[Interestingly, this same document gives 12 G as the maximum safe force allowed by standards for fall-arrestor harnesses and 20 G for the maximum safe force in ejector seats for military pilots. In both cases these standards specifically state that proper vertical alignment is necessary. This is totally contrary to kayak philosophy for waterfall impacts; the kayaker experiences much higher G's as noted above (40-60 G) and landing with the spine vertical is a big risk for spinal injury.]
As an added point, 30 ft is usually considered a maximum height for flat-landing waterfalls (only if the water is well aerated and one is fully tucked) but is not at all recommended because it is pushing the limits. At an impact depth of 6 inches that would be 60 G which would be a force of 3000 lb if only 50 lbs of the body were actually over the spine. That is just over the military maximum for ejector seats for physically fit military members. So, this is consistent with the fact that only the most physically fit paddlers would think of flat-landing a 30 footer. There are several recorded instances of paddlers accidentally flat-landing 50 footers in well aerated water without injury (while fully tucked forward) and even a 60 footer (with only a slight spinal compression). One paddler years ago flat-landed a 78 footer in poorly or normally aerated water and survived with only a broken back (if "only" is the correct phrase to use :) ).
6) Another consideration: The study linked above (on spinal impact tolerance) says that the rate of onset of the force makes a big difference (what they call "jolt"). Maybe that is a more important consideration than the actual peak G's (at least if one is fully tucked to avoid too much weight concentrated over the lower spine). If so, then shocks in the seat might be a huge help even if they didn't absorb much energy. They could make the increase of force more gradual, especially if the initial force of impact on the water is greater than the rest as one of you suggested might be the case. Maybe this would be a huge help especially when the landing is extremely flat and is like a slap as Baluncore noted earlier (but I didn't quite grasp the concept of phase velocity unfortunately)? If fully tucked forward, most of the body would be experiencing horizontal G's rather than vertical and studies by Stapp and others have shown the body can take very high horizontal G's for brief impacts without harm. The lower spine alone would experience vertical G's.
7) On Jack Action's calculations of the spring rate of the water/kayak impact: I think I followed what you said. If we took two 200lb/in springs and put them in series it would not reduce the distance of impact any more than having one 200lb/in spring alone. Agreed. However, I suspect the water doesn't act like a spring but more like a damper with uniform rate of dampening during the entire impact. I assumed the behavior of this impact followed Newtons approximations for the impact depth of blunt projectiles (as partially noted in the OP):
https://en.wikipedia.org/wiki/Impact_depth
If so, wouldn't the depth the kayak descends in the water on impact be constant since the mass of the boat and body remains the same? According to Newton's approximation, wouldn't the depth that the kayak descends be roughly equal to the depth it sits in the water at equilibrium since it displaces an equal mass of water (except that the boat does have some aerodynamics to it, so this isn't quite true during impact)? This behavior would also explain why the depth of impact seems to be the same regardless of how high the waterfall is. It seems like it goes about 6 inches into normally aerated water regardless of whether the kayaker goes off a 20 footer or a 30 footer. If this is true, would a 2 inch spring in the seat increase the total distance of impact to 8 inches (thereby providing benefit) rather than lessen the depth of water impact and average out the total impact depth to 6 inches anyway (thereby providing no benefit)?
8) Conclusion: If slowing the onset of force on the spine is more helpful than reducing maximum G's, then a spring with minimal preload and low spring rate might be best, or maybe memory foam under the seat with minimal springs to keep paddler weight from pre-compressing the foam during normal paddling. If reducing G's is the more important factor, then it would be necessary to use a high spring rate and preload to match the average force of the water damper (e.g. if the impact depth is 8 inches [6 from water damper and 2 from spring], then the average G's for landing a 30 foot waterfall with 8 inches impact depth would be 45 G's. If the weight on the spine is 50 lb then this means an average force of 2,250 lb during the entire impact. That means the spring would have to be preloaded to around this amount in order not to waste the 2 inches of stroke on going from 0 lb to 2250 lb. Being a high preload, this would not help reduce the rate of onset of this force (the "jolt" as the study quoted calls it).

I hope this makes sense. Sorry to be so long.

 

[JBA]

WW Kayaker,

Glad to find out you are still with,us. As I mentioned above, I have been investigating the concept of an under seat air cushion and below is an example of a fully contained air bladder the size of my reference seat. What you should not is the the seat deflection due to a 175 lb rider is negligible and the pressure at the full impact compression is actually very low (40 psig) and it only begins to compress when 1400 lbs of rider impact force (8 G's) is applied.

In working with this and thinking about the car seat I described made me think of pneumatic boat fenders and below is an example of what might be interesting to investigate (or play with) in testing this concept. Each fender is 3.5 in in diameter but the pressure is adjustable so they could be imflated to alow enough pressure to provide a lower seated load ht. What I envision is a number of these lying side by side, each fender is 13" long. Just a thought of maybe something to experiment with at a low cost.

http://www.overtons.com/modperl/product/details.cgi?pdesc=Dockmate-Dock-Shield-Fender-3-5-x-13&i=855000&from=grid

 

[Baluncore]

Sorry, for some reason my email stopped sending notifications of replies to this thread so I just now saw the most recent comments.

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[jack action]

However, I suspect the water doesn't act like a spring but more like a damper with uniform rate of dampening during the entire impact.

OK, let's model the water as a pure damper, that is $F= -Cv$ where $C$ is a damping coefficient.

We already know the initial velocity upon impact, i.e. $v_0 = \sqrt{2gh}$. Knowing that $v = \frac{dx}{dt}$ and $F = m\frac{dv}{dt}$, then:
$$F = mv\frac{dv}{dx}$$
$$-Cv = mv\frac{dv}{dx}$$
$$dx = -\frac{m}{C}dv$$
$$\int_0^d dx = -\frac{m}{C}\int_{v_0}^0 dv$$
$$d = \frac{m}{C}v_0$$
Thus we can estimate $C$ if we know the distance $d$ that the kayak sinks in:
$$C = \frac{mv_0}{d}$$
The maximum damping force will be at maximum velocity, which is at $v_0$:
$$F_{d\ max} = C v_0 = \frac{m}{d}v_0^2 = \frac{2mgh}{d} = \frac{2Wh}{d}$$
For $W= 175\ lb$, $h = 20\ ft$ and $d= 6\ in$, then $F_{d\ max} = 14\ 000\ lb$.

What difference will adding a spring in series do? Assuming the ideal case where the spring compresses completely before the kayak begins sinking:
$$v_0 = \sqrt{2gh - \frac{K_s}{m}x_s^2}$$
and
$$F_{s\ max}= K_s x_s$$
$$F_{d\ max} = \frac{m\sqrt{2gh}}{d}\sqrt{2gh - \frac{K_s}{m}x_s^2}$$
The spring constant necessary to achieve a compression of $2"$ without bottoming out is $5930\ lb$ which will give $F_{s\ max} = F_{d\ max} = 11\ 860\ lb$, same as with the 2 springs in series. With any other spring constant, either $F_{s\ max}$ or $F_{d\ max}$ will increase (up to $14\ 000\ lb$).

I thought that was an interesting result. I guess it means that there is a maximum value for the energy that you can absorb with a spring under the seat, no matter how the energy will be dissipated afterward.