# Mass-spring-damper problem for kayaking waterfalls

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1. May 27, 2017

### 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.

2. May 27, 2017

### 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.

3. May 27, 2017

### Staff: Mentor

Welcome to the PF.

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

4. May 27, 2017

### 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 cancelled out by the way it works in conjunction with the dampening effect of the water?

Last edited: May 27, 2017
5. May 27, 2017

### 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.

6. May 31, 2017

### 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.

7. May 31, 2017

### WW Kayaker

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.

8. May 31, 2017

### 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:

9. May 31, 2017

### 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.

#### Attached Files:

• ###### Kayak Rider Seat Damping Calc.xlsx
File size:
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Last edited: May 31, 2017
10. Jun 2, 2017

### WW Kayaker

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.

Last edited: Jun 2, 2017
11. Jun 2, 2017

### Baluncore

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.

12. Jun 2, 2017

### 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.

13. Jun 2, 2017

### 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.

14. Jun 3, 2017

### 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.

15. Jun 3, 2017

### 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?

16. Jun 3, 2017

### 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.

17. Jun 3, 2017

### Baluncore

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.

18. Jun 3, 2017

### 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.

19. Jun 3, 2017

### Baluncore

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.

20. Jun 5, 2017

### 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.)

Last edited: Jun 5, 2017