How much buoyancy is needed for a floating dog ramp?

[davidtu]

I want to create a floating boat ramp for my dogs. The dogs weigh 50 and 75 lbs each. I have seen commercial ramps using floats to stablize and support the ramp while the dog walks up it.

My question is if I make my own, how many pounds of buoyancy must the floats support in order to allow my 75lb dog to walk up it out of the water.

It seems that the dog will not "weigh" a full 75 lbs when he starts up the ramp. I guess at some point he gets out of the water and his full weight (plus water trapped on him) is upon the ramp. However, the ramp is secured at one end attached to the back of the boat so I presume there is some torque and fulcrum issues to consider.

Please refer to the attached image. The right hand side of the ramp is attached to the boat. The left hand side is supported by two floats.

So the question is how many lbs of buoyancy must be provided by the floats? Please make sure to indicate if you are answering per float or for both floats.

Thanks for your help.

 

[berkeman]

You are correct that using torques about the axis of the attachment point on the boat is the way to approach this. From the way you've drawn the sketch, I'd guess that you only need about half the bouyancy of the heaviest dog in the floats on the left. Start there and adjust it as necessary. Luck dogs!

 

[Danger]

Welcome to PF, Davidtu.
I don't know how classy you want this thing to look (nice picture, by the way). A couple of empty water jugs or 5-gallon plastic pails should give more than enough support. One of either will support my full weight (out of the water; not just as a buoyancy aid). I'm pretty light for a human, but heavier than your dogs.
As another (or auxilliary) system, you could always either spring-load the ramp in the upward direction or use a locking device on the hinges to assist in the weight-bearing.

 

[olgranpappy]

You are correct that using torques about the axis of the attachment point on the boat is the way to approach this. From the way you've drawn the sketch, I'd guess that you only need about half the bouyancy of the heaviest dog in the floats on the left

I agree somewhat with berkeman, a slightly more detailed analysis (assuming that the dog is much lighter in the water than out of the water--which is true because the density of dog is roughly equal to the density of water) shows that the upward force needed depends on the location of the point where the board first exits the water (in the picture this looks to be about halfway down the board, thus the factor of 1/2 in berkeman's analysis). Of course, the actual point where the dog-board first breaks the water will depend on the length of the ropes tied to the floats and how far the floats are themselves pulled down when the dog steps on the ramp and how high the water level on the boat is, etc.

I find that the upward force 'T' that you would need is something like:
$$T=\frac{M_{dog}g L}{\ell+L+d} + \frac{M_b g}{2}$$
where $$M_{dog}$$ is the heaviest dog mass, and L is the distance from the attachment point on the boat to the water level, and $$\ell$$
is the length of the rope attached to the bottoms of the floats, and d is the distance from the bottom of the float to the water surface, and M_b is the total mass of the board, and g is 9.8 meters per second per second. [actually the above equation is not quite right as it was derived assuming the board was not subject to a buoyant force, which is obviously incorrect--but it gives as least an upper bound on the force needed...]

In berkeman's analysis of looking at the picture, d is roughly zero, and L and $$\ell$$ are equal, and the mass of the board is neglected, which thus gives:

$$T=\frac{g}{2}(M_{dog})$$
I.e., half the weight of the dog is needed...

One can also solve for 'd' in terms of known quantities (and, unfortunately also 'T') and thus arrive at an equation for T... but oh! this is all rather academic, because there may be a simple solution...

The picture you drew shows the distance from the attachment point as being rather large, but if in fact, the board is attached to the swim platform, then the distance from attachment point to water will be very small... and in fact the dog will be very close to this point when finally its full weight is on the board, thus it will produce a very small torque. So really, the floats probably only need to support about half the weight of the board as it weighs when it is mostly submerged.

Thus, in the case of an attachment point very close to the water, your floats can be quite modest indeed.

To be on the safe side I would maybe just go with something like the 5 gallon jugs that Danger suggested, but I suspect you can get away with a lot less.

anyways, the main point is that you probably don't need much buoyant force at all, a couple very small buoys will most likely do just fine.

 

[mgb_phys]

This is going to be the most carefully designed and analysed dog rammp in history!
Remember to be careful about the surface, it needs to be something non slip but nothing the dogs can get their claws caught in if they slip off.
Rubber strips are good, chicken wire mesh or wooden runners aren't.

 

[Danger]

Might be easier to just use outdoor carpeting. Good point.