Weight/force of accelerating object

[Rreeves0802]

This is a practical physics question from a sailboat cruiser in Hawaii.

My name is Randall. Sadly, from the perspective of this forum, I was an English major, and so may not know the best way to frame the following question.

I will soon be sailing solo from Hawaii to Alaska. The proliferation of debris in the north Pacific due to the Japanese tsunami a year ago has encouraged me to purchase a radar unit for my boat that will help me keep from colliding with some of it. The radome (radar dome) mounting bracket delivered does not fit my mast, so I am having to fashion a bracket out of wood and fibergass (my location is pretty remote...can't just run down to the marine store and exchange the item).

I don't know how strong to make the bracket.

The radome weighs 20lbs. It has the general look of a wedding cake: is 19 inches around by 11 inches high. It will be mounted to the front of the mast at 15 feet above the water.

This is what the radome looks like: lowrance.com/Products/Marine/Broadband-Radar/3G-Broadband-Radar/

For perspective, this is a picture of a smaller radome mounted on a boat exactly like mine and in roughly the same position:
voy.com/119861/3947.html

Boats at sea move, sometimes violently. At dock, my bracket would only need to hold up 20lbs. But if, at 15 feet above the water, the radome is accelerating from 0 to, say, 10mph in 1 second as the mast and boat swing around in reaction to the waves, how does that effect the "weight" of the radome and/or the force on my bracket. Is the force at the above figures the rough equivalent of a factor of 10, I.e.200 pounds of "weight" on the bracket, or is it much more? What if the acceloration is 20mph in the same 1 second?

Except for the weight of the radome, these numbers are guesstimations. What I need is a sense of range. 20 to 200. Or 20 to 2000. I.e does the bracket need to be able to withstand 200 or 2000lbs of pressure.

The question is serious. If my bracket fails, it could take the mast with it, this while I'm mid ocean. Not a happy prospect.

Many thanks in advance,

Randall
Aboard MURRE
Nawiliwili Harbor, Kauai
murreandthepacific.wordpress.com

 

[jedishrfu]

your best bet is to contact the mfgr and ask them about your problem. They may give you an idea on how to best mount it given your circumstances.

 

[K^2]

You are seriously planning to take a 30-foot ketch half the way across Pacific?

In terms of forces involved, the bracket doesn't need to handle anything your mast won't. Can mast survive 10G of acceleration at mounting point? Possibly. So 200lb might be reasonable. Can it survive 100G? Definitely not. So 2000lb is certainly an overkill. I know this doesn't narrow it down too much, but if you can't find any other info, that's a start.

 

[Cleonis]

Boats at sea move, sometimes violently. [...] as the mast and boat swing around in reaction to the waves, how does that effect the "weight" of the radome and/or the force on my bracket.

You mention swinging, as in rolling of the boat.

While you do have to consider rolling of the boat, I don't think that that is when the bracket will be hit hardest.
I think the hardest blows are when the boat is lifted and then falls down again, slamming back in the water.


I have very little experience in boats, even less in rough circumstances, but I don't think rolling motions of the boat are the biggest hits.
Rising up and slamming down is so hard because of the added involvement of gravity. The boat is lifted up, then gravity gets the opportunity to accelerate the boat, the boat falls, and then it suddenly hits the buoyancy point again.

It is possible for you to rig a test setup?
You create a mockup radome, that has a comparable size and weight.
You manufacture a bracket, and you secure bracket plus mockup radome on a short pole.
You lift the pole, slam it to the ground, and you try to reproduce the hardness of the jerk that it would experience at sea.

Very labor intensive, yes, but I don't see any other way of evaluating the bracket.



If you do want to test, then I think the more worthwile test is for resilience under dynamic loads.
A static load is when you, say, tie a rope to the bracket, and then you add weight, many times the weight of the radome. Conversely, dynamic stressing is when you try to replicate the repetition of peaks in the force. So my suggestion is that is to create a mockup, and you try to reproduce typical rise-fall slams.

 

[Cleonis]

Boats at sea move, sometimes violently. [...] as the mast and boat swing around in reaction to the waves, how does that effect the "weight" of the radome and/or the force on my bracket.

It occurred to me there may be a way of comparison.

The acceleration to move an object along a circle with a radius of 1 meter, completing each circle in 1 second. The corresponding acceleration is about 4G. Hence if an object weighs 10 pounds the corresponding force is 40 pounds.

A bit of physics: motion along a circle can be thought of as a composite of two linear oscillations perpendicular to each other. Many of the numbers carry over to the component motion.

So if you have a side to side swing, swinging out 1 meter to either side, completing each cycle in 1 second, you have that at the extremals the acceleration is 4G.
This seems to put the stresses on the bracket due to side to side swinging in the range of 1G to 10G. (More precisely, stresses from the radome on the bracket. Subsequent stresses of the bracket on the mast is another matter.)
As I wrote earlier, I think peak stresses in the vertical direction are the main concern. How about a diagonal strut with, say, a 30 degrees angle between strut and mast, to take most of the vertical stress. Another concern is torsional stress from the bracket on that mast. That mast is designed to take the stresses of wind in the sails, which involves little or no torsional stress. The radome is big, so it's center of mass is quite a distance away from the mast.

I suppose this means that the bracket must not be too strong. If the connection between bracket and mast would be stronger than the connection between mast and ship then in the extremest case you could lose the mast.
Therefore in the case of catastrofic failure the break must occur in such a way that the mast remains intact. Hence my thought that the bracket must not be too strong.

 

[sophiecentaur]

The torsional force from a gust from abeam could be as much as any of the other forces, I reckon. This could stress the rigging so the pod should be mounted as close into the mast as possible.
Presumably you have the 'unsuitable' bracket with you and that should give you an idea of the sort of strength you're after. Just make your version a bit stronger feeling than that and that should be enough. How the bracket is actually fitted to the mast will be important. Several hefty Pop Rivets on each fixing plate should do the job. I see an awful lot of rivets used on mast fixings and you will probably need blind fixings for half way up as you can't get your arm with a spanner on the inside.
P.S. Have you tried any boating forums? I am always using the Westerly Owners forum and there is a wealth of valuable experience out there.

 

[Rreeves0802]

Thanks all for the quick replies.

To answer some of the comments/questions...

-Yes, am crossing the Pacific in a 30, or rather 31, foot ketch. Have already sailed solo San Francisco to Mexico to Tahiti to Hawaii, so I know it can be done. However, the leg to Alaska poses some unique challenges. Collisions with abandoned, drifting fishing trawlers and floating Harleys being but two.

-I am less concerned about the vertical stresses simply because the bracket I'm building is naturally stronger in that line.

-Yes, the tortional/twisting stresses are way out of mast design, so also had thought that the bracket should be designed to fail before the mast, but that refinement is beyond my skill.

-Cleonis, thanks for the reasoning re 1G to 10G. This suggests that my former range; i.e. the bracket should be able to withstand 200 pounds of "impact" is more likely. That is helpful. I know the reasoning is not tight, still helpful though.

-I haven't gone to other sailing boards or the manufacturer (yet) because my situation is unusual in today's world. That is, the masts are wood, box construction Sitka spruce. None of the brackets on the market take this material into account; they're all for aluminium masts, etc. But will go to a cruisers forum today per Sophiecentaur's suggestion. Thanks.

-Yes, wish I could test, but Kauai is a bit back-of-beyond...

Thanks again for the help with an unusual question.

RR