I have a couple ideas that might solve your problem.
The first will depend on weather you have a natural wood deck that you wish to keep natural. ie; a redwood deck as opposed to a douglas fir deck.
If you don't mind putting a coating on your deck you can go to the nearest marina that has a good rigging shop. There is a rubberized paint that you can purchase that they use for boat decks. It has small lumps, of what I think is latex, in it that give the surface a good traction base. I have personally used this while helping a friend get his 38' racing ketch ready for the races in San Francisco bay. And yes, I was one of the nuts hanging over the side of the boat going across the bay at 40 knots. What a rush!
The other is much cheaper. And a lot less labor intensive. Find some carpet and tack it to the deck with a heavy duty hammer tacker. Usually you can get plenty at any job site that has just had the carpeting installed. Just ask one of the workers if you can have some of the leftovers. Most are glad to get rid of it. That way they don't have to cart it off and pay to dump it.
After you are out of the wet and frosty months you can easily take it up and your deck will be ready for the BBQ season.
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Best regards; The Home Smithy
Yes there is. Give me a couple hours and Ill have a link or the information for you.
Thank you for your patience.
The Home Smithy
Here is an option that I ran across as I was searching for the rubber mats. I remember my Grandfather swore by these. Have a look while I continue the search.
These are quite pricy but are industrial stregnth
Hi again terry.
I think that I have found the material that you are thinking about. Have a look and let me know.If this is the material that you say was on the cruise ship deck, there is a good reason that you don't find it anywhere else. For a 3'x10' piece it will run you about $360.00. It is manufactured by 3M products and has a very long life expectancy. Depending on the size of your deck this may be cost prohibitive. The product is well worth what they ask though. You can order it here
If this is still not what you are thinking about I will need a better description of the matting.
Everything aside, these are about the only options available that I could find. The rest are closed bottomed and are more like foot wipers than anything else. There are other styles of the same thing but they are more expensive or just cheaply made. If it were me that wanted this I would go with the recycled tire mats. They are durable, inexpensive, easy to store, and easy to clean. The gentleman that sells these will also make you customized mats to suit your needs. Oh did I mention that they are recycled tires? Cant beat that when it comes to having an enviromentaly friendly home.