by DanaDCole on Fri Dec 19, 2014 10:31 am
Maybe I'm wrong, and someone smarter than me please correct me if I am, but I am wondering about John Harris's statement, " Someone can do the moment calc for me right quick, but the added pounds at the top of the mast will require an additional X pounds of ballast, where X is a shockingly big number." Moment calculations are pretty complicated, but to my mind a much simpler, leverage formula is needed instead. That formula is C = (A x L1)/L2, where A is the antenna weight, L1 is the distance from the heeling (roll) pivot point (fulcrum of a lever) of the boat, L2 is the distance from the pivot point to the bottom of the hull, and C is the counterweight required to counter-balance the antenna moment. (The below diagrams are not to scale.)
|<------------------------------------------------19' 3"------------------------|--------------------------------->|
[Masthead]<-------------------------------------------------------------->[Roll Point]<-------------------->[Hull]
The total distance from the hull bottom to the top of the mast is about 19' 3" (19.25 ft.). I think most 3dB VHF antennas weigh somewhere around 2 pounds, and most of this weight is at the bottom of the antenna. I don't know the all-important distance of the boat's roll pivot-point from the hull bottom, but conservatively it should be around 2' or 1' at the worst. So I'll run the formula twice for 2' and 1'. In this example A = 2lb, L1 = 17.25' or 18.25', and L2 = 2' or 1'.
A L1 L2 C
C1: |<--------------------------------17.25'------------------------------------>|<------------2'------------>|
C2: |<-----------------------------------------18.25'------------------------------------------>|<----1'----->|
C1 = (2 x 17.25)/2 = 17.25lb
C2 = (2 x 18.25)/1 = 36.50lb
That difference of 1 foot more than doubles the amount of additional ballast needed, but the amount is still manageable, not much more than the weight of a 30 AH battery, and the battery is directly below the mast. Can anyone supply the actual rolling pivot point? If it is higher than 2', the counterweight required would be considerably lower. If it is less than 1' (I don't know how it could be) the counterweight req. would be much higher, for example if it is only 6", the counterweight requirement would be 75lb, but even that much is manageable with, say, a battery and some more lead weights.
All that being said, John is more than correct to warn against the continual additions of items above the heeling point. Anything you do add should be weighed (pun intended) against other items that can be done without or moved lower down. And, I have not included anything about the fore-and-aft (pitch) pivot point, which should also be considered. That point would be further aft, so some of the counterweight should probably be placed further back. Also, the antenna is 3' tall, and even though as I said most of the weight is at the base of the antenna, perhaps the height of the antenna should be figured in somehow. This complicates things, but to my way of thinking it would only add 10% or so to the ballast requirement. To be on the safe side, add 20-25%. Nothing has been mentioned about the weight of the cable either. RG-8X would be OK for such a short run and it doesn't weigh a lot, but still there is that moment-arm thing. There was some mention of putting the cable inside the mast, which would be nice, but after all the careful work sealing the mast against water infiltration I really hate the idea of drilling holes in it.
Again, I am no engineer by any stretch. If there are flaws in my argument (and there probably are plenty) please correct me.