radar on the mast
 

I've been wondering how having a radar on the mast affects rolling... Is it possible to calculate the effect of additional weight on the mast in calm and storm conditions?



Displacement = 8,600 lbs official, 9,600 lbs real.
Ballast: 3600 lbs, lead.

Mast height above deck: 37.5 ft
Radar height above deck: 22 ft

Radar weight with mount bracket: 30 lbs

Many thanks!
Gleb

C. A. Marchaj formula
 

I found this iin 'Seaworthiness The Forgotten Factor' by C. A. Marchaj. (Equation 20A, page 128).

Tn=6.3(SQRT(Ir/(GM*displacement)))

Tn is the natural period of rolling
Ir is the mass moment of inertia, not the area moment of inertia.

Adding a weight (mass) on the mast increases Ir. But calculating Ir requires knowing the location of every mass on the boat, which is not likely to be known. So this formula probably won't help much.

Mark Gardiner

Thanks, Mark!

This is interesting... I think if it's possible to figure out the percentage of increase in rolling, it would be good enough. Basically, I wanted to figure out how bad the effect is in calm weather since I noticed that my boat rolls a lot at an anchor in waves, and whether it's worth it to take it off if bad weather is coming. Or maybe even move it to the stern preventively. It's awfully big....

Thanks!
Gleb

Roll amplitude
 

Gleb,

I think you are talking about roll amplitude, not roll period. So what I posted before doesn't apply much.

Roll amplitude seems to be a complicated mix of static stability, damping, wave energy, and wind energy. I don't understand it well enough to say much more.

Mark Gardiner

Weight
 

Hi,
Mark, you are correct, there is so much to determining stability, and I only nibble at the edges of the pertinent calculations in my work. Gleb, if you would like an empirical exercise in the effect of that weight at a given height, just secure a similar weight to the mast there. You can measure roll duration and rate at anchor, and measure heel under sail in a given windspeed. The effect will probably be dramatic. It is also possible that if your boat rolls "a lot" now, there are other issues worth addressing in any event.
Fair leads,
Brion Toss

This sounds like a great suggestion - I should have thought of this myself.

Many thanks!
Gleb