Acceleration Calculations

Hi,

I'm new to motions and acceleration calculations. I started to use maxsurf motions. What should be the value to use for sea-fastening calculations? Significant amplitude? Before we only use thr guide lines from rules. Something like Max. Roll amgle 10 degree, heave acceleration 0.1g etc.

 

You have to decide for yourself the criticality of the item and what your non-exceedance criteria is. Armed with this you can back factor your maximum expected design load from your input spectrum and significant amplitudes (knowing that the significant amplitude is 2*sqrt(m0) of the response spectra). From there you just sum all 6 DoF rigid body accelerations determining m1 (or average response period) in any way your prefer. Remember that your FoS is for the materials, not the loads.

(edited 4 to 2 for amplitude to be consistent with Ochi and Bhattacharya below, I always think of included roll vice half roll to account for list and heel <shrug>)

 

hi. thanks for reply. So i can use thr significant amplitude values for calculations.right? For example. i got 11.01degree as significant amplitude for roll angle in beam sea. can i assume that one as the maximum possible roll angle?

 

No, the significant amplitude is the expected amplitude...approximately the average of the largest 33% of all rolls from the applied spectra...so approximately every 3rd roll will exceed 11.01 degrees. You need to look up Ochi's 1973 "On Prediction of Extreme Values" paper (JoSR) or get a copy of " Dynamics of Marine Vehicles" by Bhattacharya (Bhattacharya Dynamics of Marine Vehicles https://www.scribd.com/doc/44416872/Bhattacharya-Dynamics-of-Marine-Vehicles). Your maximum roll would be = sqrt(2*ln(n))*sqrt(mo) where n is the number of expected events and mo is the area under the response curve. n is normally expressed as 1/(1-alpha) where alpha is the confidence factor of non-exceedance ...i.e. 99%, 99.9%, 99.99%, etc. In your case sqrt(m0) = 5.505 so the maximum design roll for a probability of non-exceedance of 99.9% (i.e. 1 in 1000) would be 3.74*sqrt(m0) = ~ 20.59 degrees. But with a nominal sea way of a 10 second response period, this roll would be exceeded every 2.8 hours. So often n is set on the lifetime expected maximum roll... 10 sec period over 200 days at sea for 20 years n would be 3.45E07 and maximum expected lifetime roll would then be 32.43 degrees.

 

Thank you so much for your time.

Previously, all our calculations were based on default motion criteria by Marine Warranty surveyors. For example, for benign weather area they provide a nominal value of single amplitude ie. 10degree roll .5 degree pitch and 0.1g of heave acceleration. We use that values for calculating the force of cargo acting on the deck. As you explained the highest roll angle is 32.43 degree, it's much more than we having used.

 

Yes, 32.43 degrees is a lot, but not impossible. After you have read through the first 4 or 5 chapters of Bhattacharya you can see that we never really have a single constant sea spectra or response spectra over the life of the ship. In fact we can have many sea spectra folded into a composite response spectra. This is because if the ship starts to roll too much, the conning officer is just going to change heading to make her lie better (the EL FARO not withstanding, which is why I said I typically consider total included angle of roll). Most class society rules take this into account, trading off acceptable losses verses costs. It becomes an economic decision...the cost of containers lost over the side against ship design, construction, and maintenance costs. The real issue is that the maximum response is quasi random … for any given sea spectra and ship heading, the maximum response may occur on the first wave...or the last...nothing is certain. So there is always a small, but real, probability of a roll greater than 32.43 occurring in the life of the ship. Whether this is a design case is a sperate question.

FWIW, to compare your old motions to a lot of history data, google "DOD-STD 1399 Section 301a". It also contains the 6 DoF equations for X, Y, and Z acceleration translation to any point on the vessel.

 

Thank you so much for your advices. It really helps me a lot. Now reading dynamics of marine vehicles. For my calculations, I think significant amplitudes values are closer to guidelines from rules. Although those rules can generally cover the normal operations, still want to find out the better analysis for more reasonable results. Much appreciate your help.