# Including Gravity to acceleration results

Discussion in 'Boat Design' started by b1ck0, Oct 22, 2013.

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### b1ck0Senior Member

Dear All,

What does it mean to report a point x,y,z accelerations including the gravity components?

I have done my spectral analysis and I have the accelerations and the maxima of motions for every loading condition. But I am not quite sure what exactly I need to include.

P.S: I suspect that I need to decompose the gravity acceleration vector due to my pitch and heel angles and include these horizontal accelerations to x and y components, derived from the spectral analysis. If you can send my any article about this issue it would be perfect.

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### PetrosSenior Member

when within the gravity field of a planet (like when floating on the surface of a body of water), you will always have a gravity acceleration straight down, F=ma, so the force is the weight of a vessel, supported by the displacement of the water. If the CG moves vertically it will affect the movement of the whole object.

If there is an vertical component to any movement (for example in a planing hull it lifts up out of the water as the boat accelerates), there will be a force required to lift the weight of the hull up against the force of gravity. likewise if it should squat or sink (like a submarine for example) than there is a vertical component where there is energy being given up as the sub descends. In a full description of the movement of any object in free space, all forces have to be accounted for.

Typically you will have three degrees of freedom to translate in space in any of three directions, and there degrees of freedom to rotate about three axis. So you will need six simultaneous equations to fully describe movement of any object in free space. that is assuming the cg and mass does not change.

Fortunately for most conditions you need only account for one or two degrees of freedom, and it is usually assumed the mass and the center of mass does not change. But there are many situations where you need to account for movement in all six degrees of freedom. When you include time in mix, you have fully seven variables that have to account for. And there could be more, for example as a rocket burns its fuel, the mass being accelerated is getting smaller and its CG is also changing, so all of the other equations are affected by the mass changing. Where you have a fuel or water tank sloshing around you could also have the center of mass moving around on a vessel. All conditions have to be considered and how it affects the others.

That is the way I have understood it and how I have had to use it when developing equations of motion to fully describe how a body will be affected by all the forces acting on it, gravity is just one of them.

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### jehardimanSenior Member

Google DoD-STD 1399, Section 301a. You already have your spectra so you can just plug it in rather than use the tables in the MIL-STD.

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### b1ck0Senior Member

Thanks for the reply. I found this paper very helpful, but my case is little different. I am not sure if I got this right, please refer to the attachment.

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### jehardimanSenior Member

Ok, the 5 columns of data on the left is the spectra output. Is the point you want to calculate 238.76m fwd of CG, 0m stbd of CG, and 38.10m above the CG? Then the next 3 columns on the right should be the accelerations due to roll, pitch, and yaw velocity. The middle 3 columns should be the maximum load due to the maximum roll angle (figured on you non-exceedence criteria) and the 3 columns on the right should be the un-phased maximums to provide design loads.

FWIW, look closely at the periods, you do not want to use the Tp (spectral peak period) in the 301a calculation, but the Tc (the zero crossing period).

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### b1ck0Senior Member

The accelerations, presented in the left side are not for CoG, but for the specified point.

The maximum pitch and roll angles are calculated for CoG, and I am using them directly, because I assume rigid body motion.

Then I decompose g in the local coordinate system (around CoG) and simply add these contributions to the accelerations obtained from the spectral analysis. (right 6 colums)

Should I get correct results as well ?

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### b1ck0Senior Member

Dear All,

I have checked with DNV they recommended the following approach.

1. Calculate 6 Degree of Freedom RAOs at Centre of Gravity
2. Calculate x,y,z displacement RAOs at particular point
3. Calculate x,y,z acceleration RAOs at particular point
4. Combine x acceleration and PITCH RAO. Scaling factor for PITCH is 9.81 Fx = X-ACC-RAO+9.81*PITCH
5. Combine y acceleration and ROLL RAO. Scaling factor for ROLL is 9.81 Fy = y-ACC-RAO+9.81*ROLL

The combined acceleration RAOs are then: Fx; Fy; Z-ACC-RAO

note: rotational RAOs have to be taken as [rad/m]

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