From 1e602f59e3460ed07de56c2e6e841021acb986d3 Mon Sep 17 00:00:00 2001 From: Rob McEwen Date: Tue, 28 Feb 2023 12:19:29 -0800 Subject: [PATCH 1/3] Adjusted moments of inertia. --- docs/docs/theory.md | 140 +++++++++++++++++++++----------------------- 1 file changed, 68 insertions(+), 72 deletions(-) diff --git a/docs/docs/theory.md b/docs/docs/theory.md index 8e1cb553..7f2717ba 100644 --- a/docs/docs/theory.md +++ b/docs/docs/theory.md @@ -21,22 +21,23 @@ the specific physical characteristics of the MBARI WEC are tabulated for referen Each rigid body in the simulation has a "Link Frame" coordinate system in which all other characteristics of the body are defined in for computational purposes. This link-frame coordinate system is often selected to be at the location of a joint that connects the various bodies (which are also called links in the vernacular of Gazebo). -In the following sections, all quantities are defined in the body's link frame unless otherwise noted. Also, the -description below includes alternative notation for added mass, e.g. \(\\ \mu_{xx}\), in the style of Newman. +Also, the description below includes alternative notation for added mass, e.g. \(\\ \mu_{xx}\), in the style of Newman. ### Surface Buoy | | Description | | Units | |:----------------:|:----------------------------------------------------------|:----------------:|:---------:| | \(m\) | Buoy Mass | 1400 | kg | -| \(V\) | Displacement (undisturbed buoy) | 1.0 | m\(^3\) | +| \(V\) | Displacement (undisturbed buoy) | 2.39 | m\(^3\) | | \(\bf{x}_{COG}\) | Center of Gravity in Link Frame (x,y,z) | (0.0, 0.0, 2.03) | m | | \(\bf{x}_{COB}\) | Center of Buoyancy in Link Frame (x,y,z) | (0.0, 0.0, 2.05) | m | | \(\bf{x}_{COW}\) | Center of Waterplane in Link Frame, including PTO and cone| (0.0, 0.0, 2.27) | m | -| \(I_{xx}\) | Roll Moment of Inertia (MOI), origin at pivot | 7000 | kg m\(^2\)| -| \(I_{yy}\) | Pitch Moment of Inertia origin at pivot | 7040 | kg m\(^2\)| -| \(I_{zz}\) | Yaw Moment of Inertia, origin at pivot | 670 | kg m\(^2\)| -| \(A_{wp}\) | Waterplane Area (undisturbed buoy) | 5.0 | m\(^2\) | +| \(\bf{S}_{x}\) | Second moment of area of water plane, about roll axis | 1.37 | m\(^4\) | +| \(\bf{S}_{y}\) | Second moment of area of water plane, about pitch axis | 1.37 | m\(^4\) | +| \(I_{xx}\) | Roll Moment of Inertia (MOI) about center of mass | 1450 | kg m\(^2\)| +| \(I_{yy}\) | Pitch Moment of Inertia about center of mass | 1450 | kg m\(^2\)| +| \(I_{zz}\) | Yaw Moment of Inertia about center of mass | 670 | kg m\(^2\)| +| \(A_{wp}\) | Waterplane Area (undisturbed buoy) | 5.47 | m\(^2\) | | \(X_{\dot{u}}\) | Surge Added Mass (\(\mu_{xx}\)) | 260 | kg | | \(X_{\dot{q}}\) | Surge-Pitch Added Mass, origin at pivot (\(\mu_{xq}\)) | 370 | kg | | \(Y_{\dot{v}}\) | Sway Added Mass ( \(\mu_{yy}\)) | 260 | kg | @@ -54,88 +55,83 @@ description below includes alternative notation for added mass, e.g. \(\\ \mu_{ - Buoy Link Frame is located at base of the buoy bridle at the pivot. - Unspecified stability derivative values (\(M_{\dot{r}}\), \(X_{uv}\), \(Y_{vu}\), etc) are zero. -- Inertias, Added mass inertias, and stability derivatives are all specified about the link frame origin, i.e. the pivot. +- Added mass moments of inertia and stability derivatives are all specified about the link frame origin, i.e. the pivot. +- Mass moments of inertia are specified about the center of mass. - Added mass values are infinite frequency. - Free-Surface Hydrodynamic Coefficients and Impulse Response Functions can be found here: ### Power Take-Off Device -| | Description | | Units | -|:-----------------:|:-------------------------------------------|:----------------:|:---------:| -| \(m\) | PTO Mass | 605 | kg | -| \(V\) | PTO Displacement | 1.0 | m\(^3\) | -| \(\bf{x}_{COG}\) | Center of Gravity in Link Frame (x,y,z) | (0.0, 0.0, -4.0) | m | -| \(\bf{x}_{COB}\) | Center of Buoyancy in Link Frame (x,y,z) | (0.0, 0.0, -3.0) | m | -| \(I_{xx}\) | Roll Moment of Inertia | 32600 | kg m\(^2\)| -| \(I_{yy}\) | Pitch Moment of Inertia | 32600 | kg m\(^2\)| -| \(I_{zz}\) | Yaw Moment of Inertia | 7 | kg m\(^2\)| -| \(I_{xy}\) | Roll-Pitch Product of Inertia | 0 | kg m\(^2\)| -| \(I_{xz}\) | Roll-Yaw Product of Inertia | -2 | kg m\(^2\)| -| \(I_{yz}\) | Pitch-Yaw Product of Inertia | -3 | kg m\(^2\)| -| \(X_{\dot{u}}\) | Surge Added Mass (\(\mu_{xx}\)) | 310 | kg | -| \(X_{\dot{q}}\) | Surge-Pitch Added Mass MOI (\(\mu_{xq}\)) | 1250 | kg m | -| \(Y_{\dot{v}}\) | Sway Added Mass (\(\mu_{yy}\)) | 310 | kg | -| \(Y_{\dot{p}}\) | Sway-Roll Added Mass MOI (\(\mu_{yp}\)) | -1250 | kg m | -| \(Z_{\dot{w}}\) | Heave Added Mass (\(\mu_{zz}\)) | 10 | kg | -| \(K_{\dot{p}}\) | Roll Added Mass MOI (\(\mu_{pp}\)) | 7040 | kg m\(^2\)| -| \(M_{\dot{q}}\) | Pitch Added Mass MOI (\(\mu_{qq}\)) | 7040 | kg m\(^2\)| -| \(X_{u\mid u \mid}\) | Surge Quadratic Drag | -1140 | kg/m | -| \(Y_{v\mid v \mid}\) | Sway Quadratic Drag | -1140 | kg/m | -| \(Z_{w\mid w \mid}\) | Heave Quadratic Drag | -50 | kg/m | -| \(K_{p\mid p \mid}\) | Roll Quadratic Drag | -195400 | kg m\(^2\)| -| \(M_{p\mid p \mid}\) | Pitch Quadratic Drag | -195400 | kg m\(^2\)| -| \(N_{r\mid r \mid}\) | Yaw Quadratic Drag | -50 | kg m\(^2\)| +| | Description | | Units | +|:-----------------:|:--------------------------------------------------------|:----------------:|:---------:| +| \(m\) | PTO Mass | 605 | kg | +| \(V\) | PTO Displacement | .205 | m\(^3\) | +| \(\bf{x}_{COG}\) | Center of Gravity in Link Frame (x,y,z) | (0.0, 0.0, -4.0) | m | +| \(\bf{x}_{COB}\) | Center of Buoyancy in Link Frame (x,y,z) | (0.0, 0.0, -3.0) | m | +| \(I_{xx}\) | Roll Moment of Inertia about center of mass | 3525 | kg m\(^2\)| +| \(I_{yy}\) | Pitch Moment of Inertia about center of mass | 3525 | kg m\(^2\)| +| \(I_{zz}\) | Yaw Moment of Inertia about center of mass | 10 | kg m\(^2\)| +| \(X_{\dot{u}}\) | Surge Added Mass (\(\mu_{xx}\)) | 310 | kg | +| \(X_{\dot{q}}\) | Surge-Pitch Added Mass MOI (\(\mu_{xq}\)) | 1250 | kg m | +| \(Y_{\dot{v}}\) | Sway Added Mass (\(\mu_{yy}\)) | 310 | kg | +| \(Y_{\dot{p}}\) | Sway-Roll Added Mass MOI (\(\mu_{yp}\)) | -1250 | kg m | +| \(Z_{\dot{w}}\) | Heave Added Mass (\(\mu_{zz}\)) | 10 | kg | +| \(K_{\dot{p}}\) | Roll Added Mass MOI (\(\mu_{pp}\)) | 7040 | kg m\(^2\)| +| \(M_{\dot{q}}\) | Pitch Added Mass MOI (\(\mu_{qq}\)) | 7040 | kg m\(^2\)| +| \(X_{u\mid u \mid}\) | Surge Quadratic Drag | -1140 | kg/m | +| \(Y_{v\mid v \mid}\) | Sway Quadratic Drag | -1140 | kg/m | +| \(Z_{w\mid w \mid}\) | Heave Quadratic Drag | -50 | kg/m | +| \(K_{p\mid p \mid}\) | Roll Quadratic Drag | -195400 | kg m\(^2\)| +| \(M_{p\mid p \mid}\) | Pitch Quadratic Drag | -195400 | kg m\(^2\)| +| \(N_{r\mid r \mid}\) | Yaw Quadratic Drag | -50 | kg m\(^2\)| - PTO Link Frame is located at top attachment of the PTO (where connects to the buoy). - Unspecified stability derivative values (\(M_{\dot{r}}\), \(X_{uv}\), \(Y_{vu}\), etc) are zero. -- Inertias, Added mass inertias, and stability derivatives are all specified about the link frame origin. -- Added mass values are infinite frequency. +- Added mass moments of inertia and stability derivatives are all specified about the link frame origin. +- Mass moments of inertia are specified about the center of mass. ### Piston -| | Description | | Units | -|:-----------------:|:-------------------------------------------|:-----------------:|:---------:| -| \(m\) | Piston Mass | 48.0 | kg | -| \(\bf{x}_{COG}\) | Center of Gravity in Link Frame (x,y,z) | (0.0, 0.0, -2.58) | m | -| \(I_{xx}\) | Roll Moment of Inertia | 100.0 | kg m\(^2\)| -| \(I_{yy}\) | Pitch Moment of Inertia | 100.0 | kg m\(^2\)| -| \(I_{zz}\) | Yaw Moment of Inertia | 5.0 | kg m\(^2\)| +| | Description | | Units | +|:-----------------:|:--------------------------------------------------------|:-----------------:|:---------:| +| \(m\) | Piston Mass | 48.0 | kg | +| \(\bf{x}_{COG}\) | Center of Gravity in Link Frame (x,y,z) | (0.0, 0.0, -2.58) | m | +| \(I_{xx}\) | Roll Moment of Inertia | 100.0 | kg m\(^2\)| +| \(I_{yy}\) | Pitch Moment of Inertia | 100.0 | kg m\(^2\)| +| \(I_{zz}\) | Yaw Moment of Inertia | 5.0 | kg m\(^2\)| - The piston is contained with the PTO housing, so it has mass and moments of inertial, but contributes no buoyancy, added mass, or quadratic fluid drag. ### Heave Cone -| | Description | | Units | -|:-----------------:|:-------------------------------------------|:----------------:|:---------:| -| \(m\) | Heave Cone Mass | 820 | kg | -| \(V\) | Heave Cone Displacement | 1.0 | m\(^3\) | -| \(\bf{x}_{COG}\) | Center of Gravity in Link Frame (x,y,z) | (0.0, 0.0, -1.25)| m | -| \(\bf{x}_{COB}\) | Center of Buoyancy in Link Frame (x,y,z) | (0.0, 0.0, -1.21)| m | -| \(I_{xx}\) | Roll Moment of Inertia | 4200 | kg m\(^2\)| -| \(I_{yy}\) | Pitch Moment of Inertia | 4200 | kg m\(^2\)| -| \(I_{zz}\) | Yaw Moment of Inertia | 610 | kg m\(^2\)| -| \(I_{xy}\) | Roll-Pitch Product of Inertia | 0 | kg m\(^2\)| -| \(I_{xz}\) | Roll-Yaw Product of Inertia | -1 | kg m\(^2\)| -| \(I_{yz}\) | Pitch-Yaw Product of Inertia | 0 | kg m\(^2\)| -| \(X_{\dot{u}}\) | Surge Added Mass (\(\mu_{xx}\)) | 720 | kg | -| \(X_{\dot{q}}\) | Surge-Pitch Added Mass MOI (\(\mu_{xq}\)) | 900 | kg m | -| \(Y_{\dot{v}}\) | Sway Added Mass (\(\mu_{yy}\)) | 720 | kg | -| \(Y_{\dot{p}}\) | Sway-Roll Added Mass MOI (\(\mu_{yp}\)) | -900 | kg m | -| \(Z_{\dot{w}}\) | Heave Added Mass: Doors Closed (\(\mu_{zz}\))| 9330 | kg | -| \(Z_{\dot{w}}\) | Heave Added Mass: Doors Open | 3000 | kg | -| \(K_{\dot{p}}\) | Roll Added Mass MOI (\(\mu_{pp}\)) | 3990 | kg m\(^2\)| -| \(M_{\dot{q}}\) | Pitch Added Mass MOI(\(\mu_{qq}\)) | 3990 | kg m\(^2\)| -| \(N_{\dot{r}}\) | Yaw Added Mass MOI (\(\mu_{rr}\)) | 10 | kg m\(^2\)| -| \(X_{u\mid u \mid}\) | Surge Quadratic Drag | -1580 | kg/m | -| \(Y_{v\mid v \mid}\) | Sway Quadratic Drag | -1580 | kg/m | -| \(Z_{w\mid w \mid}\) | Vertical Quadratic Drag: Doors Open | -3200 | kg/m | -| \(Z_{w\mid w \mid}\) | Vertical Quadratic Drag: Doors Closed| -3900 | kg/m | -| \(K_{p\mid p \mid}\) | Roll Quadratic Drag: | -4620 | kg m\(^2\)| -| \(M_{q\mid q \mid}\) | Pitch Quadratic Drag: | -4620 | kg m\(^2\)| -| \(N_{r\mid r \mid}\) | Yaw Quadratic Drag: | -50 | kg m\(^2\)| +| | Description | | Units | +|:-----------------:|:--------------------------------------------------------|:----------------:|:---------:| +| \(m\) | Heave Cone Mass | 820 | kg | +| \(V\) | Heave Cone Displacement | .12 | m\(^3\) | +| \(\bf{x}_{COG}\) | Center of Gravity in Link Frame (x,y,z) | (0.0, 0.0, -1.25)| m | +| \(\bf{x}_{COB}\) | Center of Buoyancy in Link Frame (x,y,z) | (0.0, 0.0, -1.21)| m | +| \(I_{xx}\) | Roll Moment of Inertia about the center of mass | 340 | kg m\(^2\)| +| \(I_{yy}\) | Pitch Moment of Inertia about the center of mass | 340 | kg m\(^2\)| +| \(I_{zz}\) | Yaw Moment of Inertia about the center of mass | 610 | kg m\(^2\)| +| \(X_{\dot{u}}\) | Surge Added Mass (\(\mu_{xx}\)) | 720 | kg | +| \(X_{\dot{q}}\) | Surge-Pitch Added Mass MOI (\(\mu_{xq}\)) | 900 | kg m | +| \(Y_{\dot{v}}\) | Sway Added Mass (\(\mu_{yy}\)) | 720 | kg | +| \(Y_{\dot{p}}\) | Sway-Roll Added Mass MOI (\(\mu_{yp}\)) | -900 | kg m | +| \(Z_{\dot{w}}\) | Heave Added Mass: Doors Closed (\(\mu_{zz}\)) | 9330 | kg | +| \(Z_{\dot{w}}\) | Heave Added Mass: Doors Open | 3000 | kg | +| \(K_{\dot{p}}\) | Roll Added Mass MOI (\(\mu_{pp}\)) | 3990 | kg m\(^2\)| +| \(M_{\dot{q}}\) | Pitch Added Mass MOI(\(\mu_{qq}\)) | 3990 | kg m\(^2\)| +| \(N_{\dot{r}}\) | Yaw Added Mass MOI (\(\mu_{rr}\)) | 10 | kg m\(^2\)| +| \(X_{u\mid u \mid}\) | Surge Quadratic Drag | -1580 | kg/m | +| \(Y_{v\mid v \mid}\) | Sway Quadratic Drag | -1580 | kg/m | +| \(Z_{w\mid w \mid}\) | Vertical Quadratic Drag: Doors Open | -3200 | kg/m | +| \(Z_{w\mid w \mid}\) | Vertical Quadratic Drag: Doors Closed | -3900 | kg/m | +| \(K_{p\mid p \mid}\) | Roll Quadratic Drag: | -4620 | kg m\(^2\)| +| \(M_{q\mid q \mid}\) | Pitch Quadratic Drag: | -4620 | kg m\(^2\)| +| \(N_{r\mid r \mid}\) | Yaw Quadratic Drag: | -50 | kg m\(^2\)| - Heave-Cone Link Frame is located at top attachment of the Heave Cone (where it connects to the tether). - Unspecified stability derivative values (\(M_{\dot{r}}\), \(X_{uv}\), \(Y_{vu}\), etc) are zero. -- Inertias, Added mass inertias, and stability derivatives are all specified about the link frame origin. -- Added mass values are infinite frequency. +- Added mass moments of inertia and stability derivatives are all specified about the link frame origin. +- Mass moments of inertia are specified about the center of mass. -------------------------------------------------------------------------------------------------------- From 1c3e4fd49637cdfeb63324e4064185a682b68de0 Mon Sep 17 00:00:00 2001 From: Rob McEwen Date: Tue, 28 Feb 2023 12:32:28 -0800 Subject: [PATCH 2/3] Fixed bold facing. --- docs/docs/theory.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/docs/docs/theory.md b/docs/docs/theory.md index 7f2717ba..8de77ecf 100644 --- a/docs/docs/theory.md +++ b/docs/docs/theory.md @@ -29,11 +29,11 @@ Also, the description below includes alternative notation for added mass, e.g. |:----------------:|:----------------------------------------------------------|:----------------:|:---------:| | \(m\) | Buoy Mass | 1400 | kg | | \(V\) | Displacement (undisturbed buoy) | 2.39 | m\(^3\) | -| \(\bf{x}_{COG}\) | Center of Gravity in Link Frame (x,y,z) | (0.0, 0.0, 2.03) | m | -| \(\bf{x}_{COB}\) | Center of Buoyancy in Link Frame (x,y,z) | (0.0, 0.0, 2.05) | m | -| \(\bf{x}_{COW}\) | Center of Waterplane in Link Frame, including PTO and cone| (0.0, 0.0, 2.27) | m | -| \(\bf{S}_{x}\) | Second moment of area of water plane, about roll axis | 1.37 | m\(^4\) | -| \(\bf{S}_{y}\) | Second moment of area of water plane, about pitch axis | 1.37 | m\(^4\) | +| \(\bf{x}\)_{COG} | Center of Gravity in Link Frame (x,y,z) | (0.0, 0.0, 2.03) | m | +| \(\bf{x}\)_{COB} | Center of Buoyancy in Link Frame (x,y,z) | (0.0, 0.0, 2.05) | m | +| \(\bf{x}\)_{COW} | Center of Waterplane in Link Frame, including PTO and cone| (0.0, 0.0, 2.27) | m | +| \(S_{x}\) | Second moment of area of water plane, about roll axis | 1.37 | m\(^4\) | +| \(S_{y}\) | Second moment of area of water plane, about pitch axis | 1.37 | m\(^4\) | | \(I_{xx}\) | Roll Moment of Inertia (MOI) about center of mass | 1450 | kg m\(^2\)| | \(I_{yy}\) | Pitch Moment of Inertia about center of mass | 1450 | kg m\(^2\)| | \(I_{zz}\) | Yaw Moment of Inertia about center of mass | 670 | kg m\(^2\)| From 8cec298b0a5cc4a15345e11e6ebf51bc094b2dc5 Mon Sep 17 00:00:00 2001 From: Rob McEwen Date: Tue, 28 Feb 2023 12:37:58 -0800 Subject: [PATCH 3/3] Restored bold face. --- docs/docs/theory.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/docs/theory.md b/docs/docs/theory.md index 8de77ecf..1f80b6c7 100644 --- a/docs/docs/theory.md +++ b/docs/docs/theory.md @@ -29,9 +29,9 @@ Also, the description below includes alternative notation for added mass, e.g. |:----------------:|:----------------------------------------------------------|:----------------:|:---------:| | \(m\) | Buoy Mass | 1400 | kg | | \(V\) | Displacement (undisturbed buoy) | 2.39 | m\(^3\) | -| \(\bf{x}\)_{COG} | Center of Gravity in Link Frame (x,y,z) | (0.0, 0.0, 2.03) | m | -| \(\bf{x}\)_{COB} | Center of Buoyancy in Link Frame (x,y,z) | (0.0, 0.0, 2.05) | m | -| \(\bf{x}\)_{COW} | Center of Waterplane in Link Frame, including PTO and cone| (0.0, 0.0, 2.27) | m | +| \(\bf{x}_{COG}\) | Center of Gravity in Link Frame (x,y,z) | (0.0, 0.0, 2.03) | m | +| \(\bf{x}_{COB}\) | Center of Buoyancy in Link Frame (x,y,z) | (0.0, 0.0, 2.05) | m | +| \(\bf{x}_{COW}\) | Center of Waterplane in Link Frame, including PTO and cone| (0.0, 0.0, 2.27) | m | | \(S_{x}\) | Second moment of area of water plane, about roll axis | 1.37 | m\(^4\) | | \(S_{y}\) | Second moment of area of water plane, about pitch axis | 1.37 | m\(^4\) | | \(I_{xx}\) | Roll Moment of Inertia (MOI) about center of mass | 1450 | kg m\(^2\)|