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Rob/documentation adjust #35

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Mar 8, 2023
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Rob/documentation adjust #35

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8c11c83
Moved reference frame origin to the c.m for both mass MOIs and added-…
robertmcewen Mar 7, 2023
61eeffc
Moved reference frame origin to the c.m for both mass MOIs and added-…
robertmcewen Mar 7, 2023
1446f5e
Merge branch 'main' into rob/documentation_adjust
robertmcewen Mar 7, 2023
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45 changes: 21 additions & 24 deletions docs/docs/theory.md
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Expand Up @@ -39,12 +39,12 @@ Also, the description below includes alternative notation for added mass, e.g.
| \(I_{zz}\) | 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 |
| \(X_{\dot{q}}\) | Surge-Pitch Added Mass, origin at c.m. (\(\mu_{xq}\)) | 150 | kg |
| \(Y_{\dot{v}}\) | Sway Added Mass ( \(\mu_{yy}\)) | 260 | kg |
| \(Y_{\dot{p}}\) | Sway-Roll Added Mass, origin at pivot (\(\mu_{yp}\)) | -370 | kg |
| \(Y_{\dot{p}}\) | Sway-Roll Added Mass, origin at c.m. (\(\mu_{yp}\)) | -150 | kg |
| \(Z_{\dot{w}}\) | Heave Added Mass (\(\mu_{zz}\)) | 3080 | kg |
| \(K_{\dot{p}}\) | Roll Added Mass MOI, origin at pivot (\(\mu_{pp}\)) | 780 | kg m\(^2\)|
| \(M_{\dot{q}}\) | Pitch Added Mass MOI, origin at pivot (\(\mu_{qq}\)) | 780 | kg m\(^2\)|
| \(K_{\dot{p}}\) | Roll Added Mass MOI, origin at c.m. (\(\mu_{pp}\)) | 330 | kg m\(^2\)|
| \(M_{\dot{q}}\) | Pitch Added Mass MOI, origin at c.m. (\(\mu_{qq}\)) | 330 | kg m\(^2\)|
| \(X_{u\mid u \mid}\) | Surge Quadratic Drag | -430 | kg/m |
| \(Y_{v\mid v \mid}\) | Sway Quadratic Drag | -430 | kg/m |
| \(Z_{w\mid w \mid}\) | Heave Quadratic Drag | -3280 | kg/m |
Expand All @@ -55,45 +55,43 @@ Also, the description below includes alternative notation for added mass, e.g.

- 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.
- 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.
- Stability derivatives are specified about the link frame origin, i.e. the pivot.
- Mass-moments of inertia and added-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 <a href="https://www.google.com/") target="_blank">here</a>:

### Power Take-Off Device
| | 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 |
| \({\bf x}_{COG}\) | 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\(^2\)|
| \(K_{\dot{p}}\) | Roll Added Mass MOI (\(\mu_{pp}\)) | 2030 | kg m\(^2\)|
| \(M_{\dot{q}}\) | Pitch Added Mass MOI (\(\mu_{qq}\)) | 2030 | 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\(^2\)|
| \(M_{q\mid q \mid}\) | 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.
- 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.
- Stability derivatives are specified about the link frame origin, i.e. the pivot.
- Mass-moments of inertia and added-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 |
| \({\bf x}_{COG}\) | 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\(^2\)|
Expand All @@ -106,19 +104,18 @@ no buoyancy, added mass, or quadratic fluid drag.
|:-----------------:|:--------------------------------------------------------|:----------------:|:---------:|
| \(m\) | 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 |
| \({\bf x}_{COG}\) | 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\(^2\)|
| \(K_{\dot{p}}\) | Roll Added Mass MOI (\(\mu_{pp}\)) | 2870 | kg m\(^2\)|
| \(M_{\dot{q}}\) | Pitch Added Mass MOI(\(\mu_{qq}\)) | 2870 | 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 |
Expand All @@ -130,8 +127,8 @@ no buoyancy, added mass, or quadratic fluid drag.

- 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.
- 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.
- Stability derivatives are specified about the link frame origin, i.e. the pivot.
- Mass-moments of inertia and added-mass-moments of inertia are specified about the center of mass.


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