Squashed 'WISDEM/' changes from 99dcf1c5..34396b9c

34396b9c instead of passing around awkward drivetrain efficiency matrix, be explicit and pass around gearbox and generator efficiency all the time 54e464cb switch to structural_mass as obj fun e67a786a remove incorrect variable descriptions d2cd7ecc Merge pull request #166 from WISDEM/drivetrain_fix ddda8015 tests now passing b4525078 Merge branch 'develop' into drivetrain_fix 561e01f2 more rigorous, tensor-based rotation transformation of inertia matrix ffcc1a09 fix small bug in double counting of delta f8c3db22 completing drivetrain documentation 1c768f85 progress git-subtree-dir: WISDEM git-subtree-split: 34396b9c22dd8f0cb8ba3306301c4ad99f207eb6
WISDEM · Nov 11, 2020 · 95d60ce · 95d60ce
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diff --git a/docs/images/drivetrainse/Ibeam_cross.pdf b/docs/images/drivetrainse/Ibeam_cross.pdf
diff --git a/docs/images/drivetrainse/Ibeam_cross.png b/docs/images/drivetrainse/Ibeam_cross.png
diff --git a/docs/images/drivetrainse/bed_diagram.pdf b/docs/images/drivetrainse/bed_diagram.pdf
diff --git a/docs/images/drivetrainse/bed_diagram.png b/docs/images/drivetrainse/bed_diagram.png
diff --git a/docs/images/drivetrainse/geared_detail.pdf b/docs/images/drivetrainse/geared_detail.pdf
diff --git a/docs/images/drivetrainse/geared_detail.png b/docs/images/drivetrainse/geared_detail.png
diff --git a/docs/images/drivetrainse/geared_diagram.pdf b/docs/images/drivetrainse/geared_diagram.pdf
diff --git a/docs/images/drivetrainse/geared_diagram.png b/docs/images/drivetrainse/geared_diagram.png
diff --git a/docs/images/drivetrainse/generatorse/NRELCSM.pdf b/docs/images/drivetrainse/generatorse/NRELCSM.pdf
diff --git a/docs/images/drivetrainse/generatorse/NRELCSM.png b/docs/images/drivetrainse/generatorse/NRELCSM.png
diff --git a/docs/images/drivetrainse/generatorse/bearingsmass.pdf b/docs/images/drivetrainse/generatorse/bearingsmass.pdf
diff --git a/docs/images/drivetrainse/generatorse/bearingsmass.png b/docs/images/drivetrainse/generatorse/bearingsmass.png
diff --git a/docs/images/drivetrainse/generatorse/bedplatemass.pdf b/docs/images/drivetrainse/generatorse/bedplatemass.pdf
diff --git a/docs/images/drivetrainse/generatorse/bedplatemass.png b/docs/images/drivetrainse/generatorse/bedplatemass.png
diff --git a/docs/images/drivetrainse/generatorse/gearboxmass.pdf b/docs/images/drivetrainse/generatorse/gearboxmass.pdf
diff --git a/docs/images/drivetrainse/generatorse/gearboxmass.png b/docs/images/drivetrainse/generatorse/gearboxmass.png
diff --git a/docs/images/drivetrainse/generatorse/hssmass.pdf b/docs/images/drivetrainse/generatorse/hssmass.pdf
diff --git a/docs/images/drivetrainse/generatorse/hssmass.png b/docs/images/drivetrainse/generatorse/hssmass.png
diff --git a/docs/images/drivetrainse/generatorse/hubmass.pdf b/docs/images/drivetrainse/generatorse/hubmass.pdf
diff --git a/docs/images/drivetrainse/generatorse/hubmass.png b/docs/images/drivetrainse/generatorse/hubmass.png
diff --git a/docs/images/drivetrainse/generatorse/hubsysmass.pdf b/docs/images/drivetrainse/generatorse/hubsysmass.pdf
diff --git a/docs/images/drivetrainse/generatorse/hubsysmass.png b/docs/images/drivetrainse/generatorse/hubsysmass.png
diff --git a/docs/images/drivetrainse/generatorse/lssmass.pdf b/docs/images/drivetrainse/generatorse/lssmass.pdf
diff --git a/docs/images/drivetrainse/generatorse/lssmass.png b/docs/images/drivetrainse/generatorse/lssmass.png
diff --git a/docs/images/drivetrainse/generatorse/nacellecovmass.pdf b/docs/images/drivetrainse/generatorse/nacellecovmass.pdf
diff --git a/docs/images/drivetrainse/generatorse/nacellecovmass.png b/docs/images/drivetrainse/generatorse/nacellecovmass.png
diff --git a/docs/images/drivetrainse/generatorse/nacellemass.pdf b/docs/images/drivetrainse/generatorse/nacellemass.pdf
diff --git a/docs/images/drivetrainse/generatorse/nacellemass.png b/docs/images/drivetrainse/generatorse/nacellemass.png
diff --git a/docs/images/drivetrainse/generatorse/pitchsysmass.pdf b/docs/images/drivetrainse/generatorse/pitchsysmass.pdf
diff --git a/docs/images/drivetrainse/generatorse/pitchsysmass.png b/docs/images/drivetrainse/generatorse/pitchsysmass.png
diff --git a/docs/images/drivetrainse/generatorse/spinnermass.pdf b/docs/images/drivetrainse/generatorse/spinnermass.pdf
diff --git a/docs/images/drivetrainse/generatorse/spinnermass.png b/docs/images/drivetrainse/generatorse/spinnermass.png
diff --git a/docs/images/drivetrainse/generatorse/yawmass.pdf b/docs/images/drivetrainse/generatorse/yawmass.pdf
diff --git a/docs/images/drivetrainse/generatorse/yawmass.png b/docs/images/drivetrainse/generatorse/yawmass.png
diff --git a/docs/images/drivetrainse/hss_diagram.pdf b/docs/images/drivetrainse/hss_diagram.pdf
diff --git a/docs/images/drivetrainse/hss_diagram.png b/docs/images/drivetrainse/hss_diagram.png
diff --git a/docs/images/drivetrainse/layout_bedplate.pdf b/docs/images/drivetrainse/layout_bedplate.pdf
diff --git a/docs/images/drivetrainse/layout_bedplate.png b/docs/images/drivetrainse/layout_bedplate.png
diff --git a/docs/images/drivetrainse/layout_detail.pdf b/docs/images/drivetrainse/layout_detail.pdf
diff --git a/docs/images/drivetrainse/layout_detail.png b/docs/images/drivetrainse/layout_detail.png
diff --git a/docs/images/drivetrainse/layout_diagram.pdf b/docs/images/drivetrainse/layout_diagram.pdf
diff --git a/docs/images/drivetrainse/layout_diagram.png b/docs/images/drivetrainse/layout_diagram.png
diff --git a/docs/images/drivetrainse/layout_lss.pdf b/docs/images/drivetrainse/layout_lss.pdf
diff --git a/docs/images/drivetrainse/layout_lss.png b/docs/images/drivetrainse/layout_lss.png
diff --git a/docs/images/drivetrainse/layout_picture.pdf b/docs/images/drivetrainse/layout_picture.pdf
diff --git a/docs/images/drivetrainse/layout_picture.png b/docs/images/drivetrainse/layout_picture.png
diff --git a/docs/images/drivetrainse/layout_stator.pdf b/docs/images/drivetrainse/layout_stator.pdf
diff --git a/docs/images/drivetrainse/layout_stator.png b/docs/images/drivetrainse/layout_stator.png
diff --git a/docs/images/drivetrainse/lss_diagram.pdf b/docs/images/drivetrainse/lss_diagram.pdf
diff --git a/docs/images/drivetrainse/lss_diagram.png b/docs/images/drivetrainse/lss_diagram.png
diff --git a/docs/images/drivetrainse/nose_diagram.pdf b/docs/images/drivetrainse/nose_diagram.pdf
diff --git a/docs/images/drivetrainse/nose_diagram.png b/docs/images/drivetrainse/nose_diagram.png
diff --git a/docs/images/drivetrainse/drivese/NRELCSM.pdf → docs/images/drivetrainse/old/NRELCSM.pdf b/docs/images/drivetrainse/drivese/NRELCSM.pdf → docs/images/drivetrainse/old/NRELCSM.pdf
diff --git a/docs/images/drivetrainse/drivese/NRELCSM.png → docs/images/drivetrainse/old/NRELCSM.png b/docs/images/drivetrainse/drivese/NRELCSM.png → docs/images/drivetrainse/old/NRELCSM.png
diff --git a/...ges/drivetrainse/drivese/bearingsmass.pdf → .../images/drivetrainse/old/bearingsmass.pdf b/...ges/drivetrainse/drivese/bearingsmass.pdf → .../images/drivetrainse/old/bearingsmass.pdf
diff --git a/...ges/drivetrainse/drivese/bearingsmass.png → .../images/drivetrainse/old/bearingsmass.png b/...ges/drivetrainse/drivese/bearingsmass.png → .../images/drivetrainse/old/bearingsmass.png
diff --git a/...ges/drivetrainse/drivese/bedplatemass.pdf → .../images/drivetrainse/old/bedplatemass.pdf b/...ges/drivetrainse/drivese/bedplatemass.pdf → .../images/drivetrainse/old/bedplatemass.pdf
diff --git a/...ges/drivetrainse/drivese/bedplatemass.png → .../images/drivetrainse/old/bedplatemass.png b/...ges/drivetrainse/drivese/bedplatemass.png → .../images/drivetrainse/old/bedplatemass.png
diff --git a/...ages/drivetrainse/drivese/gearboxmass.pdf → docs/images/drivetrainse/old/gearboxmass.pdf b/...ages/drivetrainse/drivese/gearboxmass.pdf → docs/images/drivetrainse/old/gearboxmass.pdf
diff --git a/...ages/drivetrainse/drivese/gearboxmass.png → docs/images/drivetrainse/old/gearboxmass.png b/...ages/drivetrainse/drivese/gearboxmass.png → docs/images/drivetrainse/old/gearboxmass.png
diff --git a/docs/images/drivetrainse/drivese/hssmass.pdf → docs/images/drivetrainse/old/hssmass.pdf b/docs/images/drivetrainse/drivese/hssmass.pdf → docs/images/drivetrainse/old/hssmass.pdf
diff --git a/docs/images/drivetrainse/drivese/hssmass.png → docs/images/drivetrainse/old/hssmass.png b/docs/images/drivetrainse/drivese/hssmass.png → docs/images/drivetrainse/old/hssmass.png
diff --git a/docs/images/drivetrainse/drivese/hubmass.pdf → docs/images/drivetrainse/old/hubmass.pdf b/docs/images/drivetrainse/drivese/hubmass.pdf → docs/images/drivetrainse/old/hubmass.pdf
diff --git a/docs/images/drivetrainse/drivese/hubmass.png → docs/images/drivetrainse/old/hubmass.png b/docs/images/drivetrainse/drivese/hubmass.png → docs/images/drivetrainse/old/hubmass.png
diff --git a/...mages/drivetrainse/drivese/hubsysmass.pdf → docs/images/drivetrainse/old/hubsysmass.pdf b/...mages/drivetrainse/drivese/hubsysmass.pdf → docs/images/drivetrainse/old/hubsysmass.pdf
diff --git a/...mages/drivetrainse/drivese/hubsysmass.png → docs/images/drivetrainse/old/hubsysmass.png b/...mages/drivetrainse/drivese/hubsysmass.png → docs/images/drivetrainse/old/hubsysmass.png
diff --git a/docs/images/drivetrainse/drivese/lssmass.pdf → docs/images/drivetrainse/old/lssmass.pdf b/docs/images/drivetrainse/drivese/lssmass.pdf → docs/images/drivetrainse/old/lssmass.pdf
diff --git a/docs/images/drivetrainse/drivese/lssmass.png → docs/images/drivetrainse/old/lssmass.png b/docs/images/drivetrainse/drivese/lssmass.png → docs/images/drivetrainse/old/lssmass.png
diff --git a/...s/drivetrainse/drivese/nacellecovmass.pdf → ...mages/drivetrainse/old/nacellecovmass.pdf b/...s/drivetrainse/drivese/nacellecovmass.pdf → ...mages/drivetrainse/old/nacellecovmass.pdf
diff --git a/...s/drivetrainse/drivese/nacellecovmass.png → ...mages/drivetrainse/old/nacellecovmass.png b/...s/drivetrainse/drivese/nacellecovmass.png → ...mages/drivetrainse/old/nacellecovmass.png
diff --git a/...ages/drivetrainse/drivese/nacellemass.pdf → docs/images/drivetrainse/old/nacellemass.pdf b/...ages/drivetrainse/drivese/nacellemass.pdf → docs/images/drivetrainse/old/nacellemass.pdf
diff --git a/...ages/drivetrainse/drivese/nacellemass.png → docs/images/drivetrainse/old/nacellemass.png b/...ages/drivetrainse/drivese/nacellemass.png → docs/images/drivetrainse/old/nacellemass.png
diff --git a/...ges/drivetrainse/drivese/pitchsysmass.pdf → .../images/drivetrainse/old/pitchsysmass.pdf b/...ges/drivetrainse/drivese/pitchsysmass.pdf → .../images/drivetrainse/old/pitchsysmass.pdf
diff --git a/...ges/drivetrainse/drivese/pitchsysmass.png → .../images/drivetrainse/old/pitchsysmass.png b/...ges/drivetrainse/drivese/pitchsysmass.png → .../images/drivetrainse/old/pitchsysmass.png
diff --git a/...ages/drivetrainse/drivese/spinnermass.pdf → docs/images/drivetrainse/old/spinnermass.pdf b/...ages/drivetrainse/drivese/spinnermass.pdf → docs/images/drivetrainse/old/spinnermass.pdf
diff --git a/...ages/drivetrainse/drivese/spinnermass.png → docs/images/drivetrainse/old/spinnermass.png b/...ages/drivetrainse/drivese/spinnermass.png → docs/images/drivetrainse/old/spinnermass.png
diff --git a/docs/images/drivetrainse/drivese/yawmass.pdf → docs/images/drivetrainse/old/yawmass.pdf b/docs/images/drivetrainse/drivese/yawmass.pdf → docs/images/drivetrainse/old/yawmass.pdf
diff --git a/docs/images/drivetrainse/drivese/yawmass.png → docs/images/drivetrainse/old/yawmass.png b/docs/images/drivetrainse/drivese/yawmass.png → docs/images/drivetrainse/old/yawmass.png
diff --git a/docs/wisdem/drivetrainse/components.rst b/docs/wisdem/drivetrainse/components.rst
@@ -1,5 +1,5 @@
 ****************************
-Drivetrain Component Theory
+Drivetrain Components
 ****************************
 
 This section describes the theory behind the sizing and estimation of mass properties for all of the hub and nacelle components.  Unless otherwise noted, the moment of inertia expressions are about the component center of mass.
@@ -24,8 +24,9 @@ The pitch system moment of inertia assumes that the mass is distributed as a sol
    I_0 &= m R_{hub}^2 / 2 \\
    I_1 &= I_0 / 2
 
-Main Bearing
-=============
+
+Main Bearing(s)
+=================
 
 This is a simple, regression-based sizing tool for the main bearings.  The same function is called once for configurations with one main bearing or twice for configurations with two.  It handles Compact Aligning Roller Bearings (CARB), Cylindrical Roller Bearings (CRB), Spherical Roller Bearings (SRB), and Tapered Roller Bearings (TRB).  The face width, mass, and maximum allowable deflection angle of these bearing types are,
 
@@ -189,7 +190,14 @@ For geared layouts, the bedplate consists of twin I-beams that run along the bot
    A_I  &= 2 w_f t_f + h_w t_w \\
    m_{bedplate} &= 2 \rho A_I L_{bedplate}
 
-Where :math:`w_f` and :math:`t_f` are the flange width and thickness and :math:`h_w` and :math:`t_w` are the web height and thickness.  The factor of two on the mass equation is to account for the twin I-beams.
+Where :math:`w_f` and :math:`t_f` are the flange width and thickness and :math:`h_w` and :math:`t_w` are the web height and thickness, illustrated in n:numref:`fig_ibeam_cross`.  The factor of two on the mass equation is to account for the twin I-beams.
+
+.. _fig_ibeam_cross:
+.. figure::  /images/drivetrainse/Ibeam_cross.*
+    :width: 35%
+    :align: center
+
+    I-beam cross section and dimension nomenclature.
 
 The moment of inertia for the geared bedplate is taken from standard expressions for I-beam of a finite length with a coordinate system of :math:`x` along the axial length, :math:`y` consistent with a right-hand coordinate system when :math:`z` is pointed up (from the base flange to the top flange),
 
@@ -267,3 +275,17 @@ The yaw system is approximated by assuming that the main mass contributions are
 Where :math:`D_{rotor}` is the rotor diameter in meters, :math:`D_{tt}` is the tower-top diameter, and :math:`\rho` is the density of steel.  The friction plate mass calculation is derived from assuming that the surface width is 10% of the tower top diameter and the thickness is 0.1% of the rotor diameter.
 
 Since the yaw system is at the tower top coordinate system origin, it is assumed to not contribute to the nacelle moment of inertia calculation.
+
+Nacelle and RNA mass summary
+=============================
+
+To aid in the tower structural analysis, the total mass and moment of inertia of the nacelle is summed about a coordinate system center at the tower top.  This is a straightforward summation of the mass, and a mass-weighted average of the component center of mass.  For the component moments of inertia, which are given about the component center of mass, the inertia tensor was first rotated through the driveshaft tilt, and then the parallel axis theorem was applied to move from the component center of mass to the tower top coordinate system.  These operations can be expressed as,
+
+.. math::
+   m_{nac}  &= \sum_i m_i\\
+   \vec{r}_{nac} &= \frac{1}{m_{nac}} \sum_i m_i \vec{r}_i\\
+   I_{nac} &= \sum_i \left[ R(\gamma) I_i R^T(\gamma) + m_i \left( \vec{r}_i \cdot \vec{r}_i E_3 - \vec{r}_i \otimes \vec{r}_i \right)\right]
+
+Where :math:`m_i` is the component mass, :math:`\vec{r}_i` is the vector from the tower top coordinate system origin to the component center of mass, :math:`I_i` is the component moment of inertia tensor, :math:`R(\gamma)` is the 3-D rotation matrix about the y-axis for the tilt angle, :math:`E_3` is the 3x3 identity matrix, :math:`\cdot` denotes the inner (dot) product, and :math:`\otimes` denotes the outer product.
+
+
diff --git a/docs/wisdem/drivetrainse/index.rst b/docs/wisdem/drivetrainse/index.rst
@@ -15,5 +15,6 @@ DrivetrainSE
     :maxdepth: 2
 
     intro
+    layout
     components
     structural
diff --git a/docs/wisdem/drivetrainse/intro.rst b/docs/wisdem/drivetrainse/intro.rst
@@ -2,23 +2,19 @@
 Drivetrain Model Introduction
 ******************************
 
-Introduction
-------------
+The Drivetrain Systems Engineering (DrivertainSE) module is a set of models for sizing wind turbine drivetrain components as part of the larger WISDEM design and analysis tool. Wind turbine drivetrains physically connect the rotor to the tower and serve as a load-path from one to the other.  The drivetarin is also responsible for converting the aerodynamic torque of the rotor into electrical power that can be fed to the grid. Therefore, the drivetrain model interacts with the rotor and tower designs and it is important in looking at the overall design of a wind turbine to consider the coupling that exists between these three primary subsystem.  DrivetrainSE provides the capability to take in the aerodynamic loads and rotor properties and to estimate the mass properties and dimensions for all major components; the overall nacelle properties can then be used in subsequent tower design and analysis or as part of a system-level optimization of the wind turbine.  In addition, the resulting mass and dimension estimates can then be used to feed into a turbine capital cost model as well as a balance of station cost model that considers cost of assembly and installation of a wind turbine so that a full wind plant system level cost analysis could be performed.
 
-The Drivetrain Systems Engineering (DriveSE) model is a set of models for sizing wind turbine drivetrain components that is designed for use as part of a larger wind turbine design and analysis tool.  A previous similar tool was developed in the late 1990's :cite:`harrison_cost_1993`.  This model, known as the Sunderland model, used semi-empirical formulations were developed for all major wind turbine components in order to provide the mass of each which could be then converted into cost for an overall turbine capital cost estimate. These semi-empirical formulations were based on a collected industry database that is not representative of today's multi-megawatt (MW) size wind turbines. Thus, a need exists to develop an accurate drivetrain sizing tool that can be used for dimensioning drivetrain components as part of a case study on drivetrain design or, more importantly, as part of a larger wind turbine and system study.
+DrivetrainSE uses a slightly different approach to the prior instances of DriveSE and HubSE, although some of the component sizing remains the same. Instead of analytical derivations of the forces and moments on the various elements and closed form expressions for sizing the components, we instead rely on Frame3DD to conduct the analysis and enable the use of optimization with stress constraints to ensure a valid design.  This proves to be an easier long-term approach to maintain correct code.
 
-Wind turbine drivetrains physically connect the rotor to the tower and serve as a load-path from one to the other.  The drivetarin is also responsible for converting the aerodynamic torque of the rotor into electrical power that can be fed to the grid. Therefore, the drivetrain model interacts with the rotor and tower designs and it is important in looking at the overall design of a wind turbine to consider the coupling that exists between these three primary subsystem.  DriveSE provides the capability to take in the aerodynamic loads and rotor properties and to estimate the mass properties and dimensions for all major components; the overall nacelle properties can then be used in subsequent tower design and analysis or as part of a system-level optimization of the wind turbine.  In addition, the resulting mass and dimension estimates can then be used to feed into a turbine capital cost model as well as a balance of station cost model that considers cost of assembly and installation of a wind turbine so that a full wind plant system level cost analysis could be performed.  Thus, while DriveSE can be used to do drivetrain specific analysis as illustrated in \citep{DriveStudy}, the model set can also be used as part of larger wind turbine and plant system level studies :cite:`tip_speed_2014`.
-
-DriveSE uses a more rigorous set of physics-based analyses than was used in the Sunderland model to estimate the size of a subset of the major load-bearing components (the low speed shaft, main bearing(s), gearbox and bedplate) and parametric formulations representative of current wind turbine technology for the remaining components (the hub and yaw system).  The high-speed side of the drivetrain including the high speed shaft and coupling, mechanical brake, generator and other auxiliary components are not modeled and an existing set of models based on the Sunderland Model and other more recently developed models :cite:`DriveWPACT`.  The only exception is the transformer which was not included in previous models.  A simple model of the transformer based on industry data is included since uptower transformers are relatively common to modern wind turbines and, as a heavy component, have a significant impact on the overall mass properties of the nacelle assembly.
-
-Features
+DrivetrainSE features the following capabilities:
 
 * Upwind or downwind rotor configuration
 * Direct-drive and geared
-* Lots of generator models
-* Sizing using physical constraints and utilization factors from structural analysis for optimization
+* Electromagnetic design of multiple generator technologies, including synchronous and induction generators.
+* Up-tower or down-tower electronics
+* Sizing of drivetrain components via structural analysis
 
-Components included
+DrivetrainSE includes sizing for the following components:
 
 * Hub
 * Spinner
@@ -36,18 +32,4 @@ Components included
 * Nacelle cover
 * Yaw system
 
-Layout
-
-* Direct drive
-* Geared
-
-Generator
-
-* All types, defaults and status?
-
-Nacelle and RNA mass summary
-
-* I rotation through tilt from hub-aligned coordinate system to tower-aligned coordinate system
-* Parallel axis theorem to tower top from CoM
-
-Inputs
+Some of these components are sized with very simple, empirical- or regression-based approximations.  Others involve more detailed structural analysis, cast as utilization constraints, that are meant to be included in an optimization.
diff --git a/docs/wisdem/drivetrainse/layout.rst b/docs/wisdem/drivetrainse/layout.rst
@@ -0,0 +1,108 @@
+******************
+Layout and Inputs
+******************
+The direct-drive and geared drivetrain layouts are quite different, however both use the same set of user inputs.  This was intentional to simplify the user-input burden.  The common layout parameters are,
+
+- Overhang (:math:`L_{overhang}`)
+- Height from hub to tower top (:math:`H_{htt}`)
+- Shaft tilt angle (:math:`\gamma`),
+- Generator length (:math:`L_{generator}`)
+- Distance between the hub flange and the first main bearing (:math:`L_{h1}`)
+- Distance between the main bearings (:math:`L_{12}`)
+
+Detailed diagrams of how these parameters set the sizing and layout of the drivetrain is shown in the two subsections below.
+
+Direct-Drive Layout
+========================
+
+.. _fig_layout_pic:
+.. figure::  /images/drivetrainse/layout_picture.*
+    :width: 75%
+    :align: center
+
+    Direct-drive configuration geometry
+
+The overall layout for the direct-drive configuration is shown in :numref:`fig_layout_pic` and :numref:`fig_layout_diagram`.  The hub connects to the low-speed shaft, which is a large diameter, hollow cylinder supported by two sets of main bearings attached to the nose, also called the turret.  The nose is affixed to the bedplate, which also has a circular cross-section, but follows an elliptical curve down to the tower attachment.  The total length, parallel to the ground, from the tower center line to the rotor apex, is considered the *overhang*.  The total height difference between those same two points in the *hub to tower top height*.  The outer-rotor of the generator also attaches to the low-speed shaft, and the corresponding stator attaches to the nose.
+
+.. _fig_layout_diagram:
+.. figure::  /images/drivetrainse/layout_diagram.*
+    :width: 50%
+    :align: center
+
+    Direct-drive configuration layout diagram
+
+The detailed parameters that specify the drivetrain layout are shown in :numref:`fig_layout_detail`.
+
+.. _fig_layout_detail:
+.. figure::  /images/drivetrainse/layout_detail.*
+    :width: 100%
+    :align: center
+
+    Detailed direct-drive configuration with key user inputs and derived values.
+
+In addition to the user-defined dimensions, the other values are derived in the following way,
+
+.. math::
+   L_{grs}	&= 0.5 L_{h1}\\
+   L_{gsn}	&= L_{generator} - L_{grs} - L_{12}\\
+   L_{2n}	&= 2 L_{gsn}\\
+   L_{lss}	&= L_{12} + L_{h1}\\
+   L_{nose}	&= L_{12} + L_{2n}\\
+   L_{drive}    &= L_{h1} + L_{12} + L_{2n}\\
+   L_{bedplate} &= L_{overhang} - L_{drive}\cos \gamma\\
+   H_{bedplate} &= H_{htt} - L_{drive}\sin \gamma
+
+Here the length from the hub flange to the generator rotor attachment, :math:`L_{grs}`, is assumed to be at the halfway point between the flange and the first main bearing, :math:`L_{h1}`.  Similarly, the distance between the second main bearing and the nose/turret interface with the bedplate, :math:`L_{2n}`, is twice the distance as that from the same interface to the generator stator attachment, :math:`L_{gsn}`.  After adding up the total length of the low speed shaft and nose/turret, the total drivetrain length from bedplate to hub can be determined.  Then, the bedplate dimensions are determined in order to meet the target overhang and hub-to-tower top height. To ensure that these layout dimensions are adequately satisfied during a design optimization, a constraint is enforced such that :math:`L_{bed} \geq 0.5 D_{top}`.
+
+The user must also specify diameter and thickness values for the low speed shaft (:math:`D_{lss}` and :math:`t_{lss}`) and the nose/turret (:math:`D_{nose}` and :math:`t_{nose}`).  These can also be assigned as design variables to satisfy the constraints generated in the structural analysis.
+
+The bedplate diagram is shown in :numref:`fig_layout_bedplate`, and follows an elliptical path from the tower top to the nose/turret attachment point.  The length and height of the bedplate (major and minor half axes of the ellipse) are determined from the input user dimensions.  The bedplate diameter also follows an elliptical progression from the tower top diameter at the bedplate base to the nose/turrent diameter at the top.  The wall thickness schedule is a user defined input, or can be designated as a design variable in order to meet structural constraints.
+
+.. _fig_layout_bedplate:
+.. figure::  /images/drivetrainse/layout_bedplate.*
+    :width: 65%
+    :align: center
+
+    Direct-drive configuration layout diagram
+
+The attachment of the generator stator to the nose/turret is shown in :numref:`fig_layout_stator`.  For the direct-drive configuration, we assume an outer rotor-inner stator, radial flux topology for a permanent magnet synchronous generator. The outer rotor layout facilitates a simple and rugged structure, easy manufacturing, short end windings, and better heat transfer between windings and teeth than an inner rotor configuration.
+
+.. _fig_layout_stator:
+.. figure::  /images/drivetrainse/layout_stator.*
+    :width: 70%
+    :align: center
+
+    Direct-drive configuration layout diagram
+
+
+Geared Layout
+========================
+
+The overall layout for the geared configuration is shown in :numref:`fig_geared_diagram`. The hub connects to the low-speed shaft, supported by two sets of main bearings.  The low speed shaft connects to the gearbox which converts the high-torque, low-rpm input into a low-torque, high-rpm output on the high speed shaft.  The high speed shaft feeds the generator, which is assumed to be a doubly-fed induction generator (DFIG).  The bedplate is a steel platform that sits atop two parallel I-beams to provide the structural support.  The bearings and the generator are assumed to be firmly attached to the bedplate.  The gearbox attaches to the nacelle platform atop the bedplate with a trunion.
+
+.. _fig_geared_diagram:
+.. figure::  /images/drivetrainse/geared_diagram.*
+    :width: 75%
+    :align: center
+
+    Geared configuration layout diagram
+
+The detailed parameters that specify the drivetrain geared are shown in :numref:`fig_geared_detail`.
+
+.. _fig_geared_detail:
+.. figure::  /images/drivetrainse/geared_detail.*
+    :width: 75%
+    :align: center
+
+    Geared configuration layout diagram
+
+In addition to the user-defined dimensions, the other values are derived in the following way,
+
+.. math::
+   \delta       &= 0.1\\
+   L_{lss}      &= L_{12} + L_{h1} + \delta\\
+   L_{drive}    &= L_{lss} + L_{gearbox} + L_{hss} + L_{generator}\\
+   L_{bedplate} &= L_{drive} \cos \gamma \\
+   H_{bedplate} &= H_{htt} - L_{drive} \sin \gamma
+
+The dimension, :math:`\delta` is the space between the second main bearing and the gearbox attachment where the shrink disk lies.  This is assumed to be 0.1 meters.  The bedplate height is sized to ensure that the desired height from tower top to hub is obtained.  To achieve the desired overhang distance, the tower is centered at the exact overhang distance from the hub and a constraint is enforced such that the drivetrain length is sufficient to extend past the tower, :math:`L_{drive} \cos \gamma - L_{overhang} \geq 0.5 D_{top}`.