**Appendices**

**List of Symbols**

Awp area of waterplane (ft2 or m2)

b hull beam at M2

Bwp length of a waterplane line segment (ft or m)

BDR beam/depth ratio = b/d

c1 ... c6 conic curve fit coefficients

C1 intersection of deadrise and slope through M2

C2 corner point defining flare of the topsides

C3 corner point defining deck crown

Cp prismatic coefficient

d hull depth from M2

d0, d1 approximations to d

D displacement (lb or N)

E1, E2 end points of the intersection of a cross section with the waterplane

Fx force along X axis (lb or N)

Fxh force along X axis of individual hull (lb or N)

Fy force along Y axis (lb or N)

Fyh force along Y axis of individual hull (lb or N)

Fz force along Z axis (lb or N)

Fzh force along Z axis of individual hull (lb or N)

Gwet wetted girth (ft or m)

hC2 height of C2 above design waterline

hM2 height of M2 above design waterline

hM3 height of M3 above design waterline

hM4 height of M4 above design waterline

Ixwp moment of inertia of waterplane about waterplane X axis

Iywp moment of inertia of waterplane about waterplane Y axis

lcb position of center of buoyancy aft of midships, as a fraction of waterline length

L rolling moment (ft lb or N m)

Lh rolling moment of individual hull (ft lb or N m)

Lwl length of the waterline (ft or m)

m number of sections

M pitching moment (ft lb or N m)

Mh pitching moment of individual hull (ft lb or N m)

M1 bottom centerline

M2, mold line near design waterline

M3 mold line forming chine or shear

M4 deck centerline

Mx area moment about X axis (ft3 or m3)

My area moment about Y axis (ft3 or m3)

Mz area moment about Z axis (ft3 or m3)

n number of points around a section

N yawing moment (ft lb or N m)

Nh yawing moment of individual hull (ft lb or N m)

P roll rate (deg/sec or radians/sec)

Q pitch rate (deg/sec or radians/sec)

R yaw rate (deg/sec or radians/sec)

S cross sectional area (ft2 or m2)

S0, S1 approximations to cross section area (ft2 or m2)

Swet wetted area (ft2 or m2)

Sx maximum cross sectional area (ft2 or m2)

t independent parameter

t time (seconds)

V volume (ft3 or m3)

wM3 width of hull flare, measured from extension of slope at M2

x generic spatial distance (ft or m)

x1, x3 conic curve fixed points

x2 conic curve corner point

x4 midpoint of line connecting conic curve fixed points

x5 interior fixed point of conic curve

Vertx component of vertical unit vector along direction of hull's X axis

Verty component of vertical unit vector along direction of hull's Y axis

Vertz component of vertical unit vector along direction of hull's Z axis

X distance in longitudinal coordinate direction, positive aft (ft or m)

Xcb longitudinal location of center of buoyancy (ft or m)

Xcb longitudinal location of waterplane centroid in boat body axes (ft or m)

Xcwp longitudinal location of waterplane centroid in waterplane axes (ft or m)

Xo longitudinal position of the origin of the hull axis system (ft or m)

Xref longitudinal location of boat's reference point in fixed earth axis system (ft or m)

Xs longitudinal distance in stability axis system (ft or m)

Xwp longitudinal distance in waterplane coordinate system (ft or m)

Y distance in lateral coordinate direction, positive starboard (ft or m)

Yc lateral location of the centroid of cross sectional area

Ycb lateral location of center of buoyancy (ft or m)

Ycb lateral location of waterplane centroid in boat body axes (ft or m)

Ycwp lateral location of waterplane centroid in waterplane axes (ft or m)

Yo lateral position of the origin of the hull axis system (ft or m)

Yref lateral location of boat's reference point in fixed earth axis system (ft or m)

Ys lateral distance in stability axis system (ft or m)

Ywp lateral distance in waterplane coordinate system (ft or m)

Z distance in vertical coordinate direction, positive up (ft or m)

Zc vertical position of the centroid of cross sectional area

Zcb vertical location of center of buoyancy (ft or m)

Zcb vertical location of waterplane centroid in boat body axes (ft or m)

Zo vertical position of the origin of the hull axis system (ft or m)

Zref vertical location of boat's reference point in fixed earth axis system (ft or m)

Zs vertical distance in stability axis system

Zwp vertical distance in waterplane coordinate system (ft or m)

qD deadrise angle (radians or degrees)

qF flam (radians or degrees)

qT topsides angle (radians or degrees)

i hull incidence angle (radians or degrees)

k hull cant angle (radians or degrees)

x independent parameter (radians)

r conic curve parameter

r fluid density (slug/ft3 or kg/m3)

r1 bilge curvature parameter

r2 curvature parameter for segment M2-M3

r3 curvature parameter for segment M3-M4

t hull toe angle (radians or degree)

DX distance between stations (ft or m)

DXwp distance between stations projected on the waterplane (ft or m)

Q pitch attitude (radians or degrees)

Q0 steady state pitch attitude (radians or degrees)

F roll attitude (radians or degrees)

F0 steady state roll attitude (radians or degrees)

Y heading angle (radians or degrees)

Y0 steady state heading
angle (radians or degrees)

**Appendices**

**References**

Etkin, Bernard, "Dynamics of Atmospheric Flight," John Wiley & Sons,
Inc., 1972. ISBN 0-471-24620-4.

Garrison, Peter, "Loftsman User's Manual," Aerologic, 1998.

Jinnaka, T., Tsutsumi, T., and Ogiwara, S., "Hull Form Design Derived
From Wave Analysis"

Larsson, Lars, and Eliasson, Rolf E., "Principles of Yacht Design,"
International Marine, Camden, Maine. 1994. ISBN 0-07-036492-3.

Lewis, Edward V., "Principles of Naval Architecture Second Revision,
Volume I - Stability and Strength," Society of Naval Architects and Marine
Engineers, 1988. ISBN0-939773-00-7.

Lewis, Edward V., "Principles of Naval Architecture Second Revision,
Volume II - Resistance, Propulsion and Vibration," Society of Naval Architects
and Marine Engineers, 1988. ISBN0-939773-01-5.

Lewis, Edward V., "Principles of Naval Architecture Second Revision,
Volume III - Motions in Waves and Controllability," Society of Naval Architects
and Marine Engineers, 1988. ISBN0-939773-02-3.

Raymer, Daniel P., "Aircraft Design: A Conceptual Approach," American
Instiute of Aeronautics and Astronautics, Washington, D. C. 1989. ISBN
0-930403-51-7.

Thelander, J. A., "Aircraft Motion Analysis," Technical Documentary
Report FDL-TDR-64-70, Air Force Flight Dynamics Laboratory, Wright Patterson
AFB, Ohio. 1965.