SINGLE WING LANDYACHT PERFORMANCE PREDICTIONS WITH VELOCITY DEPENDENT ROLLING RESISTANCE This is the derivation of a simple velocity prediction program (VPP) for landyachts. A working Mathcad version of this program can be found here. Although it was derived for landyachts with rigid wing rigs, the program can be adapted to any sailing vehicle by replacing the rolling resistance equations with the appropriate hull drag and sideforce model. By replacing a few key geometry and aerodynamic parameters, it is easy to see the effects of major design choices on the performance of the yacht. The following assumptions are made: 1. pilot trims sail to the angle of attack for either best L/D or maximum lift under light to medium winds, but will reduce alpha to keep wheel on ground or to avoid skidding in high winds 2. variation of yacht parasite drag with apparent wind angle is neglected 3. aerodynamic drag coefficient follows a parabolic polar based on wing lift coefficient 4. rolling resistance is linearly dependent on vertical and side loads 5. rolling resistance varies linearly with speed (consistent with the existing limited test data) Basic kinematic relationships:
Fundamental speed relationship:
Force relationships:
gamma : direction of travel relative to true wind
Balance of forces:
Moment Balance (vertical center of drag is not same as vertical center of lift because of parasite drag of body. So ignore parasite drag of wing (it may be small compared with body) and only look at lift induced forces) Di : induced drag
Sail trim for best L/D:
Sail trim if constrained by rolling moment:
Sail trim if constrained by skidding:
by substitution, yields
Approximate axle sizing (so skidding & heeling happen at about the same time)
Rolling resistance defined in terms of drag of yacht sailing at some reference wind velocity (say, 10 mph). This is to be consistent with the generic performance analysis and a convenient way of incorporating existing tow data.
Substituting into the Dw force balance equation gives the performance relationship:
COMPLETE PERFORMANCE ANALYSIS Numerical tolerance for iterative solutions:
Yacht Parameters:
Aspect Ratio :
Oswald efficiency :
Height of CE :
CDo :
CLmax :
Gross Weight :
Friction Coefficient :
Rolling Resistance :
Sideforce Resistance:
Reference Speed :
Wheel Apex Angle :
Axle Size:
Length of yacht from front wheel to c.g.:
Sail Trim:
(reset CL to CL max  the second trim strategy)
Yacht Acceleration:
10mph:
15mph:
20mph:
25mph:
30mph:
Plot excess thrust vs beta to see if there will be any problems with convergence in the iterative solution:
Final Results (wind is from 0 degrees):
