Milgram 



As an example of the use of this program, a rig evaluation of a sloop- 

 rigged offshore cruising boat is carried out. The vessel chosen is the New York 

 "32", a vessel for which the results of model tests are available. Figure 3 shows 

 three rigs which are analyzed for this vessel; the original seven-eights rig, and 

 two masthead rigs. Tables 3a through 3f show the analysis of these rigs based 

 on the theory of two interacting lifting lines. The speeds predicted by model 

 tests for the resulting forces and moments are shown in each table. The course 

 with respect to the direction of the true wind is taken as 42.5° and the wind 

 strength considered is 18 ft/sec at the midspan of the mainsail, with a velocity 

 profile slope of 0.12 per second. Table 3a shows the results for the original 

 seven-eights rig with lift coefficients of 2.0 based on the true windspeed on both 

 main and jib. Note the relatively high value used for the second Fourier coeffi- 

 cient in the circulation series on the jib. This is necessary to keep the local lift 

 coefficient near the jib head at an attainable value, because the chord lengths in 

 this region are so small. The problem is not as severe on the mainsail because 

 of the headboard and the roach. Another reason for keeping the circulation at 

 the jib head small on a seven- eights rig is that this region is near the mainsail. 

 K the jib circulation does not taper to zero gradually enough as the jib head is 

 approached from below, the mainsail shape will have to vary greatly in passing 

 from regions below the jib head to regions above the jib head, if the mainsail is 

 to attain an efficient load distribution. Table 3b shows the results for conditions 

 as above, except that the mainsail lift coefficient is increased by 15 percent. 

 Note the decrease in the drag factor, which shows that this is a better relative 

 distribution than the preceding one, provided that the mainsail lift coefficient is 

 not too large to be attained. 



Table 3c shows the results of the rig calculation for the lower of the mast- 

 head rigs shown in Fig. 3. The lift coefficient based on the true wind is 2.0 for 

 both sails, and the sail area is reduced from its value on the seven-eights rig. 

 The increase in resulting boat speed over that for the case shown in Table 3b is 

 apparent. The improved load distribution is also revealed by a reduction in drag 

 factor, which is the ratio of the drag coefficient to the square of the lift coeffi- 

 cient. Since, according to linear theory, this ratio is unchanged by multiplying 

 the lift coefficients by a factor, it is a measure of the efficiency of the rig geom- 

 etry and relative load distribution. An increase in mainsail lift coefficient of 

 10 percent increases the boat speed and leaves the drag factor unaffected 

 (Table 3d). Since the jib is taller than the mainsail, it should and does carry 

 more lift than the mainsail as shown in Tables 3c and 3d. It does so even though 

 it has a smaller lift coefficient than the mainsail, because it has more area 

 (Fig. 3). Increasing the jib lift coefficient by 10 percent so that both the jib 

 sails and the mainsails have lift coefficients of 2.2 increases the boat speed 

 further, as shown in Table 3e. An increase in rig height of 3 feet while main- 

 taining the same sail area as before improves performance, as shown in Table 3f . 



Conclusions from Numerical Examples 



The example just described indicates the beneficial effect of an increase in 

 span, as long as the heeling moment does not become excessive. It is instruc- 

 tive to take note of the magnitude of the induced drag of a sailing rig. For ex- 

 ample of Table 3f , the rig producing the highest speed of all the rigs considered 



1410 



