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```					 Grand Valley State University

WOODEN SHOE REGATTA:

MODEL SAIL BOAT REPORT
EGR 365 – FLUID MECHANICS

July 30, 2003
INTRODUCTION:
The purpose of this project is to design, build, and test a 1/12 model recreational sailboat.
After this model has been tested, calculations will then be performed to predict how the
full-scale prototype will behave. The hull for the model boat is to be made from a 2” x 4”
x 10” block of basswood. The design must be a single hull design, and the entire hull
must be made only of the basswood. The boat must also be powered only using sails to
harness the wind. The boat must also be design so that it would look appealing to
customers wanting to buy a sailboat.

PRELIMINARY DESIGN STATEMENT:
The boat I have build was designed using the following criteria:

-   high width to depth ration (for increased stability)
-   low weight
-   shape will be similar to real sailboat
-   use two sails (main sail and jib sail)
THE DESIGN:

Figure 1 below shows a picture of the model sailboat:

Figure 1 – Picture of Model Sailboat

The completed model design had a waterline length of 15”, and a wetted surface area of
67 square inches. The mast reached a height of 16” from the surface of the deck.

TESTING:

The model hull was put through a hull test in a towing tank. Drag on the model was
found for a range of different speeds. In Table 1 below, the test results can be seen.

speed_model [ft/s]    drag_model [lbf]

0.35                0.0132
0.63                0.0242
0.91                0.0165
1.18                0.0264
1.47                0.0165
1.74                0.0330
1.95                0.0308
2.22                0.0484
2.48                0.0660

Table 1 – Drag Test Results
MODEL CALCULATIONS:

Using the wetted surface area of the model and the model speed, the total resistance
coefficient can be calculated.

Drag
Ct 
0.5 AV 2

Table 2 below shows the resistance coefficient at each speed:

speed_model [ft/s]    total_resistance_coefficient_model

0.35                          0.2399
0.63                          0.1358
0.91                          0.0444
1.18                          0.0422
1.47                          0.0170
1.74                          0.0243
1.95                          0.0180
2.22                          0.0219
2.48                          0.0239

Table 2 –Total Resistance Coefficient

The Froude Number can also be calculated for each speed.

V
Fn 
gL
Table 3 below shows the Froude Number for each speed:

speed_model [ft/s]        Froude Number

0.35                    0.0552
0.63                    0.0993
0.91                    0.1434
1.18                    0.1860
1.47                    0.2317
1.74                    0.2743
1.95                    0.3074
2.22                    0.3499
2.48                    0.3909

Table 3 – Froude Number

In Figure 2 below, the hull resistance is plotted vs. the Froude Number:

Figure 2 – Drag vs. Froude Number For Model
Using the Reynolds Number for the model and the waterline length of the model and the
model speed, the friction coefficient can be calculated.

.075
Cf 
(log 10 Re  2) 2

Table 4 below shows Reynolds Number and the friction coefficent for each speed.

speed_model [ft/s]   Reynolds Number (Model)              friction_coefficient_model

0.35                    36157                              0.01146
0.63                    65083                              0.00947
0.91                    94008                              0.00848
1.18                    121901                             0.00788
1.47                    151860                             0.00741
1.74                    179752                             0.00708
1.95                    201446                             0.00687
2.22                    229339                             0.00664
2.48                    256198                             0.00646

Table 4 – Reynolds Number and Friction Coefficient

The residual coefficient can now be calculated.

C r  Ct  C f

Table 5 below shows the residual coefficient:

speed_model [ft/s]         residual_coefficent

0.35                      0.22849
0.63                      0.12630
0.91                      0.03588
1.18                      0.03434
1.47                      0.00959
1.74                      0.01719
1.95                      0.01117
2.22                      0.01523
2.48                      0.01744

Table 5 – Residual Coefficient
PROTOTYPE CALCULATIONS:

Now that the Froude Number is matched, calculations can be made for the prototype
sailboat.

Using the Froude Number, the prototype sailboat speed can be calculated.

1
 Lp  2
L 
V p  Vm     
 m

Table 6 below shows the speed of the prototype sailboat:

speed_model [ft/s]   Froude Number            prototype_velocity [ft/s]

0.35               0.0552                       1.212
0.63               0.0993                       2.182
0.91               0.1434                       3.152
1.18               0.1860                       4.088
1.47               0.2317                       5.092
1.74               0.2743                       6.028
1.95               0.3074                       6.755
2.22               0.3499                       7.690
2.48               0.3909                       8.591

Table 6 – Prototype Velocity

The Reynolds Number for the prototype can now be calculated, and using the Reynolds
Number, the prototype friction coefficient can be calculated.

.075
Cf 
(log 10 Re  2) 2
Table 7 below shows Reynolds Number and the friction coefficient for the protoype:

prototype_velocity [ft/s]     Reynolds Number (Prototype)              friction_coefficient_prototype

1.212                          1503019                                  0.00430
2.182                          2705435                                  0.00382
3.152                          3907850                                  0.00356
4.088                          5067322                                  0.00339
5.092                          6312681                                  0.00325
6.028                          7472153                                  0.00316
6.755                          8373965                                  0.00309
7.690                          9533437                                  0.00303
8.591                          10649965                                 0.00297

Table 7 – Prototype Reynolds Number and friction coefficient

The total resistance coefficient for the prototype can now be calculated.

Ct  C f  C r

Table 8 below shows the total resistance coefficient for the prototype:

prototype_velocity [ft/s]       total_resistance_coefficient_prototype

1.212                                  0.23279
2.182                                  0.13012
3.152                                  0.03944
4.088                                  0.03773
5.092                                  0.01285
6.028                                  0.02035
6.755                                  0.01426
7.690                                  0.01825
8.591                                  0.02041

Table 8 – Prototype Total Resistance Coefficient

The total drag force for the prototype can now be calculated:

Drag  0.5Ct ApV p
2
Table 9 below shows the total drag force on the prototype:

prototype_velocity [ft/s]          drag_prototype [lbf]

1.212                           22.129
2.182                           40.075
3.152                           25.346
4.088                           40.771
5.092                           21.545
6.028                           47.809
6.755                           42.083
7.690                           69.805
8.591                           97.402

Table 9 – Prototype Drag Force

The horsepower needed to overcome this drag force can also be calculated

1Hp
Hp  Drag  V p 
ft  lbf
550
sec

Table 10 below shows the horsepower calculation for the prototype:

prototype_velocity [ft/s]            EHP [hp]

1.212                         0.049
2.182                         0.159
3.152                         0.145
4.088                         0.303
5.092                         0.199
6.028                         0.524
6.755                         0.517
7.690                         0.976
8.591                         1.521

Table 10 – Prototype Horsepower Calculation
Figure 3 below shows a plot of the necessary horsepower to overcome the drag force of
the prototype:

Prototype Horsepow er

2.50

2.00

Prototype Horsepow er

1.50
EHP [hp]

1.00

0.50

0.00
0.00       0.10        0.20           0.30    0.40   0.50
Froude Num ber

Figure 3 – Horsepower Needed to Overcome Drag

SAIL CALCULATIONS:

SEE APPENDIX A FOR SAIL DATA:

To get model sail data, a copper sail was placed in a wind tunnel. This sail was also a
1/12 scale, so Reynolds scaling was used to match sail forces. The model sail was put
into a wind tunnel with a model wind velocity of 136 ft/second. This corresponds to a
prototype wind velocity 11.35 ft/s.
Table 11 below shows the forward force generated due to the wind:

yaw angle [deg]    Forward Force @ 5'' or 11`.35 ft/s [lbf]

0                                   -1.310
10                                   -1.037
20                                    0.083
30                                    2.139
40                                    3.134
50                                    3.587
60                                    3.644
70                                    3.930
80                                    4.005
90                                    4.000

Table 11 – Forward Force vs. Yaw Angle

Figure 4 below shows a plot of this data:

Forw ard Force

5.000

4.000

3.000
Forward Fo rce [lbf]

Forw ard Force
2.000

1.000

0.000
0      10        20   30        40          50        60   70       80      90

-1.000

-2.000
Yaw Angle [deg]
Figure 4 – Forward Force vs. Yaw Angle

As can be seen from this data, the maximum forward force created by the wind is 4 lbs.
This is significantly less than any prototype hull speed analyzed in this lab. Even for a
prototype speed of only 1.2 ft/s, the drag force was 22 lbs. There really is no point of sail
on the sail data chart.

Data could be extrapolated to show that the boat may have a possible point of sail when
the boat is going less than 1 ft/second. As soon as the drag force is less than the wind
force, there is a possible point of sail.

DISCUSSION:

In designing and building the model boat, two different types of scaling were used,
Froude Number scaling and Reynolds Number scaling.

The Froude Number scaling was used to match the wave-making properties of the boat,
corresponding to the hull drag. It was not possible for us to use Reynolds Number
scaling on the hull because no fluid was available that would give us proper Reynolds
scaling.

Reynolds Number scaling was used for the sail however. A model sail was placed in a
wind tunnel and the forces were measured. Using simple Reynolds Number scaling
techniques, the model sail forces were scaled to the prototype sail forces.

CONCLUSION:

In this project, a 1/12 model sailboat was designed, built, and tested. The data collected
was then scaled to a full size prototype sailboat. This data was then analyzed, and
inspected for possible points of sail. The data collected for the model sail showed that no
points of sail existed. However, this data was extrapolated to find that a possible point of
sail existed at a hull speed of about 1 ft/second, and a wind speed of 12 ft/second.

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