Testing of hull drag for a sailboat

Final report

For Autonomous Sailboat Project

In Professor Ruina’s Locomotion and Robotics Lab, Cornell

Jian Huang

jh2524@cornell.edu

Mechanical Engineering, MEng student

2016/5/12

Table of Contents

1. Background ............................................................................................................................... 3

2. Testing procedures .................................................................................................................... 3

2.1. Straight ahead motion ................................................................................................... 3

2.2. Motion with angle of attack .......................................................................................... 5

2.3. Pool test ......................................................................................................................... 6

3. Testing results ........................................................................................................................... 7

3.1. Straight ahead motion ................................................................................................... 7

3.2. Moving with an angle of attack ..................................................................................... 9

3.3. Pool test ......................................................................................................................... 9

4. Conclusion .............................................................................................................................. 11

Reference ........................................................................................................................................ 12

1. Background

The drag of a sailboat hull is an important parameter that can aid hull design process

and needs to be taken into consideration when navigating the sailboat. Previous a drag

test was conducted by the Autonomous Sailboat Team, the results of which was used in

calculating the maximum boat velocity with various attack angles between the sailboat

and the wind.[1] In that test, it was found that the overall drag force was approximately

as follows:

|�⃑�ℎ𝑢𝑙𝑙| = 2.48|�⃑⃑�𝑏𝑜𝑎𝑡|3

That test was not very detailed, however, because only drag while moving straight

ahead without attack angle was measured. Also, the amount of data collected is limited.

After the previous test, new hull designs have been completed, and a new hull drag test

on them would be beneficial to simulating and navigating them.

2. Testing procedures

Before testing the real-sized hull in a swimming pool as the previous test did, several

tests were conducted with small models of a sailboat in a bathtub. They are useful for

testing whether the planed method for testing will work, and getting a rough impression

on how the results of such drag tests might look like.

2.1. Straight ahead motion

The basic structure for testing is shown in Figue.1.

Figure.1 Basic structure of testing hull drag.

The boat is connected to a weight m by a wire, with two pulleys in between. The

weight is free to fall, exerting a tension T on the boat. The drag D acts on the boat and

increases with the boat speed. Eventually the weight falls and the boat moves at a

steady state speed, and the drag equals the tension and the gravity of the weight. By

measuring steady state velocity, recording the weight, and repeating with different

weights, a relationship between drag force and boat velocity can be made clear.

Figure.2 shows the actual testing structure. The pulleys are hung on the sprayer with

wires, with additional wires preventing spinning and swinging.

Figure.2 Pulleys hung in the air.

Figure.3 shows the model boat used. A wire is attached to its head through a hole.

Some coins are attached to the other end of the wire as the weights in Figure.1. After

the weight is free to fall, the boat starts moving and approach a steady speed before

the weight reaches minimum possible height. The motion of the boat is recorded as a

video which can be later used to measure the steady state velocity. The time between

points A and B on the boat pass a particular point on screen can be measured with any

video player, and with the distance between A and B, the velocity can be measured.

Figure.3 Model boat used for testing.

2.2. Motion with angle of attack

Besides drag when moving straight ahead, the drag force when the motion of the model

boat does not align with the body of the boat is measured in another test. The rest of the

test structure is the same, except for the way the boat is connected by the wire. Figure.4

shows the modification, where the arrow indicates another wire keeping the motion of

the boat in the center of the bathtub. This wire disables the measurement of lift force,

but it prevents the boat from swinging in the direction of minimal drag force.

The model boat is connected by two wires at both the head and the stern, which are then

connected to a single wire. The location of the intersecting point determines the angle

that the boat would be moving at. By moving this point and reconnecting the wires,

steady state velocities at various angles can be measured.

Figure.4 The model boat connected with an angle of attack.

2.3. Pool test

Multiple methods including the one used in bathtub tests above were attempted, and the

final test method is shown in Figure.5 below.

Figure.5 Test method of the pool test.

As shown in the figures, a weight is falling through the water, pulling the boat in the

process. Thus the problem of fixing the pulley system is avoided, and the test is easy to

conduct. Meanwhile, without using the pulleys, the friction between the wire and the

metal rod results in an error. The weight is now subject to buoyancy and hydraulic drag,

and the computation of these forces can also contain error.

The buoyancy force can be calculated after calculating approximate volumes of the

weights. The drag force is calculated as such: (1) let the weight fall without pulling the

boat; (2) measure the pool depth and the time it takes the weight to fall to the bottom;

(3) calculate an average drag coefficient with Gravity − Buoyancy = Cv2; (4) after

measuring boat speed, calculate the drag force of the weight with C and v.

The drag force while moving at an angle was not included in the pool test.

3. Testing results

3.1. Straight ahead motion

The main results of the straight ahead case are shown in Figure.5. Drag force with

friction measured and removed is plotted against the steady state velocity that the model

eventually achieves.

Figure.6 Drag force changing with velocity, when the boat is moving straight ahead.

While there are noise in the data, it can be seen that the drag force increases

exponentially as velocity increases. In order to compare the results to the previous tests,

Figure.6 plots the drag force against the cube of steady state velocity. After ignoring

the last point with a large drag force and connecting the remaining first and last points

with a straight line, the drag force seems to correspond to the previous conclusion that

it is proportional to the cube of velocity. The correspondence would require more data

to confirm.

Figure.7 Drag force plotted against cube of steady state velocity.

However, shown in Figure.7, the model boat clearly does not obey the coefficient of

2.48, most possibly simply due to the difference between the model boat and the full

sized boat used previously.

Figure.8 Comparison of this test and the previous test.

3.2. Moving with an angle of attack

Figure.10 shows the main results in this test. When the angle of attack increases, the

steady state velocity decreases as expected. However, in a bathtub test, there is little

room for the model boat to pass the phase of swinging and enter a status of a steady

motion at an angle, therefore it is difficult to gain more accuracy or sufficient data

points in this test for a detailed relationship between the two.

Figure.9 Steady state velocity plotted against the angle of attack.

3.3. Pool test

Figure.10 shows the results when there is no additional weight placed on the empty hull,

which weighs 0.392 kg. The hull is made of leaking materials, and the water leaking

into the hull is uncontrollable and unmeasurable, and can possibly outweigh the hull

itself. Therefore, much error and noise can be noticed in the figure. A general trend that

the drag force is larger at higher speed can still be observed.

Figure.10 Drag force changing with velocity, without additional weight.

Figure.11 shows the results when there is an additional weight of 2 kg placed in the hull.

With the hull being heavier, the water is leaking more heavily. An estimation value of

the total weight for reference including the weight of the hull is 4.392 kg. Due to error

and noise, the results show no relationship between the drag force and the cube or

square of boat velocity. Meanwhile, the general trend is more explicit than the case

without additional weight, which means water leaking in caused much of the error in

the previous case, and that the additional weight does stabilize the results.

Figure.11 Drag force changing with velocity, with additional weight.

4. Conclusion

The tests on the model boat shows trends as expected, thus validating the methods used

to test the drag force. However, the pool test is not as successful, with possible causes

being:

(1) Performing the method used in bathtub tests failed due to being unable to fix the

pulleys tight to the standing rod;

(2) Ignoring the pulleys in the new method caused additional friction;

(3) The motion of the falling weight is complicated, and approximations of the

additional drag and buoyancy are not exact enough.

Any future attempts to measure hull drag should take these causes into considerations.

Reference

[1] Bo Baker, Jesse Miller, et al., 2015, Polar Plot Generation.