Hull Test Data

Out of curiosity, I have done some testing of the hull characteristics of a Footy hull. This is part of an effort to defeat a V-12 that has been constantly beating me on the race course every Thursday, causing unbearable humiliation. My current boat is the Pepsi Torpedo, made of two 2-liter Pepsi bottles glued together lengthwise. As an improvement, I am now making a fatter and lighter hull, using a single 3-liter soda bottle. The testing was done with an empty 3-liter bottle, with moveable weights to adjust the pitch trim (nose-up vs nose-down). A skeg was added to provide some directional stability. This provides a cheap test vehicle that can be lost at sea with no regrets.

The characteristics of concern were pitch stability (submarining) and drag.

Pitch Stability
The pitch stability was measured in the bathtub by moving weights inside the bottle, on a velcro track. A 16 oz hull, using the 3-liter bottle, had a pitch stability of 32 oz-in/in, which means a 1 oz weight, 32 inches forward of center, will cause the prow to dip 1 inch. This test did not include a keel or bulb, which will add a small amount of pitch stability. This result is significantly better than the existing Pepsi Torpedo, and should allow it to carry more sail without nose-diving. It is probably not quite as good as the V-12, but it is getting close. The soda bottle hull actually sails quite well with its entire nose under water, as long as part of the rudder stays wet.

Drag was measured in two configurations. First with an approximately level 16 oz hull, which was actually about 1/4" nose-up. Secondly with a deliberately nose-down hull, also of 16 oz. The nose was 3/4" down. The data is:

Speed Drag Comments
(kt) (oz)
0 0
0.57 0.24 nose-up 1/4"
0.86 0.72 nose-up 1/4"
0.96 0.72 nose-down 3/4"
1.44 1.20 noe-down 3/4"

The probable accuracy of the data is:
Speed data = 10%
Drag data = 1/8 oz

This data was taken with very primitive methods, but the results do not appear unreasonable. The data did not go significantly past the theoretical hull speed, where I am sure the drag will rise much faster. The gain in speed at the 0.72 ounce drag point, when going from nose-up to nose-down, may not be real, as it falls within the measurement accuracy.

If you plot the data, you will see that it has an approximate square-law shape, but strangely does not rise more sharply at the higher speeds. This may be due to inaccuracy in the data, or it may be real (the high prismatic coefficient of the hull may be advantageous as the hul speed is approached). The testing method was VERY primitive.

This data is being presented because I have never found anything at all on hulls this small at such low speeds. Others are probably also looking for this kind of information, so this may be a useful starting point.

Bear in mind that the hull shape is probably nowhere close to optimal for drag, because it is essentially a long cylinder with a little rounding at the ends. But it is a better than average shape for pitch stability. Hopefully that will enable it to carry enough sail to make up for the difference.

I would be interested in any other data of this kind on other Footy hull types.

Very interesting, Walt. Can you explain your primative methods so some of us might try to do it too?

Thanks…Bill H

It is facinating and reassuring that my theoretical speculations and Brett’s and your practical tests atre all pointing in the same direction - albeit by different routes. Further, the resulting boats - Pipsqueak, Akela, MoonShadow seem to live up to the expectations generated!

The test method requires the following equipment:

  1. A light freshwater fishing rod (I used a 6 ft light action carbon spinning rod)
  2. A watch with a second hand
  3. A stiff stick taped to the fishing rod (I used 1/4" carbon fiber)
  4. A short ruler taped to the stick (I used a marked piece of paper)
  5. some sinkers of known weight (I used 3/4 oz and 1.2 oz)
  6. A scale to measure the sinkers (don’t believe the marked weight)
  7. A paper clip which can be bent into a hook to hang the sinkers from during calibration.

The force reading is taken from the deflection of the tip of the fishing rod, as compared to the stiff stick. The rod must be normal to the direction of the line, and the tip must be close to the water. Distance is measured by the number of cranks of the fishing reel, and time is measured with the watch.

The reel must be calibrated so you know how much line is taken in by each turn of the crank. The rod tip must be calibrated with some sinkers so you know how much deflection is caused per ounce of force. THe zero-force point should als be recorded.

The stick is taped to the fishing rod at several places below the top section, but the topmost secton is free to deflect.

I did the test at a section of lake shore with a clear gravel bottom devoid of weeds. The hull under test was placed in the water a few feeet off shore, then I walked down the beach about 30 feet, while letting out line. Then I reeled in the line at a speed which caused a particular constant deflection of the rod tip, keeping reeling at this constant speed as long as possible in the limted space. I started counting turns and measuring elapsed time after the rod tip had stabilized at the desired deflection. This test was then repeated at different deflections, until the full set of data was recorded.

A certain amount of practice is needed to do this correctly. Data was not recorded until after a few practice runs. Some tests were repeated as a validity check, and the data did indeed repeat.

As you can see, this test is not very fancy, and there are many improvements that can be made. A major dificulty was my 72 year old eyeballs trying to read the thin second hand of the wristwatch while counting turns and keeping the rod tip deflection under control.

A second difficulty was the paper calibration got wet and started to warp, even though it was covered with transparent tape. A piece of plastic would be better.

After reviewing the data, it is apparent that I should have made the ruler a little longer, so more data past the theoretical hull speed could have been gotten. Also, there is no point to making fine markings on the ruler. It is hard enough to keep the tip stable at 1-inch increments, and the markings should be easily seen from the other end of the rod (where your eyes will be).

With regard to the friction force on the line, it should not affect the rod tip deflection as long as the line makes a right angle turn at the rod tip.

I hope the above description is helpful.

Sir, as one of my mentors - a very great man - said, ‘An engineer is a man who can do for five shillings what any fool can do for a pound.’ Your method is worthy of him (and I mean this as a considerable compliment) and better than that of Ljungstrom as described.

Congratulatins. This is what Footys SHOULD be about.

I agreed, nice methodology. I have a question for you or the group. Where would be the best place to attach the line?

Attaching to the tip of the bow would be easy but the sails aren’t dragging the boat by the bow. Would towing from a point on the mast be better (without sails)? This would add some of the submarining force that plagues Footys.

A very excellent question. My first attempts used a short mast, with the pull force at the top of the mast. The objective was to simulate the submarining moment caused by the sail and combine it with the drag test. Unfortunately, this did not work as planned. The boat always wanted to turn. We finally came to the conclusion that the mast was not exactly vertical, which was putting a turning moment on the hull. As soon as it started turning, the turning moment increased, resulting in chaos. This could perhaps be controlled by actively using a rudder. Therefore the drag tests were run with the line attached to the prow, and the hull stayed on course because of the skeg. The skeg was about the size and shape of a typical Footy rudder, hung off the stern. It was quite rudimentary, just a piece of carbon fiber sheet, 1/16" thick.

It was decided to run a separate test for pitch stability, and run the drag test at several pitch angles. The results could later be combined.

Roll angle is not an issue with the soda bottle hull, since it has a cylindrical cross section, and should have the same drag regardless of roll angle.

Obviously more data needs to be taken. I was so surprised that this method actually worked that I was anxious to get home and plot the data, so didn’t get as much data as planned.

This data is probably not accurate enough to compare the performance of small changes in hull design, but may be useful for comparing wildly divergent designs (such as the soda bottle vs a conventional hull).

well done! it souns as though you have done some great work, in the footy spirit with great results!

The data that I had originally posted prompts some questions, which were also mentioned. Therefore some more data has been taken. First, I took 2 more data points at higher speeds. Then, a comparison test was done using a tow bar. Two identical 3-liter soda bottles were weighted to 16 oz, and towed together, at opposite ends of a 36" tow bar, as follows:

A green bottle was towed at a nose-down attitude (1" down)
A clear bottle was towed at a level attitude.

There was no obvious difference between the speeds of the two bottles. This puts some suspicion on the accuracy of the previous data, which appeared to indicate that nose-down was faster.

Then the two new data points were plotted with the original data. The results are interesting. A single smooth curve can be fitted to all the data, except for one data point, which may be questionable (it will be re-visited at the next oppportunity). The smooth curve is a simple function, Drag = K*V^2, and goes all the way out to 2 knots. I have attached a copy of the curve. It appears that pitch attitude is not a major factor, as long as it doesn’t exceed 1" nose-down.

The direction in which you are leading is that Froude was wrong - at any rate at very small sizes. I have been surmising this for some time on the basis of my own non-systematic obervations and some anecdotal information.

It would be of very great interest to now the depth of water in which yout tests were conducted. Are we possibly loking at a ‘bottom’ effect? I suppose that, if we are and Froide stands, then, so what? Model yachts should be designed for the shallow waters in which they generally sail. In either case the anseer can scarcely fail to be of great importance

A very interesting observation. I have been bothered about this also, and have been looking at possible sources of error. I thought that perhaps the drag on my fishing reel was slipping, but checked it out and it was OK. Another possibility is that all the drag is coming from the skeg, but this seems unlikely.

The testing was indeed done in shallow water. I will try to put some bounds on it:

(A) The skeg extends about 5 inches below the bottom of the hull (6 inches below the water line). There were at least a few additional inches under the skeg in all cases. This puts a lower limit on the depth of at least 8 inches.

(B) The testing was done near shore, at a boat launch that falls off rapidly. I was typically standing in water about 6 to 12 inches deep, and the boat was further out, perhaps in 2 feet of water. But I can not guarantee it.

At the higher speeds, the hull was definitely making a significant bow wave, and was trying to climb up it. When initially trimmed nose-down, it appeared to go nose-up at the higher speeds, while climbing the bow wave.

Nevertheless, I believe some more testing needs to be done to truly validate this data, and it is very beneficial that some intelligent people such as yourself are looking at it. We normally race these boats in a small pond which is 7 feet deep in the racing area, so I don’t want to be getting a shallow water effect into the data. It sounds like some testing should be done in that pond, across the full width of the pond.

There was another interesting phenomenon that was observed. Just for amusement, a band of tape was wrapped around the hull near the bow, to create a ridge of 0.020" which could perhaps trip the boundary layer. When comparing two identical hulls, towed together behind a 36" tow bar, the one with the tape appeared to be faster (possibly the golf ball dimple effect). But the validity of my tow-bar tests is not 100%, because the test area may not be long enough for the 2-hull system to reach equilibrium.

Walt, perhaps moving your tests indoors to a swimming pool would eliminate several variables in your testing (like water depth, current, or wind effect). A swimming pool would also provide a standardized length.
Many High Schools and Colleges have swimming pools, and they are not in use all the time. You might even recruit some volunteers to help from the student body!

Really interesting data, Walt…please continue to keep us posted.

Thanks…Bill H

First, my congratulations to Mudhen on his successfuul Footy regatta.

With regard to the hull test data that I have posted, there is a logical explanation.

Angus had raised the question that the wave drag seems to be missing, with its expected sharp increase at the hull speed of 1.34 kt.

The explanation is that the form drag is very high, and is overwhelming the wave drag. I have looked at the various drag terms, and that is the only explanation.

The shallow water in which the tests were performed does not appear to be an issue. Various technical articles have mentioned that shallow water effects don’t appear unless the depth is less than half the wavelength. I believe that the depth was sufficient.

The hull has a frontal wetted cross-section of about 3 square inches. When combined with the test data, this imples a dimensionless viscous drag coefficient of about 1.2, which seems like a very high number. I was expecting perhaps 0.5.

Therefore, I suspected that maybe friction drag (from wetted surface area)was a big contributor. So I took a flat aluminum plate, 12" long, and used it as a sliding damping element in a pendulum, in a trough of water. Backing out the drag from the damping ratio, I got a dimensionles friction drag coefficient of 0.007. This would imply that the friction drag is not a major contributor.

This all comes back to the form drag being the major contributor, throughout the range of test data, up to 2 knots. Also, the drag coefficient is very large. This may be caused by the unusual hull form, which is a straight cylinder, with some rounding at the ends. Because of this shape, it has a very small frontal wetted cross-section. Other shapes may have a better coefficient, but similar overall drag, because they may have a larger frontal cross-section. I would be very interested in seeing any similar data on other hull types. Since the data appears to follow a predictable curve, only one or two data points may be needed.

Please be aware that I am not experienced or educated in the art of ship design. All my knowledge in this area comes from an engineering course in fluid dynamics, 50 years ago. I have spent the intervening years in the aerospace industry, designing electronics. So much has been forgotten, and much was never learned. Any constructive comments will be appreciated.

A picture of the towing dummies is attached. The 3-liter bottles are 5.2" diameter, and draw about 1" when weighted to 16 oz.

More Testing
I did some more testing yesterday, which corroborated the previous drag test data, in at least 2 feet of water. I tried the tape ridge, which looked promising in a questionable comparison test last week, however there was no apparent advantage, at least to the accuracy limits of my test method.

Testing of Pepsi Torpedo - Problems
Then I tried testing the real Pepsi Torpedo (made from thinner 2-liter bottles, with a deeper draft), to see if it fell on the same drag curve. However, I could not get it to go straight. I mention this because others trying this method may have a similar problem. I am not entirely sure why this happened, however it may have 2 causes which worked together to cause the problem:

  1. The tow line was attached at the base of the mast, about 2" aft of the prow (the mast is well forward because of the cat-boat rig). This was also about 1" above the roll axis (note: the roll axis is well defined because of the cylindrical hull), and probably caused a small roll moment when starting out slightly off line. My previous testing, with a weighted bottle, always had the tow line connected exactly on the roll axis, at the prow, using a hole in the bottle cap as the attachment point. This implies that the tow line should be attached as low as possible on the prow. This idea is reinforced by my much earlier testing, which used the 3- liter bottles with the tow line attached further up the mast, and would not go straight.

  2. The boat had the rudder positioned in the straight position, but the rudder linkage has a little play in it, so maybe the rudder wasn’t really doing anything. The boat was not being actively controlled (the power switch was off). It had a VERY strong desire to go off at about 30 degrees, in either direction. Pulling sideways on the tow line would not turn the boat. The rudder was visibly not turned. This same hull works very well normally.

The test area was getting crowded, so I had to suspend operations before investigating this any further.

I have built a dummy Razor hull for comparison to the 3-liter hulls. The objective was to get a reasonably conventional hull shape for comparison, without too much work. Like the soda bottle hulls, it would not tow straight without a large skeg. All data was taken with 16 oz total weight, using sinkers placed in the hull, and level attitude, and skegs. For the Razor, level was defined as having the prow touching the water, which put the transom corners also touching the water.

Static testing for pitch stability
(defined as oz-in of torque to get 1 inch of prow depression)
This test does not include the additional effect of the keel bulb
3-liter hull - 32 oz-in/in
Razor hull - 20 oz-in/in

Towing test for hull drag (at 1.15 kt)
3-liter hull - 0.90 oz
Razor hull - 0.68 oz

It can be seen that the conventional hull has less drag, but also less pitch stability. But it must be noted that the tow testing is currently not very accurate, and the difference may be better or worse than indicated by these tests. Comparison testing with a tow-bar pulling 2 hulls will be needed to get better data (similar to what Brett has done).

Pitch stability, to resist submarining, is dependent on the fullness of the prow above the water line, and the fullness and depth of the stern below the water line. The conventional (Razor) hull pulls its stern completely out of the water immediately, but also has better drag characteristics. The soda bottle keeps its stern immersed a little longer, and also has a large bulbous prow above the water line. Our friend Angus has apparently taken this a little further on his Akela 2 design. It appears that he has concentrated on keeping the stern under water by reducing beam, and also has a fairly full prow. Of course, keeping the stern in the water also keeps the rudder in the water, a big advantage in a blow.

It was a real pleasure sailing and talking with you today! I now have a better appreciation for your research. Keep it up!

In the interest of getting more accurate data, a simple bathtub test was developed. The boat is towed by a pendulum. Only a stopwatch is needed to measure the test result. The pendulum was a string attached to the shower head, with weights of 1 oz and 1/4 oz. This test has several obvious advantages:

  1. It is not necessary to get your feet wet in the icy water.

  2. Accuracy is determined by the stop watch, the length of the pendulum, and the weight of the pendulous mass.

Because of the limited length of the bathtub, this test must be done at relatively slow speeds, but can be done at the lower end of the existing data taken by the fishing rod method (0.5 knot). The pulling force is not constant, but changes with the pendulum angle. A simple simulation was developed, using an Excel spreadsheet, calculating the forces and accelerations at small time increments, to compare against the test results by varying the assumed drag factor.

The results were surprising. There was no measurable drag. Previous testing with the fishing rod had indicated a drag curve of the form:

Drag = k*V^2

Drag is ounces
V is knots
k is about 1.0 for the 3-liter bottle

The pendulum test should have easily detected the drag of the fishing rod test. This implies that either the pendulum test is invalid, possibly because it didn’t give the lossy vortices suficient time to develop, or that the drag curve equation shown above isn’t valid at low speeds.

Now that spring has come, it is possible to do some more tests. I am concentrating on tow-bar tests, to compare 2 hulls. The tow bar is 30" long, with sliding attachments for the boats, and an offset connection to the tow line. This allows the percent of drag difference to be measured by looking at the tow bar angle, or moving the attachment points. The tow bar is pulled by a 10 foot cane pole, while walking along the shore, without getting my feet wet. The dimensions can be adjusted to measure large differences, or small differences.

The first testing was set up to look at large differences, comparing a dummy Razor hull with various versions of the 3-liter bottle hull. The results were not very encouraging, since the razor hull had far less drag (perhaps 50%) than any of the versions of the 3-liter hull, so much so that the differences in the 3-liter hulls could not be seen.

Then the sensitivity was goosed up, and some meaningful data was gotten comparing 2 dummy 3-liter hulls with variations. Testing was done at low speed and high speed, and the results were the same at the different speeds. All testing was done with the dummy hulls level, and weighted to 16 oz.

The 3-liter bottle is obviously sub-optimal, for several reasons:

  1. It does not quite use the full 12 inches at the water line
  2. The prow is very blunt
  3. The stern is rounded off in an obscene manner.
  4. The hull has no rocker

Two modifications were therefore tried.

A) A skirt was added to the stern, to give a more squared-off stern. The result was a 6% increase in drag (not good)

B) A false prow was added, to give it a more vertical stem, and faired into the bottle shape with foam and tape. This was a very rudimantary job, not esthetically pleasing, but it showed a 6% reduction in drag (Alleluia!!)

Conclusion: false prow is good, and deserves some more work. It will also increase the pitch stability slightly. Recent racing of the real boat against our local V-12 had shown some apparent improvement with the false prow,but this quantifies it and takes it out of the realm of subjective judgement.

Of course, any sane person would just build the boat from something else, and get a better shape to start with. But this has been fun and educational, and there is too much effort invested in the existing boat to abandon it. It is also light and strong.

I plan on testing a diagonal towing dummy next; it is probably similar to Brett’s new design, with a narrow transom, but without the vertical angle. The objective will be to see if the drag improvement is worth the pitch stability loss (of course, Brett has probably already done this). The new diagonal hull has a deep transom to improve pitch stability. Because of the small width, I am hoping it doesn’t have too much drag.

Happy to send you panel shapes to re create Bob2 if you wish.
Can you read and print CAD files? or do i need to convert to another format?