KTH

Department of Aeronautics 25 October 2002

Technical Report of Phyxius

Table of Contents 1 Introduction ............................................................................................................3 2 Design.....................................................................................................................4 3 The Human Power..................................................................................................5 4 Hull Design ............................................................................................................6 5 Propulsion...............................................................................................................6

5:1 Air propeller ....................................................................................................7 5:2 Water propeller................................................................................................7 5:3 Surface piercing propeller ..............................................................................8 5:4 Pelton turbine wheel........................................................................................8

6 Transmission ..........................................................................................................8 7 Performance ...........................................................................................................9 8 Stability and Steering ...........................................................................................11 9 Hydrofoil Design..................................................................................................12 10 Conclusion..........................................................................................................13

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Technical Report of Phyxius

1 Introduction 16 students in their last year of a Master of Science degree at KTH (the Royal Institute of Technology, Stockholm, Sweden), have formed a team with the purpose of building a waterbike. The faculty is not involved other than by advising in special matters. The work is part of a project course and the team consists of five people studying aeronautics and aerospace engineering, and the others are conducting their studies in lightweight construction. No member of the team is studying marine technology and this could have as a result that questions are raised in the report which might be easy to answer for someone with good knowledge in that subject.

The project was launched in mid August and the waterbike, called Phyxius from Latin which means “ready to lift”, is planned to be finished in late spring 2003. The economical budget for the project is $4000 and the “time” budget is 12 weeks of full time work per team member. The goal of this project is to combine the knowledge of those studying aviation, whose main task is to build the hydrofoil and the propulsion system, with the skills of those who have the task of building the watebike light and rigid. The ambition is to use the theoretical knowledge gathered during three years at school and to transform it into the practical building of a water-based vehicle. Our ambition is to learn as much as possible in ship constructing without a specific knowledge in marine technology.

The specification is fairly simple: obtain maximum velocity on water using human power only.

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2 Design

Figure 1: Phyxius with a front mounted airpropeller

To minimize the resistance while the vessel is still in displacing mode the best solution is to have just one hull and eventually two supportive pylons are needed to stabilize in roll. To stabilize in both roll and pitch in “flying” mode the vessel is equipped with two stabilizers in front. To prevent drag from the propeller, it is not to be in the water. In this example it is placed in front of the mast to get free air stream. To get the hull out of the water there are two wings: one big to get enough initial lift and one small to get the highest speed while “flying”. The big wing will leave the water when the speed is high enough.

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Figure 2: Phyxius with a front mounted surfacepiercing propeller

In this example the waterbike is equipped with a surface-piercing propeller. The propeller is placed in the very forward because of the raise of the aft. This option is now being studied considered to forces and efficiency. In other aspects this vessel is equal to the one above. The placement of the small pylons is still to be decided. Because those contribute to dead weight in flying mode they are to be dropped in this mode (see section Stability and Steering). A third propulsion system based on Pelton wheels (see section Propulsion) is under investigation and close to be abandoned since there is doubt about the efficiency of this propulsion system can achieve a velocity of 11m/s and therefore a sketch do not yet exist. The Pelton wheel is only treated in the Propulsion section.

3 The Human Power The task has been to estimate the available human power. Tests were done on a training bicycle and data from the tests were used to evaluate the time (somewhere below a minute) it would take to reach 11m/s. Tests during 30 s and 1 min have been performed for both normal position and the more laid-back one. Statistics were used to compare the results and those gave a hint of the results. A first class athlete is able to deliver 730 W during 30 s and 600 W during a minute. Tests results showed that the laid-back position was more effective than the normal bicycle position, although not by much. Since laid-back position lowers the center of gravity and gives stability

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and as well minimizes the area in the air, the upright position was abandoned. The test which was done in the laid back position resulted in the following:

t = 30 s t = 60 s n = 130 rpm n = 90 rpmP = 620 W P = 500 W

Table 1: Test result from cycling in laid back position

These results gave a hint of the available power.

4 Hull Design Data about the hull that was decided early in the project:

Max length of the hull; 6 m, LOA (Length Over All) due to practical reasons. Displacement about 0,090 m3

The hull will be optimized to achieve a low drag and highest possible speed, however since the vessel will be constructed with only one hull, the stability must be addressed. The drag in lower parts of the velocity region will be dominated by the skin friction. It is important to reduce the skin friction because the hull is entering the first flight-regime at an early stage. Reducing the wetted surface is one way to achieve a lower skin friction level. Increasing the speed, introduces another phenomena, wave drag. Analysis of the total drag clearly indicates that increasing the length of the hull will especially lower the wave drag. A flat or slightly curved hull bottom will allow a higher speed, and a rather large longitudinal curvature lowers the center of gravity and increases the stability. The freeboard has to be slightly inclined to keep the stability even when the hull is heavily loaded. To satisfy all these aforementioned shape-points an already existing hull such a K1-kayak will be a good choice.

5 Propulsion The power output available has been decided by trials to be approximately 550 W during 45 seconds keeping an rpm of about 110. These numbers has been the starting point for choosing propulsion unit. Four different propulsion solutions have been investigated: an air propeller, water propeller, surface-piercing propeller and a Pelton turbine wheel. Initially an air propeller and water propeller was compared, showing equal efficiency. The water propeller has the distinct disadvantage of having a submerged drive shaft and propeller axle, creating a significant amount of drag. The air propeller was considered to be the best solution regarding efficiency and drag though it has the disadvantage (or maybe advantage?) of being sensitive to wind. It was found that a diameter of 3.2 meters and a geometric pitch of 3.9 meters was the most efficient solution for a speed of 11 m/s.

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5:1 Air propeller When designing the air propeller the following data has been used; n = 110 rpm Pavailable = 550 W (for approx. 45 s) Vnecessary = 11 m/s CL,α = 2π (thin airfoil theory) These numbers has been derived from trials on an ergonometer in a gym and from the current world record holder. A combination of blade element and momentum theory was used to calculate the optimum propeller blade layout. Momentum theory says that it is more efficient to accelerate a large volume of air a little than accelerating a small volume much.

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 3.6

3.7 3.8

3.9 4

4.1

4.2

4.3 4.4

4.5

4.6

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.94

Figure 3: Geometric pitch (m) on the y-axis, radius (m) on the x-axis and efficiency as contours.

That, together with the foremost successful example, Decavitator, gave that a propeller diameter of 3 m was chosen initially. By changing different parameters such as geometric pitch, chord distribution and diameter the following conclusions were made regarding the efficiency over the blade radius (fig. 1). Hence a geometric pitch of 3.9 m, mean chord of 0.08 m and a diameter of 3.2 m shows to be the most “efficient” solution. The total efficiency obtained through the calculations is probably a bit too high due to simplifications made but still show the best layout. 5:2 Water propeller The same methods used for the air propeller was used in evaluating the water propeller design. It was concluded that the same efficiency could be obtained by a water propeller with a geometry adapted to water conditions. Due to the geometric constrictions and the increased drag caused by the submerged drive shaft a water-propeller seemed less interesting.

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5:3 Surface piercing propeller The definite advantage of a surface piercing propeller is that the drive shaft is above water and that there are no geometric constraints. There are also problems associated with a surface piercing propeller such as side forces and effects due to ventilation on the blade. To avoid the side forces the propeller has to be yawed, or two counteracting propellers have to be used. Since there is very little research done in this area and particularly in the low speed region there is no obvious way of designing the geometry. Further investigations have to include physical experiments with different designs. 5:4 Pelton turbine wheel The Pelton turbine wheel has been used for more than a hundred years in the production of electric power. Utilizing a water jet sream on showels results in very high efficiency. The problem in the case of using a Pelton wheel on a human powered hydrofoil is that it requires a reversal of the operating procedure and thus the method of calculations. The main advantage would be the simple power transmission and the main drawback would be the sensitivity to waves. The Pelton wheel has to be further investigated, including building and testing different designs.

6 Transmission Concerning the position of the propulsion system there are still three different alternatives.

1. Air propeller mounted in the front of the waterbike. 2. Air propeller mounted in the rear of the waterbike. 3. Surface piercing propeller mounted in the front of the waterbike.

After a thorough evaluation of different alternatives the numbers of possible transmission solutions has been narrowed down to one each for the different propeller-configurations.

1. A twisted synchronous transmission belt directly from the pedals, using four gearwheels for twisting purpose, transfers the power to the propeller shaft. This is a rather simple configuration and the efficiency factor is quite high, η ≈ 0,96 – 0,97.

2. In this configuration the chain is to go over the pilots head, this for shortening the length of the transmission. A chain transfers the power from the pedals to a 90° gearbox. The propeller is mounted on the output shaft of the gearbox. The efficiency factor is somewhat below the first configuration, η ≈ 0,93.

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3. This configuration uses a 90° gearbox placed between the pedals. A shaft connects the 90° gearbox with the propeller via a ball coupling since a single surface piercing propeller needs to be angled approximately 20°, this for eliminating the side force which is generated by a surface piercing propeller. The efficiency of this configuration has not yet been investigated.

7 Performance The performance analyze is based on “Fluid dynamic drag” by Hoerner and “Introduction to THERMAL SCIENCES” by Schmidt, Henderson and Wolgemuth. The programs that calculate lift, drag and effect required, were programmed in MATLAB. These parameter-names in the formulas are initially “written in Swedish” and means: bindex = width or cord lindex = lenght sindex = span The other parameter-names follow the conventions in: Fluid dynamic Drag by Hoerner. The formula that calculates the drag of the wings is:

+=

Re

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ACCqAD L

Dow παα

Such drag as spray drag for the wings is also considered. The strut drag , two struts that joins the wings with the rest of the vessels.

keelkeelkeelDostrut sbqCD 2= The drag ”above water” structure is estimated as an ellipsoid, the shape of the driver. And 15 meters of symmetric wing foil, the beams (pipe).

( )pipepipepipeDdriverMandriverManDStructure lbCACqD "",, += Two stabilizers. Neglecting wave induced drag and lift from the stabilizers. These are going to be taken care of in the future. Haven’t find the time to do it this far.

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++=

− )51(

Re074.02 floaterfloatertprofilstrutprofilstruutprofilestrDoprofileprofileprofileDoStabilizer lbsbCsbCqD

The drag from a water prop. The ”sword”, who joins the water prop and the rest of the vessel, is assumed to be a symmetric wing foil, and the gear as a nacelle. Neglecting the wave induced drag.

+=

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2πdCsbCqD nacelleDoprofileprofileprofileDoWaterprop

Lift from wings. sbqCL L ⋅⋅= αα

The relation between the vessel’s pitch and the angle of attack isn’t put down in MATLAB yet. The functions above are used, together with some conditioning statements, to formulate the MATLAB-functions. These MATLAB-functions generates graphs like the one below.

Figure 4: Graph of required effect as a function of speed

It is possible to see that the hull is no longer in contact with the water after approximately 6 m/s. The big wing looses its contact with the water at approximately

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9 m/s. There are plots for the two alternatives: water-propeller and air-propeller, that is the effect required due to drag for the different applications. As you can see from the graph, the big wing has a variable angle of attack. The idea is that there’s also going to be a program where the small wing has the variable angle of attack. The project doesn’t know now what’s best to achieve the highest speed. A variable angle of attack for the small wing or the big wing is the question? To have variable angle of attack of both wings at the same time seems to be too complicated. The project is in an early stage, all the input data in the formulas are within broad limits and there are quite a lot that can be refined. The MATLAB-functions that been programmed is also going to be more and more accurate, hopefully, as the project goes on. It is going to be interesting to se how accurate the calculations are in comparison with reality.

8 Stability and Steering First of all, only the static aspects of stability have yet been considered. Evaluations have been made with respect to stability in roll, pitch and surface-piercing stall. A single long hull, canard mounted stabilizers and rear lifting surfaces configuration is found to be a good solution. Of course, a catamaran configuration would give better roll stability in low speed conditions, but the lack of stability in low speed will be compensated with two small pylons mounted on each side of the pilot. The intention is that the pilot should be able to drop these small pylons as the bike lifts to decrease weight. The long-one-pylon configuration would probably give a better pitch and surface-piercing stall stability because of the increased stability margin. Since the canard mounted stabilizers must generate some of the lift to be able to keep the waterbike merged, this configuration decreases the drag compared to aft or mid mounted stabilizers. The stabilizers are placed symmetrically on each side of the main hull, as far out on each side as possible. It seems that the stiffness of the structure sets a limit on how far apart these stabilizers can be assembled. The shape of the wing seems to have little or no effect on the roll stability unless one uses a surface piercing dihedral wing configuration. However, this configuration is not acceptable when taking the drag into consideration. To avoid surface piercing stall the waterbike will be equipped with two main lifting surfaces: one low speed and one high speed wing. By mounting the high speed wing below the low speed wing, the pilot may eject the low speed wing out of the water to reduce drag. The distance from the lifting surface(s) to the center of gravity should be

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as short as possible in order to make roll stability better, but this distance is a trade off between avoiding surface-piercing and roll stability.

Estimating the pilot’s possibilities to control the bike by moving the center of gravity either to bank or dive/climb was found to be a hard task. Therefore it is assumed, with some uncertainty, that the center of gravity should be as close to the surface as possible.

The calculations showed that a keel would have been useful in low speed, both for stability and as a steering surface, but the weight and drag caused by a sufficient keel is not acceptable. The disposable small pylons are probably a better solution. Using the wing (and stabilizer) assembly(s) as steering surfaces seems to be a good idea, but no evaluations or calculations have been done on this yet. It also seems to be a good idea to use "water brakes" for steering. These can be ejected from water when not in use, and might give the pilot the possibility of braking in case of emergency.

Figure 5: using water brakes (red) Figure 6: steering surfaces

9 Hydrofoil Design The design of the foil has just begun. In order to obtain maximum velocity, the wing configuration will consist of two wings, one low-speed and one high-speed wing. Internet sites and other databases have been studied in the hunt for a well performing hydrofoil profile. Using the drag parabola and lifting curve for comparison of the different alternatives the Wortmann FX 63-137 was chosen. Further evaluation of this profile has been conducted in X-FOIL. Thickness 0.1371 Camber 0.0579 Leading edge radius 0.0094 Trailing edge angle [deg] 21.1598

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Figure 7: Wortmann hydrofoil To determine a good plan form of the wing the vortice-lattice program Tornado (by Tomas Melin, Department of aeronautics, KTH, Sweden) will be used.

10 Conclusion As seen there are many question marks that must be eliminated for the continuing development of Phyxius. The given parameters for the waterbike in present time are:

• One hull: Displacement about 0,090 m3, LOA = max 6m • Available human power • Cycling in laid back position • Two pylons for roll stability • Two canard mounted stabilizers • Two rear lifting surfaces • Hydrofoil profile: Wortmann FX 63-137 • Variable angle of attack for (at least) one wing • Maximum weight of Phyxius is set to maximum 25kg • Size of lifting surface

Critical points

• Propulsion system (air-, surface piercing propeller, Pelton wheel) • “Take off speed” needed to get Phyxius in flying mode • Design velocity for low speed wing ejection

An important parameter is the available human power over the mass cube, the ratio is to be maximized and therefore it is of big importance to reduce weight as it increase with the cube. Therefore the pilot should be as light as possible and produce much power, thus the ratio power over mass of pilot is to be maximize. The choice of pilot is therefore of great importance and the question to ask is: who is it to be? A professional cyclist, a dwarf or Carl Lewis.

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