Foiling tech­nology in E2MUT - Resis­tance saving of ships through light­weight design concepts

Dear reader,

in autumn 2021, we started working on hydro­foil concepts to increase the effi­ciency of elec­tri­cally powered ferries as part of the BMBF-funded research project E2MUT (Emis­sion-free elec­tro­mo­bility for maritime trans­port). In this article, we will intro­duce you to the tech­nical basics of a hydro­foil. You will better under­stand the advan­tages of hydro­foils and learn about their field of appli­ca­tion. In doing so, we present you with results from the research activ­i­ties of ar engi­neers GmbH, which include results of the running resis­tance calcu­la­tion of various hydro­foil vessel concepts.

Retro­spect on Foiling

As early as the begin­ning of the last century, with the devel­op­ment of the first aero­planes, the idea of using hydro­foils on ships emerged (e.g. by Enrico Forlanini around 1900). The idea was to posi­tion the wings (foils or hydro­foils) below the hull and thus be able to use the dynamic lift gener­a­tion of hydro­foils, which is effi­cient at high speeds. So the moti­va­tion was to be able to reach higher speeds with a given drive system. This moti­va­tion is also found today in sailing racing, for example in the Amer­icas Cup, where under­water wings have been used since 2013.

The French trimaran Hydrop­tère, which held the speed record for sailing over one nautical mile at 41.5 knots between 2007 and 2012, can be cited as a trend-setter here. In times of global climate change, foil tech­nology plays a central role in making urban maritime trans­port emis­sion-free. The main focus is on elec­tric drives with hydrogen or battery-based energy storage systems. In this context, the advan­tage of foil tech­nology lies partic­u­larly in energy saving, as the range is more limited by modern energy storage than compared to fossil fuels. At the same time, foil tech­nology combines the char­ac­ter­is­tics of high cruising speed and low energy consump­tion that are impor­tant for passenger trans­port. In the E2MUT research project, we would like to incor­po­rate precisely these advan­tages of foil tech­nology in order to make a contri­bu­tion to an emis­sion-free mobility future.

Hydro­static and hydro­dy­namic rela­tions on a hydro­foil ship 

A hydro­foil ship is char­ac­terised by the fact that hydro­foils are fitted in the under­water area of the ship’s hull, which generate dynamic buoy­ancy. The prop­erty dynamic” describes that the lift is depen­dent on the inflow velocity, or more precisely, that it changes propor­tion­ally to the square of the inflow velocity. In a hydro­foil, there­fore, two different types of lift gener­a­tion come into play. On the one hand, the dynamic buoy­ancy just described and, on the other, the hydro­static buoy­ancy of the ship’s hull.

In addi­tion, a ship’s hull can also generate dynamic lift at high speed, also known as planing. The planing of a ship’s hull depends to a large extent on the shape of the hull. In the class of cata­maran hulls consid­ered here, partial planing is achieved at cruising speeds of approx. 22 knots, but this is signif­i­cantly less effec­tive than the foil systems consid­ered. At low speeds, the share of dynamic lift of the fuse­lage is vanish­ingly small.

The forces acting on a generic hydro­foil, in this case with a tandem foil system, are shown in Figure 1. The hull gener­ates the buoy­ancy B, the hull resis­tance DH and the weight force W, which also includes the weight of the foil system for the sake of simplicity. Each foil then gener­ates a lift Li and drag Di, which depends on the rela­tive inci­dent flow v.The propul­sive force P of the propul­sion unit is entered at the rear foil, for example.

Figure 1: The system of forces on the foiling hull

The total drag of the hydro­foil can be calcu­lated if inter­fer­ence resis­tances are neglected:

calcu­lated In order to further illus­trate the rela­tion­ships, it is useful to intro­duce so-called glide ratios, which are commonly used in avia­tion. A glide ratio reflects the ratio of lift and drag as a dimen­sion­less number and can be under­stood as a measure of the effi­ciency of a means of trans­port. The glide ratio of the foils and the hull are defined with:

definiert. If we now assume that the hull oper­ates in pure displace­ment mode, a signif­i­cant differ­ence between hull and foils can be worked out. This differ­ence becomes clear when the depen­den­cies of the force vari­ables are included as argu­ments in the equa­tions (lift coef­fi­cient CL, density of water ρ, drag coef­fi­cient CD, accel­er­a­tion due to gravity g, displaced water volume of the hull V):

The differ­ence now is that with the foils both the lift and the drag depend quadrat­i­cally on the speed. In the case of the fuse­lage, only the drag is velocity depen­dent if the fuse­lage is oper­ating in pure displace­ment mode or the compo­nents of dynamic lift are negli­gible. In fact, the glide ratio of the foils remains approx­i­mately constant as the speed increases, provided that their angle of attack remains constant. The glide ratio of the fuse­lage is partic­u­larly high at low speed, or goes towards infinity, at zero speed. At higher speeds the fuse­lage drag increases strongly, thus the glide ratio of the fuse­lage is contin­u­ously reduced.

In the following, the eval­u­a­tion of the glide ratios of equa­tion (3) is presented on the basis of a concept of a flying hydro­foil. The concept of the hydro­foil is shown in Figure 2. The wing area of the main foil is 9.2 m x 1.5 m and gener­ates a lift of 50 tons from 28 kn. In total, the foil system is designed to generate 80 tonnes of lift.

Figure 2: Hydro­foil concept (Source: Tamsen)

To calcu­late the buoy­ancy and resis­tance of the foil system, a sepa­rate foil calcu­la­tion soft­ware was devel­oped which takes into account wave resis­tance, induced resis­tance, fric­tional and pres­sure resis­tance, as well as the effect of the water surfaces on the buoy­ancy coef­fi­cient. The resis­tance of the hull was calcu­lated over the speed range from 6 knots to 40 knots for different displace­ments with a poten­tial-theo­ret­ical CFD soft­ware by Tamsen Maritim GmbH. The perfor­mance data of the foils and the fuse­lage are fully auto­mat­i­cally merged in our in-house foil calcu­la­tion soft­ware and allow a calcu­la­tion of the drag of the hydro­foil over the entire speed range. This approach is partic­u­larly suit­able for the concept phase for the initial assess­ment of the perfor­mance of hydro­foils. Figure 3 shows the eval­u­a­tion of the glide ratio of the foil strut system and the fuse­lage and the eval­u­a­tion of the gener­ated lift by the foil system. Struts are the vertical struc­tural elements that connect the hori­zontal foils to the fuse­lage. Diese werden auch als Struts beze­ichnet.

Figure 3: Lift and glide ratio as a func­tion of velocity

It is clear from Figure 3 that the hull’s glide ratio is very high at low speeds, making the use of foil systems at low speeds imprac­tical. From a speed of about 15 knots, the foils then become contin­u­ously more effi­cient than the hull. The overall effec­tive­ness of the foil system then still depends on the buoy­ancy gener­ated, which deter­mines how far the hull is still submerged in the water. In the design phase, the lift and the effi­ciency of the foils are opposing para­me­ters, because increasing the angle of attack of the foils increases the lift but at the same time decreases the effi­ciency (glide ratio). The rela­tion­ship just described between the glide ratio and displace­ment of the fuse­lage and the lift and glide ratio of the foils can be explained by combining equa­tions (1) and (2) and B = W - L to:

where L is the total lift of the foil system and E is the glide ratio of the entire foil system. The eval­u­a­tion of equa­tion (4) is shown in figure 4 as Total drag Full Flying Cat”. In addi­tion, the resis­tance of the fuse­lage without foiling system is shown, the immer­sion depth of the fuse­lage with foiling system, the resis­tance of the fuse­lage with foiling system and the resis­tance of the pure foiling system.


Figure 4: Drag curves

Figure 4 clearly shows the effect that foiling systems can have. Drag is reduced by 44% at a speed of 32 knots compared to the drag of the bare hull at 22 knots. From a speed of 28 knots, the hull can be lifted completely out of the water, and as the speed increases, the overall drag can even be reduced as the foils are set lower. Signif­i­cant savings can also be achieved with much smaller foiling systems, which only partially lift the hull out of the water.

The hydro­foil concepts studied in the E2MUT research project will be presented in the next E2MUT blog post. Stay tuned!