Water Ski Physics

Water skiing is a highly popular sport worldwide. It has been around for quite

some time beginning in the 1920’s. Scientic approach to this kind of motion

came about in the context of seaplane landing and take-o operations in the

1930’s. Water skiing, wakeboarding, etc. rely upon the physical principle of

hydrodynamic planing, or HP for short. Research in HP has continued since the

early beginnings in the 1930’s and has been intensied in the last decade by the

needs for high-speed marine transportation like surface eect ships and

supercavitating foils. My long time of actively participating in water skiing and

some 50 years of experience and observation competing and coaching indicates

a rather slow and incomplete adaptation and application of the results of

hydrodynamic research to the design of water skis. The last two decades have

witnessed emphasis on making slalom skis lighter, (mass reduction) softer,

narrower, or wider. This is mainly achieved by the use of composite materials.

The intuitive notion is that a lighter and stier ski is advantageous for skiing with

respect to quicker turn rates, faster acceleration or deceleration. All the latter

factors contribute to the controllability of the ski’s motion by the skier. It certainly

is a valuable approach to improving water skiing. What seems to have been

widely ignored in the past is the hydrodynamic physics side of water skiing. It is

without much of speculation that further development of water skiing,

competition as well as recreational skiing, will benet from a thorough

understanding and application of hydrodynamic design principles that have

been applied successfully in engineering elds of marine engineering lately. This

short note is written to deepen this kind of view and point to potential new

developments with respect to hydrodynamics or hydrodynamic planing (HP) of

the water ski.

The scientic challenge of HP comes from the complexity of the ow produced

by an object moving along the water surface. Dierent from an airplane wing,

which is fully immersed in the medium through which it travels, a water ski

interacts only along its underside with the medium, no portion of ow will go

along the upper side of the ski. The primary eect of the water ski is generating

lift (L) to carry a skier’s weight by moving the ski at a certain speed. Generation of

Lift causes hydrodynamic Drag (D) which originates from three sources. First, D

depends on the viscosity of water. Viscosity eects the formation of a boundary

layer along the wetted surface of the ski. Second, D has a portion associated with

the production of surface waves being shed continuously o the trailing edge of

the ski into the downstream region of the ski. This drag portion is usually called

wave drag, i.e. ships that use Archimedean buoyancy rather than motion for lift

generation. Wave drag is the main contribution during deep water starts where

the ski has virtually no lift but creates a lot of water displacement. Third, there is

what hydrodynamicists call the splash drag. The splash (or sometimes spray) drag

originates from the sheets of water that the ski throws in the turn. These uid

(water) sheets are most spectacular in slalom skiing when turning around the

buoys. Experienced instructors can determine the quality of skiing from the

shape of the sheets, so they are a rather sharp diagnostic tool. The total drag D is

the sum of viscous, wave and splash drag. In the scientic literature specic types

of ski shapes are known that completely avoid splashes. All three types of drag

contribute dierently to the total drag. In competition slalom water skiing, for

instance, it’s the splash drag that is more relevant.

A phenomenon that is closely associated with splash drag is the so called

hydrodynamic mass (HM). In scientic parlance it is sometimes called ‘Added

Mass’. HM shows up during acceleration, deceleration of the ski (speed variation)

or rotating the ski around its longitudinal axis as it happens during running the

slalom course. Actually the speed variations of a skier in a slalom course are quite

considerable becoming larger with decreasing line length. Thus HM is

increasingly important with shortening the line in slalom competition. HM

means that the skier feels like moving a heavier ski. Physically HM has to do with

the water mass that is pushed around by the ski when negotiating the water

surface. The increase in mass above the actual mass of the ski has nothing

to do with the material the ski is made from, so HM cannot be reduced by

going to a dierent composite structure. HM depends essentially on the

form of the contact surface between the ski and the water and can be

kept small by shaping the ski properly. Skis that are currently on the market seem

to have a large potential of reducing HM. To be specic HM is of the same order

of magnitude as the mass of the entire material the ski is made from and by

proper shaping the HM-improved ski is much more agile with respect to turn and

acceleration.

The next point that deserves to be addressed is the lift generation mechanism in

HP. To that end is perhaps a good idea to look at an airfoil or wing traveling

through air. Dierent from water skiing HM does not play a signicant role in

aerodynamics. When a wing is accelerated from rest to take o speed its lift

needs some time to establish itself. Even if the take o speed were “switched on”

instantaneously the wing would have to travel some 20 units of its wing depth

until the full lift is established. This is sometimes called the memory eect in

aerodynamics and physically is due to the formation of vortices that spring of the

trailing edge and the tips of the wing. In the aerodynamic context they have to

be present out of the necessity to ow, both around the upper and lower side of

the wing whereas a water ski does not use lift generation by suction on its upper

side. It comes as a surprise that water skiing (and the main reason for its

feasibility as a sports instrument) uses lift generation without vortex generation

and thus has virtually no memory eect. This is not quite true since the

establishment of the splash at the front of a water ski takes some time also. But

the time delay to build up the lift is negligible compared to the aerodynamic

case. The absence of memory eects makes a planing water ski really the most

appropriate device to run a slalom course or jump. So whenever one thinks

about improving hydrodynamics of skis by immersed controlled surfaces one has

to keep them small to avoid memory eects.

Another point of importance is the slenderness of the ski’s shape. It resembles

rather a rocket in aerodynamics than a glider plane with its long span and small

wing depth. The ski has a small span compared to its length. The comparison of

hydrodynamics of ski and aerodynamics of slender wings, now suggests that a

slalom ski can be reduced in width along certain portion of its length without

loosing any of the desired lift characteristics and even a net gain in splash drag

reduction over conventional designs. Second, there is experimental evidence of

reducing splash and boundary layer drag further by providing supercavitated

portions of ow along the underside of the ski. This technique has become

known lately since it is used in the context of supercavitating torpedoes which

make use of hydrodynamic planing to control the path of the torpedo. The

speed range of water skiing is very well adapted for the exploitation of

supercavitation as a design feature.

Let us talk about another important feature. The point of attack of the lift

force in aerodynamics in called the center of pressure (CP). Air wings are

designed in such a fashion that it does not change position much when the

angle of attack of a wing changes. Analogously a CP exists for a ski as well but,

dierent from aerodynamics the particularities of slender hydrodynamic planing

cause a large travel interval of CP when changing pitch, roll and yaw angles of

skis. This is undesirable from a skier’s point of view since the travel of CP has to be

balanced by large movements of the skier’s center of mass, which may limit the

skier’s control window in turns or cross course skiing. A skier will benet from

marginal shifts in CP in the course. Now, there are ways of shaping the ski such

that the CP shift is low. In aerodynamics such wing proles are known as S-Shape

airfoils. A similar idea can be applied to water skiing as well but has not yet been

considered as far as Willi is aware.

All measures that were indicated above have the potential of improving

competition water skiing and certainly recreational skiing to a great extent. A

question that cannot be answered at the present time is if a ski designed

incorporating changes of the above kind ts to the controlling pattern of a skier.

Loads on the body will change faster so the response of the skier would have to,

on the other hand proper manipulation of CP shift, hydrodynamic mass (HM) etc.

might be tailored to the skier’s needs to make possible to go to shorter line

lengths.

Nevertheless time is about ready to look at new design principles for water skis

that include hydrodynamic ideas; of course the proper choice of composite

materials has to be ongoing. The possibilities of what one can do on a water ski

will denitely benet from this eort.

In summary let me say that the consideration of hydrodynamics of water skis

leads to the idea of improving skis by three major items

• reducing the hydrodynamic mass of skis,

• applying short-memory control devices; specically proled spoilers

• using super-cavitation

-applying model experiments in water channels. This may be a worthwhile

undertaking for water ski manufacturers since all the basics are already in

existence and await application to benet water skiing. The development eorts

and risk is within reasonable limits, as far as that may be judged at the present

time.


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