Ski jump hydraulics 
Introduction 
Ski jumps in combination with plunge pools are widely used as an economic and effective type of energy dissipator downstream of large dams (Fig. 1). Ski jumps typically consist of an approach chute with a deflector at its end  the flip bucket  deflecting the discharge into the air. In this process, air is entrained into the jet reducing its scour potential during impact in the plunge pool. An inappropriate flip bucket design may result in a scour hole at the valley sides or close to the takeoff section, endangering the stability of the valley sides or of the structure itself. An example includes the Nacimiento Dam, California, where a scour hole depth of tens of meters was observed after a flood in 1969. Despite hundreds of model studies conducted for specific prototypes, general guidelines were somehow incomplete when this research was launched in 2003. 


Personal research website of Dr Valentin Heller 
Circularshaped flip bucket 
Fig. 1. Ski jump of Karakaya Dam, Turkey, in operation (journal title page to publication Heller et al. (2004), courtesy of Pöyry Infra AG, Switzerland)

Fig. 2. Definition sketch for plane ski jump flow

Heller et al. (2005) investigated the ski jump hydraulics in a physical model. This research resulted in generic design criteria for the jet trajectories, pressures on the flip bucket, conditions of flow chocking (hydraulic jump) on flip bucket and energy dissipation as a function of the approach flow conditions (water depth h_{o}, Froude number F_{o}) and the flip bucket geometry (angle b (beta) and radius R, Fig. 2).

Fig. 3. Ski jump model with deflection angle b (beta) = 30°, radius R = 0.40 m, approach flow water depth h_{o} = 0.05 m and approach Froude number F = V_{o}/(gh_{o})^{1/2} = 10 
Triangularshaped flip bucket 
A systematic investigation of a triangularshaped flip bucket was investigated by a MSc student under Dr Heller’s cosupervision. A triangularshaped flip bucket may be both cheaper and easier to construct than the conventional geometry. However, how does it perform from a hydraulic point of view? General guidelines for this alternative geometry were established in Steiner et al. (2008), including the jet trajectories, the pressure on the flip bucket and the conditions of flow chocking on the flip bucket (Fig. 4). As expected, peak pressures on the flip buckets are larger than for the circularshaped geometry, however, the total force is smaller. No apparent disadvantage of this alternative flip bucket geometry was found. 
Selected publications 
Journals Heller, V., Pfister, M. (2009). Discussion of “Computing the trajectory of free jets” by Wahl, T.L., Frizell, K.H., Cohen, E.A. Journal of Hydraulic Engineering 135(7):622623. Steiner, R., Heller, V., Hager, W.H., Minor, H.E. (2008). Deflector ski jump hydraulics. Journal of Hydraulic Engineering 134(5):562571 (http://dx.doi.org/10.1061/(ASCE)07339429(2008)134:5(562)). Heller, V., Hager, W.H., Minor, H.E. (2006). Two Replies to Discussions of „Ski jump hydraulics“ by Khatsuria, R.M., and Novak, P. Journal of Hydraulic Engineering 132(10):1117. Heller, V., Hager, W.H., Minor, H.E. (2005). Ski jump hydraulics. Journal of Hydraulic Engineering 131(5):347354 (http://dx.doi.org/10.1061/(ASCE)07339429(2005)131:5(347)). Heller, V., Hager, W.H., Minor, H.E. (2004). Skisprung – Allgemeine Bemessungsansätze. Wasser Energie Luft (7/8):183187 (in German). Others Heller, V., Steiner, R. (2008). Skisprung  Eine alternative Deflektorgeometrie. Proc. Internationales Symposium Neue Anforderungen an den Wasserbau, VAW Mitteilung 207, 8395, Minor, H.E. ed. ETH Zurich, Zurich. Heller, V., Hager, W.H., Minor, H.E. (2007). Hydraulics of ski jumps. Proc. 32^{nd} IAHR Congress, Venice, Paper 377: 110, IAHR, Madrid. 
Fig. 4. Flow chocking observed on triangularshaped flip bucket for decreasing discharge regime 
The jet trajectory can be described with mass point dynamics given by 
z(x) = z_{o} + tana_{j}x − gx^{2}/(2V_{o} ^{2 }cos^{2}a_{j}) 
In this equation x and z are the coordinates, a_{j} (alpha) the takeoff angle for the upper (O) or lower (U) jet trajectory and V_{o} is the approach flow velocity (Fig. 2). The parameter in this equation with the largest uncertainty is a_{j} (alpha) which is not identical to the deflection angle b (beta) of the flip bucket. Effects such as jet disintegration and aerodynamic interactions result further in deviation between mass point dynamics and the observed jet throw distance X_{O} or X_{U}, respectively. 
Last modified: 24.04.2017 