Differences in the mechanics of takeoff in reverse and forward springboard somersaulting dives

ABSTRACT

Forward and reverse springboard somersaulting dives use similar approaches with a hurdle step prior to the final board contact phase during which forward rotation is produced in forward takeoffs and backward rotation in reverse takeoffs. This study compared forward and reverse takeoffs for joint strength, activation complexity, technique kinematics, and rotation potential. A planar 8-segment torque-driven computer simulation model of springboard diving takeoff was used to determine isometric joint strength by matching performances of a forward 2½ somersault dive and a reverse 1½ somersault dive. Activation complexity for the reverse takeoff was increased to achieve a similar closeness of match as for the forward takeoff. Takeoff technique was optimised to maximise rotation potential of forward and reverse somersaulting dives. Kinematics at touchdown, lowest point and takeoff were compared for the optimised forward and reverse takeoff simulations. It was found that the optimised reverse somersaulting dive exhibited greater isometric strength for ankle plantarflexion and shoulder flexion, greater joint torque activation complexity for ankle plantarflexion and for knee flexion. There was also less forward motion during board depression, more hip extension and knee flexion during the later stages of board recoil, less capacity for rotation potential, and greater vertical velocity at takeoff.

KEYWORDS:

• Technique
• subject-specific
• model
• angular momentum
• rotation potential

Introduction

Takeoffs in springboard diving differ in the four types: forward, reverse, backward, and inward. Backward and inward takeoffs use a standing start at the end of the springboard. Forward and reverse somersaulting dives employ a walking approach, followed by a hurdle step, board touchdown, springboard depression, recoil and takeoff. The last step before the hurdle flight depresses the springboard so as to increase the height of the hurdle flight in order to give a high vertical downward velocity at board touchdown (Sanders & Wilson, 1988). Prior to landing from the hurdle flight the ankle, knee and hip joints are flexed (Sanders & Gibson, 2000) and at touchdown the mass centre is behind the metatarsophalangeal (MTP) joint. Following touchdown the ankle, knee and hip joints continue to flex for up to 100 ms (Miller, 1974) and then extend vigorously during board depression (Martikkala et al., 1995). At maximum board depression most of the hip extension has been completed and the mass centre is forward of the MTP joint (Miller, 1974). During board recoil, the joints continue to extend initially and then angular momentum is developed primarily by flexing or extending the hip joint (Miller, 1974; Sanders & Wilson, 1988) so that the board reaction force acts at a greater distance from the mass centre, thereby increasing the torque about the mass centre. During the flight phase of the dive, feedback and feedforward timing adjustments to body configuration are made to reduce the orientation error at entry to the water (Sayyah et al., 2018). Typically more elite divers have less movement variability in the flight phase (Walker et al., 2017, 2019).

It has been suggested that differences in forward and reverse takeoffs exist as early as touchdown from the hurdle flight (Armbruster et al., 1973) although Miller (1974) did not find evidence of consistent differences. At maximum board depression Miller found that reverse somersaulting dives had less ankle dorsiflexion and less forward rotation of the trunk. Sayyah et al. (2020) found that the diver made adjustments during board depression in order to achieve appropriate kinematics at maximum board depression. During the board recoil phase, the hip joint flexes after an initial period of extension for forward somersaulting dives, whereas the hip joint continues to extend for reverse somersaulting dives (Miller, 1974; Sanders et al., 2002). The knees continue to extend in forward takeoffs, whereas the knees start to flex towards the end of board recoil in reverse takeoffs (Miller, 1974). During the flight phase of a dive, the body rotates forwards in a forward somersaulting dive and backwards in a reverse somersaulting dive. Differences in body configuration and orientation are clearly visible at the end of the board contact phase (Figure 1). Golden (1981) compared piked forward rotating dives with various amounts of somersault and found around 20° increase in hip flexion at the end of takeoff with each additional piked somersault. Similarly, it may be expected that hip extension in reverse takeoffs will increase with the number of somersaults.

Figure 1. Takeoff for forward somersaulting springboard dive (upper sequence) and reverse somersaulting springboard dive (lower sequence), showing hurdle takeoff, hurdle flight, hurdle landing, maximum board depression, dive takeoff, and flight.

Computer simulation models of springboard diving takeoffs have been used to investigate optimum techniques. King et al. (2019) used a planar 8-segment torque-driven computer simulation model of springboard diving takeoff to determine optimum technique for maximising rotation potential in forward somersaulting dives from the one-metre springboard. Activation profiles for each torque generator comprised simple ramp up then ramp down or ramp down then ramp up functions. These profiles were sufficient to obtain a close matching simulation to a recorded performance of a piked 2½ forward somersault from the one-metre springboard. Sprigings and Miller (2004) investigated optimal springboard takeoffs for dives from the reverse group using a 5-segment torque-driven model, which could not reproduce accurately the takeoff movements of an elite diver. Activation profiles were defined as ramp up functions and it was concluded that a more complex activation profile function was needed. Cheng et al. (2008) used a 5-segment torque-driven model with more complex activation profiles to investigate the contribution of the arms in maximising somersault rotation in standing backward springboard diving takeoffs. It was found that the arms contribute almost 60% to the total angular momentum in the maximised simulation although this resulted in flexed hips at takeoff in contrast to the hyper-extended hips evident in competitive performances. Comparing optimal forward and reverse takeoff techniques may give insight into the differences in mechanics. Simulation models have also been used to determine the isometric strength needed by joint torque generators required for the performance of springboard dives by finding a close match between simulation and recorded performance (King et al., 2009). The aim of this study was to compare forward and reverse springboard takeoffs from the perspective of isometric joint strength, activation complexity, technique kinematics, and rotation potential capacity. It is hypothesised that forward and reverse takeoffs will have characteristic differences in each of these aspects arising from their different mechanical requirements.

Methods

Previous research on a performance of a forward 2½ piked somersault dive from the one-metre springboard determined the necessary joint torque isometric strengths by closely matching takeoff performance using an 8-segment torque-driven computer simulation model and determined maximum rotation potential capacity for these strength limits (King et al., 2009, 2019). The same procedure will be used for the analysis of a performance of a reverse 1½ piked somersault from the one-metre springboard, allowing comparison of depression phase, recoil phase, isometric strength and rotation potential capacity. The forward 2½ piked somersault dive and the reverse 1½ piked somersault were the limiting dives for this competitor from the two dive groups.

Model

A planar computer simulation model of a springboard and a diver with torque generators at five joints was used (King et al., 2009) to investigate diving takeoff techniques. The springboard was modelled as a uniform rod with vertical, horizontal and rotational movements (Yeadon et al., 2006a). The Autolev 3.4TM FORTRAN code implementing the torque-driven model was based on Kane’s method of formulating equations of motion (Kane & Levinson, 1985). The diver was represented by an 8-segment link system comprising head, upper arm, lower arm, trunk, thigh, shank and a two-segment foot with wobbling masses within the trunk, thigh and shank segments to represent soft tissue movement. The foot-springboard interface was represented by three pairs of parallel and perpendicular damped springs acting at the toes, MTP joint and heel (Yeadon et al., 2006a). Extensor and flexor torque generators acted at the ankle, knee, hip and shoulder joints with an extensor torsional spring at the MTP joint. There were 18 degrees of freedom in the model: nine defining wobbling mass displacement, two defining foot position, one defining trunk angle above the horizontal, five defining joint angles at the MTP, ankle, knee, hip and shoulder joints, and one defining vertical springboard displacement. The elbow and the head angles were driven by joint angle time histories from video recordings of diving performances and defined as a function of time (King et al., 2009).

For each torque generator, the torque at a given time was the product of the activation level and the maximum voluntary torque that could be produced at a given joint angle and angular velocity (Yeadon et al., 2006b). The activation level was allowed to ramp up and ramp down between 0 (relaxed) and 1 (fully activated) using a quintic function with zero first and second endpoint derivatives (Yeadon & Hiley, 2000).

For the simulation of the forward 2½ somersault dive the extensor activation ramped up from an initial level and then ramped down towards the end of the takeoff (King et al., 2019). The flexor activation ramped down from an initial level and then ramped up towards the end to prevent hyper-extension. These profiles were chosen as the simplest that allowed two ramps (Figure 2). The shoulder flexor was regarded as an extensor since it opened up the shoulder joint angle and the shoulder extensor was regarded as a flexor. Six parameters defined the timing and level of activation for each extensor torque generator (two start times, two ramp durations, two activation levels) and seven parameters defined each flexor activation (two start times, two ramp durations, three activation levels) giving a total of 52 parameters. These profiles were chosen as the simplest that allowed two ramps. The minimum ramping duration was set to 0.1 s (Bobbert & Van Zandwijk, 1999; Duncan & McDonagh, 2000; Freund & Budingen, 1978). The maximum initial activation level at touchdown was set to 50% (Horita et al., 2002). The extensor torque at the MTP joint used a linear torsional spring (one parameter) multiplied by a flexor style activation function with seven parameters.

Figure 2. Simple and complex activation profiles for the joint torque generators. For the extensors the simple profile comprised a ramping up and then a ramping down of the activation level whereas the complex profile allowed a double ramp up. For the flexors the simple profile comprised a ramping down followed by a ramping up of the activation profile whereas the complex profile allowed a final ramping down.

For the simulation of the reverse 1½ somersault dive the extensors were allowed to ramp up twice before ramping down and the flexors were allowed to ramp down and then ramp up before ramping down again (Figure 2). This more complex activation profile introduced an additional three parameters for an extensor or flexor.

The input to the model consisted of touchdown conditions (springboard vertical displacement and velocity, foot distance from the end of the board, mass centre velocity, joint angles, trunk orientation and angular velocity) together with torque generator activation time histories. Takeoff was defined by the board reaching its neutral unloaded position. The output of the model consisted of the time histories of the springboard displacement, the angle and angular velocity of each joint, trunk orientation, mass centre velocity and whole-body angular momentum about the mass centre.

Data processing

An elite female diver (mass = 64.1 kg, height = 1.68 m) who competed at junior international level performed a forward 2½ piked somersault dive and a reverse 1½ piked somersault dive from the one-metre springboard in a research data collection session. The diver performed one satisfactory repetition of each dive as judged by the diver’s coach. The diver provided informed consent as approved by the Loughborough University ethics committee. Segmental inertia parameters of the diver were determined from 95 anthropometric measurements using the mathematical model of Yeadon (1990). Kinematic data of performances from the one-metre springboard of a forward 2½ piked somersault dive and a reverse 1½ piked somersault were obtained from high-speed video recordings from a Phantom V5 camera (Vision Research) operating at 200 Hz. An angle-driven model (Yeadon et al., 2006a) was used to determine springboard parameters and visco-elastic parameters of the wobbling masses and the foot-springboard. The isometric strength of each torque generator was determined as described in King et al. (2009) by finding a close match between simulation and recorded performance.

Matching procedure

The matching process consisted of minimising a difference score S that was the RMS difference between a simulation and the performance in terms of S₁: joint angles, S₂: trunk orientation, S₃: whole-body linear momentum, S₄: whole-body angular momentum about the mass centre, S₅: duration of springboard contact for each dive (details in King et al., 2009). All five components of the difference score were equally weighted when quantifying the difference between a simulation and performance. For the difference scores S₁ and S₂ which were calculated in degrees, 1° was considered to be equivalent to 1%. Anatomical constraints at the hip, knee and ankle were imposed to ensure that the joint angles remained within anatomical limits both at takeoff and during the first 100 ms of the simulated flight phase.

For the matching of the forward 2½ somersault dive the isometric strength of each of the eight torque generators was allowed to vary in addition to the activation parameters. The difference score S was minimised using the Simulated Annealing optimisation algorithm (Corana et al., 1987). This resulted in a difference score of 3.7% (King et al., 2009). For the matching of the reverse 1½ somersault dive the isometric strengths were initially set at those of the forward 2½ and the activation parameters were varied to minimise the difference score. As the resulting overall difference score S and joint angle score S₁ of the reverse takeoff were both greater than the corresponding forward takeoff values, a more complex activation profile for the reverse takeoff was then used in which the extensors were allowed to ramp up twice and the flexors were allowed to ramp down and then ramp up before ramping down again (Figure 2). The difference score improved sufficiently but the joint angle score, although improved, still remained greater than that of the forward takeoff and so in the next matching optimisation the isometric strength parameter of each torque generator was allowed to vary along with the activation parameters. This resulted in overall and joint angle difference scores that were comparable with the forward takeoff scores.

Optimisation

Optimised technique for maximising rotation potential in forward and reverse takeoffs was investigated subject to various constraints to ensure a realistic dive. The rotation potential score to be maximised was set equal to the product of angular momentum about the mass centre at takeoff multiplied by the flight time plus a measure of the initial rotation at takeoff (King et al., 2019) and was normalised to be expressed in straight somersault units. The vertical velocity at takeoff was constrained to be not smaller than the lower (4.39 ms⁻¹) of the two recorded dives and the horizontal travel during flight was constrained so as not to exceed the greater (1.59 m) of the two recorded dives. Joint angles were constrained to lie within anatomical limits exhibited in diving performances both at takeoff and during the first 100 ms of flight to prevent joint hyper-extension. While feedforward adjustments may be made during the board depression phase based on hurdle flight estimates of touchdown conditions (Sayyah et al., 2020) there is insufficient time for similar adjustments during the recoil phase since there will be a delay of around 0.2 s before a modification is effected (Gao & Zelaznik, 1991; Henry & Harrison, 1961).

The onset timings of the activations during the board recoil phase were perturbed systematically by 10 ms (Hiley et al., 2013) and the score to be maximised using simulated annealing was set equal to the lowest rotation potential score in the perturbed simulations (King et al., 2019). The reverse takeoff optimisation proved to be particularly sensitive to 10 ms perturbations and so the perturbations were reduced to 3 ms for both dives. From the various perturbed simulations corresponding to the maximised lowest score, one simulation closest to the mean value of the rotation potential score was chosen for both the forward and reverse optimised takeoffs. The body configurations during the flight phases of the forward somersaulting dive and reverse somersaulting dive simulations were modified from the recorded performances in order to produce realistic dives using a computer simulation model of aerial movement (Yeadon et al., 1990).

Comparison

The isometric strength and activation complexity required by the eight torque generators to obtain a close match were determined for the forward 2½ and the reverse 1½ dives. The representative optimum solutions for the perturbed optimisations were compared for technique kinematics and rotation potential capacity.

Results

In order to achieve the same closeness of matching as the forward 2½ somersault dive, both greater strength and more complex activation were required for the reverse 1½ somersault dive (Table 1). Greater isometric strength was required for ankle plantarflexion and shoulder flexion for the reverse takeoff (Table 2) and a more complex activation profile was needed for ankle plantarflexion and for knee flexion (Table 3).

Table 1. Overall and joint angle difference scores for the various matching simulations

Dive	Strength	Activation	Overall score	Joint angle score
Forward 2½	Forward	Simple	3.7%	5.5°
Reverse 1½	Forward	Simple	4.6%	7.9°
Reverse 1½	Forward	Complex	3.4%	6.5°
Reverse 1½	Increased	Complex	2.9%	5.6°

Table 2. Comparison of isometric strength parameters [Nm] determined from the matching of the two dives

Isometric parameter	Forward	Reverse
Knee extension	182	182
Knee flexion	143	143
Hip extension	318	318
Hip flexion	192	192
Shoulder extension	109	109
Shoulder flexion	63	67
Ankle plantar flexion	273	354
Ankle dorsi flexion	51	51
Mtp stiffness [nm/rad]	68	68

Table 3. Complexity of torque generator activation profiles determined from the matchings of the two dives

Torque generator	Forward	Reverse
Knee extension	Simple	Simple
Knee flexion	Simple	Complex
Hip extension	Simple	Simple
Hip flexion	Simple	Simple
Shoulder extension	Simple	Simple
Shoulder flexion	Simple	Simple
Ankle plantar flexion	Simple	Complex
Ankle dorsi flexion	Simple	Simple
Mtp extension	Simple	Simple

Differences in technique between the optimised forward and reverse takeoffs (Figure 3) are evident at touchdown (arm position), lowest point (mass centre position, horizontal velocity), and takeoff (hip angle, shoulder angle, knee angle), resulting in differences in vertical velocity and angular momentum at the end of the takeoff phase (Table 4).

Table 4. Touchdown, lowest point and takeoff kinematics for the maximal rotating forward and reverse dives: Mass centre horizontal distance from the toes, horizontal velocity of the mass centre, vertical velocity of the mass centre, angular momentum about the mass centre, trunk angle, joint angles

	Touchdown		Lowest point		Takeoff
Variable	Forward	Reverse	Forward	Reverse	Forward	Reverse
Mass centre dist. [m]	−0.23	−0.29	−0.10	−0.21	0.13	−0.08
Hori. Velocity [ms^−1]	0.47	0.48	1.05	0.42	1.19	1.03
Vert. Velocity [ms^−1]	−3.85	−3.40	0.71	0.52	4.46	4.92
Ang. Mom. [kg.m^2s^−1]	3.1	−4.1	0.8	−9.0	67.3	−57.2
Trunk angle [°]	57	65	64	69	32	107
Ball angle [°]	145	150	147	152	180	181
Ankle angle [°]	103	117	101	116	110	165
Knee angle [°]	115	138	135	138	173	150
Hip angle [°]	107	120	144	134	138	183
Shoulder angle [°]	3	−54	144	112	115	188
Elbow angle [°]	128	167	88	143	179	152

Moment of inertia in a straight position is 10.56 kg.m²

Figure 3. Maximised rotation potential simulations for forward somersaulting dive (upper sequence) and reverse somersaulting dive (lower sequence), showing hurdle flight, board touchdown, maximum depression, dive takeoff and five positions in the flight phase.

Discussion and implications

The aim of this study was to compare forward and reverse springboard diving takeoffs from the perspective of isometric joint strength, activation complexity, contact-phase technique, and rotation potential capacity. As hypothesised, it was found that forward and reverse takeoffs have characteristic differences in each of these aspects arising from their different mechanical requirements. It was found that reverse takeoff performance requires greater isometric strength for ankle plantar flexion and shoulder flexion than for the forward dive. The reverse takeoff uses greater joint torque activation complexity for ankle plantar flexion and for knee flexion than the forward takeoff. The arm swing technique is performed earlier in the forward takeoff so that the arms are overhead at the lowest point and are lowered during the recoil phase whereas the arms continue to open the shoulder angle throughout the contact phase of the reverse takeoff (Figure 3).

At the lowest point, the mass centre is in front of the MTP joint in the forward takeoff, whereas it is behind the MTP joint in the reverse takeoff (Table 4). This does not align with the results of Miller (1974) who found that the mass centre was in front of the MTP joint at the lowest point in all dives and noted that the vertical force on the feet acted behind the mass centre, contributing to forward rotation. During the later part of the board recoil, the hips flex in the forward takeoff whereas the hips continue to extend throughout the recoil phase in the reverse takeoff (Figure 3). In the later part of board recoil in the reverse takeoff the knees flex, whereas they remain extended in the forward takeoff. At the end of the takeoff phase, the optimised forward somersaulting dive has greater rotation potential but lower vertical velocity compared to the reverse somersaulting dive as also noted by Sanders et al. (2002).

The differences in technique between the contact phases of forward and reverse somersaulting dives can be understood in terms of the different mechanical requirements. In the forward takeoff the arms swing through earlier so that they are overhead at the lowest point and therefore can be lowered during board recoil to assist the hip flexion in producing forward somersault rotation. In the reverse takeoff, the arms continue to rotate backwards during board recoil to assist the hip extension in producing backward rotation. In the forward takeoff the mass centre horizontal velocity at the lowest point is greater since the action of piking during board recoil results in a backward force of the board on the feet thereby slowing the horizontal velocity. The mass centre is forward of the MTP joint at the lowest point in the forward dive (Table 4) since this results in a positive moment of the vertical reaction force, increasing the forward somersault momentum. In the reverse takeoff the mass centre is behind the MTP joint at the lowest point (Table 4) so that the vertical reaction force creates a backward rotating moment around the mass centre, increasing the backward angular momentum. For the forward takeoff, the hips flex during board recoil resulting in a backward force on the feet which increases the forward angular momentum whereas the hips extend in the reverse takeoff resulting in a forward force on the feet, increasing the backward angular momentum. The continuing flexion action of the shoulder in the later part of board recoil in the reverse takeoff places a greater demand on shoulder flexion strength (Table 2). The action of flexing the knees in the later part of board recoil in the reverse takeoff allows the mass centre to continue moving forwards without additional hip hyperextension. This knee flexion adds greater complexity to the activation profile of the knee flexor torque generator (Table 3). Knee flexion combined with the hip hyperextension results in a reaction force with the board that is resisted by the ankle plantarflexion torque and this may account for the greater plantarflexion strength and activation complexity that is needed than for the forward dive (Tables 2 and 3).

The forward somersaulting dive optimisation produces more rotation potential than the reverse somersaulting dive optimisation (Table 4) since the hips can flex through a greater angle than they can hyperextend thereby producing greater angular momentum. More hip flexion results in a greater reduction of the vertical force during recoil and a lower vertical velocity at takeoff (Miller & Sprigings, 2001). The consequent shorter flight time only partially offsets the increase in rotation potential arising from the greater angular momentum. The greater capacity of forward somersaulting dives for producing rotation potential is reflected in the greatest difficulty dives of the participating diver: 2½ piked in the forward group and 1½ piked in the reverse group. It is also reflected in the degree of difficulty (Fédération de Natation Internationale [FINA], 2017) for the forward 3½ tucked from 1 m (3.0) and reverse 2½ tucked from 1 m (3.0) although some of the difficulty score for reverse dives is associated with the more difficult viewing prior to water entry. On the other hand greater angular momentum requires greater eccentric hip flexor torque when extending the hip joint prior to water entry (Kong, 2010).

Conclusions

The findings have implications for the coaching of springboard diving. It is important to recognise that the horizontal velocity at the lowest point is dependent on the type of dive since the reaction force of the board on the feet during board recoil is backwards in forward somersaulting dives and is forwards in reverse somersaulting dives. Thus in forward somersaulting dives the horizontal velocity is high at the lowest point whereas it is lower for reverse dives. There is also evidence that this effect is greater in forward dives when the angular momentum is high (Sayyah et al., 2020). Since the somersault momentum is developed during board recoil by flexing or extending the hip joint, the body configuration at takeoff is a necessary consequence of this and may be in conflict with the expectations for good form. Thus having some flexion of the knees at takeoff in a reverse somersaulting dive should not necessarily be taken as a fault to be corrected since it facilitates the generation of angular momentum and also allows the mass centre to continue moving forward to give a safe board clearance during flight.

Disclosure statement

The authors declare no financial or other conflict of interest.

Additional information

Funding

This study was supported in part by the International Society of Biomechanics under the Matching Dissertation Grant Program.