Biomechanical Analysis and Measurement of Vertical Jump as a Performance Indicator in Basketball

Author: Suegnet Meyer

Introduction

Vertical jump (VJ) determines explosive lower limb power (Linthorne, 2001). This discussion highlights the VJ kinetic and kinematic pattern and the biomechanical factors maximising vertical jump height (VJH). Furthermore, VJ measurements are analysed and VJ as a basketball performance measure is assessed.

1. Kinetic & Kinematic analysis

Various VJ techniques take place in a sagittal plane. The squat jump (SJ) starts from a stationary semi-squat position excluding the pre-stretching phase. The countermovement jump (CMJ) phases:

Standing stationary

CMJ is performed from an upright position. The Body Mass (BM) equals ground reaction force (GRF) (Newton’s 1st law) (Blazevich, 2007).

Unweighting

The body’s inertia needs to be overcome (Newton’s 2nd law). The feet apply vertical force against the ground and vice versa (Newton’s 3rd law). Inertia is overcome and GRF cause COM acceleration downward (Linthorne, 2001).

Propulsion

The pre-stretching downwards muscle lengthening counteraction is the eccentric phase of the stretch-shortening (SSC), allowing hip and knee flexion with ankle dorsi-flexion (Komi, 1992). Muscle stretching reduces downward COM speed however downward force still causes negative acceleration. When resultant forces and COM acceleration reach zero, GRF is equal to BM marking maximum downward velocity (Linthorne, 2001). Large hip torque is produced at the first 2/3 of the propulsion phase (Feltner et al., 1999). Starting the second part of the SSC, concentric leg muscle action causes upward force while the COM is still moving downwards. Upward acceleration is initiated (Komi, 1992). At the lowest counter-movement point, COM is at rest and velocity is zero. Maximum lower limb muscle contraction produces force causing almost maximum GRF.

Take-off

Rapid upward movement due to SSC occurs until take-off (Komi, 1992). Hip extension, followed by knee and ankle plantar-flexion cause positive net joint movements (Umberger, 1998). High velocity and vertical COM displacement with maximum GRF occur early in the take-off phase. Maximum velocity is reached when GRF and BW equalise just before toes-off. Resultant forces cause COM acceleration (Linthorne, 2001). GRF is zero and COM rises higher than at the start due to ankle plantar-flexion until toes-off.

2. Biomechanics maximising VJ

Take-off parameters that influence VJ : Force(F); vertical velocity(v); acceleration(a); mass(m); and displacement of COM(dcom).

Power(P)= F. , F= m.a , Work(W)=F. dcom, Torque(τ)=F.d , Angular Momentum(H)= Inertia(I) x angular velocity(ω),
Angular acceleration(α)= τ.I, Impulse(J)=F x time(t)

Ρ = F ᵡ v
F = Μ ˣ ɑ
W = F ˣ dcom
τ = F ˣ d
H = I ˣ ω

α = τ ˣ I

J = F ˣ t

F ᵡ M ᵪ a ᵡ M ᵪ τ ˣ τ ˣ a ₓ t

Segments and joint contribution

Arm Swing (AS) raises the COM higher with increased velocity at take-off, increasing COM acceleration of all body segments. The AS contributes to reducing hip and knee torque in early propulsion. In later propulsion, AS slows trunk extension down enhancing hip torque thus prolonging the concentric extensor action leading to increased force and torque generation. (Feltner et al., 2004). During the last part of take- off, maximum energy is released, increasing power output and work that increase VJH (Vanezis & Lees, 2005).
(τ ↑ due to T=F.d, α= τ.I I=constant thus α↑ and F=ma, F ↑ , a ↑, P ↑due P=F.v and W ↑ due W= F.dcom)

If BW reduces, segmental mass will reduce resulting in reduction of segmental moments of inertia. This will lead to an increased angular velocity (H= ↓I. ↑ω). This will also contribute to vertical velocity to raise the COM (Blazevich, 2007).

Muscle capabilities

Muscles contract from proximal to distal to coordinate VJ (Pandy & Zajac, 1991). Creating force to maximise COM vertical displacement, requires optimum muscle capabilities. This is influenced by genetics (Vanezis & Lees, 2005). Muscle force is determined by the type of muscle fibre, muscle size and length, neural activation and control, calcium phosphorylation supplying energy, angular and contraction velocity and strength-to-mass ratio (Waller et al., 2013). Increased amount of fast twitch muscle fibres (IIa and IIx) characterises higher force production due to increased contraction speed and increased ATPase concentrations (Bosco & Komi, 1979; Kraemer & Spiering, 2006). (P= F.v)

Force-length relationship of muscles

This describes how muscle can produce force in relation to contractile and elastic features of the muscle (Enoka, 2008). The contractile (sarcomere) component creates maximal force when all cross-bridges are attached. If sarcomere length increases or decreases, force production reduces. The elastic component will generate force if a contracting muscle is stretched (Bobbert et al., 2001). The total force is the sum of contractile and elastic force components.

Force–Velocity relationship

This describes the muscle force production changes according to muscle length velocity. (Enoka, 2008). Maximal muscle force is created with no shortening eg. Isometric contraction. When a load exceeds the force generated by the muscle, it will lengthen and more force will be produced. The rate of change of muscle activation is determined by the muscle activation together with the force-length and force-velocity parameters (Domire & Challis, 2007).

Force-time relationship

Muscles that take more time to generate maximum force in the eccentric phase of the counter movement will produce higher force. Fast twitch muscles have faster ramping-up force qualities e.g. knee extensors. Bobbert et al. (1996), compared higher CMJ to SJ height. Increased ramp-up time during the countermovement caused the extensor muscles to take longer to reach maximum force, reducing knee joint moments with slower cross-bridging during the eccentric phase. Starting the concentric phase, more force could be produced.

Biarticular (BiM) and Monoarticular (MonoM) muscles

BiM spans over 2 joints and couples movement over these joints (Enoka, 2008). At the start of the countermovement, MonoM flexors (Iliopsoas, Biceps femoris short head, Tibialis anterior) facilitate the countermovement. MonoM extensors (Gluteus maximus, Vasti, Soleus) produce VJ propulsion energy with a high force-velocity relationship creating metabolic energy. BiM (Rectus Femoris, Hamstrings) with low work and power output, is responsible for transferring energy and refine coordination (Nagano et al., 2005). Activating BiM and MonoM in various sequences and ranges of motion, result in redistribution of extensor and flexors torque, increasing vertical translation of the COM (Jacobs et al., 1996).

Stretch-Shortening Cycle (SSC)

During CMJ the SSC is caused by the hip, knee and ankle extensors that actively stretch prior to shortening, increasing positive work and power (Cavagna, 1977 & Kwakami, 2002). The SSC contributes to VJ by:
i. Increased time to develop force in the eccentric phase.
ii. Storage and release of elastic energy causing force production when muscles are stretched (eccentric phase) hence increasing kinetic energy available and improving work capacity at the beginning of the concentric phase (Nagano et al., 2005). Kopper et al. (2013) suggest that storing and re-using elastic energy can increase vertical velocity especially with larger countermotion. Plyometric training increases the eccentric muscle activity since the release timing of stored elastic energy increases force output in the concentric phase. (McBride et al., 2008)
iii. Stretch reflex. A forced muscle lengthening causes a stretch reflex at the start of the SSC increasing muscle tension. This will improve concentric behaviour. For the stretch reflex to increase effectively, the intensity of change of direction from eccentric to concentric needs to be increased e.g. drop-jump (Waller et al., 2013)
iv. Increasing the rate of force development (RFD) during the concentric phase e.g. in SJ. By increasing knee flexion during the static starting position followed by rapid triple extension of hips, knees and ankles, RFD will increase (Wilson et al., 1995).

Take-off parameters are optimised by increasing force and power production, COM acceleration and vertical velocity and BM reduction. This will increase the COM displacement that will optimise the VJ.

3. VJ Measurements

Various VJ tests result in different measurements. Valid test methods are required to determine exercise programmes and lower limb explosive power (Bobbert & Van Soest, 1994). Validity indicates whether equipment measures what it claims to measure (Atkinson & Nevill, 1998). Reliability is the ability to reproduce a test with consistent measurements (Bruton et al., 2000). Reliability can increase by using a sizable population (50 participants) and performing 3 trials. To increase reliability, specific VJ must be performed in a homogenous population (Young et al., 1997).
Sargent’s test measures the difference between the fully extended-stand-reach and the maximal jump-and-reach height (Sargent, 1921). This is a cheap and easy test performed next to a wall, but concentrating on jumping and reaching to make a mark may be difficult. Calculation errors are possible causing low reliability and validity (Klavora, 2000). The Vertec System also tests jump-and-reach height but use equipment with horizontal vanes (Nuzzo et al., 2011). Moir et al. (2008) stated that adequate shoulder movement as well as precise timing and coordination is required to perform these measurements. Training is required to ensure that the participant makes contact with the vanes at peak height (Moir et al., 2004).
The Contact Mat (CMT) (Innervations) is sensitive to pressure during lift-off and landing, recording the flight time (Aragon–Vargas 2000). The flight time measurement is used to calculate VJH (jump height = [t2 × g] ÷ 8, where g = acceleration due to gravity with t = flight time) (Markovic et al., 2004). Leard et al. (2007) insists that accurate and reliable VJH calculations can be obtained when performing a correct CMJ and landing. The take-off and landing must be in the same foot position to not influence the CMT measurement (Markovic et al., 2004). However, Moir et al. (2008) found a systematic error using CMT: By using the flight time method, males do excessive knee flexion during flight, increasing the flight time thus overestimating VJ. Aragon–Vargas (2000) argued that a position error (COM rise-height) prior to take-off influences the calculations. However, Buckthorpe et al. (2012/) corrected the rise-height error but still found a significant difference measuring VJH by CMT versus Force Platform (FP). This demonstrates the CMT being reliable but having a weak validity.
Toronto Waist Belt tests determine height by a measuring tape that is fixed to the mat between the feet. When performing the VJ, the tape extends and stops at maximum height. No calculations are required, making the reading easy and valid (Klavora, 2000, Buckthorpe et al., 2012).
The accelerometer is a small simple device attached to the hip. The BM must be entered prior to testing. It can determine VJH on any surface (e.g. sand) by either measuring flight time or the take-off velocity (VJH=maximal velocity2/[2xg]). The latter proved unreliable (Casertelli et al., 2010). Based on the flight time, only bilateral VJH is relatively reliable (McCurdy et al., 2011; Nuzzo et al., 2011).
Optojump photoelectric cells measure GRF and flight time. Flight time and acceleration can calculate COM vertical rise (Glatthorn et al., 2011). It can be interchangeable with FP measurements (VJH = 1.02 x optoVJH + 0.29) and used in the field with good reliability and validity compared to FP (Coefficient of Variation (CV) 2.7%; Intra Class Coefficient (ICC) 0.982-0.989) (Glatthorn et al., 2011).
Young et al. (1997) found a high reliability for the Vertec jumps in a small (n=17) male population, performing a 1-arm reaching VJ. The Vertec vanes were 1cm apart. However, Nuzzo et al. (2011) compared the Vertec, CMT, and accelerometer and found highest reliability for the accelerometer followed by the CMT and the Vertec. This CMJ with bilateral arm swing study consisted of a moderate size mixed gender group. The Vertec vanes were 1.27cm placed apart for this study. They found that training of the population influenced the VJH, especially when using the Vertec. In contrast to this result Moir et al. (2008) found CMJ with arms around necks, in females (n=35) and males (n=35) tested over 4 weeks on a CMT was highly reliable with high ICC and low CV. These authors noted that it was more reliable to take the highest VJH instead of an average VJH due to fatigue and skill.
The FP and 3-D motion video analysis (3DVA) are the ‘gold standard’ for determining VJH. 3DVA calculates the precise COM position as well as COM of each body segment. VJH is calculated by the difference of standing COM and peak flight COM position (Aragon–Vargas, 2000).
FP is laboratory based; expensive; floor mounted; and can calculate numerous measurements including VJH, rate of power development, etc. (Naves et al., 2009, Buckthorpe et al., 2012). Calculations to determine VJH is more complex. GRF is measured by analysing the pressure on the FP. The quartz crystal transducer FP (Krisler) is most accurate (Buckthorpe et al., 2012). Mobile FP can also be used with high validity (Buckthorpe et al., 2012). Some of the FP calculation methods have been questioned (Aragon–Vargas, 2000). Moir et al. (2008) propose 3 different methods of calculating VJH:
1. Flight Time: VJH = 1/2g (t/2)2
2. Vertical Velocity of the COM at take-off method (TOV= TOV2/2g). This method is the most valid and reliable (Aragon–Vargas, 2000, Moir et al., 2008)
3. Adding the vertical COM displacement prior to take-off to the height calculated using TOV.
FP is the most reliable and valid VJH measurement using TOV method. Field testing with an Optojump is also highly reliable and valid whereas an accelerometer is small and simple to use but less valid and less reliable.

4. Basketball

Basketball requires maximum anaerobic power production to perform high intensity movements including, walking, short distance running and jumping in defence (blocking) and offence (shooting).
Scanlan et al. (2011), compared sub-elite and elite players. Elite players produced higher power and work production. Jumping ability is a requirement regardless of playing position. Maximising jump skill is required when defending or opposing counterparts (Ziv & Lidor, 2010).
During matches up to 46 VJ will be performed and reaching heights of up to 75cm (McInnes et al., 2010). Playing positions have different demands. Correlation between body composition, aerobic fitness, anaerobic power and positional roles exist (Ostojic et al., 2006). Delextrat & Cohen (2009) analysed basketball jumps performed in playing position with good reliability (ICC of 0.95). They found guards perform frequent 1leg-jumps during lay-ups. Forwards do not jump as high, perhaps due to a lack of coordination although power output is uniform in all positions. Forwards and centres perform frequent bilateral jumping. The CMJ with arm swing is more specific to basketball indicating that specific playing positions require specific VJ performance testing (Ziv & Lidor, 2010).
McGill et al. (2012) raised concerns that current tests may not be sport specific. However, Hoffman et al. (1991) noted that VJH and playtime have a significant correlation. Delextrat & Cohen (2008) assessed agility T-test, sprint and CMJ with AS, comparing recreational and elite players. The field tests demonstrated a significant VJ difference (8.8%), between the 2 groups. Due to variation in laboratory versus field testing reliability, isokinetic knee extensor testing was performed with the elites with significant higher peak torque values compared to their recreational counterparts. Furthermore, Alemdaroglu, (2012), determined the relationship between muscle strength, anaerobic performance, agility, sprinting and basketball VJ. It demonstrated significant correlation between isokinetic quadriceps peak power performance, CMJ and SJ.
Basketball jump-shots are frequently performed from a distance to the basket, in an attempt to score. The player is required to vary direction, generate momentum and overcome inertia by activating the leg muscle power (McInnes et al., 2010). The run-up towards the basket is in a curved line creating centripetal and centrifugal forces. Every step generates vertical and horizontal forces with increased horizontal and vertical velocity until braking force is applied. A bilateral CMJ is performed as discussed earlier. By creating a large force in a short time a higher impulse will be produced whilst lifting the arms up above head with 90° elbows flexion and then extending the elbows and increasing the COM. The ball is propelled by a projectile movement towards the basket. Balance, coordination and trunk stability is important. This shot requires power behind the ball and VJ as high as possible, especially in the presence of a blocking defender.
VJ is frequently executed in basketball. It is therefore indicative to use VJ as a performance test and predictor but must be specific to playing position.

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