Bilateral deficit has been observed in isometric, isokinetic and complex motor skill. Within jumping skill, both static vertical and countermovement jump have been examined. The purpose of this study was to compare unilateral (UL) and bilateral (BL) drop jumps from different heights with an aim to examine the phenomenon of bilateral deficit. Four male subjects performed drop jumps from 46cm (BL), 12 cm (UL) and 24 cm (BL & UL). The UL jumping height ratio in the same momentum and same potential energy trials was higher than 50%, indicating the existence of bilateral deficit. Inconsistent findings were obtained when dropping from the same height however. Generally, subjects tend to lower their center of mass before dropping, which decreases the dropping height. Patterns of resultant muscle moment in ankle, knee, hip and the total support moment are similar in all trials except an early peak in the 46 cm BL drop jump. The resultant muscle moment of knee dominates over that of ankle and hip during landing. It is suggested that concentric, eccentric and isometric contraction of the extensors of lower extremities all play a role to provide support and prevent collapse during the impact phase.

Introduction

Bilateral deficit is the phenomenon that the force produced by a muscle during a maximal bilateral action is less than the sum of the maximal unilateral action. Research have widely reported the existence of bilateral deficit and investigated the cause behind it (Vandervoort et al., 1984; Soest et al., 1985; Secher et al., 1988; Schantz et al., 1989; Oda & Moritani, 1994; Challis, 1998). For example, Vandervoort et al. (1984) compared the differences between muscle utilization during bilateral (BL) and unilateral (UL) leg extension. They found that the maximal voluntary strength of BL was significantly less than the summed UL under isometric and concentric contraction, with BL/UL ratio of 0.910. Soest et al. (1985) reported that the jumping height in UL countermovement jumps was 58.5% of that reached in BL jumps. This percentage differed significantly from theoretical value of 50%, suggesting that there was an impairing mechanism in bilateral performance. Some possible causes of bilateral deficit were the reduction of fast twitch motor neuron activation (Vandervoort et al., 1984; Oda & Moritani, 1994), muscle coordination for force production of movement (Challis, 1998), impaired neural mechanism (Vandervoort et al., 1984; Soest et al., 1985), and dispersion of concentration (Vandervoort et al., 1984).

While most studies measure isometric strength of selected muscle group, some works on isokinetic and complex motor skill like jumping have also been done. Within jumping skill, both static and countermovement jump showed similar results of bilateral deficit (Soest et al. 1985; Challis, 1998). Drop jump, another widely used technique, has not been examined however. Drop jump is a common method of plyometric training employed to enhance jumping capability. This stretch-shorten cycle exercise is believed to overload muscles and trigger improvement in mechanical output of muscles. Yet, the coordination of joint muscle movement has not been clearly understood. General kinetic and kinematic characteristics of drop jump have been reported (Aura & Viitasalo, 1989; Bobbert et al. et al., 1987a; Bobbert et al. et al., 1987b; Fowler & Lees, 1998; Horita et al., 1999). Aura & Viitasalo (1989) have studied drop jumps with UL foot contact. However, BL drop jumps, and thus bilateral deficit, were not investigated in their study.

The purpose of this study was to compare unilateral (UL) and bilateral (BL) drop jumps from different heights with an aim to examine the phenomenon of bilateral deficit. Time history of resultant muscle moment of ankle, knee and hip; and the total support muscle moment were also investigated.

Method

Experimental Design

There was three different comparisons between UL and BL drop jump in this study: 1) same momentum; 2) same potential energy; and 3) same velocity. In each design, each leg receives either same amount of momentum, potential or velocity at landing in both UL and BL drop jumps.

1) Same Momentum

The momentum in the legs can be represented by the following equations:

P = mv

where P=momentum, m=mass, v=velocity. It is assumed that the momentum in each leg during BL drop jump is half of that in both legs. In order that the leg has the same momentum during the landing of UL and BL drop jump, half of the momentum in BL jump should be obtained in UL jump.

If P_u= (1/2)P_b

mv_u= (1/2) mv_b

mv_u= m (1/2 v_b)

then v_u=1/2 v_b

where u and b indicate UL and BL respectively. It can be seen that half landing velocity results in half momentum. Theoretically, the potential and kinetic energy from dropping to landing is conserved. Therefore, different landing velocity can be obtained by dropping from different height:

mgh = (1/2)mv²

where m=mass, g=gravitational acceleration, h=height, v-velocity. In this study, 46cm was chosen for BL jump. To obtain half landing velocity, it was calculated that UL jump height should be approximately 12cm. Therefore, the BL drop jump from 46cm and the UL drop jump from 12cm should generate the same momentum, thus impulse, in each leg. It was hypothesized that the UL jumping heights should be 50% of the BL jumping heights.

2) Same Potential Energy

The energy that the legs absorbed during impact comes from the potential energy (PE) of dropping. Thus, it depends on the dropping height since

PE = mgh

If the dropping height is reduced to half of its value, PE would also be reduced by half. Therefore, if 46cm was chosen for BL drop jump, the UL jump should drop from 23cm to half the PE at landing. In this study, 24cm was used instead for convenience. Since each leg receives the same amount of PE in both jumps, it was hypothesized that the UL jumping heights should be 50% of the BL jumping heights.

3) Same Velocity

For the same dropping height, the landing velocity of both UL and BL jumps should be the same (v²- u² = 2as). Assume that maximum power can generated in each leg in both UL and BL drop jump, the UL jumping height was hypothesized to be 50% of BL jumping height. In this study, a dropping height of 24cm was chosen. Dropping from the same height is similar to the condition of the previous studies of static vertical jump or countermovement jump in which landing velocity is zero.

Data Collection

Four male subjects from the Loughborough University were recruited on voluntary basis. A practice session on UL and BL drop jump from particular dropping heights was conducted before the main trial. Subjects were instructed to jump (1) as high as possible, and (2) as quickly as possible after landing, with their hands on hip. To ensure dropping from the exact height, subjects were asked to prevent any weighting or unweighting before dropping. In UL drop jump, the landing leg was prepared in front of the supporting leg before dropping (Figure 1). In BL drop jump, the same preparatory position was adopted except landing on both legs.

Figure 1 - Preparatory position of drop jump with the front leg as the landing leg in UL drop jump.

On the main trial, landmarks were placed on the 5^th metatarsal-phalangeal joint, ankle, knee, greater trochanter and mid-neck region of each subject. They were asked to perform three trials of BL drop jump from 46cm, UL drop jump from 12cm, BL and UL drop jump from 24cm onto a Kistler 9281B force platform covered with rubberized athletics track. The force data were sampled at 1000 Hz and the force platform was connected with a Kistler 9865B 8-channel charge amplifier. Data were recorded in the Research Machines PC 5200 computer with C10-DAS16F A to D board (12 bit). A manual trigger was used to start sampling and initiate a bank of 20 LEDs which switch on at 1ms intervals for synchronization purpose. At the same time, the performance was videotaped using a Sony VX-1000E Digital Handycam operating at 50 Hz and with shuttle speed at 1/1000s. The camera was connected to a Panasonic NV-FS88 super VHS video cassette recorder and input with a timecode generator (Imp Electronics V9000). Lights (Arri 2000) from two sides were used to provide extra lighting. Before the trial, a 6-point calibration frame on the plane of motion was videotaped.

Data Reduction

The trial with the highest impulse was chosen in each type of jump. Impulse, peak vertical force and flight time during impact were recorded. The time history of the vertical (Fz) and anteroposterial horizontal (Fy) component of ground reaction force, and the coordinates of the point of force application (ay) was exported for calculation of joint moment. The corresponding video image coordinates from 4 frames before landing to 4 frames after take-off were digitized by the Target software developed by the Loughborough University. The 6 calibration points were digitized for 4 frames and the coordinate data were used to obtain image reconstructions by direct linear transform (DLT). Image coordinates (dy, dz) of ankle, knee and hip were exported for use. Data from the force platform and video digitization were synchronized in reference to the frame that the LEDs first appeared. The synchronization system was designed by the Loughborough University Biomechanics Section and made by Wee Beasty Electronics of Loughborough. Data of 46cm BL in subject 4 was lost in the process.

Landing velocity was calculated on theoretical and experimental basis. Theoretical values were calculated by the equation:

v² - u² = 2as

where v=final (landing) velocity, u=initial velocity, s=dropping height.

In 46 cm drop jump, v² – (0)² = 2(9.81)(0.46)

v = 3.00m/s

In 12 cm drop jump, v² – (0)² = 2(9.81)(0.12)

v = 1.53m/s

In 24 cm drop jump, v² – (0)² = 2(9.81)(0.24)

v = 2.17m/s

Experimental values were obtained by the digitized image coordinates. The hip coordinates and time difference of two frames previous to landing were taken to calculate the actual landing velocity (v = d/t).

Take-off velocity can be calculated from the impulse and landing velocity obtained since:

Ft = mv - mu

where v=take-off velocity and u=landing velocity. Jumping height can then be estimated by:

v² - u² = 2as

where v=final velocity (0 in this case) , u=take-off velocity, s=jumping height.

Joint moment (M_j) of ankle, knee and hip was calculated by the quasi-static method outlined by Alexander and Vernon (1975). The equation is:

M_j = Fydz + Fz (ay-dy)

Resultant muscle moment (M) was defined as

M = (-1) * M_j

so muscle moment of ankle (M_a), knee (M_k) and hip (M_h) was calculated from corresponding M_j.

Then net support moment (Ms) to prevent collapse is defined by Winter (1980) as:

M_s = M_k - M_a - M_h

This definition has assumed that only extension of the three joints contributes to support. However, even though the joints are flexing, muscles are contracting eccentrically to support. Therefore, it is suggested that both positive and negative muscle moment should be taken into account for support moment. Thus, in this study, support moment during impact is defined as the sum of absolute values of resultant muscle moment:

M_s = │M_k│ + │M_a│ + │M_h│

Results

Theoretical landing velocities calculated by the equation v² - u² = 2as were as follows:

In 46 cm drop jump, v² – (0)² = 2(9.81)(0.46)

v = 3.00m/s

In 12 cm drop jump, v² – (0)² = 2(9.81)(0.12)

v = 1.53m/s

In 24 cm drop jump, v² – (0)² = 2(9.81)(0.24)

v = 2.17m/s

Table 1 presents the actual landing velocity calculated from video data and the corresponding theoretical values. Most of the actual values are smaller than the theoretical ones except one identical to and two greater than. The actual/theoretical ratio ranges from 54.2% to 114.7%.

The impulse, peak vertical force (Fz) and flight time (t) during impact are shown in Table 2. Greater impulse and peak Fz, and longer flight time were observed in the BL trials. Calculated take-off velocity (v_t), estimated jumping heights (H) and the UL/BL ratio are also shown in Table 2.

Dropping height (cm)	Subject	Actual landing velocity (m/s)	Theoretical landing velocity (m/s)	Actual/Theoretical ratio (%)
46 (BL)	S1	2.63	3.00	87.7
	S2	3.44		114.7
	S3	2.88		96.0
	S4	/		/

12 (UL)	S1	0.83	1.53	54.2
	S2	1.53		100.0
	S3	1.46		95.4
	S4	1.00		65.4

24 (BL)	S1	2.15	2.17	99.1
	S2	2.47		113.8
	S3	2.14		98.6
	S4	1.96		88.9

24 (UL)	S1	1.84	2.17	84.8
	S2	2.00		92.2
	S3	2.14		98.6
	S4	1.84		84.8

Table 1. Theoretical and Actual Landing Velocity.

Subject	Jump type	Impulse (Ns)	Peak Fz (N)	t (s)	v_t (m/s)	H (m)	*UL/BL ratio (%)
Same Momentum
S1	BL	475	2630	0.445	2.27	0.263	76.0
	UL	333	1823	0.295	1.98	0.200	76.0
S2	BL	589	2599	0.421	1.59	0.129	67.4
	UL	395	2094	0.320	1.30	0.087	67.4
S3	BL	764	3438	0.499	1.77	0.159	74.2
	UL	526	3211	0.406	1.52	0.118	74.2
S4	BL	418	2775	0.463	/	/	/
	UL	317	1589	0.300	1.63	0.136	/
Same PE
S1	BL	475	2630	0.445	2.27	0.263	56.7
	UL	366	2113	0.356	1.71	0.149	56.7
S2	BL	589	2599	0.421	1.59	0.129	72.1
	UL	462	2088	0.230	1.35	0.093	72.1
S3	BL	764	3438	0.499	1.77	0.159	51.6
	UL	596	3229	0.406	1.26	0.082	51.6
S4	BL	418	2775	0.463	/	/	/
	UL	347	1709	0.328	1.33	0.090	/
Same Velocity
S1	BL	399	2580	0.419	1.90	0.184	81.0
	UL	366	2113	0.356	1.71	0.149	81.0
S2	BL	518	2466	0.442	1.95	0.193	48.2
	UL	462	2088	0.230	1.35	0.093	48.2
S3	BL	615	3602	0.492	2.10	0.225	36.4
	UL	596	3229	0.406	1.26	0.082	36.4
S4	BL	374	2636	0.499	2.39	0.292	30.8
	UL	347	1709	0.328	1.33	0.090	30.8

Table 2. General Variables of Drop Jump.

* UL / BL ratio is defined as the UL jumping height divided by the BL jumping height.
Typical example of resultant muscle moment in ankle, knee and hip, and the corresponding supporting moment are shown in Figure 2 to Figure5.

Figure 2 - Resultant muscle moment of ankle, knee and hip and support moment during impact of 46 cm BL drop jump.

Figure 3 - Resultant muscle moment of ankle, knee and hip and support moment during impact of 12 cm UL drop jump.

Figure 4 - Resultant muscle moment of ankle, knee and hip and support moment during impact of 24 cm BL drop jump.

Figure 5 - Resultant muscle moment of ankle, knee and hip and support moment during impact of 24 cm UL drop jump.

Knee muscle moment is dominant in all cases. Ankle muscle moment is slight negative throughout the impact while hip muscle moment varies about positive and negative near the zero line. In 24 cm and 12 cm trials, support moment starts from zero, peaks in the middle phase of impact, and returns to zero at take-off. In 46 cm trial, support moment peaks in the beginning of impact, remains high in the middle phase and drops to zero at take-off.

Discussion

Landing Velocity

The actual landing velocity calculated from the video coordinates is different from the theoretical value. There is only one trial which obtain exactly the same velocity as the theoretical value. Most of them are lower than the theoretical value, indicating that subjects drop from a lower height than the designated one. This is probably due to the knee flexion of the supporting leg, which lowers the center of mass (COM) before dropping. General actual values lie between 84.8% and 99.1 % of the theoretical values. It is interesting to note that subjects do not show higher tendency to lower the center of gravity while dropping from a higher height. Instead, the two lowest values (54.2% & 65.4%) lie in the 12 cm UL trial, which is of the least dropping height. Two trials show higher landing velocity (113.8% & 114.7%), implying that subjects have dropped from a higher height than the designated value. This might be due ankle extension which raises the COM before dropping, that is, subjects tend to jump off instead of dropping. On average, S3 demonstrates the highest consistency and the nearest to theoretical landing velocity (95.4% to 98.6%). It is suggested that proper instruction and sufficient practice time should be given to subjects in order to minimize the lowering or raising of COM before dropping.

Bilateral Deficit

Same Momentum. The UL jumping height was 67.4% to 76% of the BL jumping height in the same momentum comparison. This percentage differs from the theoretical ratio of 50%, supporting that there is bilateral deficit in drop jump. When each leg receives the same momentum at landing, the leg generates greater force in UL jump than in BL jump.

Same Potential Energy. The UL jumping height was 51.6% to 72.1% of BL jumping height in the same PE comparison. In agreement with the same momentum comparison, this result also demonstrates bilateral deficit but to a lesser extent. When each leg absorbs the same amount of PE at landing, the leg generates greater force in UL jump than in BL jump.

Same Velocity. The UL/BL ratio in drop jump from the same height was inconsistent. Two trials had low ratio of 30.8% and 36.4% while one was as high as 81%. While these three trials differ greatly from the theoretical value of 50%, the remaining trial demonstrates a close ratio of 48.2%. Soest et al. (1985) showed bilateral deficit in the countermovement jumps by the fact that the jumping height in one-legged jumps was 58.5% of that reached in two-legged jumps. Challis (1998) reported similar result of 58.1% in vertical jump. However, the finding in this study does not provide enough evident to suggest bilateral deficit in drop jump from the same height.

Yet, it should be noted that the jumping height in this study was estimated from the impulse and take-off velocity. It is assumed that the landing impulse and the take-off impulse are identical. However, in practical, such ideal condition is not possible. Energy is lost during impact (for example, sound, heat, friction) and absorbed by the human body, which is not a theoretical rigid body. Therefore, the take-off velocity calculated from the landing velocity should be different from its actual value. Thus, the jumping height estimated from the take-off velocity is not a precise measurement. Jumping height obtained from the video images might provide a more direct and accurate picture. In this study, image coordinates after take-off had not been digitized however.

Another method of estimating the jumping height is to make use of the flight time (t) obtained from the force platform data. Applying the equation s = ut + (1/2)at²,

H = (1/2) g t_1/2²

where t_1/2 = half flight time. Different jumping height might be obtained in the these three methods. This could explain why direct comparison among studies may sometimes be difficult when different methodology was employed.

Peak Vertical Force

In general, peak Fz was the largest in 46 cm BL, followed by 24cm BL, 24 cm UL and the smallest in 12 cm UL drop jump (except for S3). Peak Fz was greater in BL impact than UL impact. Besides, there is a trend that the higher the dropping height, the greater the peak Fz. This result supports a previous study which suggests that peak force increased with jumping height (Bobbert, 1987b). Bobbert et al. (1987a) reported the peak force in 20cm bounce drop jump (BDJ) and counter-movement drop jump (CDJ) were 4099±815N and 2649±499N respectively. When Bobbert et al. (1987b) repeated the BDJ from different heights, the peak force measured were 2682±368N, 3515±964N and 4496±693N for 20cm, 40cm and 60cm respectively. A higher peak force of 5001±130N was recorded by Aura (1989) in drop jump from 52cm with unilateral foot contact with two approaching steps. The peak Fz measured in this study lied between 1709N (12cm) to 3438N (46 cm). It appears that the peak Fz obtained in this study is smaller than those in previous studies. Since subject’s body weight has not been subtracted from the value presented, direct comparison to other studies cannot be made at this stage.

Muscle Moment

The dominance of knee muscle moment indicates that the concentric contraction of knee extensors contributes a great part in preventing collapse. The negative ankle muscle moment represents the concentric contraction of ankle extensors. In the hip joint, there is a fluctuation between positive and negative muscle moment. It is believed that the hip extensor is contracting throughout the impact to support. Positive muscle moment indicates eccentric contraction while negative muscle moment corresponds to concentric contraction. Even the resultant muscle moment is momentarily zero at points, the extensor muscle of the lower extremities may still be contracting isometrically. It is the summation of concentric, eccentric and isometric contraction together to provide support and prevent collapse during the impact phase.

Greatest muscle moment in knee, followed by ankle and the least in hip shown in this study supports the findings of Bobbert et al. (1987a). The early peak support moment in 46 cm trial is due to the high knee and hip muscle moment in the beginning. In all other trials, knee, hip and ankle muscle moment start from zero and increase gradually. This early peak moment is in agreement with Horita et al. (1999) who demonstrated a early peak knee moment during the contact phase in a 50 cm drop jump. The support moment in BL trials are greater than that in UL trials. This is consistent with the greater peak Fz measured in BL trials. In general, the average force during impact in BL trials is greater than that in UL trials. Therefore, greater joint moment, thus resultant muscle moment and total support moment is calculated in BL trials.

Conclusion

In conclusion, this study compares the characteristics of unilateral and bilateral drop jumps and presents the time history of resultant muscle moment and support moment of the lower extremities. The UL/BL ratio in jumping height was higher than 50% in the same momentum and same PE trials, indicating the existence of bilateral deficit. Inconsistent findings were obtained in the same velocity trial in which UL and BL trials drop from the same height. Generally, subjects tend to lower their COM before dropping, which leads to a decrease in dropping height. It is preferable to measure jumping height by video image than estimating from landing impulse. Patterns of resultant muscle moment in ankle, knee, hip and the total support moment are similar in all trials except an early peak in the 46 cm BL drop jump. The resultant muscle moment of knee dominate over that of ankle and hip during landing. It is suggested that concentric, eccentric and isometric contraction of the extensors of lower extremities all play a role to provide support and prevent collapse during the impact phase.

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