Introduction

Blunt force trauma is an injury caused by objects hitting the body occurring as a result of accidents, falls or violent crimes. In the latter case, forensic scientists are often asked for their expert opinion concerning injury and fatality risk. Applying the law of momentum conservation, accelerations and contact forces can be estimated [1]. A comparison between these estimated loads and injury thresholds taken from literature [2,3,4] provides the basis for forensic assessment at court.

The calculation of contact forces, etc. requires several input parameters that have to be estimated [5]. The velocity of an object at the time of impact represents one of the crucial input parameters that must be determined when calculating loads acting on the body.

In general, accelerations and contact forces depend on the (effective) mass, the material characteristics [6] and on the impact velocity of the striking object. The influence of the length and the mass of a longish striking implement on maximum striking velocity was investigated in [5, 7]. These studies analysed the striking velocities in one-handed strikes without paying attention to different striking techniques. In a former study, the authors [5] observed highly diverse striking movements and techniques in one-handed strikes using rods of different lengths and masses. At court, questions are raised concerning the expected striking velocity and the associated injury and fatality risk in one-handed versus two-handed strikes. Studies dealing with the striking technique especially comparing one-handed versus two-handed strikes as a potential factor affecting maximum striking velocity are not available in the forensic literature.

The purpose of this study was to measure and analyse maximum striking velocities in one-handed and two-handed strikes in female and male volunteers. We a priori hypothesised higher striking velocities in two-handed strikes compared to one-handed strikes.

Materials and methods

One-handed and two-handed strikes were performed by 21 female and 29 male volunteers using a steel rod with a diameter of 3 cm, a length of 65 cm and a mass of 1000 g. The experimental setup corresponds to the setup described in [5]. The target was made of a 5-cm-thick foam fixed on a table 72 cm above floor level. The volunteers were asked to perform one-handed and two-handed strikes without being provided with instructions in terms of striking movement. Prior to measurements, the volunteers had to sign a written informed consent and do warm-up to prevent any injuries. The ethics committee of the University Hospital Jena gave approval to conduct this study.

Reflecting markers were attached to the volunteers and to the striking implement. One marker each was fixed to the very distal end of the rod (dr marker) and 19.5 cm distally from the proximal end of the rod (pr marker). Striking velocity was defined as the resultant velocity of the distal rod marker dr.

A Qualisys™ Motion Analysis system (Qualisys Inc., Göteborg, Sweden) containing 12 ProReflex Motion Capture Unit (MCU) 1000 high speed cameras captured marker displacements and velocities over time. The sampling rate was 500 Hz resulting in 3000 frames at a recording time of 6 s. The standard deviation in system calibration was in the magnitude of 1.4 mm yielding a spatial resolution of the same magnitude.

Starting from a neutral position, volunteers performed one- and two-handed strikes until two valid measurements (less than 10 frames missing per second) had each been collected. Data processing contained the following steps:

  1. 1.

    Import of marker coordinates into MATLAB R2015b.

  2. 2.

    Application of an 11th order median filter to eliminate noise in the marker coordinates.

  3. 3.

    Computation of maximum striking velocities.

  4. 4.

    Computation of maximum rotational velocities of the rod.

  5. 5.

    Classification of two-handed strikes in ‘overhead’ and ‘overshoulder’ technique (Fig. 1) using Qualisys™ Track Manager 2.10 software.

  6. 6.

    Statistical analysis using IBM SPSS Statistics 4.

Fig. 1
figure 1

‘Overshoulder’ striking technique (left) and ‘overhead’ striking technique (right). Black dots represent the marker set, white lines represent the dr-marker trajectory

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For each setup and volunteer, the measurement with the individually achieved maximum striking velocity was regarded for statistical analysis.

Figure 1 shows examples for an ‘overshoulder’ strike (left) and an ‘overhead’ strike (right). In an ‘overhead’ strike, the rod is moved within a nearly vertical plane whereas the ‘overshoulder’ strike is characterised by a skewed marker trajectory. A reproducible classification in ‘overshoulder’ and ‘overhead’ strikes was performed manually by looking at the trajectories in the track manager as well as during the experiment by two colleagues. In terms of one-handed strikes, distinguishing individual striking techniques by means of a reproducible classification was hardly achievable.

In order to investigate potential differences in the striking movement, the rotational velocity of the rod was calculated. Let ra1, rb1 and ra2, rb2 the position vectors of the distal rod (dr) and proximal rod (pr) markers at two consecutive time points t1 and t2. The overall motion sequence of the rod considering two consecutive time points can be separated into a translational and rotational component. In the first step, we define the translational component of the rod’s motion. The difference vector ∆ between the proximal rod marker at t1 and at t2 represents the translational shift:

$$ \Delta ={r}_{a2}-{r}_{a1} $$

The second step defines the rotational component accordingly. Subtracting the translational component from the rod’s position at time point t2 yields the proximal rod marker position ra1* coinciding with the rod marker’s position ra2, while the rod marker position rb1 is shifted to rb1* by ∆:

$$ {r}_{a1}^{\ast }={r}_{a2};\kern0.75em {r}_{b1}^{\ast }={r}_{b1}+\Delta $$

Now, applying the scalar product gives the rotational angle φ.

$$ \cos \varphi =\frac{\left({r}_{b1}^{\ast }-{r}_{a1}^{\ast}\right)\bullet \left({r}_{b2}-{r}_{a2}\right)}{\left|{r}_{b1}^{\ast }-{r}_{a1}^{\ast}\right|\left|{r}_{b2}-{r}_{a2}\right|} $$

The velocities are calculated as usual.

$$ v=\frac{\Delta }{t_2-{t}_1};\kern0.5em \omega =\frac{\varphi }{t_2-{t}_1} $$

Note that the translational component v depends on the reference point chosen to calculate the shift ∆, whereas the rotational velocity ω represents a distinct measure which is independent from the translational shift. The calculation is performed for a time frame F of 125 samples (0.25 s) prior to the time of maximum striking velocity. To compare one-handed and two-handed strikes, we matched the maximum rotational velocities in the given time frame F.

Results

Twenty-one female and 29 male volunteers performed both one- and two-handed strikes with one rod of 65 cm and 1000 g. Table 1 summarises the descriptive statistics of the volunteers.

Table 1 Descriptive statistics of volunteer parameters
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In two-handed strikes, 10 out of 21 female (48%) and 20 out of 29 (69%) male volunteers performed ‘overhead’ strikes. Descriptive statistics of maximum striking velocities for the different striking techniques are shown in Table 2. The striking technique ‘two-handed’ contains all two-handed strikes regardless of being ‘overshoulder’ or ‘overhead’. Because of an injury of the non-dominant shoulder, one female volunteer did not perform the two-handed strikes. Thus, we had 21 one-handed and only 20 two-handed strikes in the female sample.

Table 2 Descriptive statistics of maximum striking velocities for different striking techniques and results of Shapiro-Wilk tests on normality
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The mean intra-individual variability of maximum striking velocities in two-handed strikes was 0.69 m/s. Figure 2 shows the distribution of the inter- and intra-individual variability for each volunteer in two-handed strikes. In one-handed strikes with the same rod, the mean intra-individual variability in [5] was 1.3 m/s.

Fig. 2
figure 2

Intra-individual variability of two repetitions of two-handed strikes by each volunteer, sorted by the maximum striking velocities they achieved. The vertical bars show the difference between both valid measurements of each volunteer marking the top and bottom end of each bar

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It is worth mentioning that mean maximum striking velocities are of the same order of magnitude regardless of striking technique. Male volunteers reached higher maximum striking velocities than female volunteers. Derived from the p values exceeding the 5% level in all of the Shapiro-Wilk tests, normal distribution can be assumed for all variables in Table 2.

Figure 3 presents a boxplot with an illustration of mean maximum striking velocities separated by sex and striking technique showing only slightly higher mean maximum velocities for two-handed strikes.

Fig. 3
figure 3

Boxplot of maximum striking velocities: Central mark is the median, bottom and top edges are the 25th and 75th percentiles, whiskers represent extreme values excluding outliers (circles)

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Male volunteers achieved significantly higher maximum striking velocities compared to female volunteers. The mean differences were about 6.65 m/s in the one-handed strikes and 5.98 m/s in the two-handed scenario (Table 3). Unpaired t tests revealed no significant differences between maximum velocities in two-handed ‘overhead’ and two-handed ‘overshoulder’ strikes for both female and male volunteers.

Table 3 Conclusive statistics. Levene’s test for homogeneity of variance in unpaired samples. t tests for inhomogeneous variances with H0 “there is no difference between two sample means”. Differences are given in m/s
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Paired t tests (Table 3) resulted in statistically significant differences between maximum velocities in two-handed and one-handed strikes for female but not for male volunteers. However, the mean difference of maximum striking velocities in the female sample is only about 1 m/s.

Figure 4 shows boxplots of maximum rotational velocities ω for male and female volunteers stratified by striking technique in terms of one- and two-handed strikes. Solely considering the rod kinematics, it can be concluded that the rotational component is nearly the same in one- and in two-handed strikes for both sexes.

Fig. 4
figure 4

Boxplot of maximum rotational rod velocities ω, maximum within a time frame of 0.25 s prior to the time of maximum striking velocity

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In Fig. 5, velocity-time courses are illustrated for the volunteers yielding the highest and the lowest maximum striking velocity in one-handed strikes of females and in two-handed strikes of males. The sample curves in Fig. 5 exhibit different shapes presumably caused by different striking movements.

Fig. 5
figure 5

Velocity-time courses (marker dr) for one-handed strikes in the female sample, volunteer V43 and V06 (left) and velocity-time courses for two-handed strikes in the male sample volunteer V38 and V13 (right), V43 and V38 yielded the highest and V06 and V13 yielded the lowest maximum striking velocity

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Discussion

The aim of this study was to investigate the influence of striking technique on maximum striking velocities using a 65-cm-long steel rod weighing 1000 g. The focus was on the comparison of one-handed and two-handed strikes. First visual inspection of measurement results in terms of movement patterns showed two distinct striking techniques in two-handed strikes but not in one-handed strikes [5]. Two-handed strikes were categorised in ‘overhead’ and ‘overshoulder’ striking techniques. The individual striking technique of each volunteer remained unchanged in all performances.

About 70% of male volunteers and about 50% of females chose to strike ‘overhead’. The preference of this technique might be explained by coordinative aspects. In ‘overhead’ strikes, the movements of both upper limbs during striking are basically the same, e.g. retroversion in both glenohumeral joints. This uniform movement may be easier to perform than an ‘overshoulder’ strike with a more complex movement pattern. According to [8], movement control strategies are determined by minimization of ‘neuro-computational’ effort which might contribute to the preference of ‘overhead’ striking.

As one would expect, female volunteers yielded significantly lower maximum striking velocities for both one-handed and two-handed strikes than men. Higher muscle masses and bigger muscle cross-sectional areas in men compared to women might be reasons for the considerable influence of sex on striking performance [9]. Gender differences in the kinematics and ball velocity in elite handball overarm throwing were investigated in [10]. The authors concluded that higher ball release velocities of the male players are generally not caused by gender-specific joint kinematics.

In our sample, there was no noteworthy influence of the striking technique on maximum striking velocities in terms of one- and two-handed strikes. In accordance with our results, no relevant differences in velocities comparing one- and double-handed tennis backhand serves were obtained in [11]. Although the net grip force can be increased by striking double-handedly, these strikes do not seem to result in higher striking velocities. Coordinative aspects including different tasks of the upper extremities in two-handed striking movements [12] and different muscle activation characteristics in different striking techniques [13] might contribute to this observation. Moreover, in a one-handed strike, the volunteer should be able to perform a more dynamic motion sequence in terms of flexion, extension and rotation involving different body segments. The non-striking hand is free to be used to maintain dynamic equilibrium during backswing and striking movement. Several studies investigated the influence of whole-body dynamics on tennis serve speed [14, 15].

Studying the two-handed striking technique comparing ‘overshoulder’ and ‘overhead’ strikes, we could not prove a statistical significant difference in maximum striking velocities. In both the male and female sample, ‘overhead’ strikes showed only a (small) tendency of slightly higher maximum striking velocities.

In [5], we hypothesised that ‘maximum striking velocities seem to depend more crucially on striking technique than on body parameters’. Considering one-handed versus two-handed strikes investigated in the present study, this hypothesis cannot be supported. Correspondingly, the maximum rod rotational velocities seem to be rather similar comparing the one-handed and the two-handed sample (see Fig. 4).

Figure 5 exemplarily shows velocity-time curves with different curve shapes for different volunteers. It therefore can be assumed that apart from ‘overhead’ and ‘overshoulder’ technique, volunteers exhibit individual striking techniques. Due to the high variability in striking movements, it seems to be rather impossible to derive distinct movement patterns or striking strategies.

Regarding the injury risk, not only the striking velocity but also the effective mass of an object determine contact forces and accelerations. Adamec et al. [16] found decreasing effective masses for increasing implement lengths in one-handed strikes using a longish instrument of variable length. As a result, they concluded that hand grip force cannot increase the effective mass. An increase of effective mass via hand grip force could only be observed in strikes with a striking direction along the longitudinal axis of the rod (stab-like movement).

In two-handed strikes, an increase of effective mass may be present [12] compared to one-handed strikes. Higher ball speeds in baseball serves performed with higher grip force may support this hypothesis [17]. Not only the higher grip force but also a stabilisation of the striking tool during impact caused by two grip forces acting at two adjacent points at the rod’s proximal end might be responsible for a potential increase of effective mass.

Applying the conservation of momentum, contact induced velocity changes and contact forces can be calculated (see ESM of [5] for a detailed description). In order to quantify the influence of an increasing effective striking mass by a factor α, we consider a strike against the head with a mass mHead and an initial head velocity vHead = 0 using a rod with an effective mass mRod. We yield the ratio of contact forces F(α·mRod)/F(mRod):

$$ \frac{\boldsymbol{F}\left(\boldsymbol{\alpha} \bullet {\boldsymbol{m}}_{\mathbf{Rod}}\right)}{\boldsymbol{F}\left({\boldsymbol{m}}_{\mathbf{Rod}}\right)}=\frac{{\boldsymbol{m}}_{\mathbf{Rod}}+{\boldsymbol{m}}_{\mathbf{Head}}}{{\boldsymbol{m}}_{\mathbf{Rod}}+\frac{\mathbf{1}}{\boldsymbol{\alpha}}{\boldsymbol{m}}_{\mathbf{Head}}}=\left\{\begin{array}{c}\mathbf{1}+\frac{{\boldsymbol{m}}_{\mathbf{Head}}}{{\boldsymbol{m}}_{\mathbf{Rod}}}\ \boldsymbol{for}\ \boldsymbol{\alpha} \to \infty \\ {}\boldsymbol{\alpha} \left(\mathbf{1}+\frac{{\boldsymbol{m}}_{\mathbf{Rod}}}{{\boldsymbol{m}}_{\mathbf{Head}}}\right)\kern0.5em \boldsymbol{for}\ \boldsymbol{\alpha} \to \mathbf{0}\end{array}\right. $$

As can be seen from the formula, the ratio depends on the parameters mRod, mHead and α. The formula also contains expressions for the extreme values of the ratio F(α·mrod)/F(mrod) for α → 0 and α → ∞. For example, assuming an increase of the effective rod mass from 1 to 1.5 kg with an α = 1.5 and an effective head mass of 4.5 kg, we yield the ratio F(α·mrod)/F(mrod) = 1.375. Thus, a 1.5 times increase of the effective rod mass yields a 1.375 times increase of the resultant contact force. Not only the striking velocity but also the effective mass influences the resultant contact force.

Our test results are in good agreement with Sprenger et al. [7] who considered only one-handed horizontal strikes. They used an aluminium rod (100 cm, 690 g). Male volunteers yielded a mean striking velocity of 30.02 m/s; female volunteers yielded one of 21.36 m/s. Our mean striking velocities (23.9 vs. 24.2 m/s and 17.2 vs. 18.3 m/s in one-handed vs. two-handed vertical strikes of males and females, respectively) are lower due to a higher rod mass and a shorter rod length. Impact velocities in double-handed baseball bat strikes (85 cm, 870 g) were investigated by Escamilla et al. [18], reporting a mean impact velocity of 30 m/s. These velocities exceed our results again attributable to deviant rod length and rod mass.

Our experimental setup is subjected to the following standardisations and limitations. Strikes were performed using one rod of 65 cm length and 1000 g weight in a vertical striking movement only. In [5], the authors proved distinct dependencies between instrument properties in terms of length and mass and maximum striking velocities. Higher maximum striking velocities could be achieved in strikes with longer rods (rods with up to 100 cm considered) and with rods of lower masses. The same crucial relationship presumably holds for two-handed strikes. Furthermore, striking tools with non-heterogeneous mass distribution and more complex geometries can exhibit divergent moments of inertia. From our point of view, particularly in strikes with heavier tools possessing greater moments of inertias, two-handed strikes are supposed to yield higher velocities than one-handed strikes. Especially in cases with long and/or heavy instruments, the difference between the achievable maximum striking velocity in one- and two-handed strikes likely increases.

The practical application of our test results in forensic case work was described in detail in [5].

Conclusions

In one-handed strikes, the mean maximum striking velocity was 17.2 m/s in the female and 23.9 m/s in the male sample. Nearly similar maximum striking velocities were found in two-handed strikes with mean values of 18.3 m/s in the female and 24.2 m/s in the male sample. Female and male volunteers also yielded similar mean maximum striking velocities in two-handed strikes comparing ‘overhead’ and ‘overshoulder’ striking techniques. Our a priori hypothesis of higher striking velocities in the two-handed scenario must be rejected. The same applies to different two-handed striking techniques in terms of striking ‘overhead’ and ‘overshoulder’.