 understanding the effects of impact location in racket or bat sports. These topics will be discussed in relation to research on the badminton smash and cricket power hitting, as well as historical racket development in tennis. Implications for other sports and research topics will also be discussed. For those who don't know me, I'm Stuart McCurlay-Nailer. I'm a senior lecturer in sport and exercise biomechanics at the University of Suffolk. My research investigates the factors influencing individual specific sporting technique, particularly in racket or bat sports, such as badminton with a specific focus on the smash and cricket with a specific focus on power hitting. As well as sporting technique, my research also focuses on the interactions between human and equipment, again in both racket and bat sports. Understanding the multi-factorial relationships determining performance within such sports has required an understanding of the interactions between individual, task and environmental constraints. However, before we can investigate the effect of any parameter on performance, we need to be able to accurately measure the performance outcome that we're interested in. Accurately determining instantaneous post-impact shuttlecock speed in badminton has proved harder than you might expect. The shuttlecock has a lower ballistic coefficient, that's a measure of its ability to overcome air resistance and a greater deceleration during flight than any other airborne sporting implement. So much so that initial shuttle velocities of 67 metres per second have been reported to decelerate in just 0.6 seconds to a terminal velocity of approximately 7 metres per second. These rapid decelerations between early motion capture frames as well as marker movements due to the spin or flip of the shuttle and tracking errors present researchers with difficulties when seeking to accurately determine post-impact shuttlecock velocity as an average between measured time points. Our solution has been to fit logarithmic curves to the displacement data and interpolate to the time of impact, enabling shuttle velocity to be calculated alongside racket shuttle impact location. We fit curves to the pre and post-impact phases separately in all three axes. The intersection of the curves enabled the estimation of impact timing with instantaneous shuttle speed at that time taken from the post-impact curve equation. The curve equations we used were based on fundamental mechanical principles, namely the fact that the drag force acting on an object is proportional to its velocity squared. The deceleration is proportional to that drag force and the additional inclusion of acceleration due to gravity in the vertical direction. Now, I promise this is the only equation in the entire presentation and I won't go into detail, but the process that I just mentioned resulted in a logarithmic equation with two constants to be varied in order to best fit the experimental shuttle displacement data. A couple of tweaks to the method were made specific for badminton that are worth mentioning at this point. Firstly, the greater the change in direction, the less influence any noise in the data will have on the estimated intersection of the pre and post-impact curves. For example, it's possible that a shuttle could be hit back over the net without its medialateral or left to right direction changing very much and so any small magnitude of noise in that direction could distort the estimated intersection point. The greatest change of direction is clearly in the anterior posterior or forward and backward direction and so this direction was used to determine impact timing. Secondly, an intermediate 1 millisecond racket shuttle contact period was added between the pre and post-impact curves with the shuttle velocity equal to that of the racket face at that time. A reminder to see this paper for details of the badminton specific methods if you're interested and for further details of how the equations were derived as well as justification of the parameters and checking of any assumptions see this paper on cricket batting where the method was first presented. Back to the badminton method. We wanted to quantify the effect this curve fitting method had on the calculated post-impact shuttle speeds before we then applied those speeds within any whole body technique analysis study. We did that in a conference paper from the World Racket Sports Congress. We attached reflective tape to the tip of the shuttle cock to be tracked by our motion capture cameras and 25 experienced male badminton players ranging from county to international standard. Each performed three maximal effort jump smashes. Because of the shuttle deceleration after impact that I mentioned earlier taking an average velocity between the first two recorded positions post-impact could be one alternative method used. So we compared the shuttle speeds calculated from our curve fitting methodology with this method as an average over one frame at 400 hertz. Although the difference between methods was reasonably small for most trials the average velocity over one frame was very susceptible to any noise in either of those two data points. When we move on to calculating impact location on the racket face from this data and this method any small differences in impact timing can have a big effect on the calculated impact location. A second method that we compared against was an average velocity over 10 frames instead something that might be used to avoid the negative effects of noise or error in those two data points. Compared to the curve fitting method on average taking the velocity over 10 frames resulted in a systematic 18% underestimation of shuttle velocity and this shows why previous methods have underestimated smash speeds due to either later recording once the shuttle has decelerated somewhat or decreased capture frequencies especially in video based systems. It's also noteworthy that there was a relationship between shuttle speed and the magnitude of the difference between the two methods the greater the smash speed the greater the difference. This is perhaps not surprising when we think that the drag force is proportional to velocity squared and the greater the shuttle the more it will decelerate. We were then able to use this method to give more accurate dependent variable measures in investigations of technique factors associated with shuttle speed and I won't go into detail at this point but we did just that in a paper in applied sciences reporting the technique aspects with the greatest correlation to shuttle speed. If anyone is interested at this point in the skeletal graphics then I did record a tutorial video showing how you can generate graphics in visual 3D with the segment color scaled to any parameter such as ground reaction force or segment angular velocity as it is in this example or any other parameter that you've investigated. We also used our method to investigate the speed accuracy tradeoff in early badminton players. A further implication is a possibility to more accurately determine the instant of impact between the two closest motion capture frames. This event can then be used to interpolate and extract kinetic or kinematic parameters at the exact time of impact particularly important when small differences in event timing could make a meaningful difference in values at fast moving joints such as the wrist or fast moving segments such as the forearm hand or racket. But the main focus of this video is the effect of impact location and luckily the same method enabled us to investigate that in quite a bit of detail. But first it's useful to fill in a bit of background information on the various theoretical methods of defining optimal impact location in battle racket sports. A few of them have been theoretically proposed. The first and perhaps the most simplest is the geometric center which is just the middle of the racket face. Secondly we've got the vibration node and center of percussion and the maximum apparent coefficient of restitution. I'll go through each of these briefly in turn these typically each occur at different locations on the racket face and the point here isn't to provide a definitive guide but simply to highlight the differences and any pros or cons of these methods when applied to a whole body technique analysis. The first is the vibration node. This is the point at which an impact on that location on the racket will result in the minimum frame vibration. As you can see from the diagram on the right. An impact location at the node results in less vibration and thus less energy loss in inverted commas due to racket vibration compared to an impact hit closer to the frame. And so that impact with less vibration will then result in more energy transferred to the shuttle. For example and I appreciate this isn't the clearest image but it's the best I could find in the literature. You can see less frame vibration or oscillation in the racket on the bottom row that's impacted near the vibration node compared to the one on the top row that's impacted closer to the throat of the racket. The vibration node relates closely to the feel of the shots reported by players but not necessarily to performance. It's dependent on the stiffness of the racket and the strings as well as the mass distribution of the strum racket. It's also dependent on the grip of the individual player. Another possible sweet spot definition is the center of percussion. That's the point at which there is no translational reaction at the frame of the racket i.e. where no jarring effect is felt in the hand. For example an impact below the center of percussion would move the racket handle towards the hand whereas an impact above the center of percussion would move the handle out of the hand. The specific location of the center of percussion relative to the center of mass is dependent on the ratio of two values. The first is the moment of inertia about a horizontal line through the racket center of mass and the second is the product of racket mass and the distance from the hand or rotation point to the center of mass. However that calculation does not mention the grip force at any point and so its relevancy in a real-world training or match play scenario is limited. Finally I want to mention the apparent coefficient of restitution. Perhaps the sweet spot definition that's the most inherently performance related is identifying the maximum apparent coefficient of restitution. That's because it's inherently dependent on the ratio of ball or shuttle speed after to before impact. This is typically recorded in a direction normal to the racket face i.e. in the direction that the racket is facing rather than in any other direction and as originally defined it also assumes an initially stationary racket so again not quite ideal in terms of application to sporting performance. It's dependent on the relative velocities of the ball or shuttle and racket and it's also dependent on the mass and moment of inertia of the racket. The last thing I want to mention in this section is the effective mass of the racket. The greater the racket's effective mass at the impact location the greater the shuttle speed if all else is equal. However in reality in applied sporting performance not all else is equal. Racket head linear velocity is likely to be higher further up the racket for any given angular velocity due to the greater distance from the axis of rotation. If it helps to imagine it this way imagine opening a door the entire door will rotate at the same angular velocity just as the entire racket will be moving and rotating at the same angular velocity. However the side of the door closest to the handle will move through a greater distance in the same amount of time as the end closer to the hinge which will move through a smaller distance in the same amount of time. And this is the same thing that applies with the racket where the racket rotates but towards the top of the racket it will move through a greater distance and therefore have a greater linear velocity at the time of impact. The effective mass of the racket will also be greater with a heavier racket. But again that has impact on racket head velocity as I'm sure you can imagine you may be likely to swing a heavier racket slower or at least if you were to achieve the same racket head speed then you would require greater joint talks to generate the same angular acceleration of the racket. It's also worth noting at this point that increases in racket swing weight or moment of inertia can cause upward shifts in the average impact location as well as in node location. This also affects the upper extremity angular kinematics and will marginally reduce the racket head speed at impact. This figure is from a study on the tennis serve but similar results have been observed by Kwan in the badminton smash. It's hopefully evident that none of the theoretical methods described so far have perfectly described performance outcomes in realistic smash movements. It was therefore necessary to investigate the combined effect of all of these factors during real smashes by elite players to quantify their ideal impact locations and their margins for error temporarily in swing timing or spatially on the racket face. We applied the same curve fitting method that I mentioned before with the addition of separate curves to the reflective tape that we attached to the racket and then we identified the shuttle location in the local coordinate system of the racket face i.e. how far longitudinally up the racket and how far medialaterally across the racket was the shuttle at the time of impact. To evaluate the method we recorded 40 smashes by one international male badminton player before later applying the method to additional players. After reflective tape was applied around the base of the shuttle the remaining cork was coated with stencil ink prior to each trial. This left an impression on the racket that could subsequently be digitized giving us a coordinate in two dimensions on the racket face of where that impact occurred. The digitization was done three times by the same investigator with results averaged. Calculated impact locations in the longitudinal axis up the racket were offset approximately by the distance between the tip of the shuttle where the impression was left on the racket and the center of the reflective tape that the motion capture system would be tracking and that our curve fitting methodology would be using just to allow a fair comparison between the two. We saw a good fit of the pre and post impact shuttle curves to the experimental data as well as a root mean squared error of three millimeters on average and the racket curves performed even better than that. When we display that as measured in blue versus calculated from curve fitting in red impact locations for the 40 trials you can see that they map on top of each other quite well and in both directions on the racket face the average error or difference was around three and a half millimeters. I say difference rather than error because neither method is perfect and so we don't have a gold standard result for comparison. Once we were happy with the method we applied it to 65 international badminton players and that's a really good sample but we were very fortunate that the project was funded by the badminton world federation and so we were able to get access to a warm up court at the world championships in Glasgow. Through support from badminton England we were also able to test 30 players at the national performance center to add to our data set with each player performing an average of 37 smashes all of which were included in our subsequent analysis. The main difference from the validation of the method was that we were now feeding from a shuttle launcher. This wasn't possible before due to the income of shuttle but it was now ensuring a consistent feed for each trial by each player within the data set. Before we link anything to performance outcomes it's useful to report just what the players did in terms of impact location. All impact locations will be described relative to the geometric center of the racket face and the main thing that stands out here visually at least is that this mean and standard deviation impact location seems to be shifted to the right of the diagram. This is viewed from in front of the badminton player and so a shift to the right for a right hander means it's closer to the medial side or closer to the player under their body. Data for left handers was flipped so that the coordinates would match for both right and left handed players. That result of a slightly medial impact location is consistently observed and in Harley-Towler's PhD thesis he measured players using five different racket stiffnesses and players were consistently hitting off center in that direction which we'll come back to when we look at performance outcomes. These boxes represent plus or minus one standard deviation in both directions so it's noteworthy that there's more variability longitudinally up the racket than there is medialaterally across the racket. But now that we know what elite players are doing in terms of impact location we can look to relate this to performance outcomes. To start with you may notice that the dependent variable here over on the right is a percentage of that participant's maximum shuttle speed. If we just used shuttle speed in meters per second then the inter-individual variation between players would cloud the results. For example it's possible that a player with a very fast racket could have a suboptimal impact location but still hit the shuttle faster than a player with a much slower swing who manages to hit it in the ideal impact location. Assigning each trial a percentage of that player's max speed was the simplest way around this. We observed negative significant quadratic relationships between impact location in both directions and shuttle speed. Practically what that means is that in both directions there's an optimal point for developing fast smashes and as you move in either direction the shuttle slows down so whether that's to the left or right or up or down on the racket. Firstly in the longitudinal direction we see that the ideal impact location for generating fast speeds of the shuttle is shifted slightly distally or slightly upwards on the racket. If we think back to the door analogy from earlier this isn't surprising. So although the apparent coefficient of restitution and the effective mass of the racket might be greater lower down we also know that the top of the racket has a greater linear velocity so there's some trade-off there that means overall when we put all of these factors together somewhere slightly higher than centre is the ideal impact location for generating fast smashes. If we then consider the side-to-side or medialateral direction we again see this shift in the medial direction. This is due to rapid radio ulnar pronation towards the end of the smash just prior to impact. If you hold out your hand with your palm facing towards you and then rotate so that your palm is facing away from you that's radio ulnar pronation. And as you do that just like the door analogy you'll hopefully see that your thumb is moving faster in a forward direction than your little finger or pinky side of your hand and that's what's happening here so because the medial side of the racket is rotating through just before impact at a faster speed as the other side rotates backwards and away hitting slightly towards the medial side of the racket actually results in a faster smash. And the point I want to reinforce here is just the importance of considering the player's technique when thinking about racket design and the equipment rather than considering the equipment in isolation. Even anecdotally players who have a faster rotation so a greater pronation or a greater polar rotation of the racket tends to hit more medial of racket centre so it seems to be a relationship there. To show this another way we lined up all of our trials by all of our participants ranging from those that were the slowest relative to that participant's max through to each participant's fastest trial. And as you can see a shuttle speed gets closer to each player's fastest trial we saw the range of impact locations narrowed more consistently around our newly defined sweet spot and this is regardless of the racket head speed or any kinematics for each of those particular trials. Whilst confounding factors such as a slow racket head speed might make it possible for relatively slow smashes to be hit close to the optimal location it would appear impossible to hit maximal speed smashes near to the racket frame due to a decreased coefficient of restitution in these locations. We've mentioned shuttle speed but what about shuttle direction which is also important for performance. You would likely expect the shuttle to be hit in a direction that the racket is facing i.e. at 90 degrees or normal to the racket face. We defined that angle as zero degrees and any deviation from this trajectory was either a positive or a negative angle. We saw a linear relationship between medialateral impact location and the actual direction that the shuttle headed off in likely due to a slight twist of the racket caused by that impact location and then subsequently a deviation in shuttle trajectory. There was no relationship between longitudinal impact location and shot direction. Lateral impacts resulted in greater deviations than equivalently medial impacts possibly due to the greater linear racket speed on the medial side of the racket as mentioned earlier and hence shorter contact durations on that side in which for racket polar rotation to occur and deviate the shuttle direction. If a player were able to maintain consistency of impact location within one pooled standard deviation of our entire cohort then they would see decreases in shuttle speed as a result of less than 5% and deviation in shuttle angle of less than 3 degrees. Contrastingly, if a player were only able to maintain their impact location within three pooled standard deviations of the whole group then their speed could reduce by up to 27% and their shuttle could depart at angles of up to 7 degrees. It's therefore practical for players and coaches to be aware of the importance and effective impact location on shot outcome where optimal impact locations occur slightly medially and slightly longitudinally distal of the racket face geometric center. Whilst this should be achieved with the greatest racket speed possible doing so at the expense of accurate and consistent impact locations may result in unwanted and perhaps unsuccessful shuttle trajectories. So our recommendation is that players should prioritize the accuracy of the impact location over shuttle speed if they can only have one or the other and once the accuracy and consistency of that impact is maintained they can then look to gradually increase the racket speed at which they are able to achieve that. By the time the shuttle has traveled half a court length forwards those one, two or three standard deviation differences in impact location would result in shuttlecock deviations of 25, 50 or 75 centimeters laterally. This shows the margin for error afforded to elite badminton players. We know where on the racket the best outcomes occur but future research should attempt to understand what techniques lead to more accurate or consistent impact locations or afford the players greater margin for error. And speaking of margin for error let's see what happened when two elite players put the accuracy of their impact locations to the test. So I've strung this racket with six strings in the mains and six strings in the crosses to test our timing and see if we can regularly hit it in the middle. So let's see how we get on. Okay, well that was pretty successful so we're going to ramp up the difficulty and reduce the size of the sweet spot to four by four strings. This is basically the same size as the shuttle so let's see how we get on. Yes. Surely two strings is impossible, right? I can't believe we didn't get that on camera. Thanks to Greg and Jenny from Badminton Insight for allowing me to use those clips. You can find the full video and many more tutorials and challenges on their Badminton Insight channel. In tennis, impact probability has been modeled as a probability density distribution shown on screen which shows the most likely or seemingly the preferred impacts by players which are centered on the vibration node. More recent research from a Wimbledon qualifying tournament supports the idea that tennis players generally hit at the node. There are possible implications for this because if players self-organize or adapt to find a movement solution where they hit the ball at the vibration node manufacturers may be incentivized to align the vibration node with the optimal performance impact location or at least be aware that players are likely to hit based on feeling. From a coaching perspective if we know that players will likely self-organize based on the feel of the shot to hit around the vibration node additional extrinsic feedback may be required to facilitate a search for alternative movement solutions in order to find a possible global optimum that considers performance outcomes and robustness to inherent variability. The important point here is the opposite one to earlier. So earlier I mentioned how it was important to consider the actual technique of the whole body when thinking about racket design. Here it's the opposite where we need to consider the equipment when investigating the player's chosen movement solution. And everything we've talked about so far has been for performance related whereas we should also not forget the importance of injury risk and injury risk reduction. One common injury is tennis elbow or lateral epicondylitis. This study by the Luftberg group showed that off longitudinal impact contributed to a forced wrist flexion and an eccentric stretch of the wrist flexors which is thought to be a contributor to tennis elbow. This is in agreement with a theoretical study by the same group where they also showed that the tighter the grip the greater the effect of impact location on these injury risk factors. So again just highlighting the importance of considering what the player is doing and not just the racket in isolation. We applied many of these same methods that I've mentioned for badminton studies to power hitting in cricket. The first of a series of studies looked at the same curve fitting methodology applied earlier in badminton to calculate impact locations using a curve fitting methodology in cricket. We had four markers on the back corners of the bat as well as five sections of reflective tape on the cricket ball and used Vicon motion capture cameras just as we did in badminton. Again we took a multi-stage approach. In stage one we passed an array of markers of a fixed separation through the capture volume just to see what the spatial reconstruction accuracy was before we then built layer upon layer of added complexity onto it leading up to the final impact location calculations. And we were pleased with the root mean squared error so we then moved on to stage two which was pre-impact ball tracking. We fired the ball from a bowling machine into a mat fitting the curves as before pre-impact and then measuring the impact location on impact paper on the mat but without the added complexity of a dynamic bat. The curve equations again fit satisfactorily well and the root mean squared errors on average were below a centimeter in all directions. When we compared the measured and calculated impact locations on that stationary mat again both directions were less than a centimeter on average. We then added a bat in but hit the ball off of a tee so we're looking at impact location calculation for a static ball. Just as with the stencil link for badminton we covered the cricket bat in developer spray that left a circular mark once the ball had been hit. This could then be digitized and compared to our calculated impact location in the local coordinate system of the bat. The curves again fit well to the data with average root mean squared errors of less than half a centimeter and when we looked at impact location for those trials we saw differences between digitized and calculated of again less than half a centimeter on average. For the final stage we put it all together so pre and post impact curves for the ball bat curves and then calculating the impact location. All curves fit well with again root mean squared errors of less than a centimeter and when we validated the impact location we had average errors or differences of around six and a half centimeters across the bat face and around seven centimeters longitudinally up the bat face so we were happy enough to use this method and take it forward in whole body analysis linked to the dependent variables of impact location and bat speed ball speed etc from the curve equation. Fundamentally we know that the distance of projectile travels is dependent on the launch angle and launch speed of that projectile. We also know and have shown that the ball launch angle is highly dependent on the bat angle at impact but we wanted to know what factors affect ball launch speed on the right of this deterministic model and we started with an investigation of the impact location using the method we had just evaluated. This led to the second paper of the series and similar graphics here to the ones for badminton we again see a negative quadratic relationship between impact location and ball velocity. This is looking across the bat face so in the transverse or medial lateral direction and we saw a similar relationship longitudinally up the bat face resulting in a kind of diamond shape of the effect of impact location on ball speed. We also looked at the effect of impact location on the twist or rotation of the bat about its longitudinal axis and this is where we saw one of the most perfect cubic relationships I've seen in biomechanics research at least in our own research and what this means is that an impact in the center of the bat so down the midline will not result in any bat rotation but there's an almost linear relationship through the majority of the bat face where the more off-center the impact occurs the more it causes the bat to twist in that same direction. This relationship then reverses close to the edges of the bat where there's more of a glancing blow that has less of an effect on the rotation of the bat and this rotation of the bat leads to a similar cubic relationship between impact location in the transverse direction and ball direction. This is similar to the measure described earlier for badminton but the results combined again show the importance of generating consistently central impacts and then doing so at increasingly greater bat speeds. So just as with badminton our recommendation is that players should prioritize consistently central impact locations rather than sacrificing the impact location in favor of a faster bat speed. It's also noteworthy that similar results have been reported in softball batting. We see here on the left the negative quadratic relationship between impact location and ball speed and then on the right we see the cubic relationship between impact location and direction or launch angle. We then used our method to look at the kinematic factors associated with performance outcomes from our curve fitting method relating to bat speed or ball speed angle or distance. The most important kinematic factor linked to bat speed was x factor at the top of the downswing. That's the angular separation between the pelvis here in red and the thorax in blue in the transverse plane or viewed from above. The second most important factor was lead elbow extension during the downswing and then wrist uncocking during the downswing. And interestingly the order of importance for our three greatest predictors followed a proximal to distal sequence. If you're interested in more on cricket batting biomechanics including the full body technique analysis and a comparison of batting against a bowling machine, a bowler or a sidearm thrower then check out my full lecture on cricket batting biomechanics. The issue of interactions between player and equipment or bat came up again in our comparison of power hitting kinematics between 15 male and 15 female batters ranging from university to international standard. There were lots of differences between male and female cricket. For example, the mass and size of the ball, mass size and moment of inertia of the bat, the boundary distance and various other factors. We were interested in the combined effects of all of these constraints on the emergent movement solutions of male and female experienced batters for their respective task of hitting the ball over the boundary of the pitch after we controlled for any differences between the genders in body height or mass. The biggest difference that we found was in lead elbow extension during the downswing. Male batters all extended their lead elbow whereas eight female batters but no males flexed their lead elbow during the downswing. On average, males extended their lead elbow by 30 degrees whereas female batters flexed theirs by three degrees. This resembles previous male and female differences reported in experienced golfers a difference that wasn't seen when testing the highest level professional golfers. We know that movement solutions are influenced by factors relating to the individual, their environment and the task itself. So the differences in observed movement solutions could be due to any number of constraints including boundary size, incoming ball speed, strength in relation to bat moment of inertia or many other constraints. Research in other sports suggests that the scaling of the bat moment of inertia to the player's strength may play a part here in terms of lead elbow extension. It's also possible that the smaller boundary size in female cricket allows female batters to prioritize the accuracy or margin for error in terms of impact location over achieving high bat speeds. So to put that another way it may be that there are different movement solutions available but to clear the longer boundary the male batters have to prioritize bat speed whereas the female batters may be able to clear a smaller boundary by focusing more on giving them a greater margin for error by focusing on impact location rather than bat speed. But we await the results of ongoing studies to give a greater indication of the interactions between these various constraints. Again I have a three minute video abstract available for that study if you want more detail. Another area of research that I want to briefly mention is the work by Tom Allen's group at Manchester Metropolitan University on the historical development of tennis rackets. This is a really interesting study working with the Wimbledon Museum to document the changes in rackets since the origins of the game. This includes both the materials where you can see here a gradual transition from wood in orange through to composite materials in blue but also in the shape of the racket. Given the medial impacts by badminton players that I've mentioned throughout this presentation and the possible performance advantages of those in terms of both speed and direction it's interesting to note the presence of early lopsided or asymmetrical tennis racket designs that look something like this. It would be fascinating to link the changes in racket design to changes in player performance over the years particularly considering how it might affect that tradeoff between performance and margin for error. I'm currently working with the Manchester Metropolitan group on a citizen science study. We're in the processes of developing this website where members of the public or museums will be able to upload photographs of any old rackets that they possess as well as taking their own measurements of the racket and uploading those through a form. And this will then add to the previous data set from the Wimbledon Museum etc. for tennis but allow us to create a similar data set for other sports such as squash or badminton. So if you do have or know anybody who has old rackets lying around then we'd be really, really appreciative if you were able to contribute to our understanding of historical racket design and if you can either please reach out and contact me or check out that website address at the bottom of the screen. I've mainly focused on badminton and cricket today but if you are interested in tennis biomechanics whether from a technique perspective or the effect of equipment scaling for junior players then I recommend this online lecture by Professor Bruce Elliott.