 Hello and welcome back to the Sports Biomechanics lecture series as always supported by the International Society of Biomechanics and Sports and sponsored by Vicon. Now hopefully over the past couple of weeks you've managed to enjoy some of the ISPS conference presentations and if you haven't then these are still available on YouTube over at the ISPS channel so do go and check those out. But for now I guess following on from a couple of excellent talks that we've already had in this series relating to athletics so both long jump with a sports prosthesis and running footwear in the two hour marathon. We've got another talk relating to athletics this time by Dr Sam Allen who is a senior lecturer at Loughborough University and Sam was also one of my PhD supervisors. So it's been really nice for me to get Sam involved in this and get him to talk to everybody today. I think it's a topic of simulating the triple jump that hopefully has quite a wide appeal. So it's really interesting or at least in my opinion from a theoretical biomechanics perspective but also has some real interest and practical applications from a sporting performance perspective. And even through to a strength and conditioning perspective of how to work with athletes and get a transference through to improvements in their actual performance. So yeah hopefully another really interesting talk. It is pre-recorded so if anybody has any questions for Sam then either drop a comment down below on YouTube and we'll try and get an answer for you. Or I think at the end of the talk Sam does have his email address on there and he said he's happy for people to email him. So hope you enjoy. Okay firstly I'd just like to say thank you very much to Stuart for the invitation to do this lecture. And thank you for his efforts in putting together this lecture series. He's got a great group of speakers and I'm really honoured to be invited to join them. So what I'd like to talk about today really is work that began with my PhD which was published more than 10 years ago now in computer simulation of the triple jump. So I'm just going to go through the evolution of the work from the very first studies I did with my PhD through to the most recent ones. The first thing I'll do is just to give you a quick recap of what the triple jump is. Most people will know obviously but just to remind you of the specifics. And then I'm just going to go through three studies really that we did myself and my co-authors Mark King and Fred Eugen. And they relate to the arm technique in triple jumping, double versus single arm technique. And then velocity trade-offs during the ground contact and lastly the effects of altering strength and approach velocity on performance. The latter two horizontal to vertical velocity trade-offs and strength and approach velocity relate to the phase ratio and I'll come on to what that means specifically in a minute. And then lastly we can draw some conclusions from all this work. So the triple jump. It's an athletic event, a track and field event which comprises an approach run where athletes try to generate pretty much maximum velocity, almost maximum velocity, followed by three consecutive phases and they are the hop which taking off from a take-off board from one leg onto the same leg, followed by a step where they go from that same leg onto the other leg and a jump which ends up in the sand pit. And the performance is the distance from the front of the take-off board to the rearmost mark they make in the sand. So they're trying to maximise that distance. So the motivation really for why we wanted to simulate this was that triple jumping is potentially one of the most, if not the most physically demanding disciplines in sport. The gram reaction forces have been measured up to 22 body weights which is enormous and I think James Hay said that was the highest force going through a human limb that had been measured in any volitional activity. So in that respect is potentially the most physically demanding discipline in sport. Also there's a control aspect with three phases put together which makes it interesting to simulate and how these phases have to be balanced in order to maximise the performance. There were lots of really good experimental studies on the triple jump and a lot of those were in the 90s by James Hay and Bing Yu and they provided lots of really good information on techniques used by the very best athletes in the world. So the motivation really to simulate this activity was to maybe add a little bit of insight into why the athletes use these techniques, why are they optimal and then possibly how might they manipulate to improve performance further. So the first thing I want to talk about is the arm technique and I'll show you a video, a couple of videos of these different arm techniques in a second. So I'm going to try to stay fairly surface level. I'm not going to go into too much detail on the methods of simulation. But if you need to know that if you want to know that I'll put the links up here to the papers where you can go and find out the specific details. So I'd just like to acknowledge my co-authors Matt King and Fred Yeadon who were also my PhD supervisors and they are my co-authors in all the papers I'm going to talk about today. So there are two techniques in triple jump and this is an example of the first one where the arms move asymmetrically back and forth through the phases. So it's a bit like running. I'll just play that again. So the arms move back and forth in opposition to the legs and he does actually bring them together. This is Jonathan Edwards, still the current world record holder jumping 70 meters and 80 something in Atlanta in 1996. Now the other technique is the double arm technique where athletes bring the arms symmetrically back and forth with each phase. So this is an example of the double arm technique. This is Christine Saylor, probably the best male triple jumper of recent years. And this is him getting very close to Jonathan Edwards world record of 1829. I think this was about 1821. So watch his arms. They move back and forth with each phase. He actually gathers them behind him before takeoff and then brings them back and forth as Jonathan Edwards sweating on his world record there in the commentary box. So I'll just play that again. So you'll see he gathers his arms behind him at touchdown of the takeoff step. And he brings them back and forwards and back and forwards with each ground contact. So two techniques on the end of this study really was to determine which one's the best. So the first thing I had to do was to construct a model of triple jumping. So the way the models work, they are representations of the body. So in this case, the model has 13 rigid segments representing the limbs that completely rigid that there's no compression at all within the segment or between the segments that are pin linked. And then on top of this we have wobbling masses. Now wobbling masses just represent the soft tissue motion so they are allowed to move. They themselves are rigid segments that they can move relative to the skeleton, the skeleton that we just saw, and they represent the movement of the wobbling mass. So the muscles and the fat and the viscera and all those kind of things, which is important especially during impacts and there's no higher impact than during a triple jump. So it's very important to include that. Now the model, this model is driven by torque. So it's a torque generator model. All the white dots here on this picture represent a torque generator. So the MCP ankle, knee, hip and shoulders were all torque generated, torque actuated and the elbow was actually angle driven. So that was taken from measured performance which I'll come onto in a minute. And the interaction with the ground is by a set of springs. So that just represents a force which, the size of which is determined by the intrusion of the foot into the ground. So that's the structure of the model. Just a quick comment on the reasons for the wobbling masses. So here's a jump take off. And if you watch you can see that the soft tissue moves substantially on impact. And that's what we include the wobbling masses in the model for to represent that motion. So effectively it means that the mass of the body is allowed to continue to move forwards and downwards on impact for a little bit longer than it would if we didn't include wobbling masses and that attenuates the impact. So if we look at the soft tissue you can see it moves around a lot. So there's quite significant movement of the soft tissue over the skeleton. So the inputs and outputs to the model are the kinematics at touchdown. So that's the way the model is moving. And we only simulated the ground contact phases and we estimated the movement in the air from measured data. So we used the angular momentum changes throughout the airborne phases to put the model in the right place, the landing if you like. So we give it the kinematics of the way it's moving. And then the thing that moves the models is the activation timings of the top generators. So the top generators can switch on and off effectively like the muscles and they can extend and flex the joints at different times in order to either match the performance or to maximize the performance. And then the outputs and the models are the kinematics and kinetics throughout each of the ground contacts. So we get all the joint motions and the ground contact forces, joints, moments, etc. And that's the case for each of the three phases of the triple jump. This is just an example of what I mean by the activation. So the activations are actually defined by activation profiles. So there are four different types representing different muscle groups if you like. So they can ramp up so they can be inactive and they can ramp up to being active or they can ramp down either active and they ramp down to not being active or they can ramp up and down or down and up depending on the requisite actions at that joint. So the first thing we needed to do was to get some representative data of a triple jumper because what we wanted to do was to make the model subject specific, that specific to a particular athlete. And the way we did that was to measure a triple jump performance and to measure various aspects of the triple jumper himself. So how strong was he based on measurements from an iso-velocity dynamometer and how long and heavy were his body segments. And we did that using anthropometric measurements and Newton's geometric models to calculate the segmental inertia parameters of each of the segments in the model. So the data collection, the top data collection resulted in surfaces like these. So what we did was to collect top data as a range of angles and angular velocities for each of the top driven joints in the model. And then we fit a surface to that data in order to specify at any given angle and any given angular velocity what the maximum joint torque achievable by the subject was. So we did that for each of the top driven, driven joints. And then this is the data collection of the triple jump. So we actually took force data. There's a force platform located just before the pit here. So we took force data of each of the phases of the triple jump. So we asked to get representative data. We asked the jumper to do the takeoff of each phase from the force place where the hop takeoff, the step takeoff and the jump takeoff. And that gave us representative force data for each of the phases. So from that we got the joint kinematics from the Vicon data. And that allowed us to use these both as an input to the simulation model and also to evaluate the simulation model challenge in just a second. So it was quite a challenge actually. This is quite a while ago now. It was quite a challenge actually to fit such a big volume into the Vicon capture. It was around 18 meters. So we really did struggle to calibrate such a huge volume just about managed it in the end by putting the calibration wand on the end of a pole or pole. So as I mentioned, the first thing in any modeling process really is to evaluate the model. So we want to establish whether the model is capable of reproducing the performance. So in this case, the computer uses an algorithm, in this case, a genetic algorithm to vary the top generator activation times in order to minimize the difference between the recorded performance and the simulation. So that's the performance of the top. This is measured from Vicon and this is the simulation model here at the bottom. And it tries to minimize an objective function which represents things like the differences in joint angle time histories, ground contact times, velocity at takeoff, angular momentum, that kind of thing. And an overall score is then achieved to establish whether it can match. So in this case, it matches quite well and results in a score of just over 2%, I think. And you can see that visually they look quite similar. I'll just see if I can play that again. Skipped a little bit. No, it's doing it again. So you can see that it results in a pretty similar movement. So we were confident that the model was capable of reproducing the performance that was actually achieved. And so from there, we thought we could go on to optimize the model. And this is a real strength of computer simulation in that you can then ask the algorithm, if you like, to vary those input parameters in order to try to maximize performance this time rather than the match performance. So this allowed us then to answer our research question, which was, which is the optimal arm technique. So we'll see in the matched simulation at the top here. Just look what the arms do in relation to the one at the bottom and the legs, in fact, the swinging legs. So in this case, here's the match simulation. This is the optimized simulation. So the objective function was the distance jumped by the model. So that's the cumulative distance of each of the three phases. So if we just run this through, you should be able to see that the techniques are quite different between the matched and the optimized simulation. Okay, so that resulted in quite a significant improvement on the measured performance, which was so on the match performance, which was 1267. It resulted in an over a meter's improvement on that. So a significant improvement on the performance on the day. I think I've got a video coming up here. So this is just a comparison of the two techniques. This is an example of the differences between the match performance and the one that the algorithm found to maximize performance. So the key thing here is to look at the differences in the swinging limbs, really, specifically the arms, which are very different. But also the swinging leg as well. So we can see that where the match performance and the experimental data represented a single arm technique where the arms were moved asymmetrically, the algorithm found that actually a double arm technique. So bringing the arms forwards together at the same time was optimal. And also it seems to have increased the flexion of the free limb as well. So trying to get that mass as far forward and as high as possible. So there are various mechanisms for why this is beneficial. I'll come on to those in just a second, but the first thing I want to show you is this. This is Jonathan Edwards again. So the first video I showed you of Jonathan Edwards was in Atlanta in 1996. This is Jonathan Edwards the previous year, 1995, breaking the world record. So in 1996, he used a single arm technique. This is in the year before. So just look at his arms and just run that through again. So a very definite double arm technique and that's still the world record. This is 1995. So one of the oldest records in the book. So it stood for 25 years now, 18 meters and 29. And he did that using this double arm technique. So this is a quote here from Jonathan Edwards suggesting that he adopted this technique in 1995. So he used a single arm technique. He adopted the double arm technique and radically improved his performance to the point where he broke the world record. He jumped a wind assisted 18 meters and 43, which is just unbelievable. But the following year and every year thereafter, he effectively couldn't reproduce that same technique. So he had this one amazing year where he broke the world record and he used this double arm technique. Then he reverted back to a single arm technique. Still jump very well, but never jumped as far again. So it would seem that the elite performers use this technique. The male elite performers use this technique. But so the females don't. And I'll show you a video of the best of a female, female jumper in just a second. So just before then, I'll just run through the mechanisms for why this technique is better. So essentially if you begin with your arms behind you at touchdown and you accelerate them downwards, that creates a reaction force on the shoulders, which accelerates the body upwards. So effectively it cushions the leg from the impact when the impacts are very, very high. Then subsequently as the arms and the swinging legs swing through, they're then accelerated upwards. And by accelerating the muscles, the leg and the arms upwards actually causes a force acting downwards on the legs. And in doing so, it slows the contraction velocity of the muscles. And we know that by slowing the contraction velocity concentrically in muscles, that allows them to produce more force. So it allows the muscles to do more work by accelerating the arms or the mass of the arms upwards and producing this reaction force downwards. This then allows the ground concept to go on for longer and allows the muscles to work for longer. And then at takeoff, it leads to the arms being higher. So that brings the centre of mass higher and also further forwards. So the centre of mass is higher and further forwards, which is exactly what you want. You want to be as high as possible and as far forward as possible. And then the last benefit potentially is that having the arms out in front of you then allows you to swing them backwards in flight, which stops you from over-rotating, which you typically do when you perform a jump takeoff. So there's lots of potential benefits to this technique. So as I mentioned, this is pretty well adopted by all elite male triple jumpers now. However, very few female triple jumpers do it. And this is a video of NSF Provence breaking the women's world record in the same year actually as Jonathan O'Boz and again. It's still the world record 25 years on. This is her doing 15 metres 50 and you can see that she uses the single arm technique. So there is certainly a scope, I think, for female athletes to adopt this technique. I know some are now and I hope to see it adopted more widely and I think it could lead to improvements in performance. So that's arm techniques. The next thing I want to come on to is velocity trade-offs. So this is what happens to the velocity of the centre of mass during the ground contact. So in each ground contact, you effectively want to trade-off horizontal velocity for vertical velocity. So just to give a bit of background on this, I just want to look at some of the mechanisms that lead to this trade-off in horizontal jump takeoffs. Or any running jump takeoff. So in a running jump, athletes generate horizontal velocity and momentum in an approach run. And then they attempt to convert some of that horizontal velocity into vertical velocity. Now the amount they require depends on the embeds, obviously. In the high jump you want to maximise that vertical velocity. In the long and triple jump, you want to maximise the distance you travel so there's an optimal trade-off. And there are really a couple of mechanisms that allow athletes to perform this trade-off. So I'll just go into them. Effectively, the first one is that the body goes from being in the air, moving linearly to rotating about the foot. And the second one is that during the ground contact the leg actually flexes and extends. So if we think about the first one, this is the only equation I'm going to put up, so I apologise for that. But it's just an example of how this trade-off occurs. So in the first diagram here, this is a very, very simplified model of the body. So we've got a rigid leg and a centre of mass. So this is a massless rigid leg and this is just a centre of mass. So the model is moving towards the ground contact, if you like. And it's got a vertical velocity and a horizontal velocity. Now, during ground contact, because the force acts to the point of contact in this model anyway, the angular momentum of the body is concerned. So the body hits the ground and then it begins to rotate about a fixed point here in a circle in circular motion. So in the first instance, there are two things really I'd like to point out. So the two things which will limit how the angular momentum after takeoff are the size of the vertical velocity and the plant angle here. So the further back this body is leaning, the smaller the angular momentum due to the horizontal velocity. So that's this component here. And the bigger the angular momentum component due to the vertical velocity. So if you want to create more vertical velocity, you have to potentially increase your plant angle. You have to lean back more. But that then does lead you to lose more linear momentum in the end. So it's a trade-off. You need to gain vertical velocity, but you only need to gain enough that it suits your purpose, which is depending on the event, either to jump as high as possible or as far as possible. And so that's why this velocity is traded off. That's one of the mechanisms for how the horizontal velocity becomes vertical velocity because you end up with this vertical component. So even if you only had a horizontal component here, you would have a vertical component here as the body started to rotate. And the amount of horizontal velocity you lose is dependent really on how big this plant angle is. So that's the first mechanism. The second one is that in reality we don't have a rigid leg. And actually what happens is the body hits the ground, the leg flexes, and then it extends. So that extension actually allows you to generate vertical velocity. So it increases this radius. So it's a radial velocity. So you end up with a positive radial velocity so that the mass is moving away from the foot. And that causes a vertical velocity. Now this again typically results in a loss in kinetic energy and hence momentum in this case of the sensor mass because there are huge impacts and during those impacts, I think on the next slide, yeah. So during those impacts as you hit the ground, you typically will have eccentric muscle actions. Now in eccentric muscle actions, you can produce a lot of force and they're also associated with losing energy. So in a jump take-off, you typically have a flexion of the limb which is likely to be associated with some eccentric muscle force. And then you have an extension of the limb which is associated with concentric muscle forces. And during these brief ground concepts, you have a high impact and then you don't have very long to kind of recoup that energy. So you tend not to recoup but you tend to lose energy, lose velocity. In this case, lose momentum of the sensor mass. So in each ground contact, we're losing momentum. And we have to trade it off this horizontal velocity for vertical velocity in order to try to maximize our performance. I'll come back to these mechanisms when we get to the results of this study. So just an example to show how effective this rotational mechanism is. So as the body hits the ground, it begins to rotate about the foot. This is a typical ground reaction force of a running jump. So you get an impact peak up here and then you get an active peak over here. And the leg actually begins to straighten somewhere over here. So most of the vertical impulse has already been generated. So actually a lot of the vertical impulse has been generated while the leg is still bending due to this rotation of the body about the foot. Okay, so just a little background on what's been done before in velocity trade-offs. So some previous studies on elite triple jumpers have found there's a subject-specific link between the gain in vertical velocity and the loss of horizontal velocity. And that determines the optimal ratio of each of the phases to the whole jump. But the effect of what the initial velocity, so whether they're large or small, on this is not known. So this is just a figure from you and Haye showing for different triple jumpers this relationship. So this is the gain in vertical velocity on the horizontal axis here. And this is the loss in horizontal velocity. So the gain in vertical velocity and the loss in horizontal velocity. And so it seems that for each individual, these are the hot phase and the step and the jump phase. They're different because in the step and the jump, the subjects are coming in with large vertical velocities. So they have to produce a lot more total change in vertical velocity. That has to go from negative to positive to get back off the ground. So for each subject, there seems to be this relationship where the gain in vertical velocity is a linear function of the loss in horizontal velocity. So we wanted to try to dig into that a little bit more with the simulation model. So I mentioned that this determines the phase ratio. So I'll just quickly clarify what I mean by this. So James Haye in 1992 said this should take priority over all of the triple jump technical problems because he considered this to be the most important one. So let's just look at what we mean by phase ratio. It's quite simple. It's just the ratio of each of the distances expressed as a percentage of the total distance jump. So it looks a bit like this. So each of the phases represented as a percentage of the whole. So a typical phase ratio might be that you'd have 35% in the hop, 30% in the step and 35% in the jump. And that would be classed as a balanced technique. So no phase is more than 2% larger than the next phase. If a phase is more than 2% larger, then it becomes, depending on the phase, if it's the hop that's larger, it's hop dominated. If it's the jump, it's jump dominated. It doesn't tend to be step dominated. So historically, these phase ratios over the years in male world record performances have changed from having very short steps in the earlier years of triple jumping. And then the steps settled at somewhere towards 30%. But in the 20 years between 1950 and 1970, they tended to be more hop dominated, so larger hops and smaller jumps. And then laterally, they became more jump dominated. So the hop distance or hop percentage went down and the jump percentage went up. So there's quite a lot of success in recent years by having a slightly longer jump phase. So the aim of this study really was to investigate these relationships in each of the three phases using the computer simulation model to establish why these relationships were as they were. And then this also affects the phase ratio. So we wanted to see how it affected the phase ratio. And I'll come on to how we did this in just a second. But what we wanted to do was to establish how changing the initial conditions might alter the trade-offs between the horizontal and the vertical velocity. So the horizontal velocity lost in order to gain vertical velocity. So the way we did this, the way we altered the initial conditions was to constrain. So by penalizing the model effectively forced it to take off with different vertical velocities. So in each case, the model still tried to maximize the distance jumped. So it was optimized for maximum distance. And based on the initial velocity from the measured performance of the match simulation, it was increased and decreased by increments of 10%, up to 30 and minus 30%. So in each case, it was then optimized to maximize the distance jumped with this vertical velocity. Then in this step in the jump phases, the initial velocities were calculated just from the take-off phases, take-off velocities at the previous phase. And they themselves were then optimized. Each was individually optimized to maximize the distance of the phase. Okay, so this is a representation of three of the optimizations, one where the vertical velocity was increased by 30%, one where it was the same as the match simulation and one where it was decreased by 30%. So the key thing really you can see here is the difference in the initial position of the model that touched down between the three, especially between minus 30 and plus 30. So we see leaning back a lot further here than it is here. And we can kind of relate that back to that pivot effect and the fact that when you need to generate vertical velocity, you have to start with a center of mass further back, so with a bigger plant angle as they call it. So I'll just try to play these videos through. So you can see the difference is really lay mostly in the hop phase and then the step phase, because of the different vertical velocities that it was landing with, by the jump phase, actually the techniques have become quite similar again. So on to the velocity trade-offs. So what we were expecting to see was what we saw in what you and I found was that there would be these two lines and they would both have similar gradients. And we didn't find that. We thought we found the same relationship in the hop take-off. But by the time we got to the step and the jump, we just didn't really see that same relationship. And we're a bit flummoxed. But actually by looking at rather than the gain in vertical velocity, and in this case this means you're having to reverse the velocity. So you come in with a negative vertical velocity and you take off with a positive one. If we plotted the loss in horizontal velocity against the take-off velocity, vertical velocity. So that's just the absolute take-off, the velocity at take-off. We do see that they actually all sit on the same line. So if we just plot that all together and say there's a pretty strong relationship, where if we take the vertical take-off velocity and the loss in horizontal velocity, do follow quite a nice relationship. Now it's hard to say why this isn't what's seen in practicing elite performers. But this is based on a simulation model which is trying to optimise techniques. So it's very specific. There's no kind of errors in there, if you like. It can operate a technique with very small tolerances, whereas humans obviously have motor noise they have to deal with. And they may not be able to operate to those kind of tolerances. This was the relationship we found. And I think the next slide I hope should indicate potentially how the model managed to do this. So if we go back to our pivot mechanism. When the body hits the ground, it re-orients the velocity of the center of mass from moving linearly to rotating about the foot. So in the first instance, this line is just to show really just for comparison of where the torso is. So you can see that when the model had to generate a lot more vertical velocity, it lent back a long way. When it didn't, it lent forward. And this then led to a high vertical velocity here. So coming into the step, it's coming down with more vertical velocity. Whereas in this case, it's coming down with less vertical velocity. And we can see the opposite is true. So when it was having to deal with really high vertical velocities, and remember this is acts against the positive angular momentum, the vertical velocity acts to rotate the body this way. We want to rotate the body this way. So what we don't want is for this to be a long way away from the foot in this case. So what the model did was to choose to place the body over the foot when the vertical velocity was high. And it chose to place the body further behind the foot when the vertical velocity was low and it still had more horizontal velocity. And so it seemed to mitigate the effects of this vertical velocity in order to try to optimize the effects on the performance. So on to the phases and the phase ratios, the distances actually were furthest. Now there's a big caveat here in that these phases were optimized independently. So humans will optimize their technique to maximize the total distance. In this case, in this particular optimization, and in later optimizations, we did optimize the entire triple jump as one optimization process. But in this one, each was optimized independently. So when the model lands here after a short hop, it will do a very long step where it might be better served to also do a short step and a very long jump. But it's not trying to do that because it's doing them independently. So in this case, the best results came here with a moderately increased hop phase from the optimized simulation. So if we look at this in percentage terms, we get something that looks like this. So as the strength, sorry, as the velocity went up, the hop, the step phase went down. So as it came in with bigger vertical velocities, the step phase got smaller and smaller and smaller. And vice-versus when the hop vertical velocity was low, the step phase was very large. But in most cases, this didn't change the phase ratio too much. So we had some hop-dominated techniques at the top here and some balance techniques at the bottom. So in short, the matched simulations of the model indicated it was accurate to do the optimization. And the loss in the horizontal velocity related really strongly to the vertical takeoff velocity and not the total change in vertical velocity. And this might be because the model was reorienting the body so that it didn't lose too much angular momentum at the impact wherein maybe that people aren't able to do that quite so accurately. And that's why we don't see it in elite performance. The phase ratio was not particularly sensitive to the length of the hop phase. And it was either hop-dominated when the vertical velocity of the hop was high or it was balanced for all the other simulations. So the last thing I want to talk to you about is the effects of increasing strength and approach velocity on performance. So the motivation for this really is that athletes train to increase both these things. They train in the gym to increase their strength by lifting weights, by doing plyometrics, and they train their sprinting ability to maximize their approach velocity. It's impossible to say how each of these things interrelates because they typically increase in tandem. Potentially, you can increase strength and it may improve your approach velocity. So computer simulation would allow each of these factors to establish how this would improve or how it would affect performance independently. Also, by simulating this, we get the idea of what optimal technique might look like for different athletes. So previous work has been based on a subject-specific model that has a particular approach velocity and particular strength. So in order to establish optimal technique for a range of athletes, by varying this approach velocity and strength, it gives us an estimate of what optimal technique might look like for different athletes with different strengths and different approach speeds. So the aim really was to alter these things and find what effect they had on both the jump distance and the phase ratios employed by these athletes. So the strength and velocity changes, the strength increases were made by effectively lifting the surface. So if you remember, I showed you that each of the top generators had a surface which determined how much torque it could produce at a given angle and a given angular velocity. So when we say increasing strength by 10%, this whole surface was just lifted up by 10%. And we just did this across the board for all of the top generators. The velocity increases were just increasing the horizontal velocity of the centre of mass of the model at the touchdown of the hop phase. So in the previous model, I showed you each phase was optimised independently. In this model, the whole triple jump is optimised. So this is a more realistic representation of how the of an optimal technique for a given approach velocity and strength. And so for each combination, we just maximise the total triple jump distance and the optimal phase ratios, et cetera, just fell out of that. So on to the results. So across the top here, we've got improvements or increases in approach velocity. So this is the measured performance here. And down side here, we've got increases in strength. So what we can see is that if we increase the approach velocity and the strength by 10%, we get a roughly, surprisingly, a 10% increase in performance and 20% and 30% similarly. So it would seem if we increase both these things by the same percentage, the outcome increases by approximately that percentage. Now that might seem obvious, but there was no real way of knowing that that would be the case without optimising it and finding it out. If we look across what the effects are of just independently increasing strength and an approach velocity, they're actually quite different. So we can see that across the top here, if we increase approach velocity without increasing strength, we actually hit a plateau when the individual is running 30% faster. They cease to jump any further because they're effectively not strong enough to benefit from it. Strength always leads to an improvement in performance, but nowhere near as much as a combination of strength and velocity at the same time. So this is a surface fixed to that data we've just seen. Just to give an indication here that there is an interrelationship of strength and velocity. So this is the distance jumped and this is strength and velocity. And you can see here there's an interrelationship term here where improving strength and velocity actually combines to improve the performance. There's an independent improvement of both, but an additive or a multiplicative benefit of improving strength and velocity on performance. So in terms of the phase ratios, we saw roughly what we saw before, really, but when approach, velocity and strength were increased in tandem, that the model retained this hot dominated technique. But when these things were altered independently, it moved to a balanced technique, but quite a different balanced technique in that when the approach velocity was increased without increasing strength, the balanced technique where the step phase was quite small and where we increased strength, the step phase got larger and larger and larger until the three phases were almost the same size which we never really see in elite performance. But surprising that we didn't see any jump-dominated techniques despite this being a technique which is used by some of the very best jumpers. So in summary, increasing velocity and strength both independently led to increasing performance, but not anywhere near as much as increasing them together. Now the optimal phase ratios were always either balanced or hot dominated. That's surprising because we know that elite performers do also use jump-dominated techniques and it may be a feature, again, of the model, that there's an aspect of a jump-dominated technique which is not represented, which is beneficial and is not represented in the model. And that could be potentially due to the fact that it's easier to control, it's more repeatable to use a jump-dominated technique. It could be because by reducing the impacts, the largest impact is typically the landing of the hop. So if that phase is smaller, then that big impact is reduced. So it could be that performers choose not to do that because the impacts are lower and it's a safer way of jumping. It could potentially be something to do with the last flight phase. We didn't optimise the flight phases and it may be that with a jump-dominated technique and a longer flight phase you can do more to reorient the body and get a better landing position, which could improve performance. But in terms of the simulations, it typically found that these hop-dominated techniques were beneficial. So that's all I've got to talk to you about today. So just to conclude, based on all the studies that I've talked about, what can we conclude on triple jumping performance and what athletes should be doing? Well, the double arm technique, it does seem that this is optimal. Male jumpers use it and some female jumpers are adopting it now, but most don't use it yet. So the real change could come with female jumpers adopting this double arm technique and that could improve that performance. In terms of the velocity trade-offs, it seems that you can mitigate your losses of horizontal velocity when vertical velocities are high if you make sure that you always orient your body over the foot at touchdown. So you allow the leg to absorb the impact, if you like, rather than to try to rotate about the foot. And then lastly, by increasing strength and velocity, we still saw that the phase ratios were typically always balanced and hop-dominated, but we see that elite performers also use jump-dominated techniques. Increasing the strength and velocity, obviously, in both cases was beneficial for the triple jumper in this study, but it seems that to be an elite performer when you're talking 18-metre jumps, you've got to be exceptionally strong and exceptionally fast. That's no real surprise, but you've really got to hit the board upwards of 10.5 metres per second, probably, in order to think about jumping 18 metres and you've also obviously got to be exceptionally strong. So that's all from me. Thank you very much for watching. Please, if you do have any questions, feel free to get in contact with me. Probably best by your email, but you can look at my staff page and give me a call if you want to. So all that remains is to say thank you again to Stuart and sorry to miss you all at ISPS this year. I hope to see you next year. Thank you very much. Thank you, Sam. And I know because it was pre-recorded, I've already thanked Sam personally, to take the opportunity again to, I guess, publicly say a huge thank you to Sam for that talk. As I said at the start, I found it really enjoyable from both a theoretical biomechanics perspective, but also because of the practical implications from a sporting perspective. So thanks, Sam. And as Sam said, feel free to either get in touch via email or leave a comment below and we can get an answer to any questions you might have that way if you prefer. But that said, I'm really happy to put up on screen now the lectures for the next five weeks, which at least for now will be the final block of lectures in this series. So starting next week, we've got Wendy Holiday talking about cycling biomechanics, then John Drazan talking about how we can use biomechanics as a vehicle, I guess, for STEM outreach to engage youth in biomechanics. Then the next few are really, I guess, by popular demand. A few people requested a talk on Bayesian statistics following Kristen Sinani's excellent statistics talk a few weeks back. So Tony Myers has offered to deliver just that. And then back by popular demand, we've got Kristen Sinani again at this time providing some tips for scientific writing. And then finally to finish off, I'm really delighted to have a talk by Walter Herzog on muscle mechanics. So thank you very much for watching. Hope you've enjoyed that and hopefully see you soon.